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1.03M
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# Called in the OrdinaryDiffEQ.__init; All `OrdinaryDiffEqAlgorithm`s have one
function OrdinaryDiffEq.initialize!(integ, cache::GaussianODEFilterCache)
if integ.opts.dense && !integ.alg.smooth
error("To use `dense=true` you need to set `smooth=true`!")
elseif !integ.opts.dense && integ.alg.smooth
@warn "If you set dense=false for efficiency, you might also want to set smooth=false."
end
if !integ.opts.save_everystep && integ.alg.smooth
error("If you do not save all values, you do not need to smooth!")
end
@assert integ.saveiter == 1
integ.kshortsize = 1
resize!(integ.k, integ.kshortsize)
integ.k[1] = integ.u
# Update the initial state to the known (given or computed with AD) initial values
initial_update!(integ, cache, integ.alg.initialization)
# These are necessary since the solution object is not 100% initialized by default
OrdinaryDiffEq.copyat_or_push!(integ.sol.x_filt, integ.saveiter, cache.x)
OrdinaryDiffEq.copyat_or_push!(
integ.sol.pu,
integ.saveiter,
mul!(cache.pu_tmp, cache.SolProj, cache.x),
)
return nothing
end
"""Perform a step
Not necessarily successful! For that, see `step!(integ)`.
Basically consists of the following steps
- Coordinate change / Predonditioning
- Prediction step
- Measurement: Evaluate f and Jf; Build z, S, H
- Calibration; Adjust prediction / measurement covs if the diffusion model "dynamic"
- Update step
- Error estimation
- Undo the coordinate change / Predonditioning
"""
function OrdinaryDiffEq.perform_step!(
integ,
cache::GaussianODEFilterCache,
repeat_step=false,
)
@unpack t, dt = integ
@unpack d, SolProj = integ.cache
@unpack x, x_pred, u_pred, x_filt, u_filt, err_tmp = integ.cache
@unpack x_tmp, x_tmp2 = integ.cache
@unpack A, Q, Ah, Qh = integ.cache
make_preconditioners!(cache, dt)
@unpack P, PI = integ.cache
tnew = t + dt
# Build the correct matrices
@. Ah = PI.diag .* A .* P.diag'
X_A_Xt!(Qh, Q, PI)
if isdynamic(cache.diffusionmodel) # Calibrate, then predict cov
# Predict
predict_mean!(x_pred, x, Ah)
mul!(view(u_pred, :), SolProj, x_pred.μ)
# Measure
evaluate_ode!(integ, x_pred, tnew)
# Estimate diffusion
cache.local_diffusion, cache.global_diffusion =
estimate_diffusion(cache.diffusionmodel, integ)
# Adjust prediction and measurement
predict_cov!(x_pred, x, Ah, Qh, cache.C1, cache.global_diffusion)
# Compute measurement covariance only now
compute_measurement_covariance!(cache)
else
predict_mean!(x_pred, x, Ah)
predict_cov!(x_pred, x, Ah, Qh, cache.C1)
mul!(view(u_pred, :), SolProj, x_pred.μ)
evaluate_ode!(integ, x_pred, tnew)
compute_measurement_covariance!(cache)
cache.local_diffusion, cache.global_diffusion =
estimate_diffusion(cache.diffusionmodel, integ)
end
# Likelihood
# cache.log_likelihood = logpdf(cache.measurement, zeros(d))
# Update
x_filt = update!(integ, x_pred)
# Estimate error for adaptive steps - can already be done before filtering
if integ.opts.adaptive
err_est_unscaled = estimate_errors(cache)
if integ.f isa DynamicalODEFunction # second-order ODE
DiffEqBase.calculate_residuals!(
err_tmp,
dt * err_est_unscaled,
integ.u[1, :],
u_pred[1, :],
integ.opts.abstol,
integ.opts.reltol,
integ.opts.internalnorm,
t,
)
else # regular first-order ODE
DiffEqBase.calculate_residuals!(
err_tmp,
dt * err_est_unscaled,
integ.u,
u_pred,
integ.opts.abstol,
integ.opts.reltol,
integ.opts.internalnorm,
t,
)
end
integ.EEst = integ.opts.internalnorm(err_tmp, t) # scalar
end
# If the step gets rejected, we don't even need to perform an update!
reject = integ.opts.adaptive && integ.EEst >= one(integ.EEst)
if !reject
# Save into u_filt and integ.u
mul!(view(u_filt, :), SolProj, x_filt.μ)
integ.u .= u_filt
# Advance the state here
copy!(integ.cache.x, integ.cache.x_filt)
integ.sol.log_likelihood += integ.cache.log_likelihood
end
end
function evaluate_ode!(
integ::OrdinaryDiffEq.ODEIntegrator{<:AbstractEK},
x_pred,
t,
second_order::Val{false},
)
@unpack f, p, dt, alg = integ
@unpack u_pred, du, ddu, measurement, R, H = integ.cache
@assert iszero(R)
@unpack E0, E1, E2 = integ.cache
z, S = measurement.μ, measurement.Σ
# Mean
_eval_f!(du, u_pred, p, t, f)
integ.destats.nf += 1
# z .= MM*E1*x_pred.μ .- du
if f.mass_matrix == I
H .= E1
elseif f.mass_matrix isa UniformScaling
H .= f.mass_matrix.λ .* E1
else
_matmul!(H, f.mass_matrix, E1)
end
_matmul!(z, H, x_pred.μ)
z .-= du[:]
# If EK1, evaluate the Jacobian and adjust H
if alg isa EK1 || alg isa IEKS
u_lin =
(alg isa IEKS && !isnothing(alg.linearize_at)) ? alg.linearize_at(t).μ : u_pred
# Jacobian is computed either with the given jac, or ForwardDiff
if !isnothing(f.jac)
_eval_f_jac!(ddu, u_lin, p, t, f)
elseif isinplace(f)
ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_lin)
integ.destats.nf += 1
else
ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_lin)
integ.destats.nf += 1
end
integ.destats.njacs += 1
# _matmul!(H, f.mass_matrix, E1) # This is already the case (see above)
_matmul!(H, ddu, E0, -1.0, 1.0)
end
return nothing
end
function evaluate_ode!(
integ::OrdinaryDiffEq.ODEIntegrator{<:EK1FDB},
x_pred,
t,
second_order::Val{false},
)
@unpack f, p, dt, alg = integ
@unpack d, u_pred, du, ddu, measurement, R, H = integ.cache
@assert iszero(R)
@unpack E0, E1, E2 = integ.cache
z, S = measurement.μ, measurement.Σ
(f.mass_matrix != I) && error("EK1FDB does not support mass-matrices right now")
# Mean
_eval_f!(du, u_pred, p, t, f)
integ.destats.nf += 1
# z .= MM*E1*x_pred.μ .- du
H1, H2 = view(H, 1:d, :), view(H, d+1:2d, :)
z1, z2 = view(z, 1:d), view(z, d+1:2d)
H1 .= E1
_matmul!(z1, H1, x_pred.μ)
z1 .-= @view du[:]
# If EK1, evaluate the Jacobian and adjust H
u_lin = u_pred
if !isnothing(f.jac)
_eval_f_jac!(ddu, u_lin, p, t, f)
elseif isinplace(f)
ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_lin)
integ.destats.nf += 1
else
ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_lin)
integ.destats.nf += 1
end
integ.destats.njacs += 1
_matmul!(H1, ddu, E0, -1.0, 1.0)
z2 .= (E2 * x_pred.μ .- ddu * du)
if integ.alg.jac_quality == 1
# EK0-type approach
H2 .= E2
elseif integ.alg.jac_quality == 2
H2 .= E2 - ddu * ddu * E0
elseif integ.alg.jac_quality == 3
_z2(m) = begin
u_pred = E0 * m
du = zeros(eltype(m), d)
ddu = zeros(eltype(m), d, d)
_eval_f!(du, u_pred, p, t, f)
if !isnothing(f.jac)
_eval_f_jac!(ddu, u_pred, p, t, f)
elseif isinplace(f)
ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_pred)
# integ.destats.nf += 1
else
ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_pred)
# integ.destats.nf += 1
end
# integ.destats.njacs += 1
return (E2 * m .- ddu * du)
end
H2 .= ForwardDiff.jacobian(_z2, x_pred.μ)
else
error("EK1FDB's `jac_quality` has to be in [1,2,3]")
end
return nothing
end
function evaluate_ode!(
integ::OrdinaryDiffEq.ODEIntegrator{<:AbstractEK},
x_pred,
t,
second_order::Val{true},
)
@unpack f, p, dt, alg = integ
@unpack d, u_pred, du, ddu, measurement, R, H = integ.cache
@assert iszero(R)
du2 = du
@unpack E0, E1, E2 = integ.cache
z, S = measurement.μ, measurement.Σ
# Mean
# _u_pred = E0 * x_pred.μ
# _du_pred = E1 * x_pred.μ
if isinplace(f)
f.f1(du2, view(u_pred, 1:d), view(u_pred, d+1:2d), p, t)
else
du2 .= f.f1(view(u_pred, 1:d), view(u_pred, d+1:2d), p, t)
end
integ.destats.nf += 1
_matmul!(z, E2, x_pred.μ)
z .-= @view du2[:]
# Cov
if alg isa EK1
(alg isa IEKS) && error("IEKS is currently not supported for SecondOrderODEProbems")
if isinplace(f)
H .= E2
J = ddu
ForwardDiff.jacobian!(
J,
(du2, du_u) -> f.f1(du2, view(du_u, 1:d), view(du_u, d+1:2d), p, t),
du2,
u_pred,
)
integ.destats.nf += 1
integ.destats.njacs += 1
_matmul!(H, J, integ.cache.SolProj, -1.0, 1.0)
else
J = ForwardDiff.jacobian(
(du_u) -> f.f1(view(du_u, 1:d), view(du_u, d+1:2d), p, t),
u_pred,
)
integ.destats.nf += 1
integ.destats.njacs += 1
H .= E2 .- J * integ.cache.SolProj
end
end
return measurement
end
evaluate_ode!(integ, x_pred, t) =
evaluate_ode!(integ, x_pred, t, Val(integ.f isa DynamicalODEFunction))
# The following functions are just there to handle both IIP and OOP easily
_eval_f!(du, u, p, t, f::AbstractODEFunction{true}) = f(du, u, p, t)
_eval_f!(du, u, p, t, f::AbstractODEFunction{false}) = (du .= f(u, p, t))
_eval_f_jac!(ddu, u, p, t, f::AbstractODEFunction{true}) = f.jac(ddu, u, p, t)
_eval_f_jac!(ddu, u, p, t, f::AbstractODEFunction{false}) = (ddu .= f.jac(u, p, t))
compute_measurement_covariance!(cache) =
X_A_Xt!(cache.measurement.Σ, cache.x_pred.Σ, cache.H)
function update!(integ, prediction)
@unpack measurement, H, R, x_filt = integ.cache
@unpack K1, K2, x_tmp2, m_tmp = integ.cache
update!(x_filt, prediction, measurement, H, K1, x_tmp2.Σ.mat, m_tmp)
return x_filt
end
function smooth_all!(integ)
integ.sol.x_smooth = copy(integ.sol.x_filt)
@unpack A, Q = integ.cache
@unpack x_smooth, t, diffusions = integ.sol
@unpack x_tmp, x_tmp2 = integ.cache
x = x_smooth
for i in length(x)-1:-1:1
dt = t[i+1] - t[i]
if iszero(dt)
copy!(x[i], x[i+1])
continue
end
make_preconditioners!(integ.cache, dt)
P, PI = integ.cache.P, integ.cache.PI
mul!(x_tmp, P, x[i])
mul!(x_tmp2, P, x[i+1])
smooth!(x_tmp, x_tmp2, A, Q, integ, diffusions[i])
mul!(x[i], PI, x_tmp)
end
end
function estimate_errors(cache::GaussianODEFilterCache)
@unpack local_diffusion, Qh, H, d = cache
if local_diffusion isa Real && isinf(local_diffusion)
return Inf
end
L = cache.m_tmp.Σ.squareroot
if local_diffusion isa Diagonal
_matmul!(L, H, sqrt.(local_diffusion) * Qh.squareroot)
error_estimate = sqrt.(diag(L * L'))
return view(error_estimate, 1:d)
elseif local_diffusion isa Number
_matmul!(L, H, Qh.squareroot)
# error_estimate = local_diffusion .* diag(L*L')
@tullio error_estimate[i] := L[i, j] * L[i, j]
error_estimate .*= local_diffusion
# @info "it's small anyways I guess?" error_estimate cache.measurement.μ .^ 2
# error_estimate .+= cache.measurement.μ .^ 2
error_estimate .= sqrt.(error_estimate)
return view(error_estimate, 1:d)
end
end
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] | 1.97438 | 6,050 |
module Day07
using Statistics
import ..data_dir # from parent module
input = read(joinpath(data_dir, "day07"), String)
export part1, part2
"""
The total fuel required to align all crab submarines to `target`
This function accepts an optional `fuel_cost_function` which calculates the fuel
required to move a crab submarine from one location to another. This function
should act on non-negative integer values (ie. absolute difference). The default
is the `identity` function, in which the distance between the two locations is
also the fuel cost.
"""
function fuel_to_align(
positions::Vector{Int64},
target::Integer,
fuel_cost_function::Function = identity
)
absolute_movements = abs.(positions .- target)
fuel_costs = fuel_cost_function.(absolute_movements)
sum(fuel_costs)
end
"""
I'm calling this `brute_force` since it inelegantly searches the entire solution
space for a minimum cost. If this function isn't good enough for part 2 I can
look for leaner search strategies (starting from median position maybe?).
Starting with the assumption that the optimal position must be somewhere between
the minimum and maximum positions, we can check each possible position between
the two to determine the minimum fuel consumption.
"""
function brute_force(positions::Vector{Int64}, fuel_cost_function::Function = identity)
minimum_fuel = Inf
for position = minimum(positions):maximum(positions)
required_fuel = fuel_to_align(positions, position, fuel_cost_function)
minimum_fuel = min(required_fuel, minimum_fuel)
end
Integer(minimum_fuel)
end
function part1(input = input)
positions = [parse(Int64, position) for position in split(input, ",")]
brute_force(positions)
end
"""
I think this is an appropriate name? We're summing an arithmetic sequence.
"""
arithmetic_fuel_cost(movement::Int64) = movement * (movement + 1) / 2
function part2(input = input)
positions = [parse(Int64, position) for position in split(input, ",")]
brute_force(positions, arithmetic_fuel_cost)
end
end # module
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437,
198,
198,
437,
1303,
8265,
198
] | 3.459866 | 598 |
module juliaAllotter
using CSV
using LinearAlgebra
using Statistics
using JLD
include("core.jl")
import Random
Random.seed!(2^13 - 1)
courseFile = "data/courseFile.csv"
studentsFile = "data/studentsFile.csv"
choiceIndices = [0, 1, 2, 3, 4, 5]
choiceWeights = [10, 1, 2, 3, 4, 5]
costWeights = [-1.0, 1.0, 1.0]
iterations = 4900
coursesDF = CSV.read(courseFile)
studentsDF = CSV.read(studentsFile)
courseCount = length(coursesDF[:, 1])
studentCount = length(studentsDF[:, 1])
cpiArray = Array(studentsDF.CPI)
times = Array(coursesDF.CourseNeeds)
choiceIdx = makeArray(studentCount, studentsDF, courseCount, coursesDF, choiceIndices)
choiceWeights = makeArray(studentCount, studentsDF, courseCount, coursesDF, choiceWeights)
initialAllotment = allotment(studentCount, courseCount, times, Matrix{Float64}(I, studentCount, studentCount))
initialAllotment = squeezeAllotment(initialAllotment)
choiceGoodnessOld, cpiGoodnessOld = calcGoodness(initialAllotment, choiceWeights, cpiArray)
finalAllottment, utility = runMCMC(initialAllotment, iterations, studentCount, courseCount, costWeights, choiceIdx, choiceWeights, studentsDF, cpiArray, times)
choiceGoodnessNew, cpiGoodnessNew = calcGoodness(finalAllottment, choiceWeights, cpiArray)
writePerformance(finalAllottment, choiceGoodnessOld, cpiGoodnessOld, choiceGoodnessNew, cpiGoodnessNew, utility)
end # module | [
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struct PolicyValueRewardTest <: TrainingTest
idx::Integer
state::AbstractEnvState
image::AbstractImage
actions::Vector{<:Integer}
value::Float32
action::Integer
reward::Float32
end
mutable struct PolicyValueRewardTests <: TrainingTests
tests::Vector{PolicyValueRewardTest}
images::AbstractArray{Float32, 4}
actual_value::AbstractArray{Float32, 2}
actual_reward::AbstractArray{Float32, 2}
period::Int
warmup::Int
function PolicyValueRewardTests(tests; period=1, warmup=0)
new(
tests,
tensorize(get_image.(tests)),
Flux.unsqueeze(get_value.(tests), 1),
Flux.unsqueeze(get_reward.(tests), 1),
period,
warmup,
)
end
end
function gettestfn(tests::PolicyValueRewardTests)
function fn(n::Network)
initial_output = initialinferencefn(tests)(n)
acc, fails = getpolicyacc(tests, initial_output)
value_mse = getvaluemse(tests, initial_output)
recurrent_output = recurrentinferencefn(tests, initial_output)(n)
reward_mse = getrewardmse(tests, recurrent_output)
acc, fails, value_mse, reward_mse
end
end
struct PolicyValueRewardTestsSVG
tests::PolicyValueRewardTests
end
svg(x::PolicyValueRewardTests) = PolicyValueRewardTestsSVG(x)
function Base.show(io::IO, m::MIME"image/svg+xml", x::PolicyValueRewardTestsSVG)
num_tests = length(x.tests)
range = 1:(min(10, num_tests))
subset = 1:num_tests
subset_indices = subset[range]
svgbatch = [gridsvg(x.tests[i]) for i in subset_indices]
Base.show(io, m, GridSVG(svgbatch, main_title="RVP Tests"))
end | [
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] | 2.401439 | 695 |
include("ToricVarieties.jl")
######################
# 1: The Julia type for ToricDivisors
######################
struct toric_divisor
GapToricDivisor::GapObj
end
export toric_divisor
######################
# 2: Generic constructors
######################
function create_divisor( coeffs::Vector{Int}, v::toric_variety )
# create the divisor
gap_coeffs = GapObj( coeffs )
gap_divisor = GAP.Globals.CreateDivisor( gap_coeffs, v.GapToricVariety )
# wrap and return
return toric_divisor( gap_divisor )
end
export create_divisor
function divisor_of_character( character::Vector{Int}, v::toric_variety )
# create the divisor
gap_character = GapObj( character )
gap_divisor = GAP.Globals.DivisorOfCharacter( gap_character, v.GapToricVariety )
# wrap and return
return toric_divisor( gap_divisor )
end
export divisor_of_character
function divisor_of_class( v::toric_variety, class::Vector{Int} )
# create the divisor
gap_class = GapObj( class )
gap_divisor = GAP.Globals.DivisorOfGivenClass( v.GapToricVariety, gap_class )
# wrap and return
return toric_divisor( gap_divisor )
end
export divisor_of_class
######################
# 3: Properties
######################
function is_cartier( d::toric_divisor )
return GAP.Globals.IsCartier( d.GapToricDivisor )::Bool
end
export is_cartier
function is_principal( d::toric_divisor )
return GAP.Globals.IsPrincipal( d.GapToricDivisor )::Bool
end
export is_principal
function is_primedivisor( d::toric_divisor )
return GAP.Globals.IsPrimedivisor( d.GapToricDivisor )::Bool
end
export is_primedivisor
function is_basepoint_free( d::toric_divisor )
return GAP.Globals.IsBasepointFree( d.GapToricDivisor )::Bool
end
export is_basepoint_free
function is_ample( d::toric_divisor )
return GAP.Globals.IsAmple( d.GapToricDivisor )::Bool
end
export is_ample
function is_very_ample( d::toric_divisor )
if ! is_ample( d )
@warn "Can (current) only tell for ample toric divisors if they are very ample."
return "fail"
end
return GAP.Globals.IsVeryAmple( d.GapToricDivisor )::Bool
end
export is_very_ample
function is_numerically_effective( d::toric_divisor )
return GAP.Globals.IsNumericallyEffective( d.GapToricDivisor )::Bool
end
export is_numerically_effective
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] | 2.462827 | 955 |
@testset "Spaces" begin
Qx, x = PolynomialRing(FlintQQ, "x")
K, a = NumberField(x^2 - 2, "a1")
Kt, t = K["t"]
E, b = NumberField(t^2 + 3)
F = GF(3)
Hecke.change_base_ring(::Hecke.NfRel, ::Hecke.gfp_mat) = error("asd")
@test_throws ErrorException hermitian_space(E, F[1 2; 2 1])
Hecke.change_base_ring(::Hecke.NfRel, x::Hecke.gfp_mat) = x
@test_throws ErrorException hermitian_space(E, F[1 2; 2 1])
V = @inferred hermitian_space(E, FlintQQ[1 2; 2 1])
@test V isa Hecke.HermSpace
end
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] | 2.09465 | 243 |
using JuMP, EAGO
m = Model()
EAGO.register_eago_operators!(m)
@variable(m, -1 <= x[i=1:3] <= 1)
@variable(m, -3.428579430434188 <= q <= 8.991868736935128)
add_NL_constraint(m, :(gelu(0.758903986598098 + 0.8106379052679875*gelu(0.47487042435595583 + 0.4488775132618512*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.015398554931854491*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3])))) + -0.6668215058198093*gelu(0.8216722410540171 + 0.5667551555087149*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.5912184082121308*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))))) + gelu(-0.09143860592972564 + 0.3407854070498746*gelu(0.47487042435595583 + 0.4488775132618512*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.015398554931854491*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3])))) + 0.24612879529032217*gelu(0.8216722410540171 + 0.5667551555087149*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.5912184082121308*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))))) - $q <= 0.0))
@objective(m, Min, q)
return m
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] | 1.764286 | 1,820 |
"""
Nghttp2 Julia bindings.
"""
"""
Items:
[x] add basic unit test, server, client
[x] unit test to submit_response with payload > 16 KB
[ ] verify trailers are sent at the end with request is send with multiple packages
[ ] add unit test with invalid response
[x] return an error if failure occurs in Http2Stream
[ ] nghttp2_on_stream_close_callback, close stream on error
[ ] ensure sessions are destroyed
[x] submit request should return correct stream
[x] create a new request stream
- nghttp2_xxx functions returns error code, except _new functions.
session reading loop
read and dispatch
single Http2Session
read()
multiple entries from read stream
until it is available
Multiple Http2Streams are reading from a single Http2Session.
┌─────────────────┐
│Http2Stream::read│─ ─ ─
└─────────────────┘ │ session.read_lock
┌─────────────────┐ ─ ─ ▶ ╔════╗ ┌─────────────┐
│Http2Stream::read│───────────────╣Lock╠─────▶│Session::read│
└─────────────────┘ ─ ─ ▶ ╚════╝ └─────────────┘
┌─────────────────┐ │
│Http2Stream::read│─ ─ ─
└─────────────────┘
"""
module Nghttp2
export Http2ClientSession, Http2ServerSession, Http2Stream, Http2ProtocolError
export send, recv, try_recv, submit_request, submit_response, read, eof, bytesavailable, close, isopen
export nghttp2_version
using nghttp2_jll
using BitFlags
using Sockets
const Option{T} = Union{Nothing,T} where {T}
"""
Error codes used by Nghttp2 library.
"""
@enum(Nghttp2Error::Int32,
# Invalid argument passed.
NGHTTP2_ERR_INVALID_ARGUMENT = -501,
# Out of buffer space.
NGHTTP2_ERR_BUFFER_ERROR = -502,
# The specified protocol version is not supported.
NGHTTP2_ERR_UNSUPPORTED_VERSION = -503,
# Used as a return value from nghttp2_send_callback, nghttp2_recv_callback and nghttp2_send_data_callback to indicate that the operation would block.
NGHTTP2_ERR_WOULDBLOCK = -504,
# General protocol error.
NGHTTP2_ERR_PROTO = -505,
# The frame is invalid.
NGHTTP2_ERR_INVALID_FRAME = -506,
# The peer performed a shutdown on the connection.
NGHTTP2_ERR_EOF = -507,
# Used as a return value from nghttp2_data_source_read_callback() to indicate that data transfer is postponed. See nghttp2_data_source_read_callback() for details.
NGHTTP2_ERR_DEFERRED = -508,
# Stream ID has reached the maximum value. Therefore no stream ID is available.
NGHTTP2_ERR_STREAM_ID_NOT_AVAILABLE = -509,
# The stream is already closed; or the stream ID is invalid.
NGHTTP2_ERR_STREAM_CLOSED = -510,
# RST_STREAM has been added to the outbound queue. The stream is in closing state.
NGHTTP2_ERR_STREAM_CLOSING = -511,
# The transmission is not allowed for this stream (e.g., a frame with END_STREAM flag set has already sent).
NGHTTP2_ERR_STREAM_SHUT_WR = -512,
# The stream ID is invalid.
NGHTTP2_ERR_INVALID_STREAM_ID = -513,
# The state of the stream is not valid (e.g., DATA cannot be sent to the stream if response HEADERS has not been sent).
NGHTTP2_ERR_INVALID_STREAM_STATE = -514,
# Another DATA frame has already been deferred.
NGHTTP2_ERR_DEFERRED_DATA_EXIST = -515,
# Starting new stream is not allowed (e.g., GOAWAY has been sent and/or received).
NGHTTP2_ERR_START_STREAM_NOT_ALLOWED = -516,
# GOAWAY has already been sent.
NGHTTP2_ERR_GOAWAY_ALREADY_SENT = -517,
# The received frame contains the invalid header block.
NGHTTP2_ERR_INVALID_HEADER_BLOCK = -518,
# Indicates that the context is not suitable to perform the requested operation.
NGHTTP2_ERR_INVALID_STATE = -519,
# The user callback function failed due to the temporal error.
NGHTTP2_ERR_TEMPORAL_CALLBACK_FAILURE = -521,
# The length of the frame is invalid, either too large or too small.
NGHTTP2_ERR_FRAME_SIZE_ERROR = -522,
# Header block inflate/deflate error.
NGHTTP2_ERR_HEADER_COMP = -523,
# Flow control error.
NGHTTP2_ERR_FLOW_CONTROL = -524,
# Insufficient buffer size given to function.
NGHTTP2_ERR_INSUFF_BUFSIZE = -525,
# Callback was paused by the application.
NGHTTP2_ERR_PAUSE = -526,
# There are too many in-flight SETTING frame and no more transmission of SETTINGS is allowed.
NGHTTP2_ERR_TOO_MANY_INFLIGHT_SETTINGS = -527,
# The server push is disabled.
NGHTTP2_ERR_PUSH_DISABLED = -528,
# DATA or HEADERS frame for a given stream has been already submitted and has not been fully processed yet.
NGHTTP2_ERR_DATA_EXIST = -529,
# The current session is closing due to a connection error or nghttp2_session_terminate_session() is called.
NGHTTP2_ERR_SESSION_CLOSING = -530,
# Invalid HTTP header field was received and stream is going to be closed.
NGHTTP2_ERR_HTTP_HEADER = -531,
# Violation in HTTP messaging rule.
NGHTTP2_ERR_HTTP_MESSAGING = -532,
# Stream was refused.
NGHTTP2_ERR_REFUSED_STREAM = -533,
# Unexpected internal error, but recovered.
NGHTTP2_ERR_INTERNAL = -534,
# Indicates that a processing was canceled.
NGHTTP2_ERR_CANCEL = -535,
# When a local endpoint expects to receive SETTINGS frame, it receives an other type of frame.
NGHTTP2_ERR_SETTINGS_EXPECTED = -536,
# When a local endpoint receives too many settings entries in a single SETTINGS frame.
NGHTTP2_ERR_TOO_MANY_SETTINGS = -537,
# The errors < nghttp2_error.NGHTTP2_ERR_FATAL mean that the library is under unexpected condition and processing was terminated.
NGHTTP2_ERR_FATAL = -900,
# Out of memory. This is a fatal error.
NGHTTP2_ERR_NOMEM = -901,
# The user callback function failed. This is a fatal error.
NGHTTP2_ERR_CALLBACK_FAILURE = -902,
# Invalid client magic (see NGHTTP2_CLIENT_MAGIC) was received and further processing is not possible.
NGHTTP2_ERR_BAD_CLIENT_MAGIC = -903,
# Possible flooding by peer was detected in this HTTP/2 session.
NGHTTP2_ERR_FLOODED = -904)
"""
The frame types in HTTP/2 specification.
"""
@enum(Nghttp2FrameType::UInt8,
# The DATA frame.
NGHTTP2_DATA = 0,
# The HEADERS frame.
NGHTTP2_HEADERS = 0x01,
# The PRIORITY frame.
NGHTTP2_PRIORITY = 0x02,
# The RST_STREAM frame.
NGHTTP2_RST_STREAM = 0x03,
# The SETTINGS frame.
NGHTTP2_SETTINGS = 0x04,
# The PUSH_PROMISE frame.
NGHTTP2_PUSH_PROMISE = 0x05,
# The PING frame.
NGHTTP2_PING = 0x06,
# The GOAWAY frame.
NGHTTP2_GOAWAY = 0x07,
# The WINDOW_UPDATE frame.
NGHTTP2_WINDOW_UPDATE = 0x08,
# The CONTINUATION frame. This frame type won't be passed to any
# callbacks because the library processes this frame type and its
# preceding HEADERS/PUSH_PROMISE as a single frame.
NGHTTP2_CONTINUATION = 0x09,
# The ALTSVC frame, which is defined in `RFC 7383
# <https://tools.ietf.org/html/rfc7838#section-4>`_.
NGHTTP2_ALTSVC = 0x0a,
# The ORIGIN frame, which is defined by `RFC 8336
# <https://tools.ietf.org/html/rfc8336>`_.
NGHTTP2_ORIGIN = 0x0c)
"""
The category of HEADERS, which indicates the role of the frame. In
HTTP/2 spec, request, response, push response and other arbitrary
headers (e.g., trailer fields) are all called just HEADERS. To
give the application the role of incoming HEADERS frame, we define
several categories.
"""
@enum(Nghttp2FrameHeadersCategory::UInt32,
# The HEADERS frame is opening new stream, which is analogous to SYN_STREAM in SPDY.
NGHTTP2_HCAT_REQUEST = 0,
# The HEADERS frame is the first response headers, which is
# analogous to SYN_REPLY in SPDY.
NGHTTP2_HCAT_RESPONSE = 1,
# The HEADERS frame is the first headers sent against reserved stream.
NGHTTP2_HCAT_PUSH_RESPONSE = 2,
# The HEADERS frame which does not apply for the above categories,
# which is analogous to HEADERS in SPDY. If non-final response
# (e.g., status 1xx) is used, final response HEADERS frame will be
# categorized here.
NGHTTP2_HCAT_HEADERS = 3)
"""
The flags for HTTP/2 frames.
This enum defines all flags for all frames.
"""
@enum(Nghttp2FrameFlags::UInt8,
# No flag set.
NGHTTP2_FLAG_NONE = 0,
# The END_STREAM flag.
# The ACK flag.
NGHTTP2_FLAG_END_STREAM = 0x01,
# The END_HEADERS flag.
NGHTTP2_FLAG_END_HEADERS = 0x04,
# The PADDED flag.
NGHTTP2_FLAG_PADDED = 0x08,
# The PRIORITY flag.
NGHTTP2_FLAG_PRIORITY = 0x20)
const NGHTTP2_FLAG_ACK = NGHTTP2_FLAG_END_STREAM
"""
The status codes for the RST_STREAM and GOAWAY frames.
"""
@enum(Nghttp2ErrorCode::UInt32,
# No errors.
NGHTTP2_NO_ERROR = 0x0,
# PROTOCOL_ERROR.
NGHTTP2_PROTOCOL_ERROR = 0x1,
# INTERNAL_ERROR.
NGHTTP2_INTERNAL_ERROR = 0x2,
# FLOW_CONTROL_ERROR.
NGHTTP2_FLOW_CONTROL_ERROR = 0x3,
# SETTINGS_TIMEOUT.
NGHTTP2_SETTINGS_TIMEOUT = 0x4,
# STREAM_CLOSED.
NGHTTP2_STREAM_CLOSED = 0x5,
# FRAME_SIZE_ERROR.
NGHTTP2_FRAME_SIZE_ERROR = 0x6,
# REFUSED_STREAM.
NGHTTP2_REFUSED_STREAM = 0x7,
# CANCEL.
NGHTTP2_CANCEL = 0x8,
# COMPRESSION_ERROR.
NGHTTP2_COMPRESSION_ERROR = 0x9,
#CONNECT_ERROR.
NGHTTP2_CONNECT_ERROR = 0xa,
# ENHANCE_YOUR_CALM.
NGHTTP2_ENHANCE_YOUR_CALM = 0xb,
# INADEQUATE_SECURITY.
NGHTTP2_INADEQUATE_SECURITY = 0xc,
# HTTP_1_1_REQUIRED.
NGHTTP2_HTTP_1_1_REQUIRED = 0xd)
"""
The flags for header field name/value pair.
"""
@enum(Nghttp2NvFlags::UInt8,
# No flag set.
NGHTTP2_NV_FLAG_NONE = 0,
# Indicates that this name/value pair must not be indexed ("Literal
# Header Field never Indexed" representation must be used in HPACK
# encoding). Other implementation calls this bit as "sensitive".
NGHTTP2_NV_FLAG_NO_INDEX = 0x01,
# This flag is set solely by application. If this flag is set, the
# library does not make a copy of header field name. This could
# improve performance.
NGHTTP2_NV_FLAG_NO_COPY_NAME = 0x02,
# This flag is set solely by application. If this flag is set, the
# library does not make a copy of header field value. This could
# improve performance.
NGHTTP2_NV_FLAG_NO_COPY_VALUE = 0x04)
"""
The SETTINGS ID.
"""
@enum(Nghttp2SettingsId::UInt32,
# SETTINGS_HEADER_TABLE_SIZE
NGHTTP2_SETTINGS_HEADER_TABLE_SIZE = 0x01,
# SETTINGS_ENABLE_PUSH, client only option.
NGHTTP2_SETTINGS_ENABLE_PUSH = 0x02,
# SETTINGS_MAX_CONCURRENT_STREAMS
NGHTTP2_SETTINGS_MAX_CONCURRENT_STREAMS = 0x03,
# SETTINGS_INITIAL_WINDOW_SIZE
NGHTTP2_SETTINGS_INITIAL_WINDOW_SIZE = 0x04,
# SETTINGS_MAX_FRAME_SIZE
NGHTTP2_SETTINGS_MAX_FRAME_SIZE = 0x05,
# SETTINGS_MAX_HEADER_LIST_SIZE
NGHTTP2_SETTINGS_MAX_HEADER_LIST_SIZE = 0x06)
"""
The flags used to set in |data_flags| output parameter in :type:`nghttp2_data_source_read_callback`.
"""
@bitflag Nghttp2DataFlags::UInt32 begin
# No flag set.
NGHTTP2_DATA_FLAG_NONE = 0
# Indicates EOF was sensed.
NGHTTP2_DATA_FLAG_EOF = 0x01
# Indicates that END_STREAM flag must not be set even if
# NGHTTP2_DATA_FLAG_EOF is set. Usually this flag is used to send
# trailer fields with `nghttp2_submit_request()` or
# `nghttp2_submit_response()`.
NGHTTP2_DATA_FLAG_NO_END_STREAM = 0x02
# Indicates that application will send complete DATA frame in
# :type:`nghttp2_send_data_callback`.
NGHTTP2_DATA_FLAG_NO_COPY = 0x04
end
"""
The SETTINGS ID/Value pair.
"""
struct SettingsEntry
settings_id::Nghttp2SettingsId
value::UInt32
end
const DEFAULT_SERVER_SETTINGS = Vector{SettingsEntry}(
[
SettingsEntry(NGHTTP2_SETTINGS_MAX_CONCURRENT_STREAMS, 100)
])
const DEFAULT_CLIENT_SETTINGS = Vector{SettingsEntry}(
[
SettingsEntry(NGHTTP2_SETTINGS_MAX_CONCURRENT_STREAMS, 100),
SettingsEntry(NGHTTP2_SETTINGS_ENABLE_PUSH, 1),
])
"""
The name/value pair, which mainly used to represent header fields.
It creates a copy of the strings using malloc.
String pointers can be safely passed to C function.
"""
struct NVPair
name::Ptr{Cchar}
value::Ptr{Cchar}
namelen::Csize_t
valuelen::Csize_t
flags::UInt8
NVPair(nothing) = new(C_NULL, C_NULL, 0, 0, UInt8(0))
NVPair(nv_pair::Pair{String,String}) = NVPair(nv_pair.first, nv_pair.second, UInt8(0))
function NVPair(name::String, value::String, flags::UInt8)
name_len = length(name)
value_len = length(value)
# Reserve 2 bytes for the string terminator
name_ptr = Ptr{UInt8}(Libc.calloc(name_len + value_len + 2, 1))
value_ptr = name_ptr + name_len + 1
GC.@preserve name unsafe_copyto!(name_ptr, pointer(name), name_len)
GC.@preserve value unsafe_copyto!(value_ptr, pointer(value), value_len)
return nv_pair = new(name_ptr, value_ptr, name_len, value_len, flags)
end
end
free(nv_pair::NVPair) = Libc.free(nv_pair.name)
"""
Helper functions to convert vector of string pairs to vector of NVPair.
"""
const NVPairs = Vector{NVPair}
const StringPairs = Vector{Pair{String,String}}
function convert_to_nvpairs(input::StringPairs)
nv_pairs = NVPairs()
foreach(pair -> push!(nv_pairs, NVPair(pair)), input)
finalizer(free, nv_pairs)
return nv_pairs
end
free(nv_pairs::NVPairs) =
for i in 1:length(nv_pairs)
free(nv_pairs[i])
nv_pairs[i] = NVPair(nothing)
end
"""
Nghttp2 library options.
"""
mutable struct Nghttp2Option
ptr::Ptr{Cvoid}
"""
Creates an instance of Nghttp2Options.
"""
function Nghttp2Option()::Nghttp2Option
nghttp2_option = new(C_NULL)
result = ccall(
(:nghttp2_option_new, libnghttp2),
Cint,
(Ref{Nghttp2Option},),
nghttp2_option)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
finalizer(free, nghttp2_option)
return nghttp2_option
end
end
function free(nghttp2_option::Nghttp2Option)
ccall(
(:nghttp2_option_del, libnghttp2),
Cvoid,
(Nghttp2Option,),
nghttp2_option)
nghttp2_option.ptr = C_NULL
return nothing
end
mutable struct Nghttp2Session
ptr::Ptr{Cvoid}
end
mutable struct Nghttp2Frame
ptr::Ptr{Cvoid}
end
"""
The frame header.
"""
struct Nghttp2FrameHeader
# The length field of this frame, excluding frame header.
length::Csize_t
# The stream identifier (aka, stream ID)
stream_id::Int32
# The type of this frame. See `nghttp2_frame_type`.
type::Nghttp2FrameType
# The flags.
flags::UInt8
# Reserved bit in frame header. Currently, this is always set to 0
# and application should not expect something useful in here.
reserved::UInt8
end
"""
The structure to specify stream dependency.
"""
struct Nghttp2PrioritySpec
# The stream ID of the stream to depend on. Specifying 0 makes stream not depend any other stream.
stream_id::Int32
# The weight of this dependency.
weight::Int32
# Nonzero means exclusive dependency.
exclusive::UInt8
end
"""
The HEADERS frame.
"""
struct Nghttp2HeadersFrame
# The frame header.
frame_header::Nghttp2FrameHeader
# The length of the padding in this frame. This includes PAD_HIGH and PAD_LOW.
pad_len::Csize_t
# The priority specification
pri_spec::Nghttp2PrioritySpec
# The name/value pairs.
nva::Ptr{Cvoid}
# The number of name/value pairs in |nva|.
nvlen::Csize_t
# The category of this HEADERS frame.
cat::Nghttp2FrameHeadersCategory
end
"""
Nghttp2 library information.
"""
struct Nghttp2Info
age::Cint
version_num::Cint
version_str::Cstring
proto_str::Cstring
end
mutable struct DataSource
send_stream::IO
trailer::NVPairs
end
mutable struct DataProvider
data_source::Ptr{DataSource}
read_callback::Ptr{Cvoid}
end
"""
Http2ProtocolError.
"""
mutable struct Http2ProtocolError <: Exception
lib_error_code::Nghttp2Error
msg::String
Http2ProtocolError(lib_error_code::Nghttp2Error, msg::String) = new(lib_error_code, msg)
function Http2ProtocolError(lib_error_code::Nghttp2Error)
str_error = ccall(
(:nghttp2_strerror, libnghttp2),
Cstring,
(Nghttp2Error,),
lib_error_code)
return new(lib_error_code, unsafe_string(str_error))
end
end
abstract type AbstractSession end
"""
Library definition.
"""
mutable struct Http2Stream <: IO
session::AbstractSession
stream_id::Int32
buffer::IOBuffer
headers::Dict{String,String}
lock::ReentrantLock
eof::Bool
Http2Stream(session::AbstractSession, stream_id::Int32) =
return new(
session,
stream_id,
PipeBuffer(),
Dict{String,String}(),
ReentrantLock(),
false)
end
"""
Tests whether an HTTP2 stream is at end-of-file.
"""
function Base.eof(http2_stream::Http2Stream)::Bool
lock(http2_stream.lock) do
return http2_stream.eof && eof(http2_stream.buffer)
end
end
"""
Returns number of bytes available for reading before a read from this stream will block.
"""
function Base.bytesavailable(http2_stream::Http2Stream)
lock(http2_stream.lock) do
return bytesavailable(http2_stream.buffer)
end
end
"""
Determines whether the underlying session IO is not yet closed. Even if the stream is closed, it may still have data to read in its buffer; use eof to check for the ability to read data.
"""
function Base.isopen(http2_stream::Http2Stream)
return isopen(http2_stream.session.io)
end
"""
Ensures there are requested number of bytes in the Http2Stream.
"""
function ensure_in_buffer(http2_stream::Http2Stream, nb::Integer)
should_read = true
# Process HTTP2 stack until there is no more available data in HTTP2 stream.
while should_read
lock(http2_stream.lock) do
if bytesavailable(http2_stream.buffer) >= nb || http2_stream.eof
should_read = false
end
end
if should_read && internal_read!(http2_stream.session)
continue
end
# Read failed
break
end
# Throw exception if session is in error state.
if has_error(http2_stream.session)
throw(http2_stream.session.exception)
end
end
"""
Reads available data from the HTTP2 stream.
"""
function Base.read(http2_stream::Http2Stream)::Vector{UInt8}
ensure_in_buffer(http2_stream, 1)
lock(http2_stream.lock) do
result_buffer = read(http2_stream.buffer)
return result_buffer
end
end
"""
Reads at most nb bytes from from the HTTP2 stream.
"""
function Base.read(http2_stream::Http2Stream, nb::Integer)::Vector{UInt8}
ensure_in_buffer(http2_stream, nb)
lock(http2_stream.lock) do
if bytesavailable(http2_stream.buffer) < nb
throw(EOFError())
end
result_buffer = read(http2_stream.buffer, nb)
return result_buffer
end
end
function Base.read(http2_stream::Http2Stream, ::Type{UInt8})::UInt8
return read(http2_stream, Core.sizeof(UInt8))[begin + 0]
end
function Base.unsafe_read(http2_stream::Http2Stream, p::Ptr{UInt8}, nb::UInt)
ensure_in_buffer(http2_stream, nb)
lock(http2_stream.lock) do
if bytesavailable(http2_stream.buffer) < nb
throw(EOFError())
end
result_buffer = read(http2_stream.buffer, nb)
GC.@preserve result_buffer unsafe_copyto!(p, pointer(result_buffer), nb)
end
end
"""
Writes the data to the Http2 stream.
"""
function Base.write(http2_stream::Http2Stream, out_buffer::Vector{UInt8})
lock(http2_stream.lock) do
# Write the data to the steam.
return write(http2_stream.buffer, out_buffer)
end
end
"""
Internal HTTP2 session.
"""
mutable struct Session <: AbstractSession
io::IO
nghttp2_session::Nghttp2Session
recv_streams::Dict{Int32,Http2Stream}
recv_streams_id::Set{Int32}
exception::Option{Exception}
lock::ReentrantLock
read_lock::ReentrantLock
function Session(io::IO, nghttp2_session::Nghttp2Session)
return new(
io,
nghttp2_session,
Dict{Int32,Http2Stream}(),
Set{Int32}(),
nothing,
ReentrantLock(),
ReentrantLock())
end
end
"""
Retrieves the Session object from the nghttp2_session data.
The Session object must be pinned.
"""
function session_from_data(user_data::Ptr{Cvoid})::Session
session::Session = unsafe_pointer_to_objref(user_data)
return session
end
"""
Sets the session object in Nghttp2Session structure.
The Session object must be pinned.
"""
function session_set_data(session::Session)
return ccall(
(:nghttp2_session_set_user_data, libnghttp2),
Cvoid,
(Nghttp2Session, Ptr{Cvoid}),
session.nghttp2_session,
pointer_from_objref(session))
end
function nghttp2_option_set_no_auto_window_update(nghttp2_option::Nghttp2Option, value::Cint)
return ccall(
(:nghttp2_option_set_no_auto_window_update, libnghttp2),
Cvoid,
(Nghttp2Option, Cint),
nghttp2_option,
value)
end
"""
Session callbacks.
"""
mutable struct Nghttp2SessionCallbacks
ptr::Ptr{Cvoid}
function Nghttp2SessionCallbacks()::Nghttp2SessionCallbacks
callbacks = new(C_NULL)
result = ccall(
(:nghttp2_session_callbacks_new, libnghttp2),
Cint,
(Ref{Nghttp2SessionCallbacks},),
callbacks)
if (result != 0)
throw(Http2ProtocolError(Nghttp2Error(result)))
end
finalizer(free, callbacks)
ccall(
(:nghttp2_session_callbacks_set_on_frame_recv_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_frame_recv_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_recv_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_recv_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_on_begin_headers_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_begin_headers_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_on_header_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_header_recv_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_on_data_chunk_recv_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_data_chunk_recv_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_send_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_send_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_error_callback2, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_error_callback_ptr)
ccall(
(:nghttp2_session_callbacks_set_on_stream_close_callback, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks, Ptr{Cvoid}),
callbacks,
NGHTTP2_CALLBACKS.x.on_stream_close_callback_ptr)
return callbacks
end
end
function free(nghttp2_callbacks::Nghttp2SessionCallbacks)
ccall(
(:nghttp2_session_callbacks_del, libnghttp2),
Cvoid,
(Nghttp2SessionCallbacks,),
nghttp2_callbacks)
nghttp2_callbacks.ptr = C_NULL
return nothing
end
"""
Server session.
Creates a new server session and stores the session object in the lookup dictionary.
"""
function server_session_new(io::IO)::Session
nghttp2_session::Nghttp2Session = Nghttp2Session(C_NULL)
nghttp2_session_callbacks = Nghttp2SessionCallbacks()
result = ccall(
(:nghttp2_session_server_new, libnghttp2),
Cint,
(Ref{Nghttp2Session}, Nghttp2SessionCallbacks, Ptr{Cvoid}),
nghttp2_session,
nghttp2_session_callbacks,
C_NULL)
if (result != 0)
throw(Http2ProtocolError(Nghttp2Error(result)))
end
finalizer(free, nghttp2_session)
session = Session(io, nghttp2_session)
finalize(nghttp2_session_callbacks)
return session
end
"""
Client session.
Creates a new client session.
"""
function client_session_new(io::IO)::Session
nghttp2_session::Nghttp2Session = Nghttp2Session(C_NULL)
nghttp2_session_callbacks = Nghttp2SessionCallbacks()
result = ccall(
(:nghttp2_session_client_new, libnghttp2),
Cint,
(Ref{Nghttp2Session}, Nghttp2SessionCallbacks, Ptr{Cvoid}),
nghttp2_session,
nghttp2_session_callbacks,
C_NULL)
if (result != 0)
throw(Http2ProtocolError(Nghttp2Error(result)))
end
finalizer(free, nghttp2_session)
session = Session(io, nghttp2_session)
finalize(nghttp2_session_callbacks)
return session
end
"""
Nghttp2Session.
"""
function is_nghttp2_server_session(nghttp2_session::Nghttp2Session)::Bool
result = ccall(
(:nghttp2_session_check_server_session, libnghttp2),
Cint,
(Nghttp2Session,),
nghttp2_session)
return result != 0
end
function free(nghttp2_session::Nghttp2Session)
ccall(
(:nghttp2_session_del, libnghttp2),
Cvoid,
(Nghttp2Session,),
nghttp2_session)
nghttp2_session.ptr = C_NULL
return nothing
end
function nghttp2_session_terminate_session(nghttp2_session::Nghttp2Session, error_code::UInt32)
return ccall(
(:nghttp2_session_terminate_session, libnghttp2),
Cint,
(Nghttp2Session, UInt32),
nghttp2_session, error_code)
end
function nghttp2_submit_shutdown_notice(nghttp2_session::Nghttp2Session)
return ccall(
(:nghttp2_submit_shutdown_notice, libnghttp2),
Cint,
(Nghttp2Session,),
nghttp2_session)
end
function nghttp2_session_send(nghttp2_session::Nghttp2Session)
return ccall(
(:nghttp2_session_send, libnghttp2),
Cint,
(Nghttp2Session,),
nghttp2_session)
end
function nghttp2_session_submit_settings(nghttp2_session::Nghttp2Session, settings::Vector{SettingsEntry})
return ccall(
(:nghttp2_submit_settings, libnghttp2),
Cint,
(Nghttp2Session, UInt8, Ptr{Cvoid}, Csize_t),
nghttp2_session,
NGHTTP2_FLAG_NONE,
pointer(settings),
length(settings))
end
function nghttp2_submit_goaway(nghttp2_session::Nghttp2Session)
return ccall(
(:nghttp2_submit_goaway, libnghttp2),
Cint,
(Nghttp2Session, UInt8, Cint, UInt32, Ptr{Cvoid}, Csize_t),
nghttp2_session,
NGHTTP2_FLAG_NONE,
0,
NGHTTP2_NO_ERROR,
C_NULL, 0)
end
function nghttp2_session_mem_recv(nghttp2_session::Nghttp2Session, input_data::Vector{UInt8})
return ccall(
(:nghttp2_session_mem_recv, libnghttp2),
Cssize_t,
(Nghttp2Session, Ptr{UInt8}, Csize_t),
nghttp2_session,
input_data,
length(input_data))
end
function nghttp2_session_recv(nghttp2_session::Nghttp2Session)
return ccall(
(:nghttp2_session_recv, libnghttp2),
Cint,
(Nghttp2Session,),
nghttp2_session)
end
function nghttp2_submit_window_update(nghttp2_session::Nghttp2Session, stream_id::Int32, window_size_increment::Int32)
return ccall(
(:nghttp2_submit_window_update, libnghttp2),
Cint,
(Nghttp2Session, UInt8, Cint, Cint),
nghttp2_session,
NGHTTP2_FLAG_NONE,
stream_id,
window_size_increment)
end
"""
Errors.
"""
nghttp2_error_to_string(error::Nghttp2Error) =
unsafe_string(
ccall(
(:nghttp2_strerror, libnghttp2),
Cstring,
(Cint,),
error))
nghttp2_version() =
unsafe_load(
ccall(
(:nghttp2_version, libnghttp2),
Ptr{Nghttp2Info},
(Cint,),
0))
function Base.show(io::IO, nghttp2_info::Nghttp2Info)
return println(
io,
"""NGHttp2 lib: $(nghttp2_info.version_num)
path: $(libnghttp2)
version: $(unsafe_string(nghttp2_info.version_str))
protocol: $(unsafe_string(nghttp2_info.proto_str))""")
end
function Base.show(io::IO, nghttp2_frame_header::Nghttp2FrameHeader)
return println(
io,
"""Frame:
length: $(nghttp2_frame_header.length)
stream_id: $(nghttp2_frame_header.stream_id)
type: $(Nghttp2FrameType(nghttp2_frame_header.type))
flags: $(nghttp2_frame_header.flags)""")
end
function Base.show(io::IO, nv_pair::NVPair)
local nv_pair_str::String
if (nv_pair.name == C_NULL)
nv_pair_str = "nothing"
else
nv_pair_str = "NVPair: { name: '$(unsafe_string(nv_pair.name)) $(nv_pair.name)', value: '$(unsafe_string(nv_pair.value)) $(nv_pair.value)' }"
end
return println(io, "NVPair: { $nv_pair_str }")
end
"""
Callback implementation.
"""
function on_recv_callback(
nghttp2_session::Nghttp2Session,
buf::Ptr{UInt8},
len::Csize_t,
flags::Cint,
user_data::Ptr{Cvoid})::Cssize_t
# Get the server session object.
session = session_from_data(user_data)
result::Cssize_t = 0
return result
end
function on_frame_recv_callback(nghttp2_session::Nghttp2Session, frame::Nghttp2Frame, user_data::Ptr{Cvoid})::Cint
# Get the server session object.
session = session_from_data(user_data)
frame_header = unsafe_load(Ptr{Nghttp2FrameHeader}(frame.ptr))
stream_id = frame_header.stream_id
last_frame = stream_id != 0 && frame_header.flags & UInt8(NGHTTP2_FLAG_END_STREAM) != 0
if last_frame
# Last frame in the stream detected, mark the stream as EOF.
local http2_stream::Http2Stream
lock(session.lock) do
return http2_stream = session.recv_streams[frame_header.stream_id]
end
lock(http2_stream.lock) do
return http2_stream.eof = true
end
end
result::Cint = 0
return result
end
function on_begin_headers_callback(nghttp2_session::Nghttp2Session, frame::Nghttp2Frame, user_data::Ptr{Cvoid})::Cint
# Get the server session object.
session = session_from_data(user_data)
frame_header = unsafe_load(Ptr{Nghttp2FrameHeader}(frame.ptr))
# Create a new stream.
lock(session.lock) do
if !haskey(session.recv_streams, frame_header.stream_id)
session.recv_streams[frame_header.stream_id] = Http2Stream(session, frame_header.stream_id)
push!(session.recv_streams_id, frame_header.stream_id)
end
end
result::Cint = 0
return result
end
function on_header_recv_callback(
nghttp2_session::Nghttp2Session,
frame::Nghttp2Frame,
name::Ptr{UInt8},
namelen::Csize_t,
value::Ptr{UInt8},
valuelen::Csize_t,
flags::UInt8,
user_data::Ptr{Cvoid})::Cint
# Get the server session object.
session = session_from_data(user_data)
frame_header = unsafe_load(Ptr{Nghttp2FrameHeader}(frame.ptr))
# Copy from received buffer to the local data.
header_name = Vector{UInt8}(undef, namelen)
GC.@preserve header_name unsafe_copyto!(pointer(header_name), name, namelen)
header_value = Vector{UInt8}(undef, valuelen)
GC.@preserve header_value unsafe_copyto!(pointer(header_value), value, valuelen)
# Store the header in the session stream.
local recv_stream::Http2Stream
lock(session.lock) do
return recv_stream = session.recv_streams[frame_header.stream_id]
end
lock(recv_stream.lock) do
return recv_stream.headers[String(header_name)] = String(header_value)
end
result::Cint = 0
return result
end
function on_data_chunk_recv_callback(
nghttp2_session::Nghttp2Session,
flags::UInt8,
stream_id::Cint,
buf::Ptr{UInt8},
len::Csize_t,
user_data::Ptr{Cvoid})::Cint
# Get the server session object.
session = session_from_data(user_data)
# Copy from received buffer to the local data.
data = Vector{UInt8}(undef, len)
GC.@preserve data unsafe_copyto!(pointer(data), buf, len)
# Write received data to the received stream buffer.
local http2_stream::Http2Stream
lock(session.lock) do
return http2_stream = session.recv_streams[stream_id]
end
write(http2_stream, data)
result::Cint = 0
return result
end
function on_send_callback(
nghttp2_session::Nghttp2Session,
data::Ptr{UInt8},
length::Csize_t,
flags::Cint,
user_data::Ptr{Cvoid})::Csize_t
# Get the server session object.
session = session_from_data(user_data)
# Copy send data to the buffer.
out_buffer = Vector{UInt8}(undef, length)
GC.@preserve out_buffer unsafe_copyto!(pointer(out_buffer), data, length)
try
write(session.io, out_buffer)
catch ex
lock(session.lock) do
return session.exception = ex
end
return Int(NGHTTP2_ERR_CALLBACK_FAILURE) % Csize_t
end
return length
end
function on_error_callback(
nghttp2_session::Nghttp2Session,
lib_error_code::Cint,
msg::Ptr{UInt8},
len::Csize_t,
user_data::Ptr{Cvoid})::Cint
# Get the server session object.
session = session_from_data(user_data)
println("on_error_callback session:$(session.nghttp2_session) nghtt2_error_code: $(lib_error_code)")
# Create HTTP2 error object, include Nghttp2 error.
http2_protocol_error = Http2ProtocolError(Nghttp2Error(lib_error_code), unsafe_string(msg))
lock(session.lock) do
return session.exception = http2_protocol_error
end
@show session.exception
result::Cint = 0
return result
end
function on_data_source_read_callback(
nghttp2_session::Nghttp2Session,
stream_id::Cint,
buf::Ptr{UInt8},
buf_length::Csize_t,
data_flags::Ptr{UInt32},
data_source::Ptr{Ptr{IOBuffer}},
user_data::Ptr{Cvoid})::Cssize_t
# Get DataSource object.
data_source = unsafe_load(data_source)
data_source = unsafe_pointer_to_objref(data_source)
# TODO on_data_source_read_callback here
in_buffer = read(data_source.send_stream, buf_length)
in_length = length(in_buffer)
GC.@preserve in_buffer unsafe_copyto!(buf, pointer(in_buffer), in_length)
source_stream_eof = eof(data_source.send_stream)
source_has_trailer = source_stream_eof && length(data_source.trailer) != 0
send_data_flags::Nghttp2DataFlags = NGHTTP2_DATA_FLAG_NONE
if source_stream_eof
send_data_flags |= NGHTTP2_DATA_FLAG_EOF
end
if source_has_trailer
send_data_flags |= NGHTTP2_DATA_FLAG_NO_END_STREAM
# Submit the trailer.
result = ccall(
(:nghttp2_submit_trailer, libnghttp2),
Cint,
(Nghttp2Session, Int32, Ptr{Cvoid}, Csize_t),
nghttp2_session,
stream_id,
pointer(data_source.trailer),
length(data_source.trailer))
end
unsafe_store!(data_flags, UInt32(send_data_flags))
result::Cssize_t = in_length
return result
end
function on_stream_close_callback(
nghttp2_session::Nghttp2Session,
stream_id::Cint,
error_code::UInt32,
user_data::Ptr{Cvoid})::Cint
# Get the server session object.
session = session_from_data(user_data)
result::Cint = 0
return result
end
"""
Nghttp2 callbacks.
"""
struct Nghttp2Callbacks
on_recv_callback_ptr::Ptr{Nothing}
on_frame_recv_callback_ptr::Ptr{Nothing}
on_begin_headers_callback_ptr::Ptr{Nothing}
on_header_recv_callback_ptr::Ptr{Nothing}
on_data_chunk_recv_callback_ptr::Ptr{Nothing}
on_send_callback_ptr::Ptr{Nothing}
on_error_callback_ptr::Ptr{Nothing}
on_data_source_read_callback_ptr::Ptr{Nothing}
on_stream_close_callback_ptr::Ptr{Nothing}
function Nghttp2Callbacks()
on_recv_callback_ptr = @cfunction on_recv_callback Cssize_t (
Nghttp2Session,
Ptr{UInt8},
Csize_t,
Cint,
Ptr{Cvoid})
on_frame_recv_callback_ptr = @cfunction on_frame_recv_callback Cint (
Nghttp2Session,
Nghttp2Frame,
Ptr{Cvoid})
on_begin_headers_callback_ptr = @cfunction on_begin_headers_callback Cint (
Nghttp2Session,
Nghttp2Frame,
Ptr{Cvoid})
on_header_recv_callback_ptr = @cfunction on_header_recv_callback Cint (
Nghttp2Session,
Nghttp2Frame,
Ptr{UInt8},
Csize_t,
Ptr{UInt8},
Csize_t,
UInt8,
Ptr{Cvoid})
on_data_chunk_recv_callback_ptr = @cfunction on_data_chunk_recv_callback Cint (
Nghttp2Session,
UInt8,
Cint,
Ptr{UInt8},
Csize_t,
Ptr{Cvoid})
on_send_callback_ptr = @cfunction on_send_callback Csize_t (
Nghttp2Session,
Ptr{UInt8},
Csize_t,
Cint,
Ptr{Cvoid})
on_error_callback_ptr = @cfunction on_error_callback Cint (
Nghttp2Session,
Cint,
Ptr{UInt8},
Csize_t,
Ptr{Cvoid})
on_data_source_read_callback_ptr = @cfunction on_data_source_read_callback Cssize_t (
Nghttp2Session,
Cint,
Ptr{UInt8},
Csize_t,
Ptr{UInt32},
Ptr{Ptr{IOBuffer}},
Ptr{Cvoid})
on_stream_close_callback_ptr = @cfunction on_stream_close_callback Cint (
Nghttp2Session,
Cint,
UInt32,
Ptr{Cvoid})
return new(
on_recv_callback_ptr,
on_frame_recv_callback_ptr,
on_begin_headers_callback_ptr,
on_header_recv_callback_ptr,
on_data_chunk_recv_callback_ptr,
on_send_callback_ptr,
on_error_callback_ptr,
on_data_source_read_callback_ptr,
on_stream_close_callback_ptr)
end
end
"""
HTTP2 session.
"""
function submit_settings(session::Session, settings::Vector{SettingsEntry})
GC.@preserve session begin
session_set_data(session)
result = nghttp2_session_submit_settings(session.nghttp2_session, settings)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
result = nghttp2_session_send(session.nghttp2_session)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
end
end
"""
Returns true, if session is in error state.
"""
function has_error(session::Session)::Bool
lock(session.lock) do
return !isnothing(session.exception)
end
end
function set_error(session::Session, http2_protocol_error::Http2ProtocolError)
lock(session.lock) do
if !isnothing(session.exception)
session.exception = http2_protocol_error
end
end
end
"""
Reads from the session input IO and sends it to HTTP2 stack.
Returns true if there is more data available.
Ensure only one task is reading from the session.
"""
function internal_read!(session::Session)::Bool
# Return if there are errors.
if has_error(session)
return false
end
lock(session.read_lock) do
if bytesavailable(session.io) != 0 || (isreadable(session.io) && !eof(session.io))
available_bytes = bytesavailable(session.io)
input_data = read(session.io, available_bytes)
GC.@preserve session begin
session_set_data(session)
result = nghttp2_session_mem_recv(session.nghttp2_session, input_data)
if result < 0
set_error(session, Http2ProtocolError(Nghttp2Error(result)))
end
result = nghttp2_session_send(session.nghttp2_session)
if result < 0
set_error(session, Http2ProtocolError(Nghttp2Error(result)))
end
end
return true
end
end
return false
end
"""
Receives next Http2Stream from the session.
"""
function Sockets.recv(session::Session)::Option{Http2Stream}
should_read = true
while should_read
lock(session.lock) do
# Throw exception if errors occurred.
if !isnothing(session.exception)
throw(session.exception)
end
# Break, if there is no data available in the session's IO and
# there are no more HTTP2 streams to return.
if !isempty(session.recv_streams_id) || eof(session.io)
should_read = false
end
end
if should_read
# Process received data through the HTTP2 stack.
internal_read!(session)
continue
end
break
end
lock(session.lock) do
# If available, return a new HTTP2 stream.
if !isempty(session.recv_streams_id)
recv_stream_id = pop!(session.recv_streams_id)
recv_stream = session.recv_streams[recv_stream_id]
return recv_stream
end
eof(session.io)
return nothing
end
end
"""
Receives expected Http2Stream from the session.
"""
function Sockets.recv(session::Session, stream_id::Int32)::Option{Http2Stream}
should_read = true
while should_read
lock(session.lock) do
# Throw exception if errors occurred.
if !isnothing(session.exception)
throw(session.exception)
end
# Break, if there is no data available in the session's IO and there are no more HTTP2 streams to return.
if stream_id in session.recv_streams_id || !isreadable(session.io) || eof(session.io)
should_read = false
end
end
if should_read
# Process received data through the HTTP2 stack.
internal_read!(session)
continue
end
break
end
lock(session.lock) do
# If available, return a new HTTP2 stream.
if stream_id in session.recv_streams_id
delete!(session.recv_streams_id, stream_id)
recv_stream = session.recv_streams[stream_id]
return recv_stream
end
if isempty(session.recv_streams_id)
eof(session.io)
end
return nothing
end
end
"""
Returns available Http2Streams.
If there are no active Http2Streams, returns nothing.
"""
function try_recv(session::Session)::Option{Http2Stream}
lock(session.lock) do
# Throw exception if errors occurred.
if !isnothing(session.exception)
throw(session.exception)
end
# If available, return Http2Stream.
if !isempty(session.recv_streams_id)
recv_stream_id = pop!(session.recv_streams_id)
recv_stream = session.recv_streams[recv_stream_id]
return recv_stream
end
return nothing
end
end
"""
Sends the data in IO stream via HTTP2 session.
"""
function send(
session::Session,
stream_id::Int32,
send_buffer::IO,
header::StringPairs=StringPairs(),
trailer::StringPairs=StringPairs())
headers::NVPairs = convert_to_nvpairs(header)
trailers::NVPairs = convert_to_nvpairs(trailer)
GC.@preserve session send_buffer headers trailers begin
session_set_data(session)
data_source = DataSource(send_buffer, trailers)
GC.@preserve data_source begin
data_provider = DataProvider(
pointer_from_objref(data_source),
NGHTTP2_CALLBACKS.x.on_data_source_read_callback_ptr)
GC.@preserve data_provider begin
# send headers, data, and trailers
result = ccall(
(:nghttp2_submit_response, libnghttp2),
Cint,
(Nghttp2Session, Int32, Ptr{Cvoid}, Csize_t, Ptr{Cvoid}),
session.nghttp2_session,
stream_id,
pointer(headers),
length(headers),
pointer_from_objref(data_provider))
if result < 0
set_error(session, Http2ProtocolError(Nghttp2Error(result)))
end
result = nghttp2_session_send(session.nghttp2_session)
if result < 0
set_error(session, Http2ProtocolError(Nghttp2Error(result)))
end
while !eof(send_buffer) && !has_error(session)
internal_read!(session)
end
end
end
end
# Release headers and trailers after sending the frame.
finalize(headers)
finalize(trailers)
# Throw if error occurred.
if has_error(session)
throw(session.exception)
end
end
function send(session::Session, send_buffer::IO, header::StringPairs=StringPairs(), trailer::StringPairs=StringPairs())
headers::NVPairs = convert_to_nvpairs(header)
trailers::NVPairs = convert_to_nvpairs(trailer)
GC.@preserve session send_buffer headers trailers begin
session_set_data(session)
data_source = DataSource(send_buffer, trailers)
GC.@preserve data_source begin
data_provider = DataProvider(
pointer_from_objref(data_source),
NGHTTP2_CALLBACKS.x.on_data_source_read_callback_ptr)
GC.@preserve data_provider begin
# send headers, data, and trailers
stream_id = ccall(
(:nghttp2_submit_request, libnghttp2),
Cint,
(Nghttp2Session, Ptr{Cvoid}, Ptr{Cvoid}, Csize_t, Ptr{Cvoid}),
session.nghttp2_session,
C_NULL,
pointer(headers),
length(headers),
pointer_from_objref(data_provider))
if stream_id < 0
throw(Http2ProtocolError(Nghttp2Error(stream_id)))
end
result = nghttp2_session_send(session.nghttp2_session)
if result < 0
set_error(session, Http2ProtocolError(Nghttp2Error(result)))
end
while !eof(send_buffer) && !has_error(session)
internal_read!(session)
end
end
end
end
# Release headers and trailers after sending the frame.
finalize(headers)
finalize(trailers)
# Throw if error occurred.
if has_error(session)
throw(session.exception)
end
return stream_id
end
function is_server_session(session::Session)::Bool
return is_nghttp2_server_session(session.nghttp2_session)
end
"""
Public API.
Wrapper classes around Http2Session.
"""
"""
Http2 client session.
"""
struct Http2ClientSession
session::Session
end
function open(io::IO)::Http2ClientSession
session = client_session_new(io)
result = submit_settings(session, DEFAULT_CLIENT_SETTINGS)
return Http2ClientSession(session)
end
"""
Submit a request.
"""
function submit_request(http2_client_session::Http2ClientSession, io::IO)
return submit_request(http2_client_session, io, StringPairs(), StringPairs())
end
function submit_request(http2_client_session::Http2ClientSession, io::IO, header::StringPairs)
return submit_request(http2_client_session, io, header, StringPairs())
end
function submit_request(
http2_client_session::Http2ClientSession,
io::IO,
header::StringPairs,
trailer::StringPairs)::Option{Http2Stream}
# Send the request.
response_stream_id = send(http2_client_session.session, io, header, trailer)
response_stream = recv(http2_client_session.session, response_stream_id)
return response_stream
end
"""
Http2 server session.
"""
struct Http2ServerSession
session::Session
end
function from_accepted(io::IO)::Http2ServerSession
session = server_session_new(io)
result = submit_settings(session, DEFAULT_SERVER_SETTINGS)
return Http2ServerSession(session)
end
function Sockets.recv(http2_server_session::Http2ServerSession)
return recv(http2_server_session.session)
end
function Base.close(http2_server_session::Http2ServerSession)
result = nghttp2_submit_shutdown_notice(http2_server_session.session.nghttp2_session)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
result = nghttp2_session_send(http2_server_session.session.nghttp2_session)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
result = nghttp2_submit_goaway(http2_server_session.session.nghttp2_session)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
result = nghttp2_session_send(http2_server_session.session.nghttp2_session)
if result != 0
throw(Http2ProtocolError(Nghttp2Error(result)))
end
return close(http2_server_session.session.io)
end
"""
Http2 stream.
"""
function submit_response(
http2_stream::Http2Stream,
io::IO,
header::StringPairs=StringPairs(),
trailer::StringPairs=StringPairs())
return send(
http2_stream.session,
http2_stream.stream_id,
io,
header,
trailer)
end
"""
Runme.
"""
const NGHTTP2_CALLBACKS = Ref{Nghttp2Callbacks}()
"""
Initialize the module.
"""
function __init__()
println("$(@__MODULE__)::__init")
NGHTTP2_CALLBACKS.x = Nghttp2Callbacks()
return nothing
end
end # module Nghttp2
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] | 2.240696 | 22,543 |
module TestProj
using Example
export hello
end
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module TiledViews
using IndexFunArrays # needed for the default window function.
using NDTools # for linear_index
# using NDTools
export TiledView, get_num_tiles, TiledWindowView, tile_centers, get_window, tiled_processing
export get_num_tiles, eachtile, eachtilenumber, eachtilerelpos
tuple_len(::NTuple{N, Any}) where {N} = Val{N}()
# T refers to the result type. N to the dimensions of the final array, and M to the dimensions of the raw array
struct TiledView{T, N, M, AA<:AbstractArray{T, M}} <: AbstractArray{T, N}
# stores the data.
parent::AA
# output size of the array
tile_size::NTuple{M, Int}
tile_period::NTuple{M, Int}
tile_offset::NTuple{M, Int} # the distance from the wrapping arrray to the start of stored data
pad_value::T
# Constructor function
function TiledView{T, N, M}(data::AA; tile_size::NTuple{M,Int}, tile_period::NTuple{M,Int}, tile_offset::NTuple{M,Int}, pad_value=nothing) where {T,M,N,AA}
if isnothing(pad_value)
if T <: NTuple
pad_value = T(Base.Iterators.repeated(0))
# elseif T <: AbstractArray
else
pad_value = convert(T,0) # this may crash, but then the user should specify a valid pad_value
end
end
return new{T, N, M, AA}(data, tile_size, tile_period, tile_offset, pad_value)
end
end
function center(data)
return size(data) .÷2 .+1
end
"""
TiledView(data::F, tile_size::NTuple{N,Int}, tile_overlap::NTuple{N,Int}, tile_center::NTuple{M,Int} = (mod.(tile_size,2) .+1); pad_value::T, keep_center=true)
Creates an 2N dimensional view of the data by tiling the N-dimensional data as
specified by tile_size, tile_overlap and optionally tile_center.
`data`. the inputdata to decompose into a TiledView. No copies are made for the TiledView and
the raw data can be accessed via myview.parent.
`tile_size`. A Tuple describing the size of each tile. This size will form the first N dimensions of the
result of size(myview). The second N dimensions refer to N-dimensional tile numbering.
`tile_overlap`. Tuple specifying the overlap between successive tiles in voxels. This implicitely
defines the pitch between tiles as (tile_size .- tile_overlap).
`pad_value`. Specifies the answer that is returned when get_index is applied to a position outside the source array.
`keep_center`. This boolean specifies whether the center of the parant `data` will be aligned with the center of the central tile. If `false`, the first tile starts at offset zero.
`tile_center`. Only used if `keep_center` is true. It defines the center position in the central tile. The default is `tile_size .÷ 2 .+1`.
# Examples
```jldoctest
julia> a = TiledView(reshape(1:49,(7,7)), (4, 4),(1, 1));
julia> a.parent
7×7 reshape(::UnitRange{Int64}, 7, 7) with eltype Int64:
1 8 15 22 29 36 43
2 9 16 23 30 37 44
3 10 17 24 31 38 45
4 11 18 25 32 39 46
5 12 19 26 33 40 47
6 13 20 27 34 41 48
7 14 21 28 35 42 49
julia> size(a)
(4, 4, 3, 3)
```
"""
function TiledView(data::AbstractArray{T,M}, tile_size::NTuple{M,Int}, tile_overlap::NTuple{M,Int}=tile_size .* 0,
tile_center::NTuple{M,Int} = (tile_size .÷ 2 .+1); pad_value=nothing, keep_center=true) where {T, M}
# Note that N refers to the original number of dimensions
tile_period = tile_size .- tile_overlap
if keep_center
data_center = center(data)
tile_offset = mod.((data_center .- tile_center), tile_period)
else
tile_offset = tile_period .* 0
end
N = 2*M
return TiledView{T,N,M}(data; tile_size=tile_size, tile_period=tile_period, tile_offset=tile_offset, pad_value=pad_value)
end
function get_num_tiles(data::TiledView)
num_tiles = ((size(data.parent) .+ data.tile_offset .- 1) .÷ data.tile_period) .+ 1
return num_tiles
end
# define AbstractArray function to allow to treat the generator as an array
# See https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-array
function Base.size(A::TiledView)
return (A.tile_size...,(get_num_tiles(A))...)
end
function zeros_like(A::TiledView, ::Type{T}=eltype(A.parent)) where {T}
TiledView{T,ndims(A),length(A.tile_size)}(zeros(T, size(A.parent)); tile_size=A.tile_size, tile_period=A.tile_period, tile_offset=A.tile_offset, pad_value=A.pad_value)
end
function ones_like(A::TiledView, ::Type{T}=eltype(A.parent)) where {T}
TiledView{T,ndims(A),length(A.tile_size)}(ones(T, size(A.parent)); tile_size=A.tile_size, tile_period=A.tile_period, tile_offset=A.tile_offset, pad_value=A.pad_value)
end
# Note that the similar function below will most of the times expand the overall required datasize
function Base.similar(A::TiledView, ::Type{T}=eltype(A.parent), dims::Dims=size(A)) where {T}
# The first N coordinates are position within a tile, the second N coordinates are tile number
#= N = length(A.tile_size)
new_tile_sz = dims[1:N]
new_num_tiles = dims[N + 1:end]
new_tile_period = A.tile_period .+ new_tile_sz .- A.tile_size
new_core_sz = new_num_tiles .* new_tile_period .- A.tile_offset # keep the overlap the same as before
TiledView{T,ndims(A),length(A.tile_size)}(similar(A.parent, T, new_core_sz); tile_size=new_tile_sz, tile_period=new_tile_period, tile_offset=A.tile_offset, pad_value=A.pad_value)
=#
similar(A.parent, T, dims) # this returns an ordinary array, but this seems the only way to handle cases like: my_tiled_array[:,:,2,3] which expect a 2D array
end
# Array{eltype(A)}(undef, size...)
# %24 = Base.getproperty(A, :parent)::AbstractMatrix{Float64}
# calculate the entry according to the index
# Base.getindex(A::IndexFunArray{T,N}, I::Vararg{B, N}) where {T,N, B} = return A.generator(I)
function pos_from_tile(A::TiledView{T,N}, TilePos::NTuple{M,Int}, TileNum::NTuple{M,Int}) where {T,N,M}
Tuple(TilePos[n] - A.tile_offset[n] + (TileNum[n]-1) * A.tile_period[n] for n in 1:M)
end
# calculate the entry according to the index
Base.@propagate_inbounds function Base.getindex(A::TiledView{T,N,M,AA}, I::Vararg{Int, N})::T where {T,N,M,AA}
@boundscheck checkbounds(A, I...)
@inbounds pos = (I[n] - A.tile_offset[n] + (I[n+M].-1) * A.tile_period[n] for n in 1:M)
if Base.checkbounds(Bool, A.parent, pos...)
return Base.getindex(A.parent, pos...)::T
else
return A.pad_value :: T;
end
end
Base.setindex!(A::TiledView{T,N,M,AA}, v, I::Vararg{Int,N}) where {T,N,M,AA} = begin
@boundscheck checkbounds(A, I...)
@inbounds pos = (I[n] - A.tile_offset[n] + (I[n+M].-1) * A.tile_period[n] for n in 1:M)
# pos = TilePos .- A.tile_offset .+ (TileNum.-1) .* A.tile_period
if Base.checkbounds(Bool, A.parent, pos...)
return setindex!(A.parent, v, pos... )
else
return convert(T,0)
end
end
## Some functions for generating useful tilings
"""
get_window(A::TiledView; window_function=window_hanning, get_norm=false, verbose=false, offset = CtrFT);
Calculates a window matching to the `TiledView`.
`window_function`. The window function as defined in IndexFunArrays to apply to the TiledView.
The result is currently not any longer a view as it is unclear how to wrap the multiplication into a view.
For this reason the TiledView without the window applied is also returned and can be used for assignments.
By default a von Hann window (window_hanning) is used. For even sizes the window is centered at the integer coordinate right of the middle position (`CtrFT`).
`get_norm`. An optional Boolean argument allowing to also obtain the normalization map for the boarder pixels, which
not necessarily undergo all required window operations. In a future version it may be possible
to automatically lay out the windowing such that this effect can be avoided.
`verbose`. If true, diagnostic information on the window layout is printed.
`offset`. defines where the center of the window is placed. See `IndexFunArrays.jl` for details.
# Returns
`matching_window`. a window that can be applied to the view via multiplication myview.*matching_window
This is intentionally not provided as a product to separate the features conceptually
when it comes to write access.
`normalized`. only returned for get_norm=true. Contains an array with the normalization information by
mapping the window back to the original data. This is useful for incomplete coverage of the tiles
as well as using windows which do not sum up to one in the tiling process.
# Examples
```jldoctest
julia> data = ones(10,10).+0.0;
julia> myview = TiledView(data, (5, 5), (2,2));
julia> win = get_window(myview, verbose=true);
Tiles with pitch (3, 3) overlap by (2, 2) pixels.
Window starts at (0.5, 0.5) and ends at (2.5, 2.5).
julia> win
5×5 IndexFunArrays.IndexFunArray{Float64, 2, IndexFunArrays.var"#329#331"{Float64, Tuple{Float64, Float64}, Tuple{Int64, Int64}, Tuple{Float64, Float64}, Tuple{Float64, Float64}}}:
0.0214466 0.125 0.146447 0.125 0.0214466
0.125 0.728553 0.853553 0.728553 0.125
0.146447 0.853553 1.0 0.853553 0.146447
0.125 0.728553 0.853553 0.728553 0.125
0.0214466 0.125 0.146447 0.125 0.0214466
see TiledWindowView() for more examples.
"""
function get_window(A::TiledView; window_function=window_hanning, get_norm=false, verbose=false, offset=CtrFT)
tile_size = A.tile_size
tile_pitch = A.tile_period
tile_overlap = tile_size .- tile_pitch
winend = (tile_size ./ 2.0)
winstart = (winend .- tile_overlap)
if verbose
print("Tiles with pitch $tile_pitch overlap by $tile_overlap pixels.\n")
print("Window starts at $winstart and ends at $winend.\n")
end
if get_norm == false
return window_function(tile_size;
scale=ScaUnit, offset=offset,
border_in=winstart, border_out= winend)
else
my_view = ones_like(A)
normalization = A.parent
normalization .= 0
my_view .+= A .*window_function(tile_size;scale=ScaUnit, offset=offset, border_in=winstart, border_out= winend)
return (window_function(tile_size;
scale=ScaUnit, offset=offset,
border_in=winstart, border_out= winend), normalization)
end
end
"""
function TiledWindowView(data::AbstractArray{T,M}, tile_size::NTuple{M,Int};
rel_overlap::NTuple{M,Float64}=tile_size .*0 .+ 1.0,
window_function=window_hanning, get_norm=false, verbose=false, offset=CtrFT) where {T, M}
Creates an 2N dimensional view of the data by tiling the N-dimensional data as
specified by tile_size, tile_overlap and optionally tile_center.
Additionally a window is applied to this view. If the window_type as defined in
IndexFunArrays sums up to one,
which is the case for window_linear and window_hanning, a linear decomposition of the
data is obtained apart from possible border effects.
`data`. the inputdata to decompose into a TiledView. No copies are made for the TiledView and
the raw data can be accessed via myview.parent.
`tile_size`. A Tuple describing the size of each tile. This size will form the first N dimensions of the
result of size(myview). The second N dimensions refer to N-dimensional tile numbering.
`rel_overlap`. Tuple specifying the relative overlap between successive tiles. The absolute overlap is then calculated as `round.(Int,tile_size./2.0 .* rel_overlap)`.
`window_function`. The window function as defined in IndexFunArrays to apply to the TiledView.
The result is currently not any longer a view as it is unclear how to wrap the multiplication into a view.
For this reason the TiledView without the window applied is also returned and can be used for assignments.
By default a von Hann window (window_hanning) is used.
`get_norm`. An optional Boolean argument allowing to also obtain the normalization map for the boarder pixels, which
not necessarily undergo all required window operations. In a future version it may be possible
to automatically lay out the windowing such that this effect can be avoided.
`verbose`. If true, diagnostic information on the window layout is printed.
`offset`. defines where the center of the window is placed. See `IndexFunArrays.jl` for details.
# Returns
myview, matching_window = TiledWindowView ...
a Tuple of two or three (get_norm=true) with
`myview`. the TiledView of the data without the window which can also be written to.
`matching_window`. a window that can be applied to the view via multiplication myview.*matching_window
This is intentionally not provided as a product to separate the features conceptually
when it comes to write access.
`normalized`. only returned for get_norm=true. Contains an array with the normalization information by
mapping the window back to the original data. This is useful for incomplete coverage of the tiles
as well as using windows which do not sum up to one in the tiling process.
Note that it may be dangerous to directly access the view via a simple .+= operation as
it is not entirely clear, whether it is always garanteed that there could not be any running
conditions with read-write operations, since some points in the referenced array are accessed
multiple times. To avoid such an effect, you can, for example, only acess every second tile along each dimension
in one call.
# Examples
```jldoctest
julia> data = ones(10,10).+0.0;
julia> myview, matching_window = TiledWindowView(data, (5, 5);verbose=true);
Tiles with pitch (3, 3) overlap by (2, 2) pixels.
Window starts at (0.5, 0.5) and ends at (2.5, 2.5).
julia> size(myview)
(5, 5, 4, 4)
julia> matching_window
5×5 IndexFunArray{Float64, 2, IndexFunArrays.var"#199#200"{Float64, Tuple{Float64, Float64}, Tuple{Int64, Int64}, Tuple{Float64, Float64}, Tuple{Float64, Float64}}}:
0.0214466 0.125 0.146447 0.125 0.0214466
0.125 0.728553 0.853553 0.728553 0.125
0.146447 0.853553 1.0 0.853553 0.146447
0.125 0.728553 0.853553 0.728553 0.125
0.0214466 0.125 0.146447 0.125 0.0214466
julia> windowed = collect(myview .* matching_window);
julia> myview[:,:,:,:].=0 # cleares the original array
julia> myview.parent
10×10 Matrix{Float64}:
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
julia> myview .+= windowed # writes the windowed data back into the array
julia> data # lets see if the weigths correctly sum to one?
10×10 Matrix{Float64}:
0.728553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
```
# This result may also be used for subsequent normalization but can also be directly obtained by
julia> myview, matching_window, normalized = TiledWindowView(rand(10,10).+0, (5, 5);get_norm=true);
"""
function TiledWindowView(data::AbstractArray{T,M}, tile_size::NTuple{M,Int};
rel_overlap::NTuple{M,Float64}=tile_size .*0 .+ 1.0,
window_function=window_hanning, get_norm=false, verbose=false, keep_center=true, offset=CtrFT) where {T, M}
tile_overlap = round.(Int,tile_size./2.0 .* rel_overlap)
changeable = TiledView(data,tile_size, tile_overlap, keep_center=keep_center);
win = get_window(changeable, window_function= window_function, get_norm=get_norm, verbose=verbose, offset=offset)
if get_norm
return (changeable, win...)
else
return (changeable, win)
end
end
"""
tile_centers(A, scale=nothing)
returns the relative center coordinates of integer tile centers with respect to the integer center `1 .+ size(A) .÷ 2 `
The tuple `scale` is used to multiply the relative position with a physical pixelsize.
See also: `eachtilerelpos` for a corresponding iterator
"""
function tile_centers(A, scale=nothing)
return collect(eachtilerelpos(A, scale))
end
"""
eachtilerelpos(A, scale=nothing)
returns a generator that iterates through the relative distance of each tile center `1 .+ size(A).÷2` to the center of the the untiled parent array `1 .+ size(parent).÷2`
The tuple `scale` is used to multiply the relative position with a physical pixelsize.
"""
function eachtilerelpos(A, scale=nothing)
nd = ndims(A)/2
ctr_array = (size(A.parent) .÷ 2) .+ 1 # center of the parent array
num_tiles = size(A)[end-nd+1:end]
# ctr_tile = (num_tiles.÷2 .+1)
tile_ctr = (size(A)[1:nd] .÷ 2) .+ 1
if isnothing(scale)
(pos_from_tile(A, tile_ctr, Tuple(idx)) .- ctr_array for idx in CartesianIndices(num_tiles)) # Only the "[" generate a 2D array
# [(Tuple(idx).-1).* A.tile_period .+ ctr for idx in CartesianIndices(num_tiles)]
else
(scale .* (pos_from_tile(A, tile_ctr, Tuple(idx)) .- ctr_array) for idx in CartesianIndices(num_tiles))
end
end
"""
eachtile(tiled_view::TiledView)
returns an iterator which iterates through all tiles. Depending on your application you may also want to use
`tiled_processing` for a convenient way to apply a function to each tile and join all tiles back together.
If you need simultaneous access to the tiles and tile numbers, you can also use `eachtilenumber`.
"""
function eachtile(tiled_view::TiledView)
nd = ndims(tiled_view)÷2
nz = ((size(tiled_view)[1:nd])..., prod(size(tiled_view)[nd+1:end]))
reshaped = reshape(tiled_view, nz)
return eachslice(reshaped, dims=nd+1)
end
"""
eachtilenumber(tiled_view::TiledView)
returns an iterator iterating though all the tile numbers. If you need access to the tiles themselves, use
`eachtile`
"""
function eachtilenumber(tiled_view::TiledView)
return (Tuple(tn) for tn in CartesianIndices(get_num_tiles(tiled_view)))
end
"""
tiled_processing(tiled_view::TiledView, fct; verbose=true, dtype=eltype(tiled_view.parent), window_function=window_hanning)
processes a raw dataset using tiled views by submitting each tile to the function `fct` and merging the results via the `window_function`.
"""
function tiled_processing(tiled_view::TiledView, fct; verbose=true, dtype=eltype(tiled_view.parent), window_function=window_hanning)
@time res = zeros_like(tiled_view, dtype)
res.parent .= zero(dtype)
@time win = get_window(tiled_view, window_function=window_function)
ttn = get_num_tiles(tiled_view)
for (src, dest, tn) in zip(eachtile(tiled_view), eachtile(res), eachtilenumber(res))
if verbose
perc = round(100 * (linear_index(tn, ttn)-1) ./ prod(ttn))
print("processing tile $(tn) out of $(ttn), $(perc)%\n")
end
size(src)
res_tile = fct(collect(src))
dest .+= win .* res_tile
end
return res
end
"""
tiled_processing(data, fct; verbose=true, dtype=eltype(data), window_function=window_hanning)
processes a raw dataset using tiled views by submitting each tile to the function `fct` and merging the results via the `window_function`.
"""
function tiled_processing(data, fct, tile_size, tile_overlap; verbose=true, dtype=eltype(data), keep_center=false, window_function=window_hanning)
tiles = TiledView(data, tile_size, tile_overlap, keep_center=keep_center);
return tiled_processing(tiles,fct; verbose=verbose, dtype=dtype, window_function=window_function)
end
end # module
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] | 2.520674 | 8,126 |
@everywhere function extForm(td, ωd, inheritData, baseProb, τ, Δt, T, fData, bData, dData, pDistr,coneBool = false)
# extensive formulation could not have variable/constraint names
# inheritData: [1]: sp, [2]: w, [3]: u (only contains the information for the linking time period)
println("========= Disruption time $(td), scenario $(ωd) modeling =========");
# precalculate data
Rdict = Dict();
Xdict = Dict();
for k in fData.brList
Rdict[k] = fData.g[k]/(fData.g[k]^2 + fData.b[k]^2);
Xdict[k] = -fData.b[k]/(fData.g[k]^2 + fData.b[k]^2);
end
Ω = [ω for ω in keys(pDistr.ωDistrn)];
Bparams = Dict();
for t in td:T
# create B parameters
for k in fData.brList
# if the line is disrupted and it is within disruption time
if (((k[1],k[2]) == ωd)|((k[2],k[1]) == ωd))&(t <= td + τ)
Bparams[k,t] = 0;
else
Bparams[k,t] = 1;
end
end
for i in fData.genIDList
if (i == ωd)&(t <= td + τ)
Bparams[i,t] = 0;
else
Bparams[i,t] = 1;
end
end
end
# set up the variables
spDict = Dict();
sqDict = Dict();
for i in fData.genIDList
for t in (td - 1):T
spDict[i,t] = @variable(mExt, lowerbound = fData.Pmin[i], upperbound = fData.Pmax[i], basename="sp_$(td)_$(i)_$(t)");
sqDict[i,t] = @variable(mExt, lowerbound = fData.Qmin[i], upperbound = fData.Qmax[i], basename="sq_$(td)_$(i)_$(t)");
end
end
sphatsum = Dict();
for t in td:T
for i in fData.IDList
sphatsum[i,t] = @expression(mExt,0.0);
if i in keys(fData.LocRev)
for j in fData.LocRev[i]
sphatsum[i,t] += spDict[j,t];
end
end
end
end
sqhatsum = Dict();
for t in td:T
for i in fData.IDList
sqhatsum[i,t] = @expression(mExt,0.0);
if i in keys(fData.LocRev)
for j in fData.LocRev[i]
sqhatsum[i,t] += sqDict[j,t];
end
end
end
end
pDict = Dict();
qDict = Dict();
vDict = Dict();
wDict = Dict();
yDict = Dict();
zpDict = Dict();
zqDict = Dict();
lppDict = Dict();
lqpDict = Dict();
lpmDict = Dict();
lqmDict = Dict();
uDict = Dict();
fsDict = Dict();
for k in fData.brList
for t in td:T
pDict[k,t] = @variable(mExt, basename="p_$(td)_$(k)_$(t)");
qDict[k,t] = @variable(mExt, basename="q_$(td)_$(k)_$(t)");
end
end
for i in fData.IDList
for t in td:T
vDict[i,t] = @variable(mExt, lowerbound = fData.Vmin[i]^2, upperbound = fData.Vmax[i]^2, basename="v_$td");
lppDict[i,t] = @variable(mExt, lowerbound = 0, basename="lpp_$(td)_$(i)_$(t)");
lqpDict[i,t] = @variable(mExt, lowerbound = 0, basename="lqp_$(td)_$(i)_$(t)");
lpmDict[i,t] = @variable(mExt, lowerbound = 0, basename="lpm_$(td)_$(i)_$(t)");
lqmDict[i,t] = @variable(mExt, lowerbound = 0, basename="lqm_$(td)_$(i)_$(t)");
end
end
for i in bData.IDList
wDict[i,td - 1] = @variable(mExt, lowerbound = 0, upperbound = bData.cap[i], basename="w_$(td)_$(i)_$(td - 1)");
uDict[i] = @variable(mExt, lowerbound = 0, upperbound = bData.uCap[i], basename="u_$(td)_$(i)");
for t in td:T
wDict[i,t] = @variable(mExt, lowerbound = 0, upperbound = bData.cap[i], basename="w_$(td)_$(i)_$(t)");
yDict[i,t] = @variable(mExt, basename="y_$(td)_$(i)_$(t)");
zpDict[i,t] = @variable(mExt, basename="zp_$(td)_$(i)_$(t)");
zqDict[i,t] = @variable(mExt, basename="zq_$(td)_$(i)_$(t)");
end
end
# set up the constraints
for i in fData.IDList
for t in td:T
@constraint(mExt, sum(zpDict[b,t] for b in bData.IDList if bData.Loc[b] == i) + lppDict[i,t] - lpmDict[i,t] +
sphatsum[i,t] - dData.pd[i][t] == sum(pDict[k,t] for k in fData.branchDict1[i]));
@constraint(mExt, sum(zqDict[b,t] for b in bData.IDList if bData.Loc[b] == i) + lqpDict[i,t] - lqmDict[i,t] +
sqhatsum[i,t] - dData.qd[i][t] == sum(qDict[k,t] for k in fData.branchDict1[i]));
end
end
for i in fData.genIDList
if td != 1
@constraint(mExt, spDict[i,td - 1] == inheritData[1][i]);
end
for t in td:T
if (t != 1)&(Bparams[i,t] == 1)
@constraint(mExt, spDict[i,t] - spDict[i,t - 1] <= fData.RU[i]);
@constraint(mExt, spDict[i,t] - spDict[i,t - 1] >= fData.RD[i]);
end
if Bparams[i,t] == 0
@constraint(mExt, spDict[i,t] == 0);
@constraint(mExt, sqDict[i,t] == 0);
end
end
end
for k in fData.brList
for t in td:T
@constraint(mExt, pDict[k,t] == -pDict[(k[2],k[1],k[3]),t]);
@constraint(mExt, qDict[k,t] == -qDict[(k[2],k[1],k[3]),t]);
if Bparams[k,t] == 1
if coneBool
@constraint(mExt, norm([pDict[k,t],qDict[k,t]]) <= fData.rateA[k]);
else
@constraint(mExt, pDict[k,t]^2 + qDict[k,t]^2 <= fData.rateA[k]^2);
end
@constraint(mExt, vDict[k[2],t] == vDict[k[1],t] - 2*(Rdict[k]*pDict[k,t] + Xdict[k]*qDict[k,t]));
else
@constraint(mExt, pDict[k,t] == 0);
@constraint(mExt, qDict[k,t] == 0);
end
end
end
for i in bData.IDList
if td != 1
@constraint(mExt, uDict[i] == inheritData[3][i]);
end
@constraint(mExt, wDict[i,td - 1] == inheritData[2][i]);
for t in td:T
@constraint(mExt, wDict[i,t] == wDict[i,t - 1] - yDict[i,t]*Δt);
if coneBool
@constraint(mExt, norm([zpDict[i,t],zqDict[i,t]]) <= uDict[i]);
else
@constraint(mExt, zpDict[i,t]^2 + zqDict[i,t]^2 <= uDict[i]^2);
end
for l in 1:length(bData.ηα[i])
@constraint(mExt, zpDict[i,t] <= bData.ηα[i][l]*yDict[i,t] + bData.ηβ[i][l]);
end
@constraint(mExt, wDict[i,t] <= bData.cap[i]);
end
end
# recursion through the possible scenario
tList = sort([t for t in keys(pDistr.tDistrn)]);
objExpr = getobjective(mExt);
if td == 1
objExpr += sum(bData.cost[i]*uDict[i] for i in bData.IDList);
# only the first pass will execute this
end
for tp in tList
if td == 1
if td + tp > T
# if the next disruption is over the time horizon
dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:T);
for t in td:T
for i in fData.genIDList
# add generator cost
if fData.cp[i].n == 3
if coneBool
fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)");
dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t];
@constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4);
else
dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t];
end
elseif fData.cp[i].n == 2
dExpr += fData.cp[i].params[1]*spDict[i,t];
end
end
end
objExpr += baseProb*pDistr.tDistrn[tp]*dExpr;
@objective(mExt, Min, objExpr);
else
# if not
dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:(td + tp - 1));
for t in td:(td + tp - 1)
for i in fData.genIDList
# add generator cost
if fData.cp[i].n == 3
if coneBool
fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)");
dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t];
@constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4);
else
dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t];
end
elseif fData.cp[i].n == 2
dExpr += fData.cp[i].params[1]*spDict[i,t];
end
end
end
for ω in Ω
objExpr += baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω]*dExpr;
spInherit = Dict();
wInherit = Dict();
uInherit = Dict();
for i in fData.genIDList
spInherit[i] = spDict[i,td + tp - 1];
end
for i in bData.IDList
wInherit[i] = wDict[i,td + tp - 1];
uInherit[i] = uDict[i];
end
inheritData = [spInherit,wInherit,uInherit];
@objective(mExt, Min, objExpr);
# println("=========================",1," ",td," ",tp,"=========================");
# println(mExt.obj);
global mExt = extForm(td + tp, ω, inheritData, baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω], τ, Δt, T, fData, bData, dData, pDistr, coneBool);
# println("=========================",11," ",td," ",tp,"=========================");
# println(mExt.obj);
objExpr = getobjective(mExt);
end
end
else
if td + τ + tp > T
# if the next disruption is over the time horizon
# add to the objective function
dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:T);
for t in td:T
for i in fData.genIDList
# add generator cost
if fData.cp[i].n == 3
if coneBool
fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)");
dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t];
@constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4);
else
dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t];
end
elseif fData.cp[i].n == 2
dExpr += fData.cp[i].params[1]*spDict[i,t];
end
end
end
objExpr += baseProb*pDistr.tDistrn[tp]*dExpr;
@objective(mExt, Min, objExpr);
else
# if not
# add the current part to the objective function
# recursion to the next disruption
dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:(td + tp + τ - 1));
for t in td:(td + tp + τ - 1)
for i in fData.genIDList
# add generator cost
if fData.cp[i].n == 3
if coneBool
fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)");
dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t];
@constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4);
else
dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t];
end
elseif fData.cp[i].n == 2
dExpr += fData.cp[i].params[1]*spDict[i,t];
end
end
end
for ω in Ω
objExpr += baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω]*dExpr;
spInherit = Dict();
wInherit = Dict();
uInherit = Dict();
for i in fData.genIDList
spInherit[i] = spDict[i,td + tp + τ - 1];
end
for i in bData.IDList
wInherit[i] = wDict[i,td + tp + τ - 1];
uInherit[i] = uDict[i];
end
inheritData = [spInherit,wInherit,uInherit];
@objective(mExt, Min, objExpr);
# println("=========================",2," ",td," ",tp,"=========================");
# println(mExt.obj);
global mExt = extForm(td + tp + τ, ω, inheritData, baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω], τ, Δt, T, fData, bData, dData, pDistr, coneBool);
# println("=========================",22," ",td," ",tp,"=========================");
# println(mExt.obj);
objExpr = getobjective(mExt);
end
end
end
end
return mExt;
end
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] | 1.588136 | 8,901 |
# \file
# \brief Callbacks, Attributes and Attribute Values definitions.
# Avoid using these definitions. Use the strings instead.
#
# See Copyright Notice in iup.h
#
# Deprecated definitions #
# Avoid using these definitions. Use the strings instead. #
# Define __IUPDEF_H to avoid the inclusion of this header #
constant RUN = "RUN"
constant ENGLISH = "ENGLISH"
constant PORTUGUESE = "PORTUGUESE"
constant SBH = "SBH"
constant SBV = "SBV"
##########################################################################
# Callbacks #
##########################################################################
constant DEFAULT_ACTION = "DEFAULT_ACTION"
constant IDLE_ACTION = "IDLE_ACTION"
constant ACTION = "ACTION"
constant GETFOCUS_CB = "GETFOCUS_CB"
constant KILLFOCUS_CB = "KILLFOCUS_CB"
constant K_ANY = "K_ANY"
constant KEYPRESS_CB = "KEYPRESS_CB"
constant HELP_CB = "HELP_CB"
constant SCROLL_CB = "SCROLL_CB"
constant RESIZE_CB = "RESIZE_CB"
constant MOTION_CB = "MOTION_CB"
constant BUTTON_CB = "BUTTON_CB"
constant ENTERWINDOW_CB = "ENTERWINDOW_CB"
constant LEAVEWINDOW_CB = "LEAVEWINDOW_CB"
constant WHEEL_CB = "WHEEL_CB"
constant MASK_CB = "MASK_CB"
constant OPEN_CB = "OPEN_CB"
constant HIGHLIGHT_CB = "HIGHLIGHT_CB"
constant MENUCLOSE_CB = "MENUCLOSE_CB"
constant MAP_CB = "MAP_CB"
constant CLOSE_CB = "CLOSE_CB"
constant SHOW_CB = "SHOW_CB"
constant DROPFILES_CB = "DROPFILES_CB"
constant WOM_CB = "WOM_CB"
##########################################################################
# Attributes #
##########################################################################
constant DIRECTION = "DIRECTION"
constant ACTIVE = "ACTIVE"
constant BGCOLOR = "BGCOLOR"
constant FRAMECOLOR = "FRAMECOLOR"
constant FGCOLOR = "FGCOLOR"
constant COLOR = "COLOR"
constant WID = "WID"
constant SIZE = "SIZE"
constant RASTERSIZE = "RASTERSIZE"
constant TITLE = "TITLE"
constant VALUE = "VALUE"
constant VISIBLE = "VISIBLE"
constant FONT = "FONT"
constant TIP = "TIP"
constant EXPAND = "EXPAND"
constant SEPARATOR = "SEPARATOR"
constant HOTSPOT = "HOTSPOT"
constant HEIGHT = "HEIGHT"
constant WIDTH = "WIDTH"
constant KEY = "KEY"
constant MULTIPLE = "MULTIPLE"
constant DROPDOWN = "DROPDOWN"
constant VISIBLE_ITEMS = "VISIBLE_ITEMS"
constant MARGIN = "MARGIN"
constant GAP = "GAP"
constant ALIGNMENT = "ALIGNMENT"
constant IMAGE = "IMAGE"
constant IMINACTIVE = "IMINACTIVE"
constant IMPRESS = "IMPRESS"
constant WIN_SAVEBITS = "WIN_SAVEBITS"
constant NC = "NC"
constant MASK = "MASK"
constant APPEND = "APPEND"
constant BORDER = "BORDER"
constant CARET = "CARET"
constant SELECTION = "SELECTION"
constant SELECTEDTEXT = "SELECTEDTEXT"
constant INSERT = "INSERT"
constant CONID = "CONID"
constant CURSOR = "CURSOR"
constant ICON = "ICON"
constant MENUBOX = "MENUBOX"
constant MINBOX = "MINBOX"
constant MAXBOX = "MAXBOX"
constant RESIZE = "RESIZE"
constant MENU = "MENU"
constant STARTFOCUS = "STARTFOCUS"
constant PARENTDIALOG = "PARENTDIALOG"
constant SHRINK = "SHRINK"
constant DEFAULTENTER = "DEFAULTENTER"
constant DEFAULTESC = "DEFAULTESC"
constant X = "X"
constant Y = "Y"
constant TOOLBOX = "TOOLBOX"
constant CONTROL = "CONTROL"
constant READONLY = "READONLY"
constant SCROLLBAR = "SCROLLBAR"
constant POSY = "POSY"
constant POSX = "POSX"
constant DX = "DX"
constant DY = "DY"
constant XMAX = "XMAX"
constant XMIN = "XMIN"
constant YMAX = "YMAX"
constant YMIN = "YMIN"
constant RED = "255 0 0"
constant GREEN = "0 255 0"
constant BLUE = "0 0 255"
constant MIN = "MIN"
constant MAX = "MAX"
constant TIME = "TIME"
constant DRAG = "DRAG"
constant DROP = "DROP"
constant REPAINT = "REPAINT"
constant TOPMOST = "TOPMOST"
constant CLIPCHILDREN = "CLIPCHILDREN"
constant DIALOGTYPE = "DIALOGTYPE"
constant FILE = "FILE"
constant MULTIPLEFILES = "MULTIPLEFILES"
constant FILTER = "FILTER"
constant FILTERUSED = "FILTERUSED"
constant FILTERINFO = "FILTERINFO"
constant EXTFILTER = "EXTFILTER"
constant DIRECTORY = "DIRECTORY"
constant ALLOWNEW = "ALLOWNEW"
constant NOOVERWRITEPROMPT = "NOOVERWRITEPROMPT"
constant NOCHANGEDIR = "NOCHANGEDIR"
constant FILEEXIST = "FILEEXIST"
constant STATUS = "STATUS"
constant LOCKLOOP = "LOCKLOOP"
constant SYSTEM = "SYSTEM"
constant DRIVER = "DRIVER"
constant SCREENSIZE = "SCREENSIZE"
constant SYSTEMLANGUAGE = "SYSTEMLANGUAGE"
constant COMPUTERNAME = "COMPUTERNAME"
constant USERNAME = "USERNAME"
constant OPEN = "OPEN"
constant SAVE = "SAVE"
constant DIR = "DIR"
constant HORIZONTAL = "HORIZONTAL"
constant VERTICAL = "VERTICAL"
##########################################################################
# Attribute Values #
##########################################################################
constant YES = "YES"
constant NO = "NO"
constant ON = "ON"
constant OFF = "OFF"
constant ACENTER = "ACENTER"
constant ALEFT = "ALEFT"
constant ARIGHT = "ARIGHT"
constant ATOP = "ATOP"
constant ABOTTOM = "ABOTTOM"
constant NORTH = "NORTH"
constant SOUTH = "SOUTH"
constant WEST = "WEST"
constant EAST = "EAST"
constant NE = "NE"
constant SE = "SE"
constant NW = "NW"
constant SW = "SW"
constant FULLSCREEN = "FULLSCREEN"
constant FULL = "FULL"
constant HALF = "HALF"
constant THIRD = "THIRD"
constant QUARTER = "QUARTER"
constant EIGHTH = "EIGHTH"
constant ARROW = "ARROW"
constant BUSY = "BUSY"
constant RESIZE_N = "RESIZE_N"
constant RESIZE_S = "RESIZE_S"
constant RESIZE_E = "RESIZE_E"
constant RESIZE_W = "RESIZE_W"
constant RESIZE_NE = "RESIZE_NE"
constant RESIZE_NW = "RESIZE_NW"
constant RESIZE_SE = "RESIZE_SE"
constant RESIZE_SW = "RESIZE_SW"
constant MOVE = "MOVE"
constant HAND = "HAND"
constant NONE = "NONE"
constant IUP = "IUP"
constant CROSS = "CROSS"
constant PEN = "PEN"
constant TEXT = "TEXT"
constant RESIZE_C = "RESIZE_C"
constant OPENHAND = "OPENHAND"
###################
# Fonts #
###################
constant HELVETICA_NORMAL_8 = "HELVETICA_NORMAL_8"
constant HELVETICA_ITALIC_8 = "HELVETICA_ITALIC_8"
constant HELVETICA_BOLD_8 = "HELVETICA_BOLD_8"
constant HELVETICA_NORMAL_10 = "HELVETICA_NORMAL_10"
constant HELVETICA_ITALIC_10 = "HELVETICA_ITALIC_10"
constant HELVETICA_BOLD_10 = "HELVETICA_BOLD_10"
constant HELVETICA_NORMAL_12 = "HELVETICA_NORMAL_12"
constant HELVETICA_ITALIC_12 = "HELVETICA_ITALIC_12"
constant HELVETICA_BOLD_12 = "HELVETICA_BOLD_12"
constant HELVETICA_NORMAL_14 = "HELVETICA_NORMAL_14"
constant HELVETICA_ITALIC_14 = "HELVETICA_ITALIC_14"
constant HELVETICA_BOLD_14 = "HELVETICA_BOLD_14"
constant COURIER_NORMAL_8 = "COURIER_NORMAL_8"
constant COURIER_ITALIC_8 = "COURIER_ITALIC_8"
constant COURIER_BOLD_8 = "COURIER_BOLD_8"
constant COURIER_NORMAL_10 = "COURIER_NORMAL_10"
constant COURIER_ITALIC_10 = "COURIER_ITALIC_10"
constant COURIER_BOLD_10 = "COURIER_BOLD_10"
constant COURIER_NORMAL_12 = "COURIER_NORMAL_12"
constant COURIER_ITALIC_12 = "COURIER_ITALIC_12"
constant COURIER_BOLD_12 = "COURIER_BOLD_12"
constant COURIER_NORMAL_14 = "COURIER_NORMAL_14"
constant COURIER_ITALIC_14 = "COURIER_ITALIC_14"
constant COURIER_BOLD_14 = "COURIER_BOLD_14"
constant TIMES_NORMAL_8 = "TIMES_NORMAL_8"
constant TIMES_ITALIC_8 = "TIMES_ITALIC_8"
constant TIMES_BOLD_8 = "TIMES_BOLD_8"
constant TIMES_NORMAL_10 = "TIMES_NORMAL_10"
constant TIMES_ITALIC_10 = "TIMES_ITALIC_10"
constant TIMES_BOLD_10 = "TIMES_BOLD_10"
constant TIMES_NORMAL_12 = "TIMES_NORMAL_12"
constant TIMES_ITALIC_12 = "TIMES_ITALIC_12"
constant TIMES_BOLD_12 = "TIMES_BOLD_12"
constant TIMES_NORMAL_14 = "TIMES_NORMAL_14"
constant TIMES_ITALIC_14 = "TIMES_ITALIC_14"
constant TIMES_BOLD_14 = "TIMES_BOLD_14"
##########################################################################
# Keys #
##########################################################################
constant K_exclam = "K_exclam"
constant K_quotedbl = "K_quotedbl"
constant K_numbersign = "K_numbersign"
constant K_dollar = "K_dollar"
constant K_percent = "K_percent"
constant K_ampersand = "K_ampersand"
constant K_quoteright = "K_quoteright"
constant K_parentleft = "K_parentleft"
constant K_parentright = "K_parentright"
constant K_asterisk = "K_asterisk"
constant K_plus = "K_plus"
constant K_comma = "K_comma"
constant K_minus = "K_minus"
constant K_period = "K_period"
constant K_slash = "K_slash"
constant K_0 = "K_0"
constant K_1 = "K_1"
constant K_2 = "K_2"
constant K_3 = "K_3"
constant K_4 = "K_4"
constant K_5 = "K_5"
constant K_6 = "K_6"
constant K_7 = "K_7"
constant K_8 = "K_8"
constant K_9 = "K_9"
constant K_colon = "K_colon"
constant K_semicolon = "K_semicolon "
constant K_less = "K_less"
constant K_equal = "K_equal"
constant K_greater = "K_greater"
constant K_question = "K_question"
constant K_at = "K_at"
constant K_A = "K_A"
constant K_B = "K_B"
constant K_C = "K_C"
constant K_D = "K_D"
constant K_E = "K_E"
constant K_F = "K_F"
constant K_G = "K_G"
constant K_H = "K_H"
constant K_I = "K_I"
constant K_J = "K_J"
constant K_K = "K_K"
constant K_L = "K_L"
constant K_M = "K_M"
constant K_N = "K_N"
constant K_O = "K_O"
constant K_P = "K_P"
constant K_Q = "K_Q"
constant K_R = "K_R"
constant K_S = "K_S"
constant K_T = "K_T"
constant K_U = "K_U"
constant K_V = "K_V"
constant K_W = "K_W"
constant K_X = "K_X"
constant K_Y = "K_Y"
constant K_Z = "K_Z"
constant K_bracketleft = "K_bracketleft"
constant K_backslash = "K_backslash"
constant K_bracketright = "K_bracketright"
constant K_circum = "K_circum"
constant K_underscore = "K_underscore"
constant K_quoteleft = "K_quoteleft"
constant K_a = "K_a"
constant K_b = "K_b"
constant K_c = "K_c"
constant K_d = "K_d"
constant K_e = "K_e"
constant K_f = "K_f"
constant K_g = "K_g"
constant K_h = "K_h"
constant K_i = "K_i"
constant K_j = "K_j"
constant K_k = "K_k"
constant K_l = "K_l"
constant K_m = "K_m"
constant K_n = "K_n"
constant K_o = "K_o"
constant K_p = "K_p"
constant K_q = "K_q"
constant K_r = "K_r"
constant K_s = "K_s"
constant K_t = "K_t"
constant K_u = "K_u"
constant K_v = "K_v"
constant K_w = "K_w"
constant K_x = "K_x"
constant K_y = "K_y"
constant K_z = "K_z"
constant K_braceleft = "K_braceleft"
constant K_bar = "K_bar"
constant K_braceright = "K_braceright"
constant K_tilde = "K_tilde"
constant K_cA = "K_cA"
constant K_cB = "K_cB"
constant K_cC = "K_cC"
constant K_cD = "K_cD"
constant K_cE = "K_cE"
constant K_cF = "K_cF"
constant K_cG = "K_cG"
constant K_cJ = "K_cJ"
constant K_cK = "K_cK"
constant K_cL = "K_cL"
constant K_cN = "K_cN"
constant K_cO = "K_cO"
constant K_cP = "K_cP"
constant K_cQ = "K_cQ"
constant K_cR = "K_cR"
constant K_cS = "K_cS"
constant K_cT = "K_cT"
constant K_cU = "K_cU"
constant K_cV = "K_cV"
constant K_cW = "K_cW"
constant K_cX = "K_cX"
constant K_cY = "K_cY"
constant K_cZ = "K_cZ"
constant K_mA = "K_mA"
constant K_mB = "K_mB"
constant K_mC = "K_mC"
constant K_mD = "K_mD"
constant K_mE = "K_mE"
constant K_mF = "K_mF"
constant K_mG = "K_mG"
constant K_mH = "K_mH"
constant K_mI = "K_mI"
constant K_mJ = "K_mJ"
constant K_mK = "K_mK"
constant K_mL = "K_mL"
constant K_mM = "K_mM"
constant K_mN = "K_mN"
constant K_mO = "K_mO"
constant K_mP = "K_mP"
constant K_mQ = "K_mQ"
constant K_mR = "K_mR"
constant K_mS = "K_mS"
constant K_mT = "K_mT"
constant K_mU = "K_mU"
constant K_mV = "K_mV"
constant K_mW = "K_mW"
constant K_mX = "K_mX"
constant K_mY = "K_mY"
constant K_mZ = "K_mZ"
constant K_BS = "K_BS"
constant K_TAB = "K_TAB"
constant K_CR = "K_CR"
constant K_SP = "K_SP"
constant K_ESC = "K_ESC"
constant K_sCR = "K_sCR"
constant K_sTAB = "K_sTAB"
constant K_cTAB = "K_cTAB"
constant K_mTAB = "K_mTAB"
constant K_HOME = "K_HOME"
constant K_UP = "K_UP"
constant K_PGUP = "K_PGUP"
constant K_LEFT = "K_LEFT"
constant K_RIGHT = "K_RIGHT"
constant K_END = "K_END"
constant K_DOWN = "K_DOWN"
constant K_PGDN = "K_PGDN"
constant K_MIDDLE = "K_MIDDLE"
constant K_INS = "K_INS"
constant K_DEL = "K_DEL"
constant K_sHOME = "K_sHOME"
constant K_sUP = "K_sUP"
constant K_sPGUP = "K_sPGUP"
constant K_sLEFT = "K_sLEFT"
constant K_sRIGHT = "K_sRIGHT"
constant K_sEND = "K_sEND"
constant K_sDOWN = "K_sDOWN"
constant K_sPGDN = "K_sPGDN"
constant K_cHOME = "K_cHOME"
constant K_cPGUP = "K_cPGUP"
constant K_cLEFT = "K_cLEFT"
constant K_cRIGHT = "K_cRIGHT"
constant K_cEND = "K_cEND"
constant K_cPGDN = "K_cPGDN"
constant K_cUP = "K_cUP"
constant K_cDOWN = "K_cDOWN"
constant K_cMIDDLE = "K_cMIDDLE"
constant K_cINS = "K_cINS"
constant K_cDEL = "K_cDEL"
constant K_mHOME = "K_mHOME"
constant K_mPGUP = "K_mPGUP"
constant K_mLEFT = "K_mLEFT"
constant K_mRIGHT = "K_mRIGHT"
constant K_mEND = "K_mEND"
constant K_mPGDN = "K_mPGDN"
constant K_mUP = "K_mUP"
constant K_mDOWN = "K_mDOWN"
constant K_mINS = "K_mINS"
constant K_mDEL = "K_mDEL"
constant K_F1 = "K_F1"
constant K_F2 = "K_F2"
constant K_F3 = "K_F3"
constant K_F4 = "K_F4"
constant K_F5 = "K_F5"
constant K_F6 = "K_F6"
constant K_F7 = "K_F7"
constant K_F8 = "K_F8"
constant K_F9 = "K_F9"
constant K_F10 = "K_F10"
constant K_F11 = "K_F11"
constant K_F12 = "K_F12"
constant K_sF1 = "K_sF1"
constant K_sF2 = "K_sF2"
constant K_sF3 = "K_sF3"
constant K_sF4 = "K_sF4"
constant K_sF5 = "K_sF5"
constant K_sF6 = "K_sF6"
constant K_sF7 = "K_sF7"
constant K_sF8 = "K_sF8"
constant K_sF9 = "K_sF9"
constant K_sF10 = "K_sF10"
constant K_sF11 = "K_sF11"
constant K_sF12 = "K_sF12"
constant K_cF1 = "K_cF1"
constant K_cF2 = "K_cF2"
constant K_cF3 = "K_cF3"
constant K_cF4 = "K_cF4"
constant K_cF5 = "K_cF5"
constant K_cF6 = "K_cF6"
constant K_cF7 = "K_cF7"
constant K_cF8 = "K_cF8"
constant K_cF9 = "K_cF9"
constant K_cF10 = "K_cF10"
constant K_cF11 = "K_cF11"
constant K_cF12 = "K_cF12"
constant K_mF1 = "K_mF1"
constant K_mF2 = "K_mF2"
constant K_mF3 = "K_mF3"
constant K_mF4 = "K_mF4"
constant K_mF5 = "K_mF5"
constant K_mF6 = "K_mF6"
constant K_mF7 = "K_mF7"
constant K_mF8 = "K_mF8"
constant K_mF9 = "K_mF9"
constant K_mF10 = "K_mF10"
constant K_m1 = "K_m1"
constant K_m2 = "K_m2"
constant K_m3 = "K_m3"
constant K_m4 = "K_m4"
constant K_m5 = "K_m5"
constant K_m6 = "K_m6"
constant K_m7 = "K_m7"
constant K_m8 = "K_m8"
constant K_m9 = "K_m9"
constant K_m0 = "K_m0"
##############
# Colorbar #
##############
constant NUM_PARTS = "NUM_PARTS"
constant NUM_CELLS = "NUM_CELLS"
constant CELL = "CELL"
constant PREVIEW_SIZE = "PREVIEW_SIZE"
constant SHOW_PREVIEW = "SHOW_PREVIEW"
constant SHOW_SECONDARY = "SHOW_SECONDARY"
constant PRIMARY_CELL = "PRIMARY_CELL"
constant SECONDARY_CELL = "SECONDARY_CELL"
constant ORIENTATION = "ORIENTATION"
constant SQUARED = "SQUARED"
constant SHADOWED = "SHADOWED"
constant BUFFERIZE = "BUFFERIZE"
constant TRANSPARENCY = "TRANSPARENCY"
constant CELL_CB = "CELL_CB"
constant EXTENDED_CB = "EXTENDED_CB"
constant SELECT_CB = "SELECT_CB"
constant SWITCH_CB = "SWITCH_CB"
constant VERTICAL = "VERTICAL"
constant HORIZONTAL = "HORIZONTAL"
##############
# Cells #
##############
constant ALL = "ALL"
constant BOXED = "BOXED"
constant CLIPPED = "CLIPPED"
constant TRANSPARENT = "TRANSPARENT"
constant NON_SCROLLABLE_LINES = "NON_SCROLLABLE_LINES"
constant NON_SCROLLABLE_COLS = "NON_SCROLLABLE_COLS"
constant ORIGIN = "ORIGIN"
constant NO_COLOR = "NO_COLOR"
constant FIRST_LINE = "FIRST_LINE"
constant FIRST_COL = "FIRST_COL"
constant DOUBLE_BUFFER = "DOUBLE_BUFFER"
constant LIMITS = "LIMITS"
constant CANVAS = "CANVAS"
constant IMAGE_CANVAS = "IMAGE_CANVAS"
constant FULL_VISIBLE = "FULL_VISIBLE"
constant MOUSECLICK_CB = "MOUSECLICK_CB"
constant MOUSEMOTION_CB = "MOUSEMOTION_CB"
constant DRAW_CB = "DRAW_CB"
constant WIDTH_CB = "WIDTH_CB"
constant HEIGHT_CB = "HEIGHT_CB"
constant NLINES_CB = "NLINES_CB"
constant NCOLS_CB = "NCOLS_CB"
constant HSPAN_CB = "HSPAN_CB"
constant VSPAN_CB = "VSPAN_CB"
constant SCROLLING_CB = "SCROLLING_CB"
###################
# ColorBrowser #
###################
constant RGB = "RGB"
constant CHANGE_CB = "CHANGE_CB"
constant DRAG_CB = "DRAG_CB"
###################
# Val #
###################
constant ICTL_MOUSEMOVE_CB = "MOUSEMOVE_CB"
constant ICTL_BUTTON_PRESS_CB = "BUTTON_PRESS_CB"
constant ICTL_BUTTON_RELEASE_CB = "BUTTON_RELEASE_CB"
constant ICTL_HORIZONTAL = "HORIZONTAL"
constant ICTL_VERTICAL = "VERTICAL"
constant ICTL_SHOWTICKS = "SHOWTICKS"
###################
# Tabs #
###################
constant ICTL_TOP = "TOP"
constant ICTL_BOTTOM = "BOTTOM"
constant ICTL_LEFT = "LEFT"
constant ICTL_RIGHT = "RIGHT"
constant ICTL_TABTYPE = "TABTYPE"
constant ICTL_TABTITLE = "TABTITLE"
constant ICTL_TABSIZE = "TABSIZE"
constant ICTL_TABCHANGE_CB = "TABCHANGE_CB"
constant ICTL_FONT = "FONT"
constant ICTL_FONT_ACTIVE = "FONT_ACTIVE"
constant ICTL_FONT_INACTIVE = "FONT_INACTIVE"
###################
# Gauge #
###################
constant ICTL_SHOW_TEXT = "SHOW_TEXT"
constant ICTL_DASHED = "DASHED"
constant ICTL_MARGIN = "MARGIN"
constant ICTL_TEXT = "TEXT"
###################
# Dial #
###################
constant ICTL_DENSITY = "DENSITY"
constant ICTL_HORIZONTAL = "HORIZONTAL"
constant ICTL_VERTICAL = "VERTICAL"
constant ICTL_CIRCULAR = "CIRCULAR"
constant ICTL_UNIT = "UNIT"
###################
# Matrix #
###################
constant ENTERITEM_CB = "ENTERITEM_CB"
constant LEAVEITEM_CB = "LEAVEITEM_CB"
constant EDITION_CB = "EDITION_CB"
constant CLICK_CB = "CLICK_CB"
constant DROP_CB = "DROP_CB"
constant DROPSELECT_CB = "DROPSELECT_CB"
constant DROPCHECK_CB = "DROPCHECK_CB"
constant SCROLL_CB = "SCROLL_CB"
constant VALUE_CB = "VALUE_CB"
constant VALUE_EDIT_CB = "VALUE_EDIT_CB"
constant FIELD_CB = "FIELD_CB"
constant RESIZEMATRIX = "RESIZEMATRIX"
constant ADDLIN = "ADDLIN"
constant ADDCOL = "ADDCOL"
constant DELLIN = "DELLIN"
constant DELCOL = "DELCOL"
constant NUMLIN = "NUMLIN"
constant NUMCOL = "NUMCOL"
constant NUMLIN_VISIBLE = "NUMLIN_VISIBLE"
constant NUMCOL_VISIBLE = "NUMCOL_VISIBLE"
constant MARKED = "MARKED"
constant WIDTHDEF = "WIDTHDEF"
constant HEIGHTDEF = "HEIGHTDEF"
constant AREA = "AREA"
constant MARK_MODE = "MARK_MODE"
constant LIN = "LIN"
constant COL = "COL"
constant LINCOL = "LINCOL"
constant CELL = "CELL"
constant EDIT_MODE = "EDIT_MODE"
constant FOCUS_CELL = "FOCUS_CELL"
constant ORIGIN = "ORIGIN"
constant REDRAW = "REDRAW"
constant PREVIOUSVALUE = "PREVIOUSVALUE"
constant MOUSEMOVE_CB = "MOUSEMOVE_CB"
###################
# Tree #
###################
constant ADDLEAF = "ADDLEAF"
constant ADDBRANCH = "ADDBRANCH"
constant DELNODE = "DELNODE"
constant IMAGELEAF = "IMAGELEAF"
constant IMAGEBRANCHCOLLAPSED = "IMAGEBRANCHCOLLAPSED"
constant IMAGEBRANCHEXPANDED = "IMAGEBRANCHEXPANDED"
constant IMAGEEXPANDED = "IMAGEEXPANDED"
constant KIND = "KIND"
constant PARENT = "PARENT"
constant DEPTH = "DEPTH"
constant MARKED = "MARKED"
constant ADDEXPANDED = "ADDEXPANDED"
constant CTRL = "CTRL"
constant SHIFT = "SHIFT"
constant STATE = "STATE"
constant STARTING = "STARTING"
constant LEAF = "LEAF"
constant BRANCH = "BRANCH"
constant SELECTED = "SELECTED"
constant CHILDREN = "CHILDREN"
constant MARKED = "MARKED"
constant ROOT = "ROOT"
constant LAST = "LAST"
constant PGUP = "PGUP"
constant PGDN = "PGDN"
constant NEXT = "NEXT"
constant PREVIOUS = "PREVIOUS"
constant INVERT = "INVERT"
constant BLOCK = "BLOCK"
constant CLEARALL = "CLEARALL"
constant MARKALL = "MARKALL"
constant INVERTALL = "INVERTALL"
constant REDRAW = "REDRAW"
constant COLLAPSED = "COLLAPSED"
constant EXPANDED = "EXPANDED"
constant SELECTION_CB = "SELECTION_CB"
constant BRANCHOPEN_CB = "BRANCHOPEN_CB"
constant BRANCHCLOSE_CB = "BRANCHCLOSE_CB"
constant RIGHTCLICK_CB = "RIGHTCLICK_CB"
constant EXECUTELEAF_CB = "EXECUTELEAF_CB"
constant RENAMENODE_CB = "RENAMENODE_CB"
constant IMGLEAF = "IMGLEAF"
constant IMGCOLLAPSED = "IMGCOLLAPSED"
constant IMGEXPANDED = "IMGEXPANDED"
constant IMGBLANK = "IMGBLANK"
constant IMGPAPER = "IMGPAPER"
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] | 2.157975 | 9,166 |
##########################################################################
# Basic functionality for doing MPS calculations with OBC #
##########################################################################
using LinearAlgebra
using Arpack
# Define sites as 3 legged tensors filled with elements of some type
Site{T} = Array{T,3}
# An MPS is an array of Sites of a certain type
MPS{T} = Vector{Site{T}}
# Define operators as 4 legged tensors filled with elements of some type
Operator{T} = Array{T,4}
# A MPO is an array of Operators
MPO{T} = Vector{Operator{T}}
"""
random_mps_obc(N::Int, D::Int, d, tensortype::Type{T}=ComplexF64)::MPS{T} where T
Function to generate a random MPS with OBC
N: Number of sites
D: Bond dimension
d: Vector of physical dimensions, if a single integer dimension is given, it is assumed that all physical dimensions are the same, if varying dimensions are wanted a vector of integers of length N has to be supplied
The convention for the 3 index tensors is that the first two are the virtual ones, the last one is the physical one
3
|
1--A--2
"""
function random_mps_obc(N::Int, D::Int, d, tensortype::Type{T} = ComplexF64)::MPS{T} where {T}
# Ensure the the system size is at least two
@assert(N > 1)
# Initialize
mps = Array{Site{T}}(undef, N)
if isa(d, Number)
# Single number, I assume all dimensions are the same
dim = d * ones(Int64, N)
else
# Make sure that the input is really a vector as julia distinguishes between nx1 matrices and column vectors
dim = vec(d)
# Make sure input is valid
@assert(length(dim) == N)
end
# Left boundary tensor (row vector)
mps[1] = rand(tensortype, 1, D, dim[1])
# Right boundary tensor (column vector)
mps[N] = rand(tensortype, D, 1, dim[N])
# Tensors in between
for i = 2:N-1
mps[i] = rand(tensortype, D, D, dim[i])
end
return mps
end
"""
basis_state_obc(configuration::Vector{<:Int}, d::Int=2)::MPS
Prepare the a product state corresponding |configuration> on N sites where configuration is an Array containing N elements from 1 to d. Each site is then initialized in the dth canonical basis state
"""
function basis_state_obc(configuration::Vector{<:Int}, d::Int = 2)::MPS{Float64}
# Some error checking
if any(x -> (x < 1 || x > d), configuration)
throw(ArgumentError("configuration must contain integer elements in the range from 1 to d, got d=$(repr(d)), configuration=$(repr(configuration))"))
end
# Generate the MPS
N = length(configuration)
psi = MPS{Float64}(undef, N)
tensors = Vector{Array{Float64,3}}(undef, d)
for i = 1:d
tmp = zeros(Float64, 1, 1, d)
tmp[1, 1, i] = 1.0
tensors[i] = tmp
end
for i = 1:N
psi[i] = tensors[configuration[i]]
end
return psi
end
"""
calculate_overlap(mps1::MPS,mps2::MPS)::Number
Given two mps, compute the overlap <mps1|mps2>.
"""
function calculate_overlap(mps1::MPS, mps2::MPS)::Number
# Make sure, that the two MPS have the same length
N1 = length(mps1)
N2 = length(mps2)
@assert(N1 == N2)
# Now compute ther overlap
overlap = ones(Float64, 1, 1)
for i = 1:N1
overlap = contract_tensors(overlap, [2], mps2[i], [1])
overlap = contract_tensors(conj(mps1[i]), [1; 3], overlap, [1; 3])
end
return overlap[1]
end
"""
expectation_value(mps::MPS, mpo::MPO)::Number
Given a MPS and a MPO compute the expectation value <mps|mpo|mps>.
"""
function expectation_value(mps::MPS, mpo::MPO)::Number
# Make sure, that the two MPS have the same length
N1 = length(mps)
N2 = length(mpo)
@assert(N1 == N2)
# Contract zipper like
val = ones(Float64, 1, 1, 1)
for i = 1:N1
val = contract_tensors(val, [1], conj(mps[i]), [1])
val = contract_tensors(val, [1; 4], mpo[i], [1; 3])
val = contract_tensors(val, [1; 4], mps[i], [1; 3])
end
return val[1]
end
"""
gaugeMPS(mps::MPS{T}, direction::Symbol=:right, normalize::Bool=false)::MPS{T}
Function to bring an MPS with OBC in canonical form
direction: tells, whether it will be left or right canonical gauge
If normalize is set to true, the resulting state will be normalized.
"""
function gaugeMPS(mps::MPS{T}, direction::Symbol = :right, normalize::Bool = false)::MPS{T} where {T}
mps_gauged = deepcopy(mps)
gaugeMPS!(mps_gauged, direction, normalize)
return mps_gauged
end
"""
gaugeMPS!(mps::MPS,direction::Dir=right,)
Bring an MPS with OBC in canonical form. Direction tells, whether it will be left or right canonical gauge If normalize is set to true, the resulting state will be
normalized. This function overwrites the input MPS with its gauged version
"""
function gaugeMPS!(mps::MPS, direction::Symbol = :right, normalize::Bool = false)
# Check that we got a meaningful direction
if (direction != :left && direction != :right)
throw(ArgumentError("direction must be :left or :right, got $(repr(direction))"))
end
# Start gauging
N = length(mps)
if (direction == :left)
# Case that I want left canonical gauge
M = mps[1]
for i = 1:N-1
mps[i], res = gauge_site(M, direction)
M = contract_tensors(res, [2], mps[i+1], [1])
if (i == (N - 1))
if (normalize)
mps[N], _ = gauge_site(M, direction)
else
mps[N] = M
end
end
end
else
# Case that I want right canonical gauge
M = mps[N]
for i = N:-1:2
mps[i], res = gauge_site(M, direction)
M = contract_tensors(mps[i-1], [2], res, [1], [1; 3; 2])
if (i == 2)
if (normalize)
mps[1], _ = gauge_site(M, direction)
else
mps[1] = M
end
end
end
end
end
"""
gauge_site(A::Site{T}, direction::Dir)::Tuple{Site{T},Matrix{T}} where T
Bring a single tensor A of an MPS with OBC in canonical form
direction tells, whether it will be left or right normalized
The new tensor is M, the residual matrix which has to be multiplied
in the next tensor is stored in res
"""
function gauge_site(A::Site{T}, direction::Symbol)::Tuple{Site{T},Matrix{T}} where {T}
if (direction == :left)
Dl, Dr, d = size(A)
M = permutedims(A, [3 1 2])
M = reshape(M, (d * Dl, Dr))
U, S, V = svd(M)
dsv = length(S)
U = reshape(U, (d, Dl, dsv))
M = permutedims(U, [2 3 1])
res = Matrix(Diagonal(S)) * V'
return M, res
else
Dl, Dr, d = size(A)
M = permutedims(A, [1 3 2])
M = reshape(M, (Dl, Dr * d))
U, S, V = svd(M)
dsv = length(S)
V = V'
V = reshape(V, (dsv, d, Dr))
M = permutedims(V, [1 3 2])
res = U * Matrix(Diagonal(S))
return M, res
end
end
"""
contract_virtual_indices(mps::MPS)::Vector{<:Number}
Given an MPS contract the virtual indices such that one obtains a dense vector. The indices are ordered such that they are compatible with the standard Julia kronecker product.
Warning: the object constructed will have exponential memory requirements in terms of the number of sites, use with care!
"""
function contract_virtual_indices(mps::MPS)::Vector{<:Number}
N = length(mps)
# Since we deal with open boundary conditions, we drop the dummy indices one on the left (right) boundary for the first (last) tensor manually. We start from the right to have the physical indices in the order compatible with Julia's kronecker product
res = mps[N][:, 1, :]
for i = N-1:-1:2
res = contract_tensors(res, [ndims(res) - 1], mps[i], [2])
end
res = contract_tensors(res, [ndims(res) - 1], mps[1][1, :, :], [1])
# Now reshape the result accordingly
res = reshape(res, prod(size(res)))
return res
end
"""
contract_virtual_indices(mps::MPO)::Matrix{<:Number}
Given an MPO contract the virtual indices such that one obtains a dense matrix. The indices are ordered such that they are compatible with the standard Julia kronecker product.
Warning: the object constructed will have exponential memory requirements in terms of the number of sites, use with care!
"""
function contract_virtual_indices(mpo::MPO)::Matrix{<:Number}
N = length(mpo)
# Since we deal with open boundary conditions, we drop the dummy indices one on the left (right) boundary for the first (last) tensor manually. We start from the right to have the physical indices in the order compatible with Julia's kronecker product
res = mpo[N][:, 1, :, :]
for i = N-1:-1:2
res = contract_tensors(res, [ndims(res) - 2], mpo[i], [2])
end
res = contract_tensors(res, [ndims(res) - 2], mpo[1][1, :, :, :], [1])
# Reshuffle the indices to be compatible with Julia's standard kronecker product
res = permutedims(res, [collect(1:2:ndims(res)); collect(2:2:ndims(res))])
# Now reshape the result accordingly
dims = size(res)
dr = prod(dims[1:N])
dc = prod(dims[N+1:end])
res = reshape(res, (dr, dc))
return res
end
"""
find_groundstate(H::Array{Operator},D::Int64,acc::Float64,max_sweeps::Int64=-1)
Given a Hamiltonian MPO H, find an MPS approximation for its ground state with bond
dimension D converged to a relative accuracy acc. If a positive number for max_sweeps
is given, the maximum amount of iterations is limited to max_sweeps
"""
function find_groundstate(H::Vector{Operator{T}}, D::Int64, d::Int64, acc::Float64, max_sweeps::Int64) where {T}
N = length(H)
# Get the physical dimensions from the Hamiltonian
d = Vector{Int64}(undef, length(H))
for i = 1:length(H)
d[i] = size(H[i], 3)
end
# Random MPS to start the calculation with
mps = random_mps_obc(N, D, d)
# Put it in right canonical gauge
gaugeMPS!(mps, :right)
# Precalculate the partial contractions
LR = setup_R(H, mps)
# Now start the sweeping
num_of_sweeps = 0
E0 = 0
Eold = 1E5
while (true)
num_of_sweeps = num_of_sweeps + 1
println("Sweep number ", num_of_sweeps)
# From left to right starting by 1 up to N-1
E_local = 0
res = 0
for i = 1:N-1
Left = LR[i]
Right = LR[i+1]
E_local, M = solve_eigenvalue_problem(Left, Right, H[i])
mps[i], _ = gauge_site(M, :left)
LR[i+1] = update_left(Left, mps[i], mps[i], H[i])
end
# From left to right starting by 1 up to N-1
for i = N:-1:2
Left = LR[i]
Right = LR[i+1]
E_local, M = solve_eigenvalue_problem(Left, Right, H[i])
mps[i], res = gauge_site(M, :right)
LR[i] = update_right(Right, mps[i], mps[i], H[i])
end
# Check convergence criterion
if (abs((Eold - E_local) / Eold) < acc)
E0 = E_local
# Restore normalisation (permutation is needed to bring the indices back into right order after contracting)
mps[1] = contract_tensors(mps[1], [2], res, [1], [1; 3; 2])
println("Convergence to desired accuracy achieved")
break
elseif (max_sweeps > 0 && num_of_sweeps >= max_sweeps)
E0 = E_local
# Restore normalisation (permutation is needed to bring the indices back into right order after contracting)
mps[1] = contract_tensors(mps[1], [2], res, [1], [1; 3; 2])
warn("Reached maximum number of iterations before convergence to desired accuracy")
break
end
Eold = E_local
end
return E0, mps, num_of_sweeps
end
"""
getHeff(Left,Right,W::Operator)
Construct the effective Hamiltonian
"""
function getHeff(Left, Right, W::Operator)
Htemp = contract_tensors(W, [2], Right, [2])
Htemp = contract_tensors(Left, [2], Htemp, [1])
Htemp = permutedims(Htemp, [1; 5; 3; 2; 6; 4])
dim1, dim2, dim3, dim4, dim5, dim6 = size(Htemp)
Heff = reshape(Htemp, (dim1 * dim2 * dim3, dim4 * dim5 * dim6))
return Heff
end
"""
solve_eigenvalue_problem(Left,Right,W)
Function to construct and solve the eigenvalue problem which arises on each site for the effective Hamiltonian
"""
function solve_eigenvalue_problem(Left, Right, W)
Htemp = contract_tensors(W, [2], Right, [2])
Htemp = contract_tensors(Left, [2], Htemp, [1])
Htemp = permutedims(Htemp, [1; 5; 3; 2; 6; 4])
dim1, dim2, dim3, dim4, dim5, dim6 = size(Htemp)
Heff = reshape(Htemp, (dim1 * dim2 * dim3, dim4 * dim5 * dim6))
E_local, M = eigs(Heff, nev = 1, which = :SR)
M = reshape(M, (dim1, dim5, dim3))
return real(E_local[1]), M
end
"""
setup_R(H::MPO{T1},mps::MPS{T2}) where {T1,T2}
Function to calculate the partial contractions needed to form the effective Hamiltonian
"""
function setup_R(H::MPO{T1}, mps::MPS{T2}) where {T1,T2}
N = length(H)
Tres = Base.return_types(*, (T1, T2))[1]
LR = Vector{Array{Tres,3}}(undef, N + 1)
# We need only N-1 partial contractions, however, we set the edges to dummy values 1 that we can recursively compute every contraction resuing the previous ones
LR[1] = ones(Tres, 1, 1, 1)
LR[N+1] = ones(Tres, 1, 1, 1)
# Now compute the partial contractions starting from the right (as I start sweeping on the left in the ground state search)
for i = N:-1:2
tmp = contract_tensors(LR[i+1], [3], mps[i], [2])
tmp = contract_tensors(H[i], [2; 4], tmp, [2; 4])
LR[i] = contract_tensors(conj(mps[i]), [2; 3], tmp, [3; 2])
end
return LR
end
"""
update_left(LR, M_left::Site, M_right::Site, W::Operator)
Function to perform an update the partial contractions required for iterative ground state search starting from the left stored in LR
"""
function update_left(LR, M_left::Site, M_right::Site, W::Operator)
res = contract_tensors(LR, [3], M_right, [1])
res = contract_tensors(W, [1; 4], res, [2; 4])
res = contract_tensors(conj(M_left), [1; 3], res, [3; 2])
return res
end
"""
update_right(LR, M_left::Site, M_right::Site, W::Operator)
Function to perform an update the partial contractions required for iterative ground state search starting from the right stored in LR
"""
function update_right(LR, M_left::Site, M_right::Site, W::Operator)
res = contract_tensors(LR, [3], M_right, [2])
res = contract_tensors(W, [2; 4], res, [2; 4])
res = contract_tensors(conj(M_left), [2; 3], res, [3; 2])
return res
end
"""
apply_operator(operator::MPO{T1}, mps::MPS{T2})::MPS where {T1,T2}
Apply an operator given as MPO to an MPS. The resulting MPS will have a bond dimension that is the product of the bond dimensions of the MPS and the MPO.
"""
function apply_operator(operator::MPO{T1}, mps::MPS{T2})::MPS where {T1,T2}
N1 = length(mps)
N2 = length(operator)
@assert(N1 == N2)
# Generate a new MPO of the correct type
Tres = Base.return_types(*, (T1, T2))[1]
res = MPS{Tres}(undef, N1)
# Apply the MPO to the MPS and generate new MPS
for i = 1:N1
temp = contract_tensors(operator[i], [4], mps[i], [3])
temp = permutedims(temp, (1, 4, 2, 5, 3))
dim1, dim2, dim3, dim4, dim5 = size(temp)
res[i] = reshape(temp, (dim1 * dim2, dim3 * dim4, dim5))
end
return res
end
"""
apply_operator!(operator::MPO{T1}, mps::MPS{T2})::MPS where {T1,T2}
Apply an operator given as MPO to an MPS. The resulting MPS will have a bond dimension that is the product of the bond dimensions of the MPS and the MPO. The input will be overwritten by the result. This requires that the type of the elements of the input MPS is able to accomodate the result of multiplying the MPO tensors into the MPS tensors (e.g. applying a complex MPO to a real MPS cannot be done inpalce as the result will be complex)
"""
function apply_operator!(operator::MPO, mps::MPS)
N1 = length(mps)
N2 = length(operator)
@assert(N1 == N2)
# Contract the tensors for each site
for i = 1:N1
temp = contract_tensors(operator[i], [4], mps[i], [3])
temp = permutedims(temp, (1, 4, 2, 5, 3))
dim1, dim2, dim3, dim4, dim5 = size(temp)
mps[i] = reshape(temp, (dim1 * dim2, dim3 * dim4, dim5))
end
end
"""
apply_operator(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2}
Multiply two MPOs together to get an expression for op2 * op1 in MPO form. The resulting MPS will have a bond dimension that is the product of the bond dimensions of both MPOs.
"""
function apply_operator(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2}
N1 = length(op1)
N2 = length(op2)
@assert(N1 == N2)
# Generate a new MPS of the correct type
Tres = Base.return_types(*, (T1, T2))[1]
res = MPO{Tres}(undef, N1)
# Contract the tensors for each site
for i = 1:N1
temp = contract_tensors(op2[i], [4], op1[i], [3])
temp = permutedims(temp, (1, 4, 2, 5, 3, 6))
dim1, dim2, dim3, dim4, dim5, dim6 = size(temp)
res[i] = reshape(temp, (dim1 * dim2, dim3 * dim4, dim5, dim6))
end
return res
end
"""
sum_states(mps1::MPS{T1}, mps2::MPS{T2})::MPS where {T1,T2}
Add two MPSs together to get an expression for mps1 + mps2 in MPS form. The resulting MPS will have a bond dimension that is the sum of the bond dimensions of both MPOs.
"""
function sum_states(mps1::MPS{T1}, mps2::MPS{T2})::MPS where {T1,T2}
N1 = length(mps1)
N2 = length(mps2)
@assert(N1 == N2)
# Generate a new MPO of the correct type
Tres = Base.return_types(+, (T1, T2))[1]
res = MPS{Tres}(undef, N1)
# The first site needs special treatment
tensor1 = mps1[1]
tensor2 = mps2[1]
_, Dr1, d1 = size(tensor1)
_, Dr2, d2 = size(tensor2)
new_tensor = zeros(Tres, 1, Dr1 + Dr2, d1)
for r = 1:d1
new_tensor[1, :, r] = [tensor1[1:1, :, r] tensor2[1:1, :, r]]
end
res[1] = new_tensor
# The tensors in between
for i = 2:N1-1
tensor1 = mps1[i]
tensor2 = mps2[i]
Dl1, Dr1, d1 = size(tensor1)
Dl2, Dr2, d2 = size(tensor2)
new_tensor = zeros(Tres, Dl1 + Dl2, Dr1 + Dr2, d1)
for r = 1:d1
new_tensor[1:Dl1, 1:Dr1, r] = tensor1[:, :, r]
new_tensor[Dl1+1:end, Dr1+1:end, r] = tensor2[:, :, r]
end
res[i] = new_tensor
end
# The last site needs special treatment
tensor1 = mps1[N1]
tensor2 = mps2[N1]
Dl1, _, d1 = size(tensor1)
Dl2, _, d2 = size(tensor2)
new_tensor = zeros(Tres, Dl1 + Dl2, 1, d1)
for r = 1:d1
new_tensor[:, 1, r] = [tensor1[:, 1, r]; tensor2[:, 1, r]]
end
res[N1] = new_tensor
return res
end
"""
sum_operators(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2}
Add two MPOs together to get an expression for op2 + op1 in MPO form. The resulting MPO will have a bond dimension that is the sum of the bond dimensions of both MPOs.
"""
function sum_operators(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2}
N1 = length(op1)
N2 = length(op2)
@assert(N1 == N2)
# Generate a new MPO of the correct type
Tres = Base.return_types(+, (T1, T2))[1]
res = MPO{Tres}(undef, N1)
# The first site needs special treatment
tensor1 = op1[1]
tensor2 = op2[1]
_, Dr1, dr1, dc1 = size(tensor1)
_, Dr2, dr2, dc2 = size(tensor2)
new_tensor = zeros(Tres, 1, Dr1 + Dr2, dr1, dc1)
for r = 1:dr1
for c = 1:dc1
new_tensor[1, :, r, c] = [tensor1[1:1, :, r, c] tensor2[1:1, :, r, c]]
end
end
res[1] = new_tensor
# The tensors in between
for i = 2:N1-1
tensor1 = op1[i]
tensor2 = op2[i]
Dl1, Dr1, dr1, dc1 = size(tensor1)
Dl2, Dr2, dr2, dc2 = size(tensor2)
new_tensor = zeros(Tres, Dl1 + Dl2, Dr1 + Dr2, dr1, dc1)
for r = 1:dr1
for c = 1:dc1
new_tensor[1:Dl1, 1:Dr1, r, c] = tensor1[:, :, r, c]
new_tensor[Dl1+1:end, Dr1+1:end, r, c] = tensor2[:, :, r, c]
end
end
res[i] = new_tensor
end
# The last site needs special treatment
tensor1 = op1[N1]
tensor2 = op2[N1]
Dl1, _, dr1, dc1 = size(tensor1)
Dl2, _, dr2, dc2 = size(tensor2)
new_tensor = zeros(Tres, Dl1 + Dl2, 1, dr1, dc1)
for r = 1:dr1
for c = 1:dc1
new_tensor[:, 1, r, c] = [tensor1[:, 1, r, c]; tensor2[:, 1, r, c]]
end
end
res[N1] = new_tensor
return res
end
"""
compute_entropy(mps::MPS, n:Int)::Float64
Compute the von Neumann along for the bipartion of the sites into two subsets A={1,...,n} and B={n+1,...,N} where N is the length of the MPS. If n<=0 is supplied, a bipartion of into A. For the result to make sense, mps has to be a normalized quantum state.
"""
function compute_entropy(mps::MPS{T}, n::Int = 0)::Float64 where {T}
# Extact the length and check if the given position is reasonable
N = length(mps)
@assert(n <= N)
# The entropy of the entire state is simply zero since it is a pure state, so nothing to compute
if n == N
return 0.0
end
# In case a value n<=0 is given, we assume the bipartion is taken in the center
if n <= 0
n = Int(round(N / 2))
end
# Get a copy of the input
mps_loc = deepcopy(mps)
# Put the sites left to n into left canonical gauge
M = mps_loc[1]
for i = 1:n
mps_loc[i], res = gauge_site(M, :left)
M = contract_tensors(res, [2], mps_loc[i+1], [1])
end
mps_loc[n+1] = M
# Now start contracting from the right boundary to obtain the reduced density operator
rdm = ones(T, 1, 1)
for i = N:-1:n+1
rdm = contract_tensors(rdm, [2], mps_loc[i], [2])
rdm = contract_tensors(conj(mps_loc[i]), [2; 3], rdm, [1; 3])
end
# Now diagonalize the reduced density matrix and compute the entropy
ev = real(eigvals(rdm))
# Eigenvalues that are numerically zero sometimes become -1E-16, to prevent problems with the logarithm we filter them
ev = filter(x -> x > 0.0, ev)
# The von Neumann entropy for the reduced density operator
entropy = -sum(ev .* log2.(ev))
return entropy
end
"""
sample_from_mps!(mps::MPS, gauge_input::Bool=true)::Vector{Int64}
Generate a sample from the probability distribution of basis states defined by the MPS following A. Ferris, G. Vidal, PRB 85 165146 (2021). If the flag gague_input is set to true, the input MPS will be put in right canoncial gauge and normalized, which is a requirement for the algorithm to work. In case one is sure that the MPS is already properly gauged and normalized the gauging step can be spared by setting the flag to false. In this case the input will stay untouched.
"""
function sample_from_mps!(mps::MPS, gauge_input::Bool = true)::Vector{Int64}
# Extact the length and check if the given position is reasonable
N = length(mps)
res = zeros(Int64, N)
# Put the state into right canonical gauge and make sure it is normalized
if gauge_input
gaugeMPS!(mps, :right, true)
end
# Now sample from the MPS
A = 0
p = 0.0
M = mps[1][1, :, :]
for i = 1:N
d = size(M, 2)
pacc = 0
r = rand()
for l = 1:d
# Prepare the basis state
basis_state = zeros(d)
basis_state[l] = 1.0
# Contract it into the physical index of the tensor
A = contract_tensors(M, [2], basis_state, [1])
# Determine the probability for the basis vector e_l
p = contract_tensors(conj(A), [1], A, [1])
pacc += real(p[1])
if r < pacc
res[i] = l
break
end
end
if i < N
# Contract the result into the next tensor
M = contract_tensors(1 / sqrt(real(p[1])) * A, [1], mps[i+1], [1])
end
end
return res
end
"""
sample_from_mps(mps::MPS)::Vector{Int64}
Generate a sample from the probability distribution of basis states defined by the MPS following A. Ferris, G. Vidal, PRB 85 165146 (2021).
"""
function sample_from_mps(mps::MPS)::Vector{Int64}
return sample_from_mps!(deepcopy(mps))
end
"""
svd_compress_mps(mps::MPS, Dmax::Int,, tol::Real = 0.0)::MPS
Compress a given MPS applying an a singular value decomposition at each bond. If Dmax > 0 is supplied (and simultaneously tol = 0.0), a maximum of Dmax singular values is kept, thus truncating the MPS to one with maximum bond dimension Dmax. If tol > 0 is given (and simultaneously Dmax = 0) then all singular values > tol are kept. If both are specified then at most Dmax singular values > tol are kept.
"""
function svd_compress_mps(mps::MPS, Dmax::Int, tol::Real = 0.0)::MPS
# One of the two parameters has to be larger than zero
@assert((Dmax > 0) || (tol > 0))
# Extract the length and prepare a result
N = length(mps)
res = deepcopy(mps)
# Gauge in both directions that redundant dimensions at the boundaries are removed
gaugeMPS!(res, :left)
gaugeMPS!(res, :right)
Dnew = 0
for i = 1:N-1
# Check if the given bond dimension is larger than Dmax
if size(res[i], 2) > Dmax
Dl1, _, d1 = size(res[i])
_, Dr2, d2 = size(res[i+1])
tmp = contract_tensors(res[i], [2], res[i+1], [1])
tmp = reshape(tmp, (Dl1 * d1, Dr2 * d2))
U, S, V = svd(tmp)
M = diagm(S) * V'
# Now truncate
if Dmax > 0 && tol == 0.0
U = U[:, 1:Dmax]
M = M[1:Dmax, :]
Dnew = Dmax
else
ind = findall(x -> x > tol, S)
if Dmax > 0 && length(ind) > Dmax
ind = ind[1:Dmax]
end
U = U[:, ind]
M = M[ind, :]
Dnew = length(ind)
end
# Reshape and set new tensors
res[i] = permutedims(reshape(U, (Dl1, d1, Dnew)), (1, 3, 2))
res[i+1] = reshape(M, (Dnew, Dr2, d2))
end
end
return res
end
"""
decompose_into_mpo(M::Matrix{T}, d::Vector{Int}) where T <:Number
Given a many-body operator in form of a dense matrix, decompose it into an MPO. It is assumed that the many-body operator follows the index convention of Julia's built-in kronecker product. The vector d specifies the local dimensions of the Hilbert space.
# Examples
Decomposing a simple two-site operator made up from sum of Pauli terms into MPO form.
```julia-repl
julia> Id = [1.0 0; 0.0 1.0]
julia> X = [0.0 1.0; 1.0 0.0]
julia> Z = [1.0 0.0; 0.0 -1.0]
julia> H = kron(X,X) + kron(Id,Z) + kron(Z,Id)
julia> mpo = decompose_into_mpo(H, 2)
```
"""
function decompose_into_mpo(M::Matrix{T}, d::Vector{Int})::MPO{T} where {T<:Number}
N = length(d)
dim = prod(d)
if size(M) != (prod(d), prod(d))
throw(ArgumentError("matrix not compatible with specified local dimensions, got size(M)=$(repr(size(M))), d=$(repr(d))"))
end
# The MPO holding the result
res = MPO{T}(undef, N)
# Reshape the matrix and rearrange the indices, such that the row and column index for each site are adjacent and add dummy indices 1 at the boundaries
A = reshape(M, (1, reverse(d)..., reverse(d)..., 1))
ind = collect(Iterators.flatten(zip(collect(N:-1:1), collect(2N:-1:N+1))))
A = permutedims(A, (1, ind .+ 1..., 2 * length(d) + 2))
# Now split it into tensors using an SVD
Dl = 1
for i = 1:N-1
# Take the first three indices together
dims = size(A)
A = reshape(A, (prod(dims[1:3]), prod(dims[4:end])))
# SVD the matrix representation
U, S, V = svd(A)
A = diagm(S) * V'
Dr = size(U, 2)
# Extract the tensor and the remaining part
U = reshape(U, (Dl, d[i], d[i], Dr))
res[i] = permutedims(U, (1, 4, 2, 3))
A = reshape(A, (Dr, dims[4:end]...))
Dl = Dr
end
res[N] = permutedims(A, (1, 4, 2, 3))
return res
end
"""
decompose_into_mpo(M::Matrix{T}, d::Int) where T <:Number
Simplified interface to the more general method assuming that all local dimensions are equal to d.
"""
function decompose_into_mpo(M::Matrix{T}, d::Int)::MPO{T} where {T<:Number}
dl, dr = size(M)
if dl != dr
throw(ArgumentError("local dimensions must all be the same, obtained a matrix with dimensions $(repr((dl,dr)))"))
end
N = Int(round(log(d, dl)))
return decompose_into_mpo(M, d * ones(Int64, N))
end | [
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] | 2.277107 | 12,663 |
module FisherySim
using Distributions
using TweedieDistributions
using StatsBase
using LinearAlgebra
using Random
using PDMats
using Arpack
using NeutralLandscapes
import Base:
rand,
+, -, *,
step,
sum,
getindex, setindex!,
size, length, eachindex,
copy
import StatsBase:
sample,
cov
import Distributions:
location
include("fisherydomain.jl")
export
AbstractFisheryDomain,
DiscreteFisheryDomain,
GriddedFisheryDomain,
size,
length,
eachindex,
sample
include("covkernels.jl")
export
AbstractCovarianceKernel,
ExpCov,
Matérn32Cov,
Matern32Cov,
AR1,
cov
# include("matrixlognormal.jl")
# export
# MatrixLogNormal,
# location
include("domaindistributions.jl")
export
AbstractDomainDistribution,
DomainDistribution,
MultiDomainDistribution,
BlendedDomainDistribution,
ClassifiedDomainDistribution,
domain,
getindex,
length
include("habitat.jl")
export
Habitat,
getindex,
length,
HabitatPreference
include("bathymetry.jl")
export
BathymetryModel,
Bathymetry,
rand
include("pop_dynamics.jl")
export
PopulationDynamicsModel,
PopState,
Schaefer,
PellaTomlinson,
StochasticProduction,
vecstate,
step,
sum,
setindex!,
copy
include("movement.jl")
export
MovementModel,
eqdist,
MovementRate
include("targeting.jl")
export
AbstractTargetingBehavior,
RandomTargeting,
FixedTargeting,
AbstractPreferentialTargeting,
PreferentialTargeting,
DynamicPreferentialTargeting,
target,
reset!
include("catchability.jl")
export
AbstractCatchability,
Catchability,
DensityDependentCatchability,
HabitatCatchability,
*
include("vessels.jl")
export
Vessel,
Catch,
CPUE,
+, -,
fish!,
getindex,
Fleet,
vessels
include("simulation.jl")
export
simulate
end # module
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220,
220,
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11,
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220,
220,
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198,
39344,
198,
220,
220,
220,
29308,
198,
198,
437,
1303,
8265,
198
] | 2.484694 | 784 |
module CLI # Bukdu
import ..Bukdu: Routing, Naming
"""
CLI.routes()
Showing the routing table.
"""
function routes()
A = Routing.store[:routing_tables]
isempty(A) && return
ncols = 5 # verb url C action pipe
nrows = Int(length(A)/ncols)
rt = reshape(A, ncols, nrows)
paddings = maximum((length ∘ string).(rt), dims=2) .+ 2
function f(idx, el, lastcolumn)
if idx == lastcolumn
el
else
rpad(el, paddings[idx])
end
end
for rowidx in 1:nrows
row = rt[:, rowidx]
lastcolumn = isempty(row[ncols]) ? ncols-1 : ncols
print.([f(idx, el, lastcolumn) for (idx, el) in enumerate(row[1:lastcolumn])])
println()
end
end
end # module Bukdu.CLI
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] | 2.06267 | 367 |
### A Pluto.jl notebook ###
# v0.18.0
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 451ae3a0-8068-4747-95a7-d31955808f29
begin
# external packages -
using PlutoUI
using Plots
using PrettyTables
end
# ╔═╡ 8ba6a00a-7a53-4dcc-af4d-cb85aa9b4d68
md"""
### Simple and Complex Models of Enzyme Kinetics
The flux bounds are essential constraints in flux balance analysis calculations and the convex decomposition of the stoichiometric array. Beyond their role in the flux estimation problem, the flux bounds are _integrative_, i.e., these constraints integrate many types of genetic and biochemical information into the flux estimation problem.
Flux bounds constrain the values that each reaction in a metabolic network can take. A general model for these bounds is given by:
$$-\delta_{j}\left[{V_{max,j}^{\circ}}\left(\frac{e}{e^{\circ}}\right)\theta_{j}\left(\dots\right){f_{j}\left(\dots\right)}\right]\leq{v_{j}}\leq{V_{max,j}^{\circ}}\left(\frac{e}{e^{\circ}}\right)\theta_{j}\left(\dots\right){f_{j}\left(\dots\right)}$$
where $V_{max,j}^{\circ}$ denotes the maximum reaction velocity (units: flux) computed at some characteristic enzyme abundance (units: concentration), the ratio $e/e^{\circ}$ is a correction for enzyme abundance (units: dimensioness), $\theta_{j}\left(\dots\right)\in\left[0,1\right]$ is the fraction of maximial enzyme activity (a function or measurement producing units: dimensionless), and $f_{j}\left(\dots\right)$ is a function describing the substrate dependence of the reaction rate $j$ (units: dimensionless). Both $\theta_{j}\left(\dots\right)$ and $f_{j}\left(\dots\right)$ could have associated parameters, e.g., saturation or binding constants, etc. Finally, the quanity $\delta_{j}\in\left\{0,1\right\}$ is a _binary_ variable:
* If reaction $j$ is __reversible__ $\delta_{j}=1$ or,
* If reaction $j$ is __irreversible__ $\delta_{j}=0$
Today, let's focus on approaches for computing the value of these bounds, i.e., the form and value of the terms in the brackets. In this lecture, we will:
1. Develop simple models of enzyme kinetics using the Michaelis–Menten approach
1. Introduce the fundamental concepts underlying more complex models of allosteric regulation (the fast control mechanisms that we mentioned previously)
1. Introduce effective discrete regulation models to capture allosteric regulation
"""
# ╔═╡ 8869f117-1fc6-4cc5-9803-b8ec72a109a6
md"""
### What is allosteric regulation?
Allosteric regulation modulates enzyme activity by binding effector molecules to sites other than the enzyme's active site. These events can activate (enhances rate) and inhibit (decreases rate). Allosteric regulation operates on a fast time scale compared to gene expression (synthesis of the enzyme).
Allosteric mechanisms in Central Carbon Metabolism:
* [Reznik E, Christodoulou D, Goldford JE, Briars E, Sauer U, Segrè D, Noor E. Genome-Scale Architecture of Small Molecule Regulatory Networks and the Fundamental Trade-Off between Regulation and Enzymatic Activity. Cell Rep. 2017 Sep 12;20(11):2666-2677. doi: 10.1016/j.celrep.2017.08.066. PMID: 28903046; PMCID: PMC5600504.](https://pubmed.ncbi.nlm.nih.gov/28903046/)
"""
# ╔═╡ 17724757-604e-4c77-a42b-238ba121e88f
md"""
### Simple: Michaelis–Menten kinetics
Let's assume we have a well-mixed test tube containing an enzyme $E$ (a protein that catalyzes chemical reactions), which converts substrate $S$ (the starting compound)
into product $P$ according to three elementary reactions:
$$\begin{eqnarray}
E+S&\rightleftharpoons&{E:S}\\
{E:S}&\longrightarrow&E+P
\end{eqnarray}$$
The kinetics of each elementary step can be written using mass-action kinetics, i.e.,
$$\begin{eqnarray}
r_{1} & = & k_{1}\left[E\right]\left[S\right]\\
r_{2} & = & k_{2}\left[E:S\right]\\
r_{3} & = & k_{3}\left[E:S\right]
\end{eqnarray}$$
where $\left[\cdot\right]$ denotes a species concentration, and $k_{j}$ denotes the rate constant governing the $jth$ elementary reaction:
* The rate $r_{1}$ describes the _association_ rate between the enzyme and substrate,
* The rate $r_{2}$ represents the rate of _dissociation_ of the enzyme-substrate complex, and
* The $r_{3}$ denotes the rate of _chemical conversion_ of the bound substrate into the product (we assume the dissociation of the product from the enzyme is fast).
The enzyme must obey the relationship:
$$\left[E_{T}\right] = \left[E\right] + \left[E:S\right]$$
where $\left[E_{T}\right]$ denotes the total enzyme concentration in the tube,
$\left[E\right]$ denotes the free enzyme concentration (not bound to substrate) while
$\left[E:S\right]$ denotes the enzyme-substrate complex.
To estimate the _overall_ rate $v$, we stipulate a single rate-limiting step out of the set of elementary reactions. Let's assume that the rate of chemical conversion ($r_{3}$) is the slowest step, i.e., the substrate bounces on/off the enzyme quickly with only a tiny fraction of these binding events resulting in a successful chemical transformation. Thus, the overall rate is then given by:
$$v = k_{3}\left[E:S\right]$$
Let's also assume that we already know (or can estimate) the rate constants $k_{1},k_{2}$ and $k_{3}$. When this is true, the only unknown is $\left[E:S\right]$.
However, we can relate $\left[E:S\right]$ to variables we know ($E_{T}$ and at least initially $S$) through the enzyme balance, and the _pseudo-steady-state assumption_ for the reaction intermediate
$\left[E:S\right]$:
$$\frac{d\left[E:S\right]}{dt} = k_{1}\left[E\right]\left[S\right] - k_{2}\left[E:S\right] - k_{3}\left[E:S\right]\simeq{0}$$
Rearranging and solving for $\left[E:S\right]$ gives the relationship:
$$\left[E:S\right]\simeq\frac{k_{1}}{k_{2}+k_{3}}\left[E\right]\left[S\right]$$
where the ratio of constants is defined as the Michaelis-Menten saturation coefficient or $K_{M}$:
$$\frac{1}{K_{M}}\equiv\frac{k_{1}}{k_{2}+k_{3}}$$
Substituting the definition of $K_{M}$ into the overall rate yields:
$$v = k_{3}\frac{\left[E\right]\left[S\right]}{K_{M}}$$
However, we do not know the free enzyme concentration of $\left[E\right]$; to find $\left[E\right]$
we subsitute $\left[E:S\right]$ into the enzyme balance and solving for $\left[E\right]$:
$$\left[E\right] = \frac{\left[E_T\right]K_{M}}{K_{M}+\left[S\right]}$$
Lastly, we substitute $\left[E\right]$ into the overall rate to arrive at the final expression for $v$:
$$v = V_{max}\frac{\left[S\right]}{K_{M}+\left[S\right]}$$
where $V_{max}\equiv{k_{3}}\left[E_{T}\right]$.
__Limiting cases:__
* when $S\gg{K}_{M}$, the rate becomes close to $V_{max}$.
* when $S\ll{K}_{M}$ the rate appears to be linear with respect to substrate concentration.
* when $K_{M}\simeq S$ the reaction rate equals $v\simeq 1/2V_{max}$.
"""
# ╔═╡ 431ccdf0-93a9-4b3c-9576-8854ba2f1fad
@bind MM_parameters PlutoUI.combine() do Child
md"""
##### Michaelis–Menten Parameters
\[E\] $(
Child(Slider(1:5))
) (μM) and Kₘ $(
Child(Slider(5:100))
) (mM)
"""
end
# ╔═╡ 7efaf27c-8e0a-40f9-ac28-af90357450a3
begin
# get MM parameter values -
E = MM_parameters[1]
Kₘ = MM_parameters[2]
kcat = 13.7 # units: s^-1
number_of_steps = 1000
# substrate range -
S_array = range(0.0,stop=100.0,length=number_of_steps) |> collect;
# initialize space -
v_array = Array{Float64,1}(undef,number_of_steps)
# compute the rate -
for (i,S) ∈ enumerate(S_array)
# compute the rate -
v_array[i] = (kcat*E)*(S/(S+Kₘ))
end
# plot -
plot(S_array,v_array,xlims=(0.0,100.0),ylims=(0.0,14), label="v: E = $(E) μM and Kₘ = $(Kₘ) (mM)")
xlabel!("Substrate S (mM)",fontsize=18)
ylabel!("Rate v (μM/s)",fontsize=18)
end
# ╔═╡ 55ea8324-f36d-40bd-99e3-92e7fcbafca9
md"""
### Complex: MWC and Sequential kinetic models
The Monod-Wyman-Changeux model (MWC model, also known as the symmetry model) describes allosteric transitions of proteins made up of identical subunits. Effector binding modulates the state of the entire protein.
* [MONOD J, WYMAN J, CHANGEUX JP. ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. J Mol Biol. 1965 May;12:88-118. doi: 10.1016/s0022-2836(65)80285-6. PMID: 14343300.](https://pubmed.ncbi.nlm.nih.gov/14343300/)
The sequential model (KNF model) of allosteric regulation posits that enzyme subunits are independent.
Thus, binding substrate (or effector) to a subunit results in only slight conformational changes to adjacent subunits. KNF model can do describe both positive and negative cooperativity:
* [Koshland D Jr, Némethy G, Filmer D. Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry. 1966 Jan;5(1):365-85. doi: 10.1021/bi00865a047. PMID: 5938952.](https://pubmed.ncbi.nlm.nih.gov/5938952/)
"""
# ╔═╡ 3502da52-7d2b-4c79-82ce-7424d756cd9b
md"""
### Effective discrete state kinetic models
Michaelis–Menten kinetics are easy to understand, but they neglect many factors, e.g., the influence of allosteric regulators. On the other hand, MWC/sequential models are detailed but case-specific (and too complex). It would be great if we could correct Michaelis–Menten kinetics to capture the influence of allosteric factors.
Suppose we model the rate $v_{j}$ as the product of a kinetic limit (a simple model of the rate) and a correction term that accounts for the missing regulation:
$$v_{j} = r_{j}\theta\left(...\right)_{j}$$
where $v_{j}$ denotes the overall rate (units: $\mu$M/time), $r_{j}$ denotes the kinetic limit i.e., the maximum rate of conversion (units: $\mu$M/time) and
$0\leq \theta\left(...\right)_{j}\leq 1$ (units: dimensionless) is a control function that describes the influence of effector molecules.
"""
# ╔═╡ c392c8a9-361d-47e4-933e-2e51b793e069
md"""
##### Discrete state control function model
There is a wide variety of different possible ways we can build the $\theta\left(...\right)_{j}$ control functions. Ultimately, it doesn't matter what we choose, as long as it gives a good performance. However, let's introduce an idea that we will revisit later, namely a discrete probabilistic approach.
###### Theory
Suppose an enzyme $E$ can exits in one of $s=1,2\dots,\mathcal{S}$ possible microstates, where each microstate $s$ has some pseudo energy $\epsilon_{s}$. Some microstates will lead to activity (the ability to carry out the chemical reactions, while others will not). For each microstate $s$, let's assign a pseudo energy $\epsilon_{s}$, where by definition $\epsilon_{1}=0$; we assume the base state has the lowest energy. Next, suppose the probability that enzyme $E$ is in microstate $s$ follows a [Boltzmann distribution](https://en.wikipedia.org/wiki/Boltzmann_distribution) which says:
$$p_{i} = \frac{1}{Z} \times f_{i}\exp\left(-\beta\epsilon_{i}\right)\qquad{i=1,2,\dots,\mathcal{S}}$$
where $p_{i}$ denotes the probability that enzyme $E$ is in microstate $i=1,2,\dots,\mathcal{S}$, $f_{i}$ denotes a state-specific factor $f_{i}\in\left[0,1\right]$, $\beta$ denotes the [thermodynamic beta](https://en.wikipedia.org/wiki/Thermodynamic_beta) and $Z$ denotes a normalization factor (called the [Partiton function](https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)) in the statistical physics community). We can find $Z$ using the summation law of discrete probolity e.g., $\sum_{s}p_{s} = 1$ which gives:
$$Z = \sum_{s=1}^{\mathcal{S}}f_{i}\exp\left(-\beta\epsilon_{i}\right)$$
which gives:
$$p_{i} = \frac{f_{i}\exp\left(-\beta\epsilon_{i}\right)}{\displaystyle \sum_{s=1}^{\mathcal{S}}f_{i}\exp\left(-\beta\epsilon_{i}\right)}\qquad{i=1,2,\dots,\mathcal{S}}$$.
Finally, we relate the probability that enzyme $E$ is in microstate $s$ back to the $\theta$ control function by computing the overall probability that the desired event happens, e.g., enzyme $E$ catalyzes the reaction of interests. We know if $\Omega = \left\{1,2,\dots,\mathcal{S}\right\}$, then we can define the subset $\mathcal{A}\subseteq\Omega$ in which the desired event happens. Given $\mathcal{A}$, the $\theta$ function becomes:
$$\theta=\sum_{s\in{\mathcal{A}}}p_{s}$$
###### Conceptual exampleTo illustrate this idea, consider an enzyme inhibited by a downstream product (this is a common allosteric motif known as [feedback inhibition](Pedreño S, Pisco JP, Larrouy-Maumus G, Kelly G, de Carvalho LP. Mechanism of feedback allosteric inhibition of ATP phosphoribosyltransferase. Biochemistry. 2012;51(40):8027-8038. doi:10.1021/bi300808b)). In this case, suppose enzyme $E$, which is inhibited by compound $I$, can exist in one of three possible microstates:
* __State s = 1__: No substrate $S$ is bound, $E$ is floating around in solution minding its own business (base state, no reaction)
* __State s = 2__: Substrate $S$ is bound to enzyme $E$, but inhibitor $I$ is not bound (reaction possible)
* __State s = 3__: Both the substrate $S$ and inhibitor $I$ are bound to enzyme $E$ (no reaction possible)
Given these microstates (and their functional assignment) we know that enzyme $E$ can only catalyze its reaction in microstate $s=2$, thus:
$$\theta = \frac{f_{2}\exp\left(-\beta\epsilon_{i}\right)}{\displaystyle \sum_{s=1}^{\mathcal{3}}f_{s}\exp\left(-\beta\epsilon_{s}\right)}$$
###### What are the state-specific factors?
The state-specific factors $f_{i}\in\left[0,1\right]$ control the reachability of a microstate:
* if $f_{\star} = 0$, then microstate $\star$ can __never__ be obtained
* if $f_{\star} = 1$, then microstate $\star$ can __always__ be obtained
As a modeler, you can choose the form (or value) that $f_{\star}$ takes. These factors can
be set to a specific value by definition (depending upon the state) or can be used to describe events associated with state $i$, e.g., such as binding events. For example, suppose state $i$ involved binding an effector molecule $x$ to the enzyme $E$. In this case, we could model the state-specific factor $f_{i}$ as:
$$f_{i} = (x/K_{i})^{n_{i}}/(1+(x/K_{i})^{n_{i}})$$
where $x\geq{0}$ denotes effector abundance, $K_{i}\geq{0}$ denotes a binding constant and $n_{i}\geq{0}$ denotes a binding order parameter.
"""
# ╔═╡ 91345d04-f502-4e90-935e-a4dc250244db
@bind DSM_parameters PlutoUI.combine() do Child
md"""
\[I\] $(
Child(Slider(0:100))
) (μM) K $(
Child(Slider(1:1:100))
) (mM) ϵ₂ $(
Child(Slider(0.001:0.1:100))
) (J/mol) ϵ₃ $(
Child(Slider(0.001:0.1:100))
) (J/mol)
"""
end
# ╔═╡ 719784fe-3ef6-4e53-ad52-82140e3d0b5e
begin
# get I -
Iₒ = DSM_parameters[1]
Kd = DSM_parameters[2]
ϵ₂ = (DSM_parameters[3])/100
ϵ₃ = (DSM_parameters[4])/100
# setup system -
R = 8.314 # units: J/mol-K
T = 273.15 + 25.0 # units: K
β = 1/R*T
# setup binding parameters for state 3 -
n = 2.0
# setup energy array -
ϵ_array = [
0.0 ; # state 1 (just E)
-ϵ₂ ; # state 2 (E bound to S, but no I)
-ϵ₃ ; # state 3 (E bound to I)
];
# compute W -
W_array = exp.(-β*ϵ_array)
# let's compute the state-specific factor array -
f_array = [
1.0 ; # state 1
1.0 ; # state 2
((Iₒ/Kd)^(n))/(1+(Iₒ/Kd)^(n))
];
# compute the θ variable -
microstate_array = f_array.*W_array;
Z = sum(microstate_array)
p_array = (1/Z)*microstate_array
θ = p_array[2]
# show -
with_terminal() do
println("θ = $(θ)")
end
end
# ╔═╡ 1d4d6059-5b79-43cd-ac17-ef2aa057ecad
with_terminal() do
# initialize -
𝒮 = 3
state_table = Array{Any,2}(undef,𝒮,4)
# populate the state array -
for s ∈ 1:𝒮
state_table[s,1] = s
state_table[s,2] = f_array[s]
state_table[s,3] = W_array[s]
state_table[s,4] = p_array[s]
end
# header -
header_row = (["s","fₛ","Wₛ","pₛ"])
pretty_table(state_table;header=header_row)
end
# ╔═╡ d46ced14-a5d3-45a9-9d43-38dc7879b0c7
let
# get MM parameter values -
E = 1.0 # units: μM
Kₘ = 5 # units: mM
kcat = 13.7 # units: s^-1
number_of_steps = 1000
# substrate range -
S_array = range(0.0,stop=100.0,length=number_of_steps) |> collect;
# initialize space -
v_array = Array{Float64,1}(undef,number_of_steps)
# compute the rate -
for (i,S) ∈ enumerate(S_array)
# compute the rate -
v_array[i] = (kcat*E)*(S/(S+Kₘ))*θ
end
# plot -
plot(S_array,v_array,xlims=(0.0,100.0),ylims=(0.0,14), label="v: I = $(Iₒ) mM and Kd = $(Kd) (mM)")
xlabel!("Substrate S (mM)",fontsize=18)
ylabel!("Rate v (μM/s)",fontsize=18)
end
# ╔═╡ d3568c5d-16bf-4698-9891-0be65d62b36c
md"""
### Summary and Conclusions
In this lecture we:
1. Developed simple models of enzyme kinetics using the Michaelis–Menten approach
1. Introduced the fundamental concepts underlying more complex models of allosteric regulation (the fast control mechanisms that we mentioned previously)
1. Introduced effective discrete regulation models to simulate allosteric regulation
"""
# ╔═╡ 55d4ab48-9589-4fd9-ac06-3338fdb418c4
md"""
### Next Time
* What about multiple substrates?
* Does the discrete state model work?
* How do we implement these bounds models in a flux balance analysis calculation?
"""
# ╔═╡ 54370424-3add-4f93-91b0-e136166842ae
TableOfContents(title="📚 Lecture Outline", indent=true, depth=5, aside=true)
# ╔═╡ 06a90381-b4cb-4d32-af0d-2f084364129c
html"""
<script>
// initialize -
var section = 0;
var subsection = 0;
var subsubsection = 0;
var headers = document.querySelectorAll('h3, h5, h6');
// main loop -
for (var i=0; i < headers.length; i++) {
var header = headers[i];
var text = header.innerText;
var original = header.getAttribute("text-original");
if (original === null) {
// Save original header text
header.setAttribute("text-original", text);
} else {
// Replace with original text before adding section number
text = header.getAttribute("text-original");
}
var numbering = "";
switch (header.tagName) {
case 'H3':
section += 1;
numbering = section + ".";
subsection = 0;
break;
case 'H5':
subsection += 1;
numbering = section + "." + subsection;
break;
case 'H6':
subsubsection += 1;
numbering = section + "." + subsection + "." + subsubsection;
break;
}
// update the header text
header.innerText = numbering + " " + text;
};
</script>"""
# ╔═╡ b6890de0-8923-11ec-3552-3113bdd53f86
html"""
<style>
main {
max-width: 860px;
width: 70%;
margin: auto;
font-family: "Roboto, monospace";
}
a {
color: blue;
text-decoration: none;
}
</style>"""
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
[compat]
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"
[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"
[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"
[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"
[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"
[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"
[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"
[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"
[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"
[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"
[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"
[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"
[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"
[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"
[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
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[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"
[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"
[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"
[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"
[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"
[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
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[[deps.gdk_pixbuf_jll]]
deps = ["Artifacts", "Glib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Xorg_libX11_jll", "libpng_jll"]
git-tree-sha1 = "c23323cd30d60941f8c68419a70905d9bdd92808"
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git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"
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uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
[[deps.libfdk_aac_jll]]
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git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
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[[deps.libpng_jll]]
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git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"
[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"
[[deps.nghttp2_jll]]
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uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"
[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"
[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""
# ╔═╡ Cell order:
# ╟─8ba6a00a-7a53-4dcc-af4d-cb85aa9b4d68
# ╟─8869f117-1fc6-4cc5-9803-b8ec72a109a6
# ╟─17724757-604e-4c77-a42b-238ba121e88f
# ╟─431ccdf0-93a9-4b3c-9576-8854ba2f1fad
# ╟─7efaf27c-8e0a-40f9-ac28-af90357450a3
# ╟─55ea8324-f36d-40bd-99e3-92e7fcbafca9
# ╟─3502da52-7d2b-4c79-82ce-7424d756cd9b
# ╟─c392c8a9-361d-47e4-933e-2e51b793e069
# ╟─91345d04-f502-4e90-935e-a4dc250244db
# ╟─719784fe-3ef6-4e53-ad52-82140e3d0b5e
# ╟─1d4d6059-5b79-43cd-ac17-ef2aa057ecad
# ╟─d46ced14-a5d3-45a9-9d43-38dc7879b0c7
# ╟─d3568c5d-16bf-4698-9891-0be65d62b36c
# ╟─55d4ab48-9589-4fd9-ac06-3338fdb418c4
# ╟─54370424-3add-4f93-91b0-e136166842ae
# ╠═451ae3a0-8068-4747-95a7-d31955808f29
# ╠═06a90381-b4cb-4d32-af0d-2f084364129c
# ╠═b6890de0-8923-11ec-3552-3113bdd53f86
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
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] | 2.051136 | 26,283 |
#!/bin/bash
#=
exec julia -O3 --color=yes -qi "${BASH_SOURCE[0]}"
=#
using Pkg
cd(@__DIR__)
Pkg.activate("..")
using Retest
@retest(@__DIR__)
# Local Variables:
# mode: julia
# End:
| [
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] | 2.126437 | 87 |
mutable struct Position
x::Int
y::Int
end
struct Size
width::Int
height::Int
end
s1 = Spaceship(Position(0,0), Size(30,5), Missile);
s2 = Spaceship(Position(10,0), Size(30,5), Laser);
a1 = Asteroid(Position(20,0), Size(20,20));
a2 = Asteroid(Position(0,20), Size(20,20));
struct Rectangle
top::Int
left::Int
bottom::Int
right::Int
# return the upper-left and lower-right points
Rectangle(p::Position, s::Size) =
new(p.y + s.height, p.x, p.y, p.x+s.width)
end
# check if the 2 rectangles (A & B) overlap
function overlap(A::Rectangle, B::Rectangle)
return A.left < B.right && A.right > B.left &&
A.top > B.bottom && A.bottom < B.top
end
function collide(A::Thing, B::Thing)
println("Checking collision of thing vs. thing")
rectA = Rectangle(position(A), size(A))
rectB = Rectangle(position(B), size(B))
return overlap(rectA, rectB)
end
function collide(A::Spaceship, B::Spaceship)
println("Checking collision of spaceship vs. spaceship")
return true # just a test
end
# Randomly pick two things and check
function check_randomly(things)
for i in 1:5
two = rand(things, 2)
collide(two...)
end
end | [
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] | 2.487705 | 488 |
############################################################
# judiWavefield ##############################################
############################################################
# Authors: Philipp Witte (pwitte@eos.ubc.ca), Henryk Modzelewski (hmodzelewski@eos.ubc.ca)
# Date: June 2017
export judiWavefield, fft, ifft
############################################################
mutable struct judiWavefield{T} <: judiMultiSourceVector{T}
nsrc::Integer
dt::Vector{T}
data::Vector{<:Union{Array{T, N}, PyArray}} where N
end
############################################################
## outer constructors
"""
judiWavefield
nsrc::Integer
dt::AbstractFloat
data
Abstract vector for seismic wavefields.
Constructors
============
Construct wavefield vector from an info structure, a cell array of wavefields and the computational \\
time step dt:
judiWavefield(nsrc, dt, data)
"""
function judiWavefield(nsrc::Integer, dt::AbstractFloat, data::Array{T, N}) where {T<:Number, N}
# length of vector
dataCell = [convert(Array{Float32, N}, data) for j=1:nsrc]
return judiWavefield{Float32}(nsrc, [Float32(dt) for i=1:nsrc], dataCell)
end
function judiWavefield(dt::AbstractFloat, data::Vector{Array{T, N}}) where {T, N}
# length of vector
nsrc = length(data)
T != Float32 && (data = tof32.(data))
return judiWavefield{Float32}(nsrc, [Float32(dt) for i=1:nsrc], data)
end
judiWavefield(dt::AbstractFloat, nsrc::Integer, data::Array{T, N}) where {T<:Number, N} = judiWavefield(nsrc, dt, data)
judiWavefield(dt::AbstractFloat, data::Vector{Any}) = judiWavefield(dt, tof32.(data))
judiWavefield(dt::AbstractFloat, data::Array{T, N}) where {T<:Number, N} = judiWavefield(1, dt, data)
conj(w::judiWavefield{T}) where {T<:Complex} = judiWavefield{R}(w.nsrc, w.dt, conj(w.data))
############################################################
## overloaded multi_source functions
time_sampling(jv::judiWavefield) = jv.dt
####################################################################
# JOLI conversion
jo_convert(::Type{T}, jw::judiWavefield{T}, ::Bool) where {T<:Number} = jw
jo_convert(::Type{T}, jw::judiWavefield{vT}, B::Bool) where {T<:Number, vT} = judiWavefield{T}(jw.nsrc, jv.dt, jo_convert.(T, jw.data, B))
zero(::Type{T}, v::judiWavefield{vT}; nsrc::Integer=v.nsrc) where {T, vT} = judiWavefield{T}(nsrc, v.dt, T(0) .* v.data[1:nsrc])
zero(::Type{T}, v::judiWavefield{vT}; nsrc::Integer=v.nsrc) where {T<:AbstractFloat, vT<:Complex} = judiWavefield{T}(nsrc, v.dt, T(0) .* real(v.data[1:nsrc]))
(w::judiWavefield)(x::Vector{<:Array}) = judiWavefield(w.dt, x)
function copy!(jv::judiWavefield, jv2::judiWavefield)
v.data .= jv2.data
jv.dt = jv2.dt
jv
end
copyto!(jv::judiWavefield, jv2::judiWavefield) = copy!(jv, jv2)
make_input(w::judiWavefield) = w.data[1]
check_compat(ms::Vararg{judiWavefield, N}) where N = all(y -> y.dt == first(ms).dt, ms)
getindex(a::judiWavefield{T}, srcnum::RangeOrVec) where T = judiWavefield{T}(length(srcnum), a.dt[srcnum], a.data[srcnum])
####################################################################
function push!(a::judiWavefield{T}, b::judiWavefield{T}) where T
append!(a.data, b.data)
append!(a.dt, b.dt)
a.nsrc += b.nsrc
end
# DFT operator for wavefields, acts along time dimension
function fft(x_in::judiWavefield{T}) where T
x = similar(x_in, Complex{Float32})
for i=1:x_in.nsrc
x.data[i] = fft(x_in.data[i], 1)/sqrt(size(x_in.data[i], 1))
end
return x
end
function ifft(x_in::judiWavefield{T}) where T
x = similar(x_in, Float32)
for i=1:x_in.nsrc
x.data[i] = real(ifft(x_in.data[i], 1)) * sqrt(size(x_in.data[i], 1))
end
return x
end
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] | 2.557613 | 1,458 |
export pswap, singlet_block, basis_rotor
using YaoBlocks
using YaoArrayRegister: mulrow!, u1rows!
function Yao.apply!(reg::ArrayReg, pb::PutBlock{N,2,RotationGate{2,T,G}}) where {N,T,G<:SWAPGate}
mask1 = bmask(pb.locs[1])
mask2 = bmask(pb.locs[2])
mask12 = mask1|mask2
a, c, b_, d = mat(Rx(pb.content.theta))
e = exp(-im/2*pb.content.theta)
state = statevec(reg)
for b in basis(reg)
if b&mask1==0
i = b+1
i_ = b ⊻ mask12 + 1
if b&mask2==mask2
u1rows!(state, i, i_, a, b_, c, d)
else
mulrow!(state, i, e)
mulrow!(state, i_, e)
end
end
end
return reg
end
mutable struct Bag{N}<:TagBlock{AbstractBlock, N}
content::AbstractBlock{N}
end
Yao.content(bag) = bag.content
Yao.chcontent(bag::Bag, content) = Bag(content)
Yao.mat(bag::Bag) = mat(bag.content)
Yao.apply!(reg::AbstractRegister, bag::Bag) = apply!(reg, bag.content)
YaoBlocks.PreserveStyle(::Bag) = YaoBlocks.PreserveAll()
setcontent!(bag::Bag, content) = (bag.content = content; bag)
function YaoBlocks.print_annotation(io::IO, bag::Bag)
printstyled(io, "[⊞] "; bold=true, color=:blue)
end
"""parametrized swap gate."""
function pswap(nbit::Int, i::Int, j::Int)
put(nbit, (i,j)=>rot(SWAP, 0.0))
end
"""block for generating singlets."""
function singlet_block(nbit::Int, i::Int, j::Int)
unit = chain(nbit)
push!(unit, put(nbit, i=>chain(X, H)))
push!(unit, control(nbit, -i, j=>X))
end
basis_rotor(::ZGate) = I2Gate()
basis_rotor(::XGate) = Ry(-0.5π)
basis_rotor(::YGate) = Rx(0.5π)
basis_rotor(basis::PauliGate, nbit, locs) = repeat(nbit, basis_rotor(basis), locs)
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] | 2.040476 | 840 |
# this takes a load of spikes and plots them on an animated graph
function spiketrain(t, spikes)
# get co-ordinates for the spikes
spiked= findall(spikes)
spcoords = (t .* ones(length(spiked)), spiked)
sc = scatter!(spcoords,xlims=(0,1000),marker=1, legend=false)
display(sc)
end
function spiketrain(t, matrix::Array{<:Any,2}, spikes::BitArray{1})
matrix[:,t] = spikes
imshow(matrix)
return(matrix)
end
function visualiseweights(weights)
GR.imshow(repeat(weights))
end
function dashboard(plt, t, weights, activation, spt, da, rec)
plt.p1 = plotact!(plt.p1, activation)
plt.p2 = plotspt!(plt.p2, spt, t)
plt.p3 = plotda!(plt.p3, [da], [t])
plt.p4 = plotrec!(plt.p4, rec)
p = plot(plt.p1, plt.p2, plt.p3, plt.p4, layout = grid(2,2), legend=false, show=true)
display(p)
end
function dashboard(plt, t, l, m::MatrixTypes, da)
plt.p1 = plotact!(plt.p1, m.activation.layers[l])
plt.p2 = plotspt!(plt.p2, m.spt.layers[l], t)
plt.p3 = plotda!(plt.p3, [da], [t])
plt.p4 = plotrec!(plt.p4, m.rec.layers[l])
p = plot(plt.p1, plt.p2, plt.p3, plt.p4, layout = grid(2,2), legend=false, show=true)
display(p)
end
mutable struct Dashplot
p1::Plots.Plot{<:AbstractBackend}
p2::Plots.Plot{<:AbstractBackend}
p3::Plots.Plot{<:AbstractBackend}
p4::Plots.Plot{<:AbstractBackend}
Dashplot() = new(heatmap(),heatmap(), scatter(), heatmap())
end
function initialiseplot(plottype::Function)
return plottype()
end
function plotact!(p1, activation)
heatmap!(p1, reshape(activation, length(activation), 1))
end
function plotspt!(p2, spt, t)
spiked = spt.==t
heatmap!(p2, reshape(spiked, length(spiked),1))
end
function plotda!(p3, t, da)
scatter!(p3, da, t)
end
function plotrec!(p4, rec)
heatmap!(p4, reshape(rec,length(rec),1))
end | [
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7,
8344,
11,
13664,
7,
8344,
828,
16,
4008,
198,
437
] | 2.245839 | 781 |
using Escher
using FactCheck
using Compat
include("macros.jl")
include("interop.jl")
FactCheck.exitstatus()
| [
3500,
16319,
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198,
3500,
3082,
265,
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198,
17256,
7203,
20285,
4951,
13,
20362,
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198,
17256,
7203,
3849,
404,
13,
20362,
4943,
198,
29054,
9787,
13,
37023,
13376,
3419,
198
] | 3.027778 | 36 |
include("c-lib-p2f-test.jl")
include("c-lib-f2p-test.jl")
include("c-lib-add-test.jl")
include("c-lib-mul-test.jl")
include("c-lib-div-test.jl")
include("c-lib-mode-test.jl")
| [
17256,
7203,
66,
12,
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79,
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12,
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12,
9288,
13,
20362,
4943,
198
] | 2.108434 | 83 |
"""
Cropbox
Declarative crop modeling framework. https://github.com/cropbox/Cropbox.jl
See also: [`@system`](@ref), [`@config`](@ref), [`simulate`](@ref), [`evaluate`](@ref), [`calibrate`](@ref), [`visualize`](@ref), [`manipulate`](@ref)
"""
module Cropbox
include("system.jl")
include("unit.jl")
include("random.jl")
include("graph.jl")
include("macro.jl")
include("state.jl")
include("bundle.jl")
include("config.jl")
include("system/clock.jl")
include("system/context.jl")
include("system/controller.jl")
include("system/calendar.jl")
include("system/store.jl")
include("system/thermaltime.jl")
include("util/simulate.jl")
include("util/calibrate.jl")
include("util/evaluate.jl")
include("util/gather.jl")
include("util/color.jl")
include("util/dive.jl")
include("util/hierarchy.jl")
include("util/plot.jl")
include("util/visualize.jl")
include("util/manipulate.jl")
end
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14,
805,
541,
5039,
13,
20362,
4943,
198,
198,
437,
198
] | 2.68693 | 329 |
function Log_LikeliHood(m::AbstractModel, om, leaves)
if leaves
#= if the animal has left we want the probability of this to happen
at that omission, given that it has not left before.
Since we assume that the events are independent the product of each likelihood
should give me the total probability. Using the log we can simply sum them =#
return log(cdf(m,om) - cdf(m,om-1))
else
#= if the animal hasn't left we want the probability of not leaving until om =#
# this is equivalent log(1-cdf(dist,om)) but it's safe when cdf is near 1
return log(1-cdf(m, om))
end
end
function nll_data(m::AbstractModel,cm::Dict)
-sum(v*Log_LikeliHood(m, k...) for (k, v) in cm)
end
function Distributions.fit(::Type{T}, b::DataFrames.AbstractDataFrame) where T<:AbstractModel
cm = countmap(StructArray((Omissions_plus_one = b.Omissions_plus_one, Leave = b.Leave)))
p = init(T, cm)
res = optimize(params(p)) do param
all(param .> 1e-10) || return 1e10
params(p) .= param
return nll_data(p, cm)
end
params(p) .= Optim.minimizer(res)
return p
end
###
function simulate(m::AbstractModel,n_samples=1)
w = [cdf(m,x)-cdf(m,x-1) for x in 1:maximum(m)]
weights = StatsBase.weights(w)
[sample(1:maximum(m),weights) for _ in 1:n_samples]
end
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287,
352,
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437,
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] | 2.479053 | 549 |
# implementation of the GPUCompiler interfaces for generating WASM code
## target
export WASMCompilerTarget
Base.@kwdef struct WASMCompilerTarget <: AbstractCompilerTarget
end
llvm_triple(::WASMCompilerTarget) = "wasm32-unknown-unknown"
function llvm_machine(target::WASMCompilerTarget)
triple = llvm_triple(target)
t = Target(triple=triple)
cpu = ""
feat = ""
tm = TargetMachine(t, triple, cpu, feat)
asm_verbosity!(tm, true)
return tm
end
function process_entry!(job::CompilerJob{WASMCompilerTarget}, mod::LLVM.Module, entry::LLVM.Function)
push!(function_attributes(entry), StringAttribute("wasm-export-name", String(chop(LLVM.name(entry), tail=4)), context(mod)))
invoke(process_entry!, Tuple{CompilerJob, LLVM.Module, LLVM.Function}, job, mod, entry)
end
## job
runtime_slug(job::CompilerJob{WASMCompilerTarget}) = "wasm"
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] | 2.862876 | 299 |
"""
reproduce!(bact::Bacterium, model::ABM)
Simulates reproduction of bacteria. Energy is halved after subtracting a cost. Inherited
features are varied.
"""
function reproduce!(bact::Bacterium, model::ABM)
add_agent!(
bact.pos,
Bacterium,
model,
bact.species,
0,
(bact.energy - model.reproduction_energy_cost) / 2.0,
inherit(bact.sensory_radius, model.rng, model.σ_sensory_radius),
inherit(bact.reproduction_threshold, model.rng, model.σ_reproduction_threshold),
inherit(bact.speed, model.rng, model.σ_speed),
bact.food_target,
)
bact.age = 0
bact.energy = (bact.energy - model.reproduction_energy_cost) / 2.0
bact.sensory_radius = inherit(bact.sensory_radius, model.rng, model.σ_sensory_radius)
bact.reproduction_threshold =
inherit(bact.reproduction_threshold, model.rng, model.σ_reproduction_threshold)
bact.speed = inherit(bact.speed, model.rng, model.σ_speed)
end
function agent_step!(bact::Bacterium, model::ABM)
# die of age or starvation
(bact.age > model.lifetime || bact.energy <= 0) && (kill_agent!(bact, model); return)
# grow older
bact.age += 1
# reproduce if possible
bact.energy >= bact.reproduction_threshold && reproduce!(bact, model)
# if currently on a food source
if model.food[bact.pos...] > 0.0
# eat
eaten = min(model.food[bact.pos...], bact.speed * model.eat_rate_factor)
model.food[bact.pos...] -= eaten
bact.energy += eaten
return
else
# can't eat, so look for something else
bact.food_target = (-1, -1)
end
# if bact doesn't see any food
if bact.food_target == (-1, -1)
best_pos = (-1, -1)
# look for the best food nearby
for pos in nearby_positions(bact.pos, model, bact.sensory_radius)
best_pos == (-1, -1) || model.food[best_pos...] < model.food[pos...] || continue
best_pos = pos
end
best_pos != (-1, -1) && (bact.food_target = best_pos)
end
# if we found some food or already had eyes on it
if bact.food_target != (-1, -1)
# move toward target
delta = bact.food_target .- bact.pos
#move as many steps diagonally as possible
diag = min(abs.(delta)..., bact.speed)
steps = diag
movement = sign.(delta) .* diag
# move the rest steps axially, if possible
delta = delta .- movement
while steps < bact.speed && any(delta .> 0)
movement = movement .+ sign.(delta)
delta = delta .- sign.(delta)
steps += 1
end
else
# move randomly if there's no food nearby
movement = rand.(model.rng, (AXIAL_DIRECTIONS, AXIAL_DIRECTIONS)) .* bact.speed
end
# move
move_agent!(bact, clamp.(bact.pos .+ movement, 1, size(model.space.s)), model)
# subtract cost of movement and looking
bact.energy -=
model.sensory_radius_cost * bact.sensory_radius +
model.distance_cost * max(abs.(movement)...)
end
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] | 2.293769 | 1,348 |
include("Batcher.jl")
include("ForwardBatcher.jl")
| [
17256,
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4943,
198,
17256,
7203,
39746,
24541,
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] | 3 | 17 |
@testset "chi-square-analysis" begin
msr_path = joinpath(mktempdir(),"temp.csv")
data = _PMD.parse_file(_PMDSE.get_enwl_dss_path(ntw, fdr))
if rm_transfo _PMDSE.rm_enwl_transformer!(data) end
if rd_lines _PMDSE.reduce_enwl_lines_eng!(data) end
data["settings"]["sbase_default"] = 100.0
# insert the load profiles
_PMDSE.insert_profiles!(data, season, elm, pfs, t = time_step)
# transform data model
data = _PMD.transform_data_model(data);
_PMDSE.reduce_single_phase_loadbuses!(data)
# solve the power flow
pf_result = _PMD.solve_mc_pf(data, _PMD.ACPUPowerModel, ipopt_solver)
key = "1" # or "sourcebus"
v_pu = data["settings"]["vbases_default"][key]* data["settings"]["voltage_scale_factor"] # divider [V] to get the voltage in per units.
v_max_err = 1.15 # maximum error of voltage measurement = 0.5% or 1.15 V
σ_v = 1/3*v_max_err/v_pu
p_pu = data["settings"]["sbase"] # divider [kW] to get the power in per units.
p_max_err = 0.01 # maximum error of power measurement = 10W, or 0.01 kW
σ_p = 1/3*p_max_err/p_pu
# sigma_dict
σ_dict = Dict("load" => Dict("load" => σ_p,
"bus" => σ_v),
"gen" => Dict("gen" => σ_p/100,
"bus" => σ_v/100)
)
# write measurements based on power flow
_PMDSE.write_measurements!(_PMD.ACPUPowerModel, data, pf_result, msr_path, exclude = ["vi","vr"], σ = σ_dict)
# read-in measurement data and set initial values
_PMDSE.add_measurements!(data, msr_path, actual_meas = true)
data["se_settings"] = Dict{String,Any}("criterion" => "rwlav", "rescaler" => 1)
se_result = _PMDSE.solve_acp_red_mc_se(data, ipopt_solver)
@test _PMDSE.get_degrees_of_freedom(data) == 34
chi_result = _PMDSE.exceeds_chi_squares_threshold(se_result, data)
@test chi_result[1] == false
@test isapprox(chi_result[2], 0.0, atol = 1e-8)
@test isapprox(chi_result[3], 48.60, atol = 1e-2)
_PMDSE.add_measurements!(data, msr_path, actual_meas = false)
se_result = _PMDSE.solve_acp_red_mc_se(data, ipopt_solver)
chi_result = _PMDSE.exceeds_chi_squares_threshold(se_result, data)
@test chi_result[1] == true #TODO: there's no real bad data, check whether there is a problem with write_meas
@test isapprox(chi_result[2], 963.32, atol = 1e-2)
@test isapprox(chi_result[3], 48.60, atol = 1e-2)
end
@testset "h_functions" begin
# NB: the length (in terms of lines of code) of this sub-test could/should be significantly result but have no time now
msr_path = joinpath(mktempdir(),"temp.csv")
data = _PMD.parse_file(joinpath(BASE_DIR, "test/data/extra/networks/case3_unbalanced.dss"); data_model=MATHEMATICAL)
#reduce grid
[delete!(data["load"], l) for (l, load) in data["load"] if l!="1"]
_PMDSE.reduce_single_phase_loadbuses!(data)
pf_result = _PMD.solve_mc_pf(data, _PMD.ACPUPowerModel, ipopt_solver)
_PMDSE.write_measurements!(_PMD.ACPUPowerModel, data, pf_result, msr_path, exclude = ["vr","vi"])
_PMDSE.add_measurements!(data, msr_path, actual_meas = true)
# state is the result of the power flow
vv = pf_result["solution"]["bus"]
state = [ vv["4"]["vm"][1], vv["4"]["vm"][2], vv["4"]["vm"][3], vv["1"]["vm"][1], vv["1"]["vm"][2], vv["1"]["vm"][3], vv["2"]["vm"][1], vv["2"]["vm"][2], vv["2"]["vm"][3], vv["3"]["vm"][1],
vv["1"]["va"][1], vv["1"]["va"][2], vv["1"]["va"][3], vv["2"]["va"][1], vv["2"]["va"][2], vv["2"]["va"][3], vv["3"]["va"][1] ]
variable_dict = _PMDSE.build_variable_dictionary(data)
state_array = _PMDSE.build_state_array(pf_result, variable_dict)
@test state_array == state
# push h functions
functions = []
ref_bus = 4
_PMDSE.add_h_function!(:pd, "4", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:qd, "5", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:pg, "1", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:qg, "2", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:vm, "3", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:vm, "6", data, ref_bus, variable_dict, functions)
@test isapprox( functions[1](state), -_DST.mean(data["meas"]["4"]["dst"][1]) ) #pd
@test isapprox( functions[2](state), -_DST.mean(data["meas"]["5"]["dst"][1]) ) # qd
@test isapprox( functions[3](state), pf_result["solution"]["gen"]["1"]["pg"][1], atol=1e-8 )
@test isapprox( functions[4](state), pf_result["solution"]["gen"]["1"]["pg"][2], atol=1e-8 )
@test isapprox( functions[5](state), pf_result["solution"]["gen"]["1"]["pg"][3], atol=1e-8 )
@test isapprox( functions[6](state), pf_result["solution"]["gen"]["1"]["qg"][1], atol=1e-8 )
@test isapprox( functions[7](state), pf_result["solution"]["gen"]["1"]["qg"][2], atol=1e-8 )
@test isapprox( functions[8](state), pf_result["solution"]["gen"]["1"]["qg"][3], atol=1e-8 )
@test isapprox( functions[9](state), pf_result["solution"]["bus"]["4"]["vm"][1] )
@test isapprox( functions[10](state), pf_result["solution"]["bus"]["4"]["vm"][2] )
@test isapprox( functions[11](state), pf_result["solution"]["bus"]["4"]["vm"][3] )
@test isapprox( functions[12](state), pf_result["solution"]["bus"]["3"]["vm"][1] )
_PMDSE.add_measurement!(data, :p, :branch, 1, pf_result["solution"]["branch"]["1"]["pt"], [0.0003])
_PMDSE.add_measurement!(data, :q, :branch, 3, pf_result["solution"]["branch"]["3"]["qf"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :q, :branch, 1, pf_result["solution"]["branch"]["1"]["qf"], [0.0003])
_PMDSE.add_h_function!(:p, "7", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:q, "8", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:q, "9", data, ref_bus, variable_dict, functions)
cm3 = sqrt.(pf_result["solution"]["branch"]["3"]["pf"].^2+pf_result["solution"]["branch"]["3"]["qf"].^2)./(pf_result["solution"]["bus"]["4"]["vm"])
cm1 = sqrt(pf_result["solution"]["branch"]["1"]["pf"][1]^2+pf_result["solution"]["branch"]["1"]["qf"][1]^2)/(pf_result["solution"]["bus"]["1"]["vm"][2])
_PMDSE.add_measurement!(data, :cm, :branch, 3, cm3, [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :cm, :branch, 1, [cm1], [0.0003])
_PMDSE.add_measurement!(data, :va, :bus, 2, pf_result["solution"]["bus"]["2"]["va"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_h_function!(:cm, "10", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:cm, "11", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:va, "12", data, ref_bus, variable_dict, functions)
@test isapprox( functions[13](state), pf_result["solution"]["branch"]["1"]["pf"][1] )
@test isapprox( functions[14](state), pf_result["solution"]["branch"]["3"]["qf"][1], atol=1e-8 )
@test isapprox( functions[15](state), pf_result["solution"]["branch"]["3"]["qf"][2], atol=1e-8 )
@test isapprox( functions[16](state), pf_result["solution"]["branch"]["3"]["qf"][3], atol=1e-8 )
@test isapprox( functions[17](state), pf_result["solution"]["branch"]["1"]["qf"][1] )
@test isapprox( functions[18](state), cm3[1] , atol=1e-8)
@test isapprox( functions[19](state), cm3[2] , atol=1e-8)
@test isapprox( functions[20](state), cm3[3], atol=1e-8 )
@test isapprox( functions[21](state), cm1 )
@test isapprox( functions[22](state), pf_result["solution"]["bus"]["2"]["va"][1])
@test isapprox( functions[23](state), pf_result["solution"]["bus"]["2"]["va"][2])
@test isapprox( functions[24](state), pf_result["solution"]["bus"]["2"]["va"][3])
pf_result_ivr = _PMD.solve_mc_pf(data, _PMD.IVRUPowerModel, ipopt_solver)
_PMDSE.add_measurement!(data, :cr, :branch, 3, pf_result_ivr["solution"]["branch"]["3"]["cr_fr"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :ci, :branch, 3, pf_result_ivr["solution"]["branch"]["3"]["ci_fr"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :crd, :branch, 1, pf_result_ivr["solution"]["load"]["1"]["crd_bus"], [0.0003])
_PMDSE.add_measurement!(data, :cid, :branch, 1, pf_result_ivr["solution"]["load"]["1"]["cid_bus"], [0.0003])
_PMDSE.add_h_function!(:cr, "13", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:ci, "14", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:crd, "15", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:cid, "16", data, ref_bus, variable_dict, functions)
@test isapprox( functions[25](state), pf_result_ivr["solution"]["branch"]["3"]["cr_fr"][1], atol=1e-8)
@test isapprox( functions[26](state), pf_result_ivr["solution"]["branch"]["3"]["cr_fr"][2], atol=4e-5)
@test isapprox( functions[27](state), pf_result_ivr["solution"]["branch"]["3"]["cr_fr"][3], atol=1e-8)
@test isapprox( functions[28](state), pf_result_ivr["solution"]["branch"]["3"]["ci_fr"][1], atol=1e-5)
@test isapprox( functions[29](state), pf_result_ivr["solution"]["branch"]["3"]["ci_fr"][2], atol=2e-5)
@test isapprox( functions[30](state), pf_result_ivr["solution"]["branch"]["3"]["ci_fr"][3], atol=2e-5)
@test isapprox( functions[31](state), -pf_result_ivr["solution"]["load"]["1"]["crd_bus"][1], atol=2e-4)
@test isapprox( functions[32](state), -pf_result_ivr["solution"]["load"]["1"]["cid_bus"][1], atol=2e-4)
_PMDSE.add_measurement!(data, :p, :branch, 2, pf_result["solution"]["branch"]["2"]["pf"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :q, :branch, 2, pf_result["solution"]["branch"]["2"]["qf"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :cr, :branch, 2, pf_result_ivr["solution"]["branch"]["2"]["cr_fr"], [0.0003, 0.0003, 0.0003])
_PMDSE.add_measurement!(data, :ci, :branch, 2, pf_result_ivr["solution"]["branch"]["2"]["ci_fr"], [0.0003, 0.0003, 0.0003])
cmfr = sqrt.(pf_result_ivr["solution"]["branch"]["2"]["cr_fr"].^2 + pf_result_ivr["solution"]["branch"]["2"]["ci_fr"].^2)
_PMDSE.add_measurement!(data, :cm, :branch, 2, cmfr, [0.0003, 0.0003, 0.0003])
_PMDSE.add_h_function!(:p, "17", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:q, "18", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:cr, "19", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:ci, "20", data, ref_bus, variable_dict, functions)
_PMDSE.add_h_function!(:cm, "21", data, ref_bus, variable_dict, functions)
@test isapprox( functions[33](state), pf_result["solution"]["branch"]["2"]["pf"][1], atol=1e-8)
@test isapprox( functions[34](state), pf_result["solution"]["branch"]["2"]["pf"][2], atol=1e-8)
@test isapprox( functions[35](state), pf_result["solution"]["branch"]["2"]["pf"][3], atol=1e-8)
@test isapprox( functions[36](state), pf_result["solution"]["branch"]["2"]["qf"][1], atol=1e-8)
@test isapprox( functions[37](state), pf_result["solution"]["branch"]["2"]["qf"][2], atol=1e-8)
@test isapprox( functions[38](state), pf_result["solution"]["branch"]["2"]["qf"][3], atol=1e-8)
@test isapprox( functions[39](state), pf_result_ivr["solution"]["branch"]["2"]["cr_fr"][1], atol=1e-4)
@test isapprox( functions[40](state), pf_result_ivr["solution"]["branch"]["2"]["cr_fr"][2], atol=1e-4)
@test isapprox( functions[41](state), pf_result_ivr["solution"]["branch"]["2"]["cr_fr"][3], atol=1e-4)
@test isapprox( functions[42](state), pf_result_ivr["solution"]["branch"]["2"]["ci_fr"][1], atol=1e-4)
@test isapprox( functions[43](state), pf_result_ivr["solution"]["branch"]["2"]["ci_fr"][2], atol=1e-4)
@test isapprox( functions[44](state), pf_result_ivr["solution"]["branch"]["2"]["ci_fr"][3], atol=1e-4)
@test isapprox( functions[45](state), cmfr[1], atol=1e-6)
@test isapprox( functions[46](state), cmfr[2], atol=1e-6)
@test isapprox( functions[47](state), cmfr[3], atol=1e-6)
end
@testset "BadData_matrices_and_LNR" begin
msr_path = joinpath(mktempdir(),"temp.csv")
data = _PMD.parse_file(joinpath(BASE_DIR, "test/data/extra/networks/case3_unbalanced.dss"); data_model=MATHEMATICAL)
#reduce grid
[delete!(data["load"], l) for (l, load) in data["load"] if l!="1"]
_PMDSE.reduce_single_phase_loadbuses!(data)
pf_result = _PMD.solve_mc_pf(data, _PMD.ACPUPowerModel, ipopt_solver)
_PMDSE.write_measurements!(_PMD.ACPUPowerModel, data, pf_result, msr_path, exclude = ["vr","vi"])
_PMDSE.add_measurements!(data, msr_path, actual_meas = true)
_PMDSE.assign_start_to_variables!(data)
data["se_settings"] = Dict{String,Any}("criterion" => "wls", "rescaler" => 1)
se_result = _PMDSE.solve_acp_red_mc_se(data, ipopt_solver)
_PMDSE.add_zib_virtual_meas!(data, 0.00000001, exclude = [2])
_PMDSE.add_zib_virtual_residuals!(se_result, data)
variable_dict = _PMDSE.build_variable_dictionary(data)
h_array = _PMDSE.build_measurement_function_array(data, variable_dict)
state_array = _PMDSE.build_state_array(pf_result, variable_dict)
stored_H_matrix = h5open(joinpath(BASE_DIR, "test/data/H_matrix.h5"), "r") do file
read(file, "H")
end
stored_G_matrix = h5open(joinpath(BASE_DIR, "test/data/G_matrix.h5"), "r") do file
read(file, "G")
end
stored_R_matrix = h5open(joinpath(BASE_DIR, "test/data/R_matrix.h5"), "r") do file
read(file, "R")
end
stored_Ω_matrix = h5open(joinpath(BASE_DIR, "test/data/Ω_matrix.h5"), "r") do file
read(file, "Ω")
end
H = _PMDSE.build_H_matrix(h_array, state_array)
R = _PMDSE.build_R_matrix(data)
G = _PMDSE.build_G_matrix(stored_H_matrix, R)
Ω = _PMDSE.build_omega_matrix(R, stored_H_matrix, G)
@test all(isapprox.(H, stored_H_matrix, atol=1))
@test all(isapprox.(R, stored_R_matrix, atol=1))
#@test all(isapprox.(G, stored_G_matrix, atol=1))
@test all(isapprox.(Ω, stored_Ω_matrix, atol=1))
id_val, exc = _PMDSE.normalized_residuals(data, se_result, Ω)
#@test !exc
#@test id_val[1] == "3"
#@test isapprox(id_val[2], 0.11035175, atol=1e-8)
_PMDSE.simple_normalized_residuals(data, se_result, R)
@test haskey(se_result["solution"]["meas"]["5"], "nr")
end | [
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] | 2.067679 | 6,915 |
module CUDNN
using CUDA
include("../libcudnn-5/libcudnn.jl")
include("../libcudnn-5/libcudnn_types.jl")
@windows? (
begin
const libcudnn = Libdl.find_library(["cudnn64_5"])
end : begin
const libcudnn = Libdl.find_library(["libcudnn"])
end)
isempty(libcudnn) && throw("CUDNN library cannot be found.")
function checkstatus(status)
if status != CUDNN_STATUS_SUCCESS
Base.show_backtrace(STDOUT, backtrace())
throw(bytestring(cudnnGetErrorString(status)))
end
end
datatype(::Type{Float32}) = CUDNN_DATA_FLOAT
datatype(::Type{Float64}) = CUDNN_DATA_DOUBLE
datatype(::Type{Float16}) = CUDNN_DATA_HALF
include("handle.jl")
include("tensor.jl")
include("activation.jl")
include("convolution.jl")
include("filter.jl")
include("softmax.jl")
end
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] | 2.453674 | 313 |
import Base: .+, .-, .*, ./, .^, max, min, .==, .>, .>=, .<, .<=, +, -
# Broadcasting binary functions (uses the same list as same size arrays)
cuda12 = cuda11
# Broadcast max/min haven't been defined:
max(a::Array,b::Array)=broadcast(max,a,b)
min(a::Array,b::Array)=broadcast(min,a,b)
function vbroadcast_shape(x,y)
nz = max(ndims(x),ndims(y))
dz = ones(Int,nz)
xdims = ydims = xsame = ysame = xlast = ylast = 0; zlen = 1
for i=1:nz
if size(x,i) > 1
xdims += 1; xlast = i
dz[i] = size(x,i)
end
if size(y,i) > 1
ydims += 1; ylast = i
if dz[i] == 1
dz[i] = size(y,i)
else
dz[i] == size(y,i) || throw(DimensionMismatch("arrays could not be broadcast to a common size"))
end
end
xsame += (dz[i] == size(x,i))
ysame += (dz[i] == size(y,i))
zlen *= dz[i]
end
xsame == nz || xdims <= 1 || error("Only vector broadcasting supported")
ysame == nz || ydims <= 1 || error("Only vector broadcasting supported")
if xdims == 0
sx = zlen; nx = 1
elseif xdims == 1
sx = prod(dz[1:xlast-1]); nx=dz[xlast]
elseif xsame == nz
sx = 1; nx=zlen
else
error("Broadcasting error")
end
if ydims == 0
sy = zlen; ny = 1
elseif ydims == 1
sy = prod(dz[1:ylast-1]); ny=dz[ylast]
elseif ysame == nz
sy = 1; ny=zlen
else
error("Broadcasting error")
end
return (tuple(dz...), sx, nx, sy, ny)
end
function cuda12def(f, j=f, o...)
J=Symbol(j)
for S in (32,64)
T = Symbol("Float$S")
F11 = "$(f)_$(S)_11"
F12 = "$(f)_$(S)_12"
@eval begin
function $J(x::KnetArray{$T},y::KnetArray{$T})
if size(x)==size(y)
z = similar(x)
ccall(($F11,$libknet8),Void,(Cint,$Ptr{$T},Ptr{$T},Ptr{$T}),length(z),x,y,z)
return z
else
(dz,sx,nx,sy,ny) = vbroadcast_shape(x,y)
z = similar(x,dz)
ccall(($F12,$libknet8),Void,(Cint,$Ptr{$T},Cint,Cint,Ptr{$T},Cint,Cint,Ptr{$T}),length(z),x,sx,nx,y,sy,ny,z)
return z
end
end
end
end
end
#if isdefined(:libknet8)
for f in cuda12
isa(f,Tuple) || (f=(f,))
cuda12def(f...)
end
#end
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] | 1.710306 | 1,436 |
@testset "8.8 Polylogarithm function" begin
(F, a, b, c, d, e, f, g, h, m, n, p, q, x, ) = @variables F a b c d e f g h m n p q x
#= ::Package:: =#
#= ::Title:: =#
#=Integration*Problems*Involving*the*Polylogarithm*Function=#
#= ::Section::Closed:: =#
#=Integrands*of*the*form*(d*x)^m*PolyLog(n, a*x^q)=#
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*PolyLog(n, a*x^q)=#
#= ::Subsubsection::Closed:: =#
#=q=1=#
@test_int [x^4*PolyLog(2, a*x), x, 4, -(x/(25*a^4)) - x^2/(50*a^3) - x^3/(75*a^2) - x^4/(100*a) - x^5/125 - log(1 - a*x)/(25*a^5) + (1/25)*x^5*log(1 - a*x) + (1/5)*x^5*PolyLog(2, a*x)]
@test_int [x^3*PolyLog(2, a*x), x, 4, -(x/(16*a^3)) - x^2/(32*a^2) - x^3/(48*a) - x^4/64 - log(1 - a*x)/(16*a^4) + (1/16)*x^4*log(1 - a*x) + (1/4)*x^4*PolyLog(2, a*x)]
@test_int [x^2*PolyLog(2, a*x), x, 4, -(x/(9*a^2)) - x^2/(18*a) - x^3/27 - log(1 - a*x)/(9*a^3) + (1/9)*x^3*log(1 - a*x) + (1/3)*x^3*PolyLog(2, a*x)]
@test_int [x^1*PolyLog(2, a*x), x, 4, -(x/(4*a)) - x^2/8 - log(1 - a*x)/(4*a^2) + (1/4)*x^2*log(1 - a*x) + (1/2)*x^2*PolyLog(2, a*x)]
@test_int [x^0*PolyLog(2, a*x), x, 3, -x - ((1 - a*x)*log(1 - a*x))/a + x*PolyLog(2, a*x)]
@test_int [PolyLog(2, a*x)/x^1, x, 1, PolyLog(3, a*x)]
@test_int [PolyLog(2, a*x)/x^2, x, 5, a*log(x) - a*log(1 - a*x) + log(1 - a*x)/x - PolyLog(2, a*x)/x]
@test_int [PolyLog(2, a*x)/x^3, x, 4, -(a/(4*x)) + (1/4)*a^2*log(x) - (1/4)*a^2*log(1 - a*x) + log(1 - a*x)/(4*x^2) - PolyLog(2, a*x)/(2*x^2)]
@test_int [PolyLog(2, a*x)/x^4, x, 4, -(a/(18*x^2)) - a^2/(9*x) + (1/9)*a^3*log(x) - (1/9)*a^3*log(1 - a*x) + log(1 - a*x)/(9*x^3) - PolyLog(2, a*x)/(3*x^3)]
@test_int [PolyLog(2, a*x)/x^5, x, 4, -(a/(48*x^3)) - a^2/(32*x^2) - a^3/(16*x) + (1/16)*a^4*log(x) - (1/16)*a^4*log(1 - a*x) + log(1 - a*x)/(16*x^4) - PolyLog(2, a*x)/(4*x^4)]
@test_int [x^3*PolyLog(3, a*x), x, 5, x/(64*a^3) + x^2/(128*a^2) + x^3/(192*a) + x^4/256 + log(1 - a*x)/(64*a^4) - (1/64)*x^4*log(1 - a*x) - (1/16)*x^4*PolyLog(2, a*x) + (1/4)*x^4*PolyLog(3, a*x)]
@test_int [x^2*PolyLog(3, a*x), x, 5, x/(27*a^2) + x^2/(54*a) + x^3/81 + log(1 - a*x)/(27*a^3) - (1/27)*x^3*log(1 - a*x) - (1/9)*x^3*PolyLog(2, a*x) + (1/3)*x^3*PolyLog(3, a*x)]
@test_int [x^1*PolyLog(3, a*x), x, 5, x/(8*a) + x^2/16 + log(1 - a*x)/(8*a^2) - (1/8)*x^2*log(1 - a*x) - (1/4)*x^2*PolyLog(2, a*x) + (1/2)*x^2*PolyLog(3, a*x)]
@test_int [x^0*PolyLog(3, a*x), x, 4, x + ((1 - a*x)*log(1 - a*x))/a - x*PolyLog(2, a*x) + x*PolyLog(3, a*x)]
@test_int [PolyLog(3, a*x)/x^1, x, 1, PolyLog(4, a*x)]
@test_int [PolyLog(3, a*x)/x^2, x, 6, a*log(x) - a*log(1 - a*x) + log(1 - a*x)/x - PolyLog(2, a*x)/x - PolyLog(3, a*x)/x]
@test_int [PolyLog(3, a*x)/x^3, x, 5, -(a/(8*x)) + (1/8)*a^2*log(x) - (1/8)*a^2*log(1 - a*x) + log(1 - a*x)/(8*x^2) - PolyLog(2, a*x)/(4*x^2) - PolyLog(3, a*x)/(2*x^2)]
@test_int [PolyLog(3, a*x)/x^4, x, 5, -(a/(54*x^2)) - a^2/(27*x) + (1/27)*a^3*log(x) - (1/27)*a^3*log(1 - a*x) + log(1 - a*x)/(27*x^3) - PolyLog(2, a*x)/(9*x^3) - PolyLog(3, a*x)/(3*x^3)]
#= ::Subsubsection::Closed:: =#
#=q=2=#
@test_int [x^5*PolyLog(2, a*x^2), x, 5, -(x^2/(18*a^2)) - x^4/(36*a) - x^6/54 - log(1 - a*x^2)/(18*a^3) + (1/18)*x^6*log(1 - a*x^2) + (1/6)*x^6*PolyLog(2, a*x^2)]
@test_int [x^3*PolyLog(2, a*x^2), x, 5, -(x^2/(8*a)) - x^4/16 - log(1 - a*x^2)/(8*a^2) + (1/8)*x^4*log(1 - a*x^2) + (1/4)*x^4*PolyLog(2, a*x^2)]
@test_int [x^1*PolyLog(2, a*x^2), x, 4, -(x^2/2) - ((1 - a*x^2)*log(1 - a*x^2))/(2*a) + (1/2)*x^2*PolyLog(2, a*x^2)]
@test_int [PolyLog(2, a*x^2)/x^1, x, 1, (1/2)*PolyLog(3, a*x^2)]
@test_int [PolyLog(2, a*x^2)/x^3, x, 6, a*log(x) - (1/2)*a*log(1 - a*x^2) + log(1 - a*x^2)/(2*x^2) - PolyLog(2, a*x^2)/(2*x^2)]
@test_int [PolyLog(2, a*x^2)/x^5, x, 5, -(a/(8*x^2)) + (1/4)*a^2*log(x) - (1/8)*a^2*log(1 - a*x^2) + log(1 - a*x^2)/(8*x^4) - PolyLog(2, a*x^2)/(4*x^4)]
@test_int [PolyLog(2, a*x^2)/x^7, x, 5, -(a/(36*x^4)) - a^2/(18*x^2) + (1/9)*a^3*log(x) - (1/18)*a^3*log(1 - a*x^2) + log(1 - a*x^2)/(18*x^6) - PolyLog(2, a*x^2)/(6*x^6)]
@test_int [x^4*PolyLog(2, a*x^2), x, 5, -((4*x)/(25*a^2)) - (4*x^3)/(75*a) - (4*x^5)/125 + (4*atanh(sqrt(a)*x))/(25*a^(5/2)) + (2/25)*x^5*log(1 - a*x^2) + (1/5)*x^5*PolyLog(2, a*x^2)]
@test_int [x^2*PolyLog(2, a*x^2), x, 5, -((4*x)/(9*a)) - (4*x^3)/27 + (4*atanh(sqrt(a)*x))/(9*a^(3/2)) + (2/9)*x^3*log(1 - a*x^2) + (1/3)*x^3*PolyLog(2, a*x^2)]
@test_int [x^0*PolyLog(2, a*x^2), x, 4, -4*x + (4*atanh(sqrt(a)*x))/sqrt(a) + 2*x*log(1 - a*x^2) + x*PolyLog(2, a*x^2)]
@test_int [PolyLog(2, a*x^2)/x^2, x, 3, 4*sqrt(a)*atanh(sqrt(a)*x) + (2*log(1 - a*x^2))/x - PolyLog(2, a*x^2)/x]
@test_int [PolyLog(2, a*x^2)/x^4, x, 4, -((4*a)/(9*x)) + (4/9)*a^(3/2)*atanh(sqrt(a)*x) + (2*log(1 - a*x^2))/(9*x^3) - PolyLog(2, a*x^2)/(3*x^3)]
@test_int [PolyLog(2, a*x^2)/x^6, x, 5, -((4*a)/(75*x^3)) - (4*a^2)/(25*x) + (4/25)*a^(5/2)*atanh(sqrt(a)*x) + (2*log(1 - a*x^2))/(25*x^5) - PolyLog(2, a*x^2)/(5*x^5)]
@test_int [x^5*PolyLog(3, a*x^2), x, 6, x^2/(54*a^2) + x^4/(108*a) + x^6/162 + log(1 - a*x^2)/(54*a^3) - (1/54)*x^6*log(1 - a*x^2) - (1/18)*x^6*PolyLog(2, a*x^2) + (1/6)*x^6*PolyLog(3, a*x^2)]
@test_int [x^3*PolyLog(3, a*x^2), x, 6, x^2/(16*a) + x^4/32 + log(1 - a*x^2)/(16*a^2) - (1/16)*x^4*log(1 - a*x^2) - (1/8)*x^4*PolyLog(2, a*x^2) + (1/4)*x^4*PolyLog(3, a*x^2)]
@test_int [x^1*PolyLog(3, a*x^2), x, 5, x^2/2 + ((1 - a*x^2)*log(1 - a*x^2))/(2*a) - (1/2)*x^2*PolyLog(2, a*x^2) + (1/2)*x^2*PolyLog(3, a*x^2)]
@test_int [PolyLog(3, a*x^2)/x^1, x, 1, (1/2)*PolyLog(4, a*x^2)]
@test_int [PolyLog(3, a*x^2)/x^3, x, 7, a*log(x) - (1/2)*a*log(1 - a*x^2) + log(1 - a*x^2)/(2*x^2) - PolyLog(2, a*x^2)/(2*x^2) - PolyLog(3, a*x^2)/(2*x^2)]
@test_int [PolyLog(3, a*x^2)/x^5, x, 6, -(a/(16*x^2)) + (1/8)*a^2*log(x) - (1/16)*a^2*log(1 - a*x^2) + log(1 - a*x^2)/(16*x^4) - PolyLog(2, a*x^2)/(8*x^4) - PolyLog(3, a*x^2)/(4*x^4)]
@test_int [PolyLog(3, a*x^2)/x^7, x, 6, -(a/(108*x^4)) - a^2/(54*x^2) + (1/27)*a^3*log(x) - (1/54)*a^3*log(1 - a*x^2) + log(1 - a*x^2)/(54*x^6) - PolyLog(2, a*x^2)/(18*x^6) - PolyLog(3, a*x^2)/(6*x^6)]
@test_int [x^4*PolyLog(3, a*x^2), x, 6, (8*x)/(125*a^2) + (8*x^3)/(375*a) + (8*x^5)/625 - (8*atanh(sqrt(a)*x))/(125*a^(5/2)) - (4/125)*x^5*log(1 - a*x^2) - (2/25)*x^5*PolyLog(2, a*x^2) + (1/5)*x^5*PolyLog(3, a*x^2)]
@test_int [x^2*PolyLog(3, a*x^2), x, 6, (8*x)/(27*a) + (8*x^3)/81 - (8*atanh(sqrt(a)*x))/(27*a^(3/2)) - (4/27)*x^3*log(1 - a*x^2) - (2/9)*x^3*PolyLog(2, a*x^2) + (1/3)*x^3*PolyLog(3, a*x^2)]
@test_int [x^0*PolyLog(3, a*x^2), x, 5, 8*x - (8*atanh(sqrt(a)*x))/sqrt(a) - 4*x*log(1 - a*x^2) - 2*x*PolyLog(2, a*x^2) + x*PolyLog(3, a*x^2)]
@test_int [PolyLog(3, a*x^2)/x^2, x, 4, 8*sqrt(a)*atanh(sqrt(a)*x) + (4*log(1 - a*x^2))/x - (2*PolyLog(2, a*x^2))/x - PolyLog(3, a*x^2)/x]
@test_int [PolyLog(3, a*x^2)/x^4, x, 5, -((8*a)/(27*x)) + (8/27)*a^(3/2)*atanh(sqrt(a)*x) + (4*log(1 - a*x^2))/(27*x^3) - (2*PolyLog(2, a*x^2))/(9*x^3) - PolyLog(3, a*x^2)/(3*x^3)]
@test_int [PolyLog(3, a*x^2)/x^6, x, 6, -((8*a)/(375*x^3)) - (8*a^2)/(125*x) + (8/125)*a^(5/2)*atanh(sqrt(a)*x) + (4*log(1 - a*x^2))/(125*x^5) - (2*PolyLog(2, a*x^2))/(25*x^5) - PolyLog(3, a*x^2)/(5*x^5)]
#= ::Subsubsection::Closed:: =#
#=q*symbolic=#
@test_int [x^2*PolyLog(2, a*x^q), x, 3, (a*q^2*x^(3 + q)*HypergeometricFunctions._₂F₁(1, (3 + q)/q, 2 + 3/q, a*x^q))/(9*(3 + q)) + (1/9)*q*x^3*log(1 - a*x^q) + (1/3)*x^3*PolyLog(2, a*x^q)]
@test_int [x^1*PolyLog(2, a*x^q), x, 3, (a*q^2*x^(2 + q)*HypergeometricFunctions._₂F₁(1, (2 + q)/q, 2*(1 + 1/q), a*x^q))/(4*(2 + q)) + (1/4)*q*x^2*log(1 - a*x^q) + (1/2)*x^2*PolyLog(2, a*x^q)]
@test_int [x^0*PolyLog(2, a*x^q), x, 3, (a*q^2*x^(1 + q)*HypergeometricFunctions._₂F₁(1, 1 + 1/q, 2 + 1/q, a*x^q))/(1 + q) + q*x*log(1 - a*x^q) + x*PolyLog(2, a*x^q)]
@test_int [PolyLog(2, a*x^q)/x^1, x, 1, PolyLog(3, a*x^q)/q]
@test_int [PolyLog(2, a*x^q)/x^2, x, 3, -((a*q^2*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, -((1 - q)/q), 2 - 1/q, a*x^q))/(1 - q)) + (q*log(1 - a*x^q))/x - PolyLog(2, a*x^q)/x]
@test_int [PolyLog(2, a*x^q)/x^3, x, 3, -((a*q^2*x^(-2 + q)*HypergeometricFunctions._₂F₁(1, -((2 - q)/q), 2*(1 - 1/q), a*x^q))/(4*(2 - q))) + (q*log(1 - a*x^q))/(4*x^2) - PolyLog(2, a*x^q)/(2*x^2)]
@test_int [PolyLog(2, a*x^q)/x^4, x, 3, -((a*q^2*x^(-3 + q)*HypergeometricFunctions._₂F₁(1, -((3 - q)/q), 2 - 3/q, a*x^q))/(9*(3 - q))) + (q*log(1 - a*x^q))/(9*x^3) - PolyLog(2, a*x^q)/(3*x^3)]
@test_int [x^2*PolyLog(3, a*x^q), x, 4, -((a*q^3*x^(3 + q)*HypergeometricFunctions._₂F₁(1, (3 + q)/q, 2 + 3/q, a*x^q))/(27*(3 + q))) - (1/27)*q^2*x^3*log(1 - a*x^q) - (1/9)*q*x^3*PolyLog(2, a*x^q) + (1/3)*x^3*PolyLog(3, a*x^q)]
@test_int [x^1*PolyLog(3, a*x^q), x, 4, -((a*q^3*x^(2 + q)*HypergeometricFunctions._₂F₁(1, (2 + q)/q, 2*(1 + 1/q), a*x^q))/(8*(2 + q))) - (1/8)*q^2*x^2*log(1 - a*x^q) - (1/4)*q*x^2*PolyLog(2, a*x^q) + (1/2)*x^2*PolyLog(3, a*x^q)]
@test_int [x^0*PolyLog(3, a*x^q), x, 4, -((a*q^3*x^(1 + q)*HypergeometricFunctions._₂F₁(1, 1 + 1/q, 2 + 1/q, a*x^q))/(1 + q)) - q^2*x*log(1 - a*x^q) - q*x*PolyLog(2, a*x^q) + x*PolyLog(3, a*x^q)]
@test_int [PolyLog(3, a*x^q)/x^1, x, 1, PolyLog(4, a*x^q)/q]
@test_int [PolyLog(3, a*x^q)/x^2, x, 4, -((a*q^3*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, -((1 - q)/q), 2 - 1/q, a*x^q))/(1 - q)) + (q^2*log(1 - a*x^q))/x - (q*PolyLog(2, a*x^q))/x - PolyLog(3, a*x^q)/x]
@test_int [PolyLog(3, a*x^q)/x^3, x, 4, -((a*q^3*x^(-2 + q)*HypergeometricFunctions._₂F₁(1, -((2 - q)/q), 2*(1 - 1/q), a*x^q))/(8*(2 - q))) + (q^2*log(1 - a*x^q))/(8*x^2) - (q*PolyLog(2, a*x^q))/(4*x^2) - PolyLog(3, a*x^q)/(2*x^2)]
@test_int [PolyLog(3, a*x^q)/x^4, x, 4, -((a*q^3*x^(-3 + q)*HypergeometricFunctions._₂F₁(1, -((3 - q)/q), 2 - 3/q, a*x^q))/(27*(3 - q))) + (q^2*log(1 - a*x^q))/(27*x^3) - (q*PolyLog(2, a*x^q))/(9*x^3) - PolyLog(3, a*x^q)/(3*x^3)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*(d*x)^(m/2)*PolyLog(n, a*x^q)=#
#= ::Subsubsection::Closed:: =#
#=q=1=#
@test_int [(d*x)^(3/2)*PolyLog(2, a*x), x, 7, -((8*d*sqrt(d*x))/(25*a^2)) - (8*(d*x)^(3/2))/(75*a) - (8*(d*x)^(5/2))/(125*d) + (8*d^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(25*a^(5/2)) + (4*(d*x)^(5/2)*log(1 - a*x))/(25*d) + (2*(d*x)^(5/2)*PolyLog(2, a*x))/(5*d)]
@test_int [(d*x)^(1/2)*PolyLog(2, a*x), x, 6, -((8*sqrt(d*x))/(9*a)) - (8*(d*x)^(3/2))/(27*d) + (8*sqrt(d)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(9*a^(3/2)) + (4*(d*x)^(3/2)*log(1 - a*x))/(9*d) + (2*(d*x)^(3/2)*PolyLog(2, a*x))/(3*d)]
@test_int [PolyLog(2, a*x)/(d*x)^(1/2), x, 5, -((8*sqrt(d*x))/d) + (8*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(sqrt(a)*sqrt(d)) + (4*sqrt(d*x)*log(1 - a*x))/d + (2*sqrt(d*x)*PolyLog(2, a*x))/d]
@test_int [PolyLog(2, a*x)/(d*x)^(3/2), x, 4, (8*sqrt(a)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (4*log(1 - a*x))/(d*sqrt(d*x)) - (2*PolyLog(2, a*x))/(d*sqrt(d*x))]
@test_int [PolyLog(2, a*x)/(d*x)^(5/2), x, 5, -((8*a)/(9*d^2*sqrt(d*x))) + (8*a^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(9*d^(5/2)) + (4*log(1 - a*x))/(9*d*(d*x)^(3/2)) - (2*PolyLog(2, a*x))/(3*d*(d*x)^(3/2))]
@test_int [PolyLog(2, a*x)/(d*x)^(7/2), x, 6, -((8*a)/(75*d^2*(d*x)^(3/2))) - (8*a^2)/(25*d^3*sqrt(d*x)) + (8*a^(5/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(25*d^(7/2)) + (4*log(1 - a*x))/(25*d*(d*x)^(5/2)) - (2*PolyLog(2, a*x))/(5*d*(d*x)^(5/2))]
@test_int [(d*x)^(5/2)*PolyLog(3, a*x), x, 9, (16*d^2*sqrt(d*x))/(343*a^3) + (16*d*(d*x)^(3/2))/(1029*a^2) + (16*(d*x)^(5/2))/(1715*a) + (16*(d*x)^(7/2))/(2401*d) - (16*d^(5/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(343*a^(7/2)) - (8*(d*x)^(7/2)*log(1 - a*x))/(343*d) - (4*(d*x)^(7/2)*PolyLog(2, a*x))/(49*d) + (2*(d*x)^(7/2)*PolyLog(3, a*x))/(7*d)]
@test_int [(d*x)^(3/2)*PolyLog(3, a*x), x, 8, (16*d*sqrt(d*x))/(125*a^2) + (16*(d*x)^(3/2))/(375*a) + (16*(d*x)^(5/2))/(625*d) - (16*d^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(125*a^(5/2)) - (8*(d*x)^(5/2)*log(1 - a*x))/(125*d) - (4*(d*x)^(5/2)*PolyLog(2, a*x))/(25*d) + (2*(d*x)^(5/2)*PolyLog(3, a*x))/(5*d)]
@test_int [(d*x)^(1/2)*PolyLog(3, a*x), x, 7, (16*sqrt(d*x))/(27*a) + (16*(d*x)^(3/2))/(81*d) - (16*sqrt(d)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(27*a^(3/2)) - (8*(d*x)^(3/2)*log(1 - a*x))/(27*d) - (4*(d*x)^(3/2)*PolyLog(2, a*x))/(9*d) + (2*(d*x)^(3/2)*PolyLog(3, a*x))/(3*d)]
@test_int [PolyLog(3, a*x)/(d*x)^(1/2), x, 6, (16*sqrt(d*x))/d - (16*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(sqrt(a)*sqrt(d)) - (8*sqrt(d*x)*log(1 - a*x))/d - (4*sqrt(d*x)*PolyLog(2, a*x))/d + (2*sqrt(d*x)*PolyLog(3, a*x))/d]
@test_int [PolyLog(3, a*x)/(d*x)^(3/2), x, 5, (16*sqrt(a)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (8*log(1 - a*x))/(d*sqrt(d*x)) - (4*PolyLog(2, a*x))/(d*sqrt(d*x)) - (2*PolyLog(3, a*x))/(d*sqrt(d*x))]
@test_int [PolyLog(3, a*x)/(d*x)^(5/2), x, 6, -((16*a)/(27*d^2*sqrt(d*x))) + (16*a^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(27*d^(5/2)) + (8*log(1 - a*x))/(27*d*(d*x)^(3/2)) - (4*PolyLog(2, a*x))/(9*d*(d*x)^(3/2)) - (2*PolyLog(3, a*x))/(3*d*(d*x)^(3/2))]
@test_int [PolyLog(3, a*x)/(d*x)^(7/2), x, 7, -((16*a)/(375*d^2*(d*x)^(3/2))) - (16*a^2)/(125*d^3*sqrt(d*x)) + (16*a^(5/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(125*d^(7/2)) + (8*log(1 - a*x))/(125*d*(d*x)^(5/2)) - (4*PolyLog(2, a*x))/(25*d*(d*x)^(5/2)) - (2*PolyLog(3, a*x))/(5*d*(d*x)^(5/2))]
#= ::Subsubsection::Closed:: =#
#=q=2=#
@test_int [(d*x)^(3/2)*PolyLog(2, a*x^2), x, 9, -((32*d*sqrt(d*x))/(25*a)) - (32*(d*x)^(5/2))/(125*d) + (16*d^(3/2)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*a^(5/4)) + (16*d^(3/2)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*a^(5/4)) + (8*(d*x)^(5/2)*log(1 - a*x^2))/(25*d) + (2*(d*x)^(5/2)*PolyLog(2, a*x^2))/(5*d)]
@test_int [(d*x)^(1/2)*PolyLog(2, a*x^2), x, 8, -((32*(d*x)^(3/2))/(27*d)) - (16*sqrt(d)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*a^(3/4)) + (16*sqrt(d)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*a^(3/4)) + (8*(d*x)^(3/2)*log(1 - a*x^2))/(9*d) + (2*(d*x)^(3/2)*PolyLog(2, a*x^2))/(3*d)]
@test_int [PolyLog(2, a*x^2)/(d*x)^(1/2), x, 8, -((32*sqrt(d*x))/d) + (16*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) + (16*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) + (8*sqrt(d*x)*log(1 - a*x^2))/d + (2*sqrt(d*x)*PolyLog(2, a*x^2))/d]
@test_int [PolyLog(2, a*x^2)/(d*x)^(3/2), x, 7, -((16*a^(1/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2)) + (16*a^(1/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (8*log(1 - a*x^2))/(d*sqrt(d*x)) - (2*PolyLog(2, a*x^2))/(d*sqrt(d*x))]
@test_int [PolyLog(2, a*x^2)/(d*x)^(5/2), x, 7, (16*a^(3/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*d^(5/2)) + (16*a^(3/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*d^(5/2)) + (8*log(1 - a*x^2))/(9*d*(d*x)^(3/2)) - (2*PolyLog(2, a*x^2))/(3*d*(d*x)^(3/2))]
@test_int [PolyLog(2, a*x^2)/(d*x)^(7/2), x, 8, -((32*a)/(25*d^3*sqrt(d*x))) - (16*a^(5/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*d^(7/2)) + (16*a^(5/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*d^(7/2)) + (8*log(1 - a*x^2))/(25*d*(d*x)^(5/2)) - (2*PolyLog(2, a*x^2))/(5*d*(d*x)^(5/2))]
@test_int [(d*x)^(5/2)*PolyLog(3, a*x^2), x, 10, (128*d*(d*x)^(3/2))/(1029*a) + (128*(d*x)^(7/2))/(2401*d) + (64*d^(5/2)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*a^(7/4)) - (64*d^(5/2)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*a^(7/4)) - (32*(d*x)^(7/2)*log(1 - a*x^2))/(343*d) - (8*(d*x)^(7/2)*PolyLog(2, a*x^2))/(49*d) + (2*(d*x)^(7/2)*PolyLog(3, a*x^2))/(7*d)]
@test_int [(d*x)^(3/2)*PolyLog(3, a*x^2), x, 10, (128*d*sqrt(d*x))/(125*a) + (128*(d*x)^(5/2))/(625*d) - (64*d^(3/2)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*a^(5/4)) - (64*d^(3/2)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*a^(5/4)) - (32*(d*x)^(5/2)*log(1 - a*x^2))/(125*d) - (8*(d*x)^(5/2)*PolyLog(2, a*x^2))/(25*d) + (2*(d*x)^(5/2)*PolyLog(3, a*x^2))/(5*d)]
@test_int [(d*x)^(1/2)*PolyLog(3, a*x^2), x, 9, (128*(d*x)^(3/2))/(81*d) + (64*sqrt(d)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*a^(3/4)) - (64*sqrt(d)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*a^(3/4)) - (32*(d*x)^(3/2)*log(1 - a*x^2))/(27*d) - (8*(d*x)^(3/2)*PolyLog(2, a*x^2))/(9*d) + (2*(d*x)^(3/2)*PolyLog(3, a*x^2))/(3*d)]
@test_int [PolyLog(3, a*x^2)/(d*x)^(1/2), x, 9, (128*sqrt(d*x))/d - (64*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) - (64*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) - (32*sqrt(d*x)*log(1 - a*x^2))/d - (8*sqrt(d*x)*PolyLog(2, a*x^2))/d + (2*sqrt(d*x)*PolyLog(3, a*x^2))/d]
@test_int [PolyLog(3, a*x^2)/(d*x)^(3/2), x, 8, -((64*a^(1/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2)) + (64*a^(1/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (32*log(1 - a*x^2))/(d*sqrt(d*x)) - (8*PolyLog(2, a*x^2))/(d*sqrt(d*x)) - (2*PolyLog(3, a*x^2))/(d*sqrt(d*x))]
@test_int [PolyLog(3, a*x^2)/(d*x)^(5/2), x, 8, (64*a^(3/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*d^(5/2)) + (64*a^(3/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*d^(5/2)) + (32*log(1 - a*x^2))/(27*d*(d*x)^(3/2)) - (8*PolyLog(2, a*x^2))/(9*d*(d*x)^(3/2)) - (2*PolyLog(3, a*x^2))/(3*d*(d*x)^(3/2))]
@test_int [PolyLog(3, a*x^2)/(d*x)^(7/2), x, 9, -((128*a)/(125*d^3*sqrt(d*x))) - (64*a^(5/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*d^(7/2)) + (64*a^(5/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*d^(7/2)) + (32*log(1 - a*x^2))/(125*d*(d*x)^(5/2)) - (8*PolyLog(2, a*x^2))/(25*d*(d*x)^(5/2)) - (2*PolyLog(3, a*x^2))/(5*d*(d*x)^(5/2))]
@test_int [PolyLog(3, a*x^2)/(d*x)^(9/2), x, 9, -((128*a)/(1029*d^3*(d*x)^(3/2))) + (64*a^(7/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*d^(9/2)) + (64*a^(7/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*d^(9/2)) + (32*log(1 - a*x^2))/(343*d*(d*x)^(7/2)) - (8*PolyLog(2, a*x^2))/(49*d*(d*x)^(7/2)) - (2*PolyLog(3, a*x^2))/(7*d*(d*x)^(7/2))]
#= ::Subsubsection::Closed:: =#
#=q*symbolic=#
@test_int [(d*x)^(3/2)*PolyLog(2, a*x^q), x, 4, (8*a*d*q^2*x^(2 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (5/2 + q)/q, (1/2)*(4 + 5/q), a*x^q))/(25*(5 + 2*q)) + (4*q*(d*x)^(5/2)*log(1 - a*x^q))/(25*d) + (2*(d*x)^(5/2)*PolyLog(2, a*x^q))/(5*d)]
@test_int [(d*x)^(1/2)*PolyLog(2, a*x^q), x, 4, (8*a*q^2*x^(1 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (3/2 + q)/q, (1/2)*(4 + 3/q), a*x^q))/(9*(3 + 2*q)) + (4*q*(d*x)^(3/2)*log(1 - a*x^q))/(9*d) + (2*(d*x)^(3/2)*PolyLog(2, a*x^q))/(3*d)]
@test_int [PolyLog(2, a*x^q)/(d*x)^(1/2), x, 4, (8*a*q^2*x^q*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (1/2 + q)/q, (1/2)*(4 + 1/q), a*x^q))/(d*(1 + 2*q)) + (4*q*sqrt(d*x)*log(1 - a*x^q))/d + (2*sqrt(d*x)*PolyLog(2, a*x^q))/d]
@test_int [PolyLog(2, a*x^q)/(d*x)^(3/2), x, 4, -((8*a*q^2*x^q*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 1/q), (1/2)*(4 - 1/q), a*x^q))/(d*(1 - 2*q)*sqrt(d*x))) + (4*q*log(1 - a*x^q))/(d*sqrt(d*x)) - (2*PolyLog(2, a*x^q))/(d*sqrt(d*x))]
@test_int [PolyLog(2, a*x^q)/(d*x)^(5/2), x, 4, -((8*a*q^2*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 3/q), (1/2)*(4 - 3/q), a*x^q))/(9*d^2*(3 - 2*q)*sqrt(d*x))) + (4*q*log(1 - a*x^q))/(9*d*(d*x)^(3/2)) - (2*PolyLog(2, a*x^q))/(3*d*(d*x)^(3/2))]
@test_int [(d*x)^(3/2)*PolyLog(3, a*x^q), x, 5, -((16*a*d*q^3*x^(2 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (5/2 + q)/q, (1/2)*(4 + 5/q), a*x^q))/(125*(5 + 2*q))) - (8*q^2*(d*x)^(5/2)*log(1 - a*x^q))/(125*d) - (4*q*(d*x)^(5/2)*PolyLog(2, a*x^q))/(25*d) + (2*(d*x)^(5/2)*PolyLog(3, a*x^q))/(5*d)]
@test_int [(d*x)^(1/2)*PolyLog(3, a*x^q), x, 5, -((16*a*q^3*x^(1 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (3/2 + q)/q, (1/2)*(4 + 3/q), a*x^q))/(27*(3 + 2*q))) - (8*q^2*(d*x)^(3/2)*log(1 - a*x^q))/(27*d) - (4*q*(d*x)^(3/2)*PolyLog(2, a*x^q))/(9*d) + (2*(d*x)^(3/2)*PolyLog(3, a*x^q))/(3*d)]
@test_int [PolyLog(3, a*x^q)/(d*x)^(1/2), x, 5, -((16*a*q^3*x^q*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (1/2 + q)/q, (1/2)*(4 + 1/q), a*x^q))/(d*(1 + 2*q))) - (8*q^2*sqrt(d*x)*log(1 - a*x^q))/d - (4*q*sqrt(d*x)*PolyLog(2, a*x^q))/d + (2*sqrt(d*x)*PolyLog(3, a*x^q))/d]
@test_int [PolyLog(3, a*x^q)/(d*x)^(3/2), x, 5, -((16*a*q^3*x^q*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 1/q), (1/2)*(4 - 1/q), a*x^q))/(d*(1 - 2*q)*sqrt(d*x))) + (8*q^2*log(1 - a*x^q))/(d*sqrt(d*x)) - (4*q*PolyLog(2, a*x^q))/(d*sqrt(d*x)) - (2*PolyLog(3, a*x^q))/(d*sqrt(d*x))]
@test_int [PolyLog(3, a*x^q)/(d*x)^(5/2), x, 5, -((16*a*q^3*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 3/q), (1/2)*(4 - 3/q), a*x^q))/(27*d^2*(3 - 2*q)*sqrt(d*x))) + (8*q^2*log(1 - a*x^q))/(27*d*(d*x)^(3/2)) - (4*q*PolyLog(2, a*x^q))/(9*d*(d*x)^(3/2)) - (2*PolyLog(3, a*x^q))/(3*d*(d*x)^(3/2))]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*PolyLog(n/2, a*x^q)=#
@test_int [PolyLog(3/2, a*x), x, 2, (-x)*PolyLog(1/2, a*x) + x*PolyLog(3/2, a*x) + Unintegrable(PolyLog(-(1/2), a*x), x)]
@test_int [PolyLog(1/2, a*x), x, 1, x*PolyLog(1/2, a*x) - Unintegrable(PolyLog(-(1/2), a*x), x)]
@test_int [PolyLog(-1/2, a*x), x, 0, Unintegrable(PolyLog(-(1/2), a*x), x)]
@test_int [PolyLog(-3/2, a*x), x, 1, x*PolyLog(-(1/2), a*x) - Unintegrable(PolyLog(-(1/2), a*x), x)]
@test_int [PolyLog(-5/2, a*x), x, 2, x*PolyLog(-(3/2), a*x) - x*PolyLog(-(1/2), a*x) + Unintegrable(PolyLog(-(1/2), a*x), x)]
@test_int [PolyLog(-3/2, a*x) + PolyLog(-1/2, a*x), x, 2, x*PolyLog(-1/2, a*x)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*(d*x)^m*PolyLog(n, a*x^q)*with*m*symbolic=#
@test_int [(d*x)^m*PolyLog(2, a*x), x, 3, (a*(d*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, a*x))/(d^2*(1 + m)^2*(2 + m)) + ((d*x)^(1 + m)*log(1 - a*x))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(3, a*x), x, 4, -((a*(d*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, a*x))/(d^2*(1 + m)^3*(2 + m))) - ((d*x)^(1 + m)*log(1 - a*x))/(d*(1 + m)^3) - ((d*x)^(1 + m)*PolyLog(2, a*x))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(4, a*x), x, 5, (a*(d*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, a*x))/(d^2*(1 + m)^4*(2 + m)) + ((d*x)^(1 + m)*log(1 - a*x))/(d*(1 + m)^4) + ((d*x)^(1 + m)*PolyLog(2, a*x))/(d*(1 + m)^3) - ((d*x)^(1 + m)*PolyLog(3, a*x))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(2, a*x^2), x, 4, (4*a*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (5 + m)/2, a*x^2))/(d^3*(1 + m)^2*(3 + m)) + (2*(d*x)^(1 + m)*log(1 - a*x^2))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x^2))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(3, a*x^2), x, 5, -((8*a*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (5 + m)/2, a*x^2))/(d^3*(1 + m)^3*(3 + m))) - (4*(d*x)^(1 + m)*log(1 - a*x^2))/(d*(1 + m)^3) - (2*(d*x)^(1 + m)*PolyLog(2, a*x^2))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x^2))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(4, a*x^2), x, 6, (16*a*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (5 + m)/2, a*x^2))/(d^3*(1 + m)^4*(3 + m)) + (8*(d*x)^(1 + m)*log(1 - a*x^2))/(d*(1 + m)^4) + (4*(d*x)^(1 + m)*PolyLog(2, a*x^2))/(d*(1 + m)^3) - (2*(d*x)^(1 + m)*PolyLog(3, a*x^2))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x^2))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(2, a*x^3), x, 4, (9*a*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/3, (7 + m)/3, a*x^3))/(d^4*(1 + m)^2*(4 + m)) + (3*(d*x)^(1 + m)*log(1 - a*x^3))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x^3))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(3, a*x^3), x, 5, -((27*a*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/3, (7 + m)/3, a*x^3))/(d^4*(1 + m)^3*(4 + m))) - (9*(d*x)^(1 + m)*log(1 - a*x^3))/(d*(1 + m)^3) - (3*(d*x)^(1 + m)*PolyLog(2, a*x^3))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x^3))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(4, a*x^3), x, 6, (81*a*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/3, (7 + m)/3, a*x^3))/(d^4*(1 + m)^4*(4 + m)) + (27*(d*x)^(1 + m)*log(1 - a*x^3))/(d*(1 + m)^4) + (9*(d*x)^(1 + m)*PolyLog(2, a*x^3))/(d*(1 + m)^3) - (3*(d*x)^(1 + m)*PolyLog(3, a*x^3))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x^3))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(2, a*x^q), x, 4, (a*q^2*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q))/((1 + m)^2*(1 + m + q)) + (q*(d*x)^(1 + m)*log(1 - a*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x^q))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(3, a*x^q), x, 5, -((a*q^3*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q))/((1 + m)^3*(1 + m + q))) - (q^2*(d*x)^(1 + m)*log(1 - a*x^q))/(d*(1 + m)^3) - (q*(d*x)^(1 + m)*PolyLog(2, a*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x^q))/(d*(1 + m))]
@test_int [(d*x)^m*PolyLog(4, a*x^q), x, 6, (a*q^4*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q))/((1 + m)^4*(1 + m + q)) + (q^3*(d*x)^(1 + m)*log(1 - a*x^q))/(d*(1 + m)^4) + (q^2*(d*x)^(1 + m)*PolyLog(2, a*x^q))/(d*(1 + m)^3) - (q*(d*x)^(1 + m)*PolyLog(3, a*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x^q))/(d*(1 + m))]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*(d*x)^m*PolyLog(n, a*x^q)*with*n*symbolic=#
@test_int [x^1*PolyLog(n, a*x), x, 0, Unintegrable(x*PolyLog(n, a*x), x)]
@test_int [x^0*PolyLog(n, a*x), x, 0, Unintegrable(PolyLog(n, a*x), x)]
@test_int [PolyLog(n, a*x)/x^1, x, 1, PolyLog(1 + n, a*x)]
@test_int [PolyLog(n, a*x)/x^2, x, 0, Unintegrable(PolyLog(n, a*x)/x^2, x)]
@test_int [PolyLog(n, a*x)/x^3, x, 0, Unintegrable(PolyLog(n, a*x)/x^3, x)]
@test_int [x^1*PolyLog(n, a*x^q), x, 0, Unintegrable(x*PolyLog(n, a*x^q), x)]
@test_int [x^0*PolyLog(n, a*x^q), x, 0, Unintegrable(PolyLog(n, a*x^q), x)]
@test_int [PolyLog(n, a*x^q)/x^1, x, 1, PolyLog(1 + n, a*x^q)/q]
@test_int [PolyLog(n, a*x^q)/x^2, x, 0, Unintegrable(PolyLog(n, a*x^q)/x^2, x)]
@test_int [PolyLog(n, a*x^q)/x^3, x, 0, Unintegrable(PolyLog(n, a*x^q)/x^3, x)]
#= ::Section::Closed:: =#
#=Integrands*of*the*form*(d*x)^m*PolyLog(n, c*(a+b*x))=#
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*PolyLog(n, c*(a+b*x))=#
@test_int [x^2*PolyLog(2, c*(a + b*x)), x, 13, -((a^2*x)/(3*b^2)) + (a*(1 - a*c)*x)/(6*b^2*c) - ((1 - a*c)^2*x)/(9*b^2*c^2) + (a*x^2)/(12*b) - ((1 - a*c)*x^2)/(18*b*c) - x^3/27 + (a*(1 - a*c)^2*log(1 - a*c - b*c*x))/(6*b^3*c^2) - ((1 - a*c)^3*log(1 - a*c - b*c*x))/(9*b^3*c^3) - (a*x^2*log(1 - a*c - b*c*x))/(6*b) + (1/9)*x^3*log(1 - a*c - b*c*x) - (a^2*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(3*b^3*c) + (a^3*PolyLog(2, c*(a + b*x)))/(3*b^3) + (1/3)*x^3*PolyLog(2, c*(a + b*x))]
@test_int [x^1*PolyLog(2, c*(a + b*x)), x, 10, (a*x)/(2*b) - ((1 - a*c)*x)/(4*b*c) - x^2/8 - ((1 - a*c)^2*log(1 - a*c - b*c*x))/(4*b^2*c^2) + (1/4)*x^2*log(1 - a*c - b*c*x) + (a*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(2*b^2*c) - (a^2*PolyLog(2, c*(a + b*x)))/(2*b^2) + (1/2)*x^2*PolyLog(2, c*(a + b*x))]
@test_int [x^0*PolyLog(2, c*(a + b*x)), x, 7, -x - ((1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (a*PolyLog(2, c*(a + b*x)))/b + x*PolyLog(2, c*(a + b*x))]
@test_int [PolyLog(2, c*(a + b*x))/x^1, x, 3, log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)) + (1/2)*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2 + (1/2)*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2 + (log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)) + log(x)*PolyLog(2, c*(a + b*x)) + log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))) - log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))) + (log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)) - PolyLog(3, -((b*x)/a)) + PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))) - PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))) - PolyLog(3, 1 - c*(a + b*x))]
@test_int [PolyLog(2, c*(a + b*x))/x^2, x, 7, -((b*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/a) - (b*PolyLog(2, c*(a + b*x)))/a - PolyLog(2, c*(a + b*x))/x - (b*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a]
@test_int [PolyLog(2, c*(a + b*x))/x^3, x, 11, (b^2*c*log(x))/(2*a*(1 - a*c)) - (b^2*c*log(1 - a*c - b*c*x))/(2*a*(1 - a*c)) + (b*log(1 - a*c - b*c*x))/(2*a*x) + (b^2*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2) + (b^2*PolyLog(2, c*(a + b*x)))/(2*a^2) - PolyLog(2, c*(a + b*x))/(2*x^2) + (b^2*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2)]
@test_int [PolyLog(2, c*(a + b*x))/x^4, x, 14, -((b^2*c)/(6*a*(1 - a*c)*x)) + (b^3*c^2*log(x))/(6*a*(1 - a*c)^2) - (b^3*c*log(x))/(3*a^2*(1 - a*c)) - (b^3*c^2*log(1 - a*c - b*c*x))/(6*a*(1 - a*c)^2) + (b^3*c*log(1 - a*c - b*c*x))/(3*a^2*(1 - a*c)) + (b*log(1 - a*c - b*c*x))/(6*a*x^2) - (b^2*log(1 - a*c - b*c*x))/(3*a^2*x) - (b^3*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(3*a^3) - (b^3*PolyLog(2, c*(a + b*x)))/(3*a^3) - PolyLog(2, c*(a + b*x))/(3*x^3) - (b^3*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3)]
@test_int [x^2*PolyLog(3, c*(a + b*x)), x, 33, (11*a^2*x)/(18*b^2) - (5*a*(1 - a*c)*x)/(36*b^2*c) + ((1 - a*c)^2*x)/(27*b^2*c^2) - (5*a*x^2)/(72*b) + ((1 - a*c)*x^2)/(54*b*c) + x^3/81 - (5*a*(1 - a*c)^2*log(1 - a*c - b*c*x))/(36*b^3*c^2) + ((1 - a*c)^3*log(1 - a*c - b*c*x))/(27*b^3*c^3) + (5*a*x^2*log(1 - a*c - b*c*x))/(36*b) - (1/27)*x^3*log(1 - a*c - b*c*x) + (11*a^2*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(18*b^3*c) - (11*a^3*PolyLog(2, c*(a + b*x)))/(18*b^3) - (a^2*x*PolyLog(2, c*(a + b*x)))/(3*b^2) + (a*x^2*PolyLog(2, c*(a + b*x)))/(6*b) - (1/9)*x^3*PolyLog(2, c*(a + b*x)) + (2*a^3*PolyLog(3, c*(a + b*x)))/(3*b^3) - ((a^3 - b^3*x^3)*PolyLog(3, c*(a + b*x)))/(3*b^3)]
@test_int [x^1*PolyLog(3, c*(a + b*x)), x, 19, -((3*a*x)/(4*b)) + ((1 - a*c)*x)/(8*b*c) + x^2/16 + ((1 - a*c)^2*log(1 - a*c - b*c*x))/(8*b^2*c^2) - (1/8)*x^2*log(1 - a*c - b*c*x) - (3*a*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b^2*c) + (3*a^2*PolyLog(2, c*(a + b*x)))/(4*b^2) + (a*x*PolyLog(2, c*(a + b*x)))/(2*b) - (1/4)*x^2*PolyLog(2, c*(a + b*x)) - ((a^2 - b^2*x^2)*PolyLog(3, c*(a + b*x)))/(2*b^2)]
@test_int [x^0*PolyLog(3, c*(a + b*x)), x, 9, x + ((1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) - (a*PolyLog(2, c*(a + b*x)))/b - x*PolyLog(2, c*(a + b*x)) + (a*PolyLog(3, c*(a + b*x)))/b + x*PolyLog(3, c*(a + b*x))]
@test_int [PolyLog(3, c*(a + b*x))/x^1, x, 1, Int(PolyLog(3, a*c + b*c*x)/x, x)]
@test_int [PolyLog(3, c*(a + b*x))/x^2, x, 6, (b*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/a + (b*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(2*a) + (b*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(2*a) + (b*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/a + (b*log(x)*PolyLog(2, c*(a + b*x)))/a + (b*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/a - (b*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/a + (b*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/a - (b*PolyLog(3, -((b*x)/a)))/a - (2*b*PolyLog(3, c*(a + b*x)))/a + ((b - a/x)*PolyLog(3, c*(a + b*x)))/a + (b*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/a - (b*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/a - (b*PolyLog(3, 1 - c*(a + b*x)))/a]
@test_int [PolyLog(3, c*(a + b*x))/x^3, x, 12, -((b^2*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2)) - (b^2*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/(2*a^2) - (b^2*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(4*a^2) - (b^2*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(4*a^2) - (b^2*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/(2*a^2) - (b^2*PolyLog(2, c*(a + b*x)))/(2*a^2) - (b*PolyLog(2, c*(a + b*x)))/(2*a*x) - (b^2*log(x)*PolyLog(2, c*(a + b*x)))/(2*a^2) - (b^2*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) - (b^2*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*a^2) + (b^2*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/(2*a^2) - (b^2*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/(2*a^2) + (b^2*PolyLog(3, -((b*x)/a)))/(2*a^2) + ((b^2 - a^2/x^2)*PolyLog(3, c*(a + b*x)))/(2*a^2) - (b^2*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*a^2) + (b^2*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/(2*a^2) + (b^2*PolyLog(3, 1 - c*(a + b*x)))/(2*a^2)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*(d+e*x)^m*PolyLog(n,c*(a+b*x))=#
@test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^3, x, 16, -(((b*d - a*e)^3*x)/(4*b^3)) - ((b*d - a*e)^2*(b*c*d + e - a*c*e)*x)/(8*b^3*c) - ((b*d - a*e)*(b*c*d + e - a*c*e)^2*x)/(12*b^3*c^2) - ((b*c*d + e - a*c*e)^3*x)/(16*b^3*c^3) - ((b*d - a*e)^2*(d + e*x)^2)/(16*b^2*e) - ((b*d - a*e)*(b*c*d + e - a*c*e)*(d + e*x)^2)/(24*b^2*c*e) - ((b*c*d + e - a*c*e)^2*(d + e*x)^2)/(32*b^2*c^2*e) - ((b*d - a*e)*(d + e*x)^3)/(36*b*e) - ((b*c*d + e - a*c*e)*(d + e*x)^3)/(48*b*c*e) - (d + e*x)^4/(64*e) - ((b*d - a*e)^2*(b*c*d + e - a*c*e)^2*log(1 - a*c - b*c*x))/(8*b^4*c^2*e) - ((b*d - a*e)*(b*c*d + e - a*c*e)^3*log(1 - a*c - b*c*x))/(12*b^4*c^3*e) - ((b*c*d + e - a*c*e)^4*log(1 - a*c - b*c*x))/(16*b^4*c^4*e) - ((b*d - a*e)^3*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b^4*c) + ((b*d - a*e)^2*(d + e*x)^2*log(1 - a*c - b*c*x))/(8*b^2*e) + ((b*d - a*e)*(d + e*x)^3*log(1 - a*c - b*c*x))/(12*b*e) + ((d + e*x)^4*log(1 - a*c - b*c*x))/(16*e) - ((b*d - a*e)^4*PolyLog(2, c*(a + b*x)))/(4*b^4*e) + ((d + e*x)^4*PolyLog(2, c*(a + b*x)))/(4*e)]
@test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^2, x, 13, -(((b*d - a*e)^2*x)/(3*b^2)) - ((b*d - a*e)*(b*c*d + e - a*c*e)*x)/(6*b^2*c) - ((b*c*d + e - a*c*e)^2*x)/(9*b^2*c^2) - ((b*d - a*e)*(d + e*x)^2)/(12*b*e) - ((b*c*d + e - a*c*e)*(d + e*x)^2)/(18*b*c*e) - (d + e*x)^3/(27*e) - ((b*d - a*e)*(b*c*d + e - a*c*e)^2*log(1 - a*c - b*c*x))/(6*b^3*c^2*e) - ((b*c*d + e - a*c*e)^3*log(1 - a*c - b*c*x))/(9*b^3*c^3*e) - ((b*d - a*e)^2*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(3*b^3*c) + ((b*d - a*e)*(d + e*x)^2*log(1 - a*c - b*c*x))/(6*b*e) + ((d + e*x)^3*log(1 - a*c - b*c*x))/(9*e) - ((b*d - a*e)^3*PolyLog(2, c*(a + b*x)))/(3*b^3*e) + ((d + e*x)^3*PolyLog(2, c*(a + b*x)))/(3*e)]
@test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^1, x, 10, -(((b*d - a*e)*x)/(2*b)) - ((b*c*d + e - a*c*e)*x)/(4*b*c) - (d + e*x)^2/(8*e) - ((b*c*d + e - a*c*e)^2*log(1 - a*c - b*c*x))/(4*b^2*c^2*e) - ((b*d - a*e)*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(2*b^2*c) + ((d + e*x)^2*log(1 - a*c - b*c*x))/(4*e) - ((b*d - a*e)^2*PolyLog(2, c*(a + b*x)))/(2*b^2*e) + ((d + e*x)^2*PolyLog(2, c*(a + b*x)))/(2*e)]
@test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^0, x, 7, -x - ((1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (a*PolyLog(2, c*(a + b*x)))/b + x*PolyLog(2, c*(a + b*x))]
@test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^1, x, 3, ((log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*e) + (log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/e - ((log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*e) + (log(d + e*x)*PolyLog(2, c*(a + b*x)))/e + ((log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/e + ((log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/e - (log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/e + (log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/e - PolyLog(3, (b*(d + e*x))/(b*d - a*e))/e - PolyLog(3, 1 - c*(a + b*x))/e - PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x))))/e + PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x)))/e]
@test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^2, x, 8, (b*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(e*(b*d - a*e)) + (b*PolyLog(2, c*(a + b*x)))/(e*(b*d - a*e)) - PolyLog(2, c*(a + b*x))/(e*(d + e*x)) + (b*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(e*(b*d - a*e))]
@test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^3, x, 12, (b^2*c*log(1 - a*c - b*c*x))/(2*e*(b*d - a*e)*(b*c*d + e - a*c*e)) - (b*log(1 - a*c - b*c*x))/(2*e*(b*d - a*e)*(d + e*x)) - (b^2*c*log(d + e*x))/(2*e*(b*d - a*e)*(b*c*d + e - a*c*e)) + (b^2*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*e*(b*d - a*e)^2) + (b^2*PolyLog(2, c*(a + b*x)))/(2*e*(b*d - a*e)^2) - PolyLog(2, c*(a + b*x))/(2*e*(d + e*x)^2) + (b^2*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(2*e*(b*d - a*e)^2)]
@test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^4, x, 15, (b^2*c)/(6*e*(b*d - a*e)*(b*c*d + e - a*c*e)*(d + e*x)) + (b^3*c^2*log(1 - a*c - b*c*x))/(6*e*(b*d - a*e)*(b*c*d + e - a*c*e)^2) + (b^3*c*log(1 - a*c - b*c*x))/(3*e*(b*d - a*e)^2*(b*c*d + e - a*c*e)) - (b*log(1 - a*c - b*c*x))/(6*e*(b*d - a*e)*(d + e*x)^2) - (b^2*log(1 - a*c - b*c*x))/(3*e*(b*d - a*e)^2*(d + e*x)) - (b^3*c^2*log(d + e*x))/(6*e*(b*d - a*e)*(b*c*d + e - a*c*e)^2) - (b^3*c*log(d + e*x))/(3*e*(b*d - a*e)^2*(b*c*d + e - a*c*e)) + (b^3*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*e*(b*d - a*e)^3) + (b^3*PolyLog(2, c*(a + b*x)))/(3*e*(b*d - a*e)^3) - PolyLog(2, c*(a + b*x))/(3*e*(d + e*x)^3) + (b^3*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(3*e*(b*d - a*e)^3)]
#= Following*integrands*are*equal. =#
@test_int [PolyLog(2, x)/(-1 + x), x, 5, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)]
@test_int [-PolyLog(2, x)/(1 - x), x, 5, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)]
@test_int [PolyLog(2, x)/((-1 + x)*x), x, 8, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)-PolyLog(3,x)]
@test_int [-PolyLog(2, x)/((1 - x)*x), x, 8, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)-PolyLog(3,x)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*PolyLog(n, e*((a + b*x) / (c + d*x))^n) / ((a + b*x)*(c + d*x))=#
@test_int [PolyLog(n, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(1 + n, e*((a + b*x)/(c + d*x))^n)/((b*c - a*d)*n)]
@test_int [PolyLog(3, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(4, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))]
@test_int [PolyLog(2, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(3, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))]
@test_int [PolyLog(1, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(2, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))]
@test_int [PolyLog(0, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 2, PolyLog(1, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))]
@test_int [PolyLog(-1, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 2, 1/((b*c - a*d)*n*(1 - e*((a + b*x)/(c + d*x))^n))]
@test_int [PolyLog(-2, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 4, PolyLog(-1, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))]
#= ::Section::Closed:: =#
#=Integrands*of*the*form*(d*x)^m*PolyLog(n, d*(F^(c*(a + b*x)))^p)=#
@test_int [x^3*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 5, (x^3*PolyLog(1 + n, d*(F^(c*(a + b*x)))^p))/(b*c*p*log(F)) - (3*x^2*PolyLog(2 + n, d*(F^(c*(a + b*x)))^p))/(b^2*c^2*p^2*log(F)^2) + (6*x*PolyLog(3 + n, d*(F^(c*(a + b*x)))^p))/(b^3*c^3*p^3*log(F)^3) - (6*PolyLog(4 + n, d*(F^(c*(a + b*x)))^p))/(b^4*c^4*p^4*log(F)^4)]
@test_int [x^2*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 4, (x^2*PolyLog(1 + n, d*(F^(c*(a + b*x)))^p))/(b*c*p*log(F)) - (2*x*PolyLog(2 + n, d*(F^(c*(a + b*x)))^p))/(b^2*c^2*p^2*log(F)^2) + (2*PolyLog(3 + n, d*(F^(c*(a + b*x)))^p))/(b^3*c^3*p^3*log(F)^3)]
@test_int [x^1*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 3, (x*PolyLog(1 + n, d*(F^(c*(a + b*x)))^p))/(b*c*p*log(F)) - PolyLog(2 + n, d*(F^(c*(a + b*x)))^p)/(b^2*c^2*p^2*log(F)^2)]
@test_int [x^0*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 2, PolyLog(1 + n, d*(F^(c*(a + b*x)))^p)/(b*c*p*log(F))]
@test_int [PolyLog(n, d*(F^(c*(a + b*x)))^p)/x^1, x, 1, CannotIntegrate(PolyLog(n, d*(F^(a*c + b*c*x))^p)/x, x)]
#= ::Section::Closed:: =#
#=Integrands*of*the*form*(d*x)^m*P(x)*(g+h*log(f*(d+e*x)^n))*PolyLog(2, c*(a+b*x))=#
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*log(1-c*x)*PolyLog(2, c*x)=#
@test_int [x^3*log(1 - c*x)*PolyLog(2, c*x), x, 38, (355*x)/(576*c^3) + (139*x^2)/(1152*c^2) + (67*x^3)/(1728*c) + (3*x^4)/256 + (139*log(1 - c*x))/(576*c^4) - (x^2*log(1 - c*x))/(8*c^2) - (5*x^3*log(1 - c*x))/(72*c) - (3/64)*x^4*log(1 - c*x) + (3*(1 - c*x)*log(1 - c*x))/(8*c^4) - log(1 - c*x)^2/(16*c^4) + (1/16)*x^4*log(1 - c*x)^2 - (log(c*x)*log(1 - c*x)^2)/(4*c^4) - (x*PolyLog(2, c*x))/(4*c^3) - (x^2*PolyLog(2, c*x))/(8*c^2) - (x^3*PolyLog(2, c*x))/(12*c) - (1/16)*x^4*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(4*c^4) + (1/4)*x^4*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, 1 - c*x))/(2*c^4) + PolyLog(3, 1 - c*x)/(2*c^4)]
@test_int [x^2*log(1 - c*x)*PolyLog(2, c*x), x, 31, (31*x)/(36*c^2) + (11*x^2)/(72*c) + x^3/27 + (11*log(1 - c*x))/(36*c^3) - (7*x^2*log(1 - c*x))/(36*c) - (1/9)*x^3*log(1 - c*x) + (5*(1 - c*x)*log(1 - c*x))/(9*c^3) - log(1 - c*x)^2/(9*c^3) + (1/9)*x^3*log(1 - c*x)^2 - (log(c*x)*log(1 - c*x)^2)/(3*c^3) - (x*PolyLog(2, c*x))/(3*c^2) - (x^2*PolyLog(2, c*x))/(6*c) - (1/9)*x^3*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(3*c^3) + (1/3)*x^3*log(1 - c*x)*PolyLog(2, c*x) - (2*log(1 - c*x)*PolyLog(2, 1 - c*x))/(3*c^3) + (2*PolyLog(3, 1 - c*x))/(3*c^3)]
@test_int [x^1*log(1 - c*x)*PolyLog(2, c*x), x, 22, (13*x)/(8*c) + x^2/16 + (1 - c*x)^2/(8*c^2) + log(1 - c*x)/(8*c^2) - (1/8)*x^2*log(1 - c*x) + (3*(1 - c*x)*log(1 - c*x))/(2*c^2) - ((1 - c*x)^2*log(1 - c*x))/(4*c^2) - ((1 - c*x)*log(1 - c*x)^2)/(2*c^2) + ((1 - c*x)^2*log(1 - c*x)^2)/(4*c^2) - (log(c*x)*log(1 - c*x)^2)/(2*c^2) - (x*PolyLog(2, c*x))/(2*c) - (1/4)*x^2*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(2*c^2) + (1/2)*x^2*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, 1 - c*x))/c^2 + PolyLog(3, 1 - c*x)/c^2]
@test_int [x^0*log(1 - c*x)*PolyLog(2, c*x), x, 15, 3*x + (3*(1 - c*x)*log(1 - c*x))/c - ((1 - c*x)*log(1 - c*x)^2)/c - (log(c*x)*log(1 - c*x)^2)/c - x*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/c + x*log(1 - c*x)*PolyLog(2, c*x) - (2*log(1 - c*x)*PolyLog(2, 1 - c*x))/c + (2*PolyLog(3, 1 - c*x))/c]
@test_int [log(1 - c*x)*PolyLog(2, c*x)/x^1, x, 1, (-(1/2))*PolyLog(2, c*x)^2]
@test_int [log(1 - c*x)*PolyLog(2, c*x)/x^2, x, 10, ((1 - c*x)*log(1 - c*x)^2)/x + c*log(c*x)*log(1 - c*x)^2 - 2*c*PolyLog(2, c*x) + c*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/x + 2*c*log(1 - c*x)*PolyLog(2, 1 - c*x) - c*PolyLog(3, c*x) - 2*c*PolyLog(3, 1 - c*x)]
@test_int [log(1 - c*x)*PolyLog(2, c*x)/x^3, x, 23, (-c^2)*log(x) + c^2*log(1 - c*x) - (c*log(1 - c*x))/x - (1/4)*c^2*log(1 - c*x)^2 + log(1 - c*x)^2/(4*x^2) + (1/2)*c^2*log(c*x)*log(1 - c*x)^2 - (1/2)*c^2*PolyLog(2, c*x) + (c*PolyLog(2, c*x))/(2*x) + (1/2)*c^2*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(2*x^2) + c^2*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/2)*c^2*PolyLog(3, c*x) - c^2*PolyLog(3, 1 - c*x)]
@test_int [log(1 - c*x)*PolyLog(2, c*x)/x^4, x, 30, (7*c^2)/(36*x) - (3/4)*c^3*log(x) + (3/4)*c^3*log(1 - c*x) - (7*c*log(1 - c*x))/(36*x^2) - (5*c^2*log(1 - c*x))/(9*x) - (1/9)*c^3*log(1 - c*x)^2 + log(1 - c*x)^2/(9*x^3) + (1/3)*c^3*log(c*x)*log(1 - c*x)^2 - (2/9)*c^3*PolyLog(2, c*x) + (c*PolyLog(2, c*x))/(6*x^2) + (c^2*PolyLog(2, c*x))/(3*x) + (1/3)*c^3*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(3*x^3) + (2/3)*c^3*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/3)*c^3*PolyLog(3, c*x) - (2/3)*c^3*PolyLog(3, 1 - c*x)]
@test_int [log(1 - c*x)*PolyLog(2, c*x)/x^5, x, 37, (5*c^2)/(144*x^2) + (7*c^3)/(36*x) - (41/72)*c^4*log(x) + (41/72)*c^4*log(1 - c*x) - (5*c*log(1 - c*x))/(72*x^3) - (c^2*log(1 - c*x))/(8*x^2) - (3*c^3*log(1 - c*x))/(8*x) - (1/16)*c^4*log(1 - c*x)^2 + log(1 - c*x)^2/(16*x^4) + (1/4)*c^4*log(c*x)*log(1 - c*x)^2 - (1/8)*c^4*PolyLog(2, c*x) + (c*PolyLog(2, c*x))/(12*x^3) + (c^2*PolyLog(2, c*x))/(8*x^2) + (c^3*PolyLog(2, c*x))/(4*x) + (1/4)*c^4*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(4*x^4) + (1/2)*c^4*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/4)*c^4*PolyLog(3, c*x) - (1/2)*c^4*PolyLog(3, 1 - c*x)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*(g+h*log(1-c*x))*PolyLog(2, c*x)=#
@test_int [x^2*(g + h*log(1 - c*x))*PolyLog(2, c*x), x, 25, (121*h*x)/(108*c^2) + (13*h*x^2)/(216*c) + (h*x^3)/81 + (h*(1 - c*x)^2)/(6*c^3) - (2*h*(1 - c*x)^3)/(81*c^3) + (13*h*log(1 - c*x))/(108*c^3) - (h*x^2*log(1 - c*x))/(12*c) - (1/27)*h*x^3*log(1 - c*x) + (h*(1 - c*x)*log(1 - c*x))/(3*c^3) + (h*log(1 - c*x)^2)/(9*c^3) - (h*log(c*x)*log(1 - c*x)^2)/(3*c^3) + (1/9)*x^3*log(1 - c*x)*(g + h*log(1 - c*x)) + ((1 - c*x)*(g + 2*h*log(1 - c*x)))/(3*c^3) - ((1 - c*x)^2*(g + 2*h*log(1 - c*x)))/(6*c^3) + ((1 - c*x)^3*(g + 2*h*log(1 - c*x)))/(27*c^3) - (log(1 - c*x)*(g + 2*h*log(1 - c*x)))/(9*c^3) - (h*x*PolyLog(2, c*x))/(3*c^2) - (h*x^2*PolyLog(2, c*x))/(6*c) - (1/9)*h*x^3*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, c*x))/(3*c^3) + (1/3)*x^3*(g + h*log(1 - c*x))*PolyLog(2, c*x) - (2*h*log(1 - c*x)*PolyLog(2, 1 - c*x))/(3*c^3) + (2*h*PolyLog(3, 1 - c*x))/(3*c^3)]
@test_int [x^1*(g + h*log(1 - c*x))*PolyLog(2, c*x), x, 21, (13*h*x)/(8*c) + (h*x^2)/16 + (h*(1 - c*x)^2)/(8*c^2) + (h*log(1 - c*x))/(8*c^2) - (1/8)*h*x^2*log(1 - c*x) + (h*(1 - c*x)*log(1 - c*x))/(2*c^2) + (h*log(1 - c*x)^2)/(4*c^2) - (h*log(c*x)*log(1 - c*x)^2)/(2*c^2) + (1/4)*x^2*log(1 - c*x)*(g + h*log(1 - c*x)) + ((1 - c*x)*(g + 2*h*log(1 - c*x)))/(2*c^2) - ((1 - c*x)^2*(g + 2*h*log(1 - c*x)))/(8*c^2) - (log(1 - c*x)*(g + 2*h*log(1 - c*x)))/(4*c^2) - (h*x*PolyLog(2, c*x))/(2*c) - (1/4)*h*x^2*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, c*x))/(2*c^2) + (1/2)*x^2*(g + h*log(1 - c*x))*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, 1 - c*x))/c^2 + (h*PolyLog(3, 1 - c*x))/c^2]
@test_int [x^0*(g + h*log(1 - c*x))*PolyLog(2, c*x), x, 18, (-g)*x + 3*h*x - (g*(1 - c*x)*log(1 - c*x))/c + (3*h*(1 - c*x)*log(1 - c*x))/c - (h*(1 - c*x)*log(1 - c*x)^2)/c - (h*log(c*x)*log(1 - c*x)^2)/c - h*x*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, c*x))/c + x*(g + h*log(1 - c*x))*PolyLog(2, c*x) - (2*h*log(1 - c*x)*PolyLog(2, 1 - c*x))/c + (2*h*PolyLog(3, 1 - c*x))/c]
@test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^1, x, 3, (-(1/2))*h*PolyLog(2, c*x)^2 + g*PolyLog(3, c*x)]
@test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^2, x, 12, c*h*log(c*x)*log(1 - c*x)^2 + (log(1 - c*x)*(g + h*log(1 - c*x)))/x + c*(g + 2*h*log(1 - c*x))*log(1 - 1/(1 - c*x)) + c*h*log(1 - c*x)*PolyLog(2, c*x) - ((g + h*log(1 - c*x))*PolyLog(2, c*x))/x - 2*c*h*PolyLog(2, 1/(1 - c*x)) + 2*c*h*log(1 - c*x)*PolyLog(2, 1 - c*x) - c*h*PolyLog(3, c*x) - 2*c*h*PolyLog(3, 1 - c*x)]
@test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^3, x, 20, (-c^2)*h*log(x) + (1/2)*c^2*h*log(1 - c*x) - (c*h*log(1 - c*x))/(2*x) + (1/2)*c^2*h*log(c*x)*log(1 - c*x)^2 + (log(1 - c*x)*(g + h*log(1 - c*x)))/(4*x^2) - (c*(1 - c*x)*(g + 2*h*log(1 - c*x)))/(4*x) + (1/4)*c^2*(g + 2*h*log(1 - c*x))*log(1 - 1/(1 - c*x)) + (c*h*PolyLog(2, c*x))/(2*x) + (1/2)*c^2*h*log(1 - c*x)*PolyLog(2, c*x) - ((g + h*log(1 - c*x))*PolyLog(2, c*x))/(2*x^2) - (1/2)*c^2*h*PolyLog(2, 1/(1 - c*x)) + c^2*h*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/2)*c^2*h*PolyLog(3, c*x) - c^2*h*PolyLog(3, 1 - c*x)]
@test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^4, x, 28, (7*c^2*h)/(36*x) - (3/4)*c^3*h*log(x) + (19/36)*c^3*h*log(1 - c*x) - (c*h*log(1 - c*x))/(12*x^2) - (c^2*h*log(1 - c*x))/(3*x) + (1/3)*c^3*h*log(c*x)*log(1 - c*x)^2 + (log(1 - c*x)*(g + h*log(1 - c*x)))/(9*x^3) - (c*(g + 2*h*log(1 - c*x)))/(18*x^2) - (c^2*(1 - c*x)*(g + 2*h*log(1 - c*x)))/(9*x) + (1/9)*c^3*(g + 2*h*log(1 - c*x))*log(1 - 1/(1 - c*x)) + (c*h*PolyLog(2, c*x))/(6*x^2) + (c^2*h*PolyLog(2, c*x))/(3*x) + (1/3)*c^3*h*log(1 - c*x)*PolyLog(2, c*x) - ((g + h*log(1 - c*x))*PolyLog(2, c*x))/(3*x^3) - (2/9)*c^3*h*PolyLog(2, 1/(1 - c*x)) + (2/3)*c^3*h*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/3)*c^3*h*PolyLog(3, c*x) - (2/3)*c^3*h*PolyLog(3, 1 - c*x)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*(g+h*log(f*(d+e*x)^n))*PolyLog(2, c*(a+b*x))=#
@test_int [x^2*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)), x, 108, -((a^2*g*x)/(3*b^2)) + (a*(1 - a*c)*g*x)/(6*b^2*c) - ((1 - a*c)^2*g*x)/(9*b^2*c^2) + (7*a^2*h*n*x)/(9*b^2) - (11*a*(1 - a*c)*h*n*x)/(36*b^2*c) + (5*(1 - a*c)^2*h*n*x)/(27*b^2*c^2) + (13*d^2*h*n*x)/(27*e^2) + (5*a*d*h*n*x)/(12*b*e) - (7*(1 - a*c)*d*h*n*x)/(36*b*c*e) - (a*h*n*x^2)/(9*b) + (7*(1 - a*c)*h*n*x^2)/(108*b*c) - (19*d*h*n*x^2)/(216*e) + (1/27)*h*n*x^3 - (5*a*(1 - a*c)^2*h*n*log(1 - a*c - b*c*x))/(36*b^3*c^2) + (2*(1 - a*c)^3*h*n*log(1 - a*c - b*c*x))/(27*b^3*c^3) - (5*(1 - a*c)^2*d*h*n*log(1 - a*c - b*c*x))/(36*b^2*c^2*e) + (5*a*h*n*x^2*log(1 - a*c - b*c*x))/(36*b) + (5*d*h*n*x^2*log(1 - a*c - b*c*x))/(36*e) - (2/27)*h*n*x^3*log(1 - a*c - b*c*x) + (4*a^2*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(9*b^3*c) + (4*d^2*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(9*b*c*e^2) + (a*d*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(3*b^2*c*e) - (d^3*h*n*log(d + e*x))/(27*e^3) - (a*d^2*h*n*log(d + e*x))/(12*b*e^2) + ((1 - a*c)*d^2*h*n*log(d + e*x))/(18*b*c*e^2) + (d^3*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(9*e^3) + (a*d^2*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*b*e^2) + (a^2*d*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*b^2*e) - (a^2*h*(d + e*x)*log(f*(d + e*x)^n))/(3*b^2*e) + (a*(1 - a*c)*h*(d + e*x)*log(f*(d + e*x)^n))/(6*b^2*c*e) - ((1 - a*c)^2*h*(d + e*x)*log(f*(d + e*x)^n))/(9*b^2*c^2*e) + (a*x^2*(g + h*log(f*(d + e*x)^n)))/(12*b) - ((1 - a*c)*x^2*(g + h*log(f*(d + e*x)^n)))/(18*b*c) - (1/27)*x^3*(g + h*log(f*(d + e*x)^n)) + (a^2*x*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(3*b^2) - (a*x^2*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(6*b) + (1/9)*x^3*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)) - (a^2*(1 - a*c)*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(3*b^3*c) + (a*(1 - a*c)^2*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(6*b^3*c^2) - ((1 - a*c)^3*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(9*b^3*c^3) - (a^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*b^3) + (d^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*e^3) - (a^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*b^3) + (d^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*e^3) + (a^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*b^3) - (d^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*e^3) + (a^3*g*PolyLog(2, c*(a + b*x)))/(3*b^3) - (a^3*h*n*PolyLog(2, c*(a + b*x)))/(9*b^3) - (a*d^2*h*n*PolyLog(2, c*(a + b*x)))/(3*b*e^2) - (a^2*d*h*n*PolyLog(2, c*(a + b*x)))/(6*b^2*e) - (d^2*h*n*x*PolyLog(2, c*(a + b*x)))/(3*e^2) + (d*h*n*x^2*PolyLog(2, c*(a + b*x)))/(6*e) - (1/9)*h*n*x^3*PolyLog(2, c*(a + b*x)) + (d^3*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(3*e^3) - (a^3*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(3*b^3) + (1/3)*x^3*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)) + (d^3*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(9*e^3) + (a*d^2*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(6*b*e^2) + (a^2*d*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(3*b^2*e) - (a^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*b^3) + (d^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*e^3) - (a^2*(1 - a*c)*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*b^3*c) + (a*(1 - a*c)^2*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*b^3*c^2) - ((1 - a*c)^3*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(9*b^3*c^3) - (a^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*b^3) + (d^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*e^3) + (a^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*b^3) - (d^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*e^3) - (a^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*b^3) + (d^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*e^3) + (a^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*b^3) - (d^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*e^3) + (a^3*h*n*PolyLog(3, 1 - c*(a + b*x)))/(3*b^3) - (d^3*h*n*PolyLog(3, 1 - c*(a + b*x)))/(3*e^3) + (a^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*b^3) - (d^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*e^3) - (a^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*b^3) + (d^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*e^3)]
@test_int [x^1*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)), x, 67, (a*g*x)/(2*b) - ((1 - a*c)*g*x)/(4*b*c) - (5*a*h*n*x)/(4*b) + ((1 - a*c)*h*n*x)/(2*b*c) - (7*d*h*n*x)/(8*e) + (3/16)*h*n*x^2 + ((1 - a*c)^2*h*n*log(1 - a*c - b*c*x))/(4*b^2*c^2) - (1/4)*h*n*x^2*log(1 - a*c - b*c*x) - (3*a*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b^2*c) - (3*d*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b*c*e) + (d^2*h*n*log(d + e*x))/(8*e^2) - (d^2*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(4*e^2) - (a*d*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*b*e) + (a*h*(d + e*x)*log(f*(d + e*x)^n))/(2*b*e) - ((1 - a*c)*h*(d + e*x)*log(f*(d + e*x)^n))/(4*b*c*e) - (1/8)*x^2*(g + h*log(f*(d + e*x)^n)) - (a*x*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(2*b) + (1/4)*x^2*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)) + (a*(1 - a*c)*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(2*b^2*c) - ((1 - a*c)^2*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(4*b^2*c^2) + (a^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*b^2) - (d^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*e^2) + (a^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*b^2) - (d^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*e^2) - (a^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*b^2) + (d^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*e^2) - (a^2*g*PolyLog(2, c*(a + b*x)))/(2*b^2) + (a^2*h*n*PolyLog(2, c*(a + b*x)))/(4*b^2) + (a*d*h*n*PolyLog(2, c*(a + b*x)))/(2*b*e) + (d*h*n*x*PolyLog(2, c*(a + b*x)))/(2*e) - (1/4)*h*n*x^2*PolyLog(2, c*(a + b*x)) - (d^2*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(2*e^2) + (a^2*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(2*b^2) + (1/2)*x^2*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)) - (d^2*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(4*e^2) - (a*d*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(2*b*e) + (a^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*b^2) - (d^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*e^2) + (a*(1 - a*c)*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*b^2*c) - ((1 - a*c)^2*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(4*b^2*c^2) + (a^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*b^2) - (d^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*e^2) - (a^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*b^2) + (d^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*e^2) + (a^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*b^2) - (d^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*e^2) - (a^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*b^2) + (d^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*e^2) - (a^2*h*n*PolyLog(3, 1 - c*(a + b*x)))/(2*b^2) + (d^2*h*n*PolyLog(3, 1 - c*(a + b*x)))/(2*e^2) - (a^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*b^2) + (d^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*e^2) + (a^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*b^2) - (d^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*e^2)]
@test_int [x^0*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)), x, 42, (-g)*x + 3*h*n*x - (g*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (2*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (d*h*n*log(c*(a + b*x))*log(1 - a*c - b*c*x)*log(-d - e*x))/e + (d*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/e + (d*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x)))^2)/(2*e) - (d*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log(1 - a*c - b*c*x) + log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x))))^2)/(2*e) - (h*(d + e*x)*log(f*(d + e*x)^n))/e + h*x*log(1 - a*c - b*c*x)*log(f*(d + e*x)^n) - ((1 - a*c)*h*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*log(f*(d + e*x)^n))/(b*c) - (a*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*b) - (a*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/b + (a*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*b) + (a*g*PolyLog(2, c*(a + b*x)))/b - (a*h*n*PolyLog(2, c*(a + b*x)))/b - (a*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/b + x*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)) + (d*h*n*(log(-d - e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x))))*PolyLog(2, 1 - a*c - b*c*x))/e + (d*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/e - h*n*x*PolyLog(2, a*c + b*c*x) + (d*h*n*log(-d - e*x)*PolyLog(2, a*c + b*c*x))/e - (d*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/e + (d*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x)))*PolyLog(2, ((b*d - a*e)*(1 - a*c - b*c*x))/(b*(d + e*x))))/e + (d*h*n*(log(1 - a*c - b*c*x) + log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x))))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/e - (a*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/b - ((1 - a*c)*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(b*c) - (a*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/b + (a*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/b - (a*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/b - (d*h*n*PolyLog(3, 1 - a*c - b*c*x))/e - (d*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/e + (d*h*n*PolyLog(3, ((b*d - a*e)*(1 - a*c - b*c*x))/(b*(d + e*x))))/e + (a*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/b - (d*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/e + (a*h*n*PolyLog(3, 1 - c*(a + b*x)))/b + (a*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/b - (a*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/b]
@test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^1, x, 0, Unintegrable(((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/x, x)]
@test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^2, x, 22, -((b*g*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/a) - (b*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*log(d + e*x))/a - (b*h*n*(log((b*c*x)/(1 - a*c)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*x)/((1 - a*c)*(d + e*x))))*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))^2)/(2*a) + (b*h*n*(log((b*c*x)/(1 - a*c)) - log(-((e*x)/d)))*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))^2)/(2*a) + (b*h*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*(n*log(d + e*x) - log(f*(d + e*x)^n)))/a + (b*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*a) - (e*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*d) + (e*h*n*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/d + (b*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/a - (e*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/d - (b*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*a) + (e*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*d) + (e*h*n*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(2*d) + (e*h*n*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(2*d) + (e*h*n*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/d - (b*g*PolyLog(2, c*(a + b*x)))/a + (e*h*n*log(x)*PolyLog(2, c*(a + b*x)))/d - (e*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/d + (b*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/a - ((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/x - (b*g*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a - (b*h*n*(log(d + e*x) - log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a + (b*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a - (b*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/a + (b*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/a + (b*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/a - (e*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/d - (b*h*n*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 + (e*x)/d))/a + (e*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/d - (e*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/d + (b*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/a - (e*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/d + (e*h*n*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/d - (b*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/a + (e*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/d + (b*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/a - (e*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/d - (e*h*n*PolyLog(3, -((b*x)/a)))/d + (b*h*n*PolyLog(3, 1 - (b*c*x)/(1 - a*c)))/a - (b*h*n*PolyLog(3, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/a + (b*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/a - (b*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/a + (e*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/d + (b*h*n*PolyLog(3, 1 + (e*x)/d))/a + (e*h*n*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/d - (e*h*n*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/d - (b*h*n*PolyLog(3, 1 - c*(a + b*x)))/a - (b*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/a + (e*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/d + (b*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/a - (e*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/d]
@test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^3, x, 44, (b^2*g*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2) - (b*e*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(a*d) + (b^2*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*log(d + e*x))/(2*a^2) + (b*e*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*a*d) + (b^2*h*n*(log((b*c*x)/(1 - a*c)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*x)/((1 - a*c)*(d + e*x))))*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))^2)/(4*a^2) - (b^2*h*n*(log((b*c*x)/(1 - a*c)) - log(-((e*x)/d)))*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))^2)/(4*a^2) - (b^2*h*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*(n*log(d + e*x) - log(f*(d + e*x)^n)))/(2*a^2) + (b^2*c*log(-((e*x)/d))*(g + h*log(f*(d + e*x)^n)))/(2*a*(1 - a*c)) + (b*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(2*a*x) - (b^2*c*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(2*a*(1 - a*c)) - (b^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*a^2) + (e^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*d^2) - (e^2*h*n*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/(2*d^2) - (b^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*a^2) + (e^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*d^2) + (b^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*a^2) - (e^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*d^2) - (e^2*h*n*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(4*d^2) - (e^2*h*n*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(4*d^2) - (e^2*h*n*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/(2*d^2) + (b^2*g*PolyLog(2, c*(a + b*x)))/(2*a^2) - (b*e*h*n*PolyLog(2, c*(a + b*x)))/(2*a*d) - (e*h*n*PolyLog(2, c*(a + b*x)))/(2*d*x) - (e^2*h*n*log(x)*PolyLog(2, c*(a + b*x)))/(2*d^2) + (e^2*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(2*d^2) - (b^2*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(2*a^2) - ((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(2*x^2) + (b*e*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(2*a*d) + (b^2*g*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) - (b*e*h*n*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(a*d) + (b^2*h*n*(log(d + e*x) - log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) - (b^2*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) + (b^2*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(2*a^2) - (b^2*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(2*a^2) - (b^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*a^2) + (e^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*d^2) - (b^2*c*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*a*(1 - a*c)) + (b^2*c*h*n*PolyLog(2, 1 + (e*x)/d))/(2*a*(1 - a*c)) + (b^2*h*n*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 + (e*x)/d))/(2*a^2) - (e^2*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*d^2) + (e^2*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/(2*d^2) - (b^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*a^2) + (e^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*d^2) - (e^2*h*n*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/(2*d^2) + (b^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*a^2) - (e^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*d^2) - (b^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*a^2) + (e^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*d^2) + (e^2*h*n*PolyLog(3, -((b*x)/a)))/(2*d^2) - (b^2*h*n*PolyLog(3, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) + (b^2*h*n*PolyLog(3, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(2*a^2) - (b^2*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(2*a^2) + (b^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*a^2) - (e^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*d^2) - (b^2*h*n*PolyLog(3, 1 + (e*x)/d))/(2*a^2) - (e^2*h*n*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*d^2) + (e^2*h*n*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/(2*d^2) + (b^2*h*n*PolyLog(3, 1 - c*(a + b*x)))/(2*a^2) + (b^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*a^2) - (e^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*d^2) - (b^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*a^2) + (e^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*d^2)]
@test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^4, x, 78, (b^2*c*e*h*n*log(x))/(2*a*(1 - a*c)*d) - (b^2*c*e*h*n*log(1 - a*c - b*c*x))/(3*a*(1 - a*c)*d) + (b*e*h*n*log(1 - a*c - b*c*x))/(3*a*d*x) - (b^3*g*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(3*a^3) + (b^2*e*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2*d) + (b*e^2*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a*d^2) - (b^2*c*e*h*n*log(d + e*x))/(6*a*(1 - a*c)*d) - (b^3*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*log(d + e*x))/(3*a^3) - (b^2*e*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*a^2*d) - (b*e^2*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*a*d^2) - (b^3*h*n*(log((b*c*x)/(1 - a*c)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*x)/((1 - a*c)*(d + e*x))))*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))^2)/(6*a^3) + (b^3*h*n*(log((b*c*x)/(1 - a*c)) - log(-((e*x)/d)))*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))^2)/(6*a^3) + (b^3*h*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*(n*log(d + e*x) - log(f*(d + e*x)^n)))/(3*a^3) - (b^2*c*(g + h*log(f*(d + e*x)^n)))/(6*a*(1 - a*c)*x) + (b^3*c^2*log(-((e*x)/d))*(g + h*log(f*(d + e*x)^n)))/(6*a*(1 - a*c)^2) - (b^3*c*log(-((e*x)/d))*(g + h*log(f*(d + e*x)^n)))/(3*a^2*(1 - a*c)) + (b*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(6*a*x^2) - (b^2*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(3*a^2*x) - (b^3*c^2*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(6*a*(1 - a*c)^2) + (b^3*c*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(3*a^2*(1 - a*c)) + (b^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*a^3) - (e^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*d^3) + (e^3*h*n*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/(3*d^3) + (b^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*a^3) - (e^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*d^3) - (b^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*a^3) + (e^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*d^3) + (e^3*h*n*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(6*d^3) + (e^3*h*n*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(6*d^3) + (e^3*h*n*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/(3*d^3) - (b^3*g*PolyLog(2, c*(a + b*x)))/(3*a^3) + (b^2*e*h*n*PolyLog(2, c*(a + b*x)))/(6*a^2*d) + (b*e^2*h*n*PolyLog(2, c*(a + b*x)))/(3*a*d^2) - (e*h*n*PolyLog(2, c*(a + b*x)))/(6*d*x^2) + (e^2*h*n*PolyLog(2, c*(a + b*x)))/(3*d^2*x) + (e^3*h*n*log(x)*PolyLog(2, c*(a + b*x)))/(3*d^3) - (e^3*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(3*d^3) + (b^3*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(3*a^3) - ((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(3*x^3) - (b^2*e*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(3*a^2*d) - (b*e^2*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(6*a*d^2) - (b^3*g*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) + (b^2*e*h*n*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2*d) + (b*e^2*h*n*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a*d^2) - (b^3*h*n*(log(d + e*x) - log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) + (b^3*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) - (b^3*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(3*a^3) + (b^3*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(3*a^3) + (b^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*a^3) - (e^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*d^3) - (b^3*c^2*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*a*(1 - a*c)^2) + (b^3*c*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*a^2*(1 - a*c)) + (b^3*c^2*h*n*PolyLog(2, 1 + (e*x)/d))/(6*a*(1 - a*c)^2) - (b^3*c*h*n*PolyLog(2, 1 + (e*x)/d))/(3*a^2*(1 - a*c)) - (b^3*h*n*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 + (e*x)/d))/(3*a^3) + (e^3*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/(3*d^3) - (e^3*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/(3*d^3) + (b^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*a^3) - (e^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*d^3) + (e^3*h*n*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/(3*d^3) - (b^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*a^3) + (e^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*d^3) + (b^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*a^3) - (e^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*d^3) - (e^3*h*n*PolyLog(3, -((b*x)/a)))/(3*d^3) + (b^3*h*n*PolyLog(3, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) - (b^3*h*n*PolyLog(3, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(3*a^3) + (b^3*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(3*a^3) - (b^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*a^3) + (e^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*d^3) + (b^3*h*n*PolyLog(3, 1 + (e*x)/d))/(3*a^3) + (e^3*h*n*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/(3*d^3) - (e^3*h*n*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/(3*d^3) - (b^3*h*n*PolyLog(3, 1 - c*(a + b*x)))/(3*a^3) - (b^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*a^3) + (e^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*d^3) + (b^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*a^3) - (e^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*d^3)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*(a+b*x)*log(1-c*x)*PolyLog(2, c*x)=#
@test_int [x^2*(a + b*x)*log(1 - c*x)*PolyLog(2, c*x), x, 52, (53*b*x)/(192*c^3) + (11*a*x)/(27*c^2) + (49*(3*b + 4*a*c)*x)/(432*c^3) + (29*b*x^2)/(384*c^2) + (5*a*x^2)/(54*c) + (13*(3*b + 4*a*c)*x^2)/(864*c^2) + (2*a*x^3)/81 + (17*b*x^3)/(576*c) + ((3*b + 4*a*c)*x^3)/(324*c) + (3*b*x^4)/256 + (29*b*log(1 - c*x))/(192*c^4) + (5*a*log(1 - c*x))/(27*c^3) + (13*(3*b + 4*a*c)*log(1 - c*x))/(432*c^4) - (b*x^2*log(1 - c*x))/(16*c^2) - (a*x^2*log(1 - c*x))/(9*c) - ((3*b + 4*a*c)*x^2*log(1 - c*x))/(48*c^2) - (2/27)*a*x^3*log(1 - c*x) - (b*x^3*log(1 - c*x))/(24*c) - ((3*b + 4*a*c)*x^3*log(1 - c*x))/(108*c) - (3/64)*b*x^4*log(1 - c*x) + (b*(1 - c*x)*log(1 - c*x))/(8*c^4) + (2*a*(1 - c*x)*log(1 - c*x))/(9*c^3) + ((3*b + 4*a*c)*(1 - c*x)*log(1 - c*x))/(12*c^4) - (b*log(1 - c*x)^2)/(16*c^4) - (a*log(1 - c*x)^2)/(9*c^3) + (1/9)*a*x^3*log(1 - c*x)^2 + (1/16)*b*x^4*log(1 - c*x)^2 - ((3*b + 4*a*c)*log(c*x)*log(1 - c*x)^2)/(12*c^4) - ((3*b + 4*a*c)*x*PolyLog(2, c*x))/(12*c^3) - ((3*b + 4*a*c)*x^2*PolyLog(2, c*x))/(24*c^2) - ((3*b + 4*a*c)*x^3*PolyLog(2, c*x))/(36*c) - (1/16)*b*x^4*PolyLog(2, c*x) - ((3*b + 4*a*c)*log(1 - c*x)*PolyLog(2, c*x))/(12*c^4) + (1/12)*(4*a*x^3 + 3*b*x^4)*log(1 - c*x)*PolyLog(2, c*x) - ((3*b + 4*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x))/(6*c^4) + ((3*b + 4*a*c)*PolyLog(3, 1 - c*x))/(6*c^4)]
@test_int [x^1*(a + b*x)*log(1 - c*x)*PolyLog(2, c*x), x, 40, (4*b*x)/(9*c^2) + (a*x)/c + (5*(2*b + 3*a*c)*x)/(24*c^2) + (b*x^2)/(9*c) + ((2*b + 3*a*c)*x^2)/(48*c) + (b*x^3)/27 + (a*(1 - c*x)^2)/(8*c^2) + (2*b*log(1 - c*x))/(9*c^3) + ((2*b + 3*a*c)*log(1 - c*x))/(24*c^3) - (b*x^2*log(1 - c*x))/(9*c) - ((2*b + 3*a*c)*x^2*log(1 - c*x))/(24*c) - (1/9)*b*x^3*log(1 - c*x) + (2*b*(1 - c*x)*log(1 - c*x))/(9*c^3) + (a*(1 - c*x)*log(1 - c*x))/c^2 + ((2*b + 3*a*c)*(1 - c*x)*log(1 - c*x))/(6*c^3) - (a*(1 - c*x)^2*log(1 - c*x))/(4*c^2) - (b*log(1 - c*x)^2)/(9*c^3) + (1/9)*b*x^3*log(1 - c*x)^2 - (a*(1 - c*x)*log(1 - c*x)^2)/(2*c^2) + (a*(1 - c*x)^2*log(1 - c*x)^2)/(4*c^2) - ((2*b + 3*a*c)*log(c*x)*log(1 - c*x)^2)/(6*c^3) - ((2*b + 3*a*c)*x*PolyLog(2, c*x))/(6*c^2) - ((2*b + 3*a*c)*x^2*PolyLog(2, c*x))/(12*c) - (1/9)*b*x^3*PolyLog(2, c*x) - ((2*b + 3*a*c)*log(1 - c*x)*PolyLog(2, c*x))/(6*c^3) + (1/6)*(3*a*x^2 + 2*b*x^3)*log(1 - c*x)*PolyLog(2, c*x) - ((2*b + 3*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x))/(3*c^3) + ((2*b + 3*a*c)*PolyLog(3, 1 - c*x))/(3*c^3)]
@test_int [x^0*(a + b*x)*log(1 - c*x)*PolyLog(2, c*x), x, 26, 2*a*x + (9*b*x)/(8*c) + ((b + 2*a*c)*x)/(2*c) + (b*x^2)/16 + (b*(1 - c*x)^2)/(8*c^2) + (b*log(1 - c*x))/(8*c^2) - (1/8)*b*x^2*log(1 - c*x) + (b*(1 - c*x)*log(1 - c*x))/c^2 + (2*a*(1 - c*x)*log(1 - c*x))/c + ((b + 2*a*c)*(1 - c*x)*log(1 - c*x))/(2*c^2) - (b*(1 - c*x)^2*log(1 - c*x))/(4*c^2) - (b*(1 - c*x)*log(1 - c*x)^2)/(2*c^2) - (a*(1 - c*x)*log(1 - c*x)^2)/c + (b*(1 - c*x)^2*log(1 - c*x)^2)/(4*c^2) - ((b + 2*a*c)*log(c*x)*log(1 - c*x)^2)/(2*c^2) - ((b + 2*a*c)*x*PolyLog(2, c*x))/(2*c) - (1/4)*b*x^2*PolyLog(2, c*x) - ((b + 2*a*c)*log(1 - c*x)*PolyLog(2, c*x))/(2*c^2) + (1/2)*(2*a*x + b*x^2)*log(1 - c*x)*PolyLog(2, c*x) - ((b + 2*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x))/c^2 + ((b + 2*a*c)*PolyLog(3, 1 - c*x))/c^2]
@test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^1, x, 18, 3*b*x + (3*b*(1 - c*x)*log(1 - c*x))/c - (b*(1 - c*x)*log(1 - c*x)^2)/c - (b*log(c*x)*log(1 - c*x)^2)/c - b*x*PolyLog(2, c*x) - (b*log(1 - c*x)*PolyLog(2, c*x))/c + b*x*log(1 - c*x)*PolyLog(2, c*x) - (1/2)*a*PolyLog(2, c*x)^2 - (2*b*log(1 - c*x)*PolyLog(2, 1 - c*x))/c + (2*b*PolyLog(3, 1 - c*x))/c]
@test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^2, x, 13, (a*(1 - c*x)*log(1 - c*x)^2)/x + a*c*log(c*x)*log(1 - c*x)^2 - 2*a*c*PolyLog(2, c*x) + a*c*log(1 - c*x)*PolyLog(2, c*x) - (a*log(1 - c*x)*PolyLog(2, c*x))/x - (1/2)*b*PolyLog(2, c*x)^2 + 2*a*c*log(1 - c*x)*PolyLog(2, 1 - c*x) - a*c*PolyLog(3, c*x) - 2*a*c*PolyLog(3, 1 - c*x)]
@test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^3, x, 30, (-a)*c^2*log(x) + a*c^2*log(1 - c*x) - (a*c*log(1 - c*x))/x - (1/4)*a*c^2*log(1 - c*x)^2 + (a*log(1 - c*x)^2)/(4*x^2) + (b*(1 - c*x)*log(1 - c*x)^2)/x - (b^2*log(c*x)*log(1 - c*x)^2)/(2*a) + ((b + a*c)^2*log(c*x)*log(1 - c*x)^2)/(2*a) - 2*b*c*PolyLog(2, c*x) - (1/2)*a*c^2*PolyLog(2, c*x) + (a*c*PolyLog(2, c*x))/(2*x) + ((b + a*c)^2*log(1 - c*x)*PolyLog(2, c*x))/(2*a) - ((a + b*x)^2*log(1 - c*x)*PolyLog(2, c*x))/(2*a*x^2) - (b^2*log(1 - c*x)*PolyLog(2, 1 - c*x))/a + ((b + a*c)^2*log(1 - c*x)*PolyLog(2, 1 - c*x))/a - (1/2)*c*(2*b + a*c)*PolyLog(3, c*x) + (b^2*PolyLog(3, 1 - c*x))/a - ((b + a*c)^2*PolyLog(3, 1 - c*x))/a]
@test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^4, x, 41, (7*a*c^2)/(36*x) - (1/2)*b*c^2*log(x) - (5/12)*a*c^3*log(x) - (1/6)*c^2*(3*b + 2*a*c)*log(x) + (1/2)*b*c^2*log(1 - c*x) + (5/12)*a*c^3*log(1 - c*x) + (1/6)*c^2*(3*b + 2*a*c)*log(1 - c*x) - (7*a*c*log(1 - c*x))/(36*x^2) - (b*c*log(1 - c*x))/(2*x) - (2*a*c^2*log(1 - c*x))/(9*x) - (c*(3*b + 2*a*c)*log(1 - c*x))/(6*x) - (1/4)*b*c^2*log(1 - c*x)^2 - (1/9)*a*c^3*log(1 - c*x)^2 + (a*log(1 - c*x)^2)/(9*x^3) + (b*log(1 - c*x)^2)/(4*x^2) + (1/6)*c^2*(3*b + 2*a*c)*log(c*x)*log(1 - c*x)^2 - (1/2)*b*c^2*PolyLog(2, c*x) - (2/9)*a*c^3*PolyLog(2, c*x) + (a*c*PolyLog(2, c*x))/(6*x^2) + (c*(3*b + 2*a*c)*PolyLog(2, c*x))/(6*x) + (1/6)*c^2*(3*b + 2*a*c)*log(1 - c*x)*PolyLog(2, c*x) - (1/6)*((2*a)/x^3 + (3*b)/x^2)*log(1 - c*x)*PolyLog(2, c*x) + (1/3)*c^2*(3*b + 2*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/6)*c^2*(3*b + 2*a*c)*PolyLog(3, c*x) - (1/3)*c^2*(3*b + 2*a*c)*PolyLog(3, 1 - c*x)]
@test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^5, x, 51, (5*a*c^2)/(144*x^2) + (b*c^2)/(9*x) + (19*a*c^3)/(144*x) + (c^2*(4*b + 3*a*c))/(48*x) - (1/3)*b*c^3*log(x) - (37/144)*a*c^4*log(x) - (5/48)*c^3*(4*b + 3*a*c)*log(x) + (1/3)*b*c^3*log(1 - c*x) + (37/144)*a*c^4*log(1 - c*x) + (5/48)*c^3*(4*b + 3*a*c)*log(1 - c*x) - (5*a*c*log(1 - c*x))/(72*x^3) - (b*c*log(1 - c*x))/(9*x^2) - (a*c^2*log(1 - c*x))/(16*x^2) - (c*(4*b + 3*a*c)*log(1 - c*x))/(48*x^2) - (2*b*c^2*log(1 - c*x))/(9*x) - (a*c^3*log(1 - c*x))/(8*x) - (c^2*(4*b + 3*a*c)*log(1 - c*x))/(12*x) - (1/9)*b*c^3*log(1 - c*x)^2 - (1/16)*a*c^4*log(1 - c*x)^2 + (a*log(1 - c*x)^2)/(16*x^4) + (b*log(1 - c*x)^2)/(9*x^3) + (1/12)*c^3*(4*b + 3*a*c)*log(c*x)*log(1 - c*x)^2 - (2/9)*b*c^3*PolyLog(2, c*x) - (1/8)*a*c^4*PolyLog(2, c*x) + (a*c*PolyLog(2, c*x))/(12*x^3) + (c*(4*b + 3*a*c)*PolyLog(2, c*x))/(24*x^2) + (c^2*(4*b + 3*a*c)*PolyLog(2, c*x))/(12*x) + (1/12)*c^3*(4*b + 3*a*c)*log(1 - c*x)*PolyLog(2, c*x) - (1/12)*((3*a)/x^4 + (4*b)/x^3)*log(1 - c*x)*PolyLog(2, c*x) + (1/6)*c^3*(4*b + 3*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/12)*c^3*(4*b + 3*a*c)*PolyLog(3, c*x) - (1/6)*c^3*(4*b + 3*a*c)*PolyLog(3, 1 - c*x)]
#= ::Subsection::Closed:: =#
#=Integrands*of*the*form*x^m*(a+b*x+c*x^2)*log(1-d*x)*PolyLog(2, d*x)=#
@test_int [x^1*(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x), x, 60, (53*c*x)/(192*d^3) + (11*b*x)/(27*d^2) + (a*x)/d + ((3*c + 4*b*d)*x)/(108*d^3) + (5*(3*c + 4*b*d + 6*a*d^2)*x)/(48*d^3) + (29*c*x^2)/(384*d^2) + (5*b*x^2)/(54*d) + ((3*c + 4*b*d)*x^2)/(216*d^2) + ((3*c + 4*b*d + 6*a*d^2)*x^2)/(96*d^2) + (2*b*x^3)/81 + (17*c*x^3)/(576*d) + ((3*c + 4*b*d)*x^3)/(324*d) + (3*c*x^4)/256 + (a*(1 - d*x)^2)/(8*d^2) + (29*c*log(1 - d*x))/(192*d^4) + (5*b*log(1 - d*x))/(27*d^3) + ((3*c + 4*b*d)*log(1 - d*x))/(108*d^4) + ((3*c + 4*b*d + 6*a*d^2)*log(1 - d*x))/(48*d^4) - (c*x^2*log(1 - d*x))/(16*d^2) - (b*x^2*log(1 - d*x))/(9*d) - ((3*c + 4*b*d + 6*a*d^2)*x^2*log(1 - d*x))/(48*d^2) - (2/27)*b*x^3*log(1 - d*x) - (c*x^3*log(1 - d*x))/(24*d) - ((3*c + 4*b*d)*x^3*log(1 - d*x))/(108*d) - (3/64)*c*x^4*log(1 - d*x) + (c*(1 - d*x)*log(1 - d*x))/(8*d^4) + (2*b*(1 - d*x)*log(1 - d*x))/(9*d^3) + (a*(1 - d*x)*log(1 - d*x))/d^2 + ((3*c + 4*b*d + 6*a*d^2)*(1 - d*x)*log(1 - d*x))/(12*d^4) - (a*(1 - d*x)^2*log(1 - d*x))/(4*d^2) - (c*log(1 - d*x)^2)/(16*d^4) - (b*log(1 - d*x)^2)/(9*d^3) + (1/9)*b*x^3*log(1 - d*x)^2 + (1/16)*c*x^4*log(1 - d*x)^2 - (a*(1 - d*x)*log(1 - d*x)^2)/(2*d^2) + (a*(1 - d*x)^2*log(1 - d*x)^2)/(4*d^2) - ((3*c + 4*b*d + 6*a*d^2)*log(d*x)*log(1 - d*x)^2)/(12*d^4) - ((3*c + 4*b*d + 6*a*d^2)*x*PolyLog(2, d*x))/(12*d^3) - ((3*c + 4*b*d + 6*a*d^2)*x^2*PolyLog(2, d*x))/(24*d^2) - ((3*c + 4*b*d)*x^3*PolyLog(2, d*x))/(36*d) - (1/16)*c*x^4*PolyLog(2, d*x) - ((3*c + 4*b*d + 6*a*d^2)*log(1 - d*x)*PolyLog(2, d*x))/(12*d^4) + (1/12)*(6*a*x^2 + 4*b*x^3 + 3*c*x^4)*log(1 - d*x)*PolyLog(2, d*x) - ((3*c + 4*b*d + 6*a*d^2)*log(1 - d*x)*PolyLog(2, 1 - d*x))/(6*d^4) + ((3*c + 4*b*d + 6*a*d^2)*PolyLog(3, 1 - d*x))/(6*d^4)]
@test_int [x^0*(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x), x, 43, 2*a*x + (4*c*x)/(9*d^2) + (b*x)/d + ((2*c + 3*b*d)*x)/(24*d^2) + ((2*c + 3*d*(b + 2*a*d))*x)/(6*d^2) + (c*x^2)/(9*d) + ((2*c + 3*b*d)*x^2)/(48*d) + (c*x^3)/27 + (b*(1 - d*x)^2)/(8*d^2) + (2*c*log(1 - d*x))/(9*d^3) + ((2*c + 3*b*d)*log(1 - d*x))/(24*d^3) - (c*x^2*log(1 - d*x))/(9*d) - ((2*c + 3*b*d)*x^2*log(1 - d*x))/(24*d) - (1/9)*c*x^3*log(1 - d*x) + (2*c*(1 - d*x)*log(1 - d*x))/(9*d^3) + (b*(1 - d*x)*log(1 - d*x))/d^2 + (2*a*(1 - d*x)*log(1 - d*x))/d + ((2*c + 3*d*(b + 2*a*d))*(1 - d*x)*log(1 - d*x))/(6*d^3) - (b*(1 - d*x)^2*log(1 - d*x))/(4*d^2) - (c*log(1 - d*x)^2)/(9*d^3) + (1/9)*c*x^3*log(1 - d*x)^2 - (b*(1 - d*x)*log(1 - d*x)^2)/(2*d^2) - (a*(1 - d*x)*log(1 - d*x)^2)/d + (b*(1 - d*x)^2*log(1 - d*x)^2)/(4*d^2) - ((2*c + 3*d*(b + 2*a*d))*log(d*x)*log(1 - d*x)^2)/(6*d^3) - ((2*c + 3*d*(b + 2*a*d))*x*PolyLog(2, d*x))/(6*d^2) - ((2*c + 3*b*d)*x^2*PolyLog(2, d*x))/(12*d) - (1/9)*c*x^3*PolyLog(2, d*x) - ((2*c + 3*d*(b + 2*a*d))*log(1 - d*x)*PolyLog(2, d*x))/(6*d^3) + (1/6)*(6*a*x + 3*b*x^2 + 2*c*x^3)*log(1 - d*x)*PolyLog(2, d*x) - ((2*c + 3*d*(b + 2*a*d))*log(1 - d*x)*PolyLog(2, 1 - d*x))/(3*d^3) + ((2*c + 3*d*(b + 2*a*d))*PolyLog(3, 1 - d*x))/(3*d^3)]
@test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^1, x, 29, 2*b*x + (9*c*x)/(8*d) + ((c + 2*b*d)*x)/(2*d) + (c*x^2)/16 + (c*(1 - d*x)^2)/(8*d^2) + (c*log(1 - d*x))/(8*d^2) - (1/8)*c*x^2*log(1 - d*x) + (c*(1 - d*x)*log(1 - d*x))/d^2 + (2*b*(1 - d*x)*log(1 - d*x))/d + ((c + 2*b*d)*(1 - d*x)*log(1 - d*x))/(2*d^2) - (c*(1 - d*x)^2*log(1 - d*x))/(4*d^2) - (c*(1 - d*x)*log(1 - d*x)^2)/(2*d^2) - (b*(1 - d*x)*log(1 - d*x)^2)/d + (c*(1 - d*x)^2*log(1 - d*x)^2)/(4*d^2) - ((c + 2*b*d)*log(d*x)*log(1 - d*x)^2)/(2*d^2) - ((c + 2*b*d)*x*PolyLog(2, d*x))/(2*d) - (1/4)*c*x^2*PolyLog(2, d*x) - ((c + 2*b*d)*log(1 - d*x)*PolyLog(2, d*x))/(2*d^2) + (1/2)*(2*b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x) - (1/2)*a*PolyLog(2, d*x)^2 - ((c + 2*b*d)*log(1 - d*x)*PolyLog(2, 1 - d*x))/d^2 + ((c + 2*b*d)*PolyLog(3, 1 - d*x))/d^2]
@test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^2, x, 19, 3*c*x + (3*c*(1 - d*x)*log(1 - d*x))/d - (c*(1 - d*x)*log(1 - d*x)^2)/d + (a*(1 - d*x)*log(1 - d*x)^2)/x + (a - c/d^2)*d*log(d*x)*log(1 - d*x)^2 - 2*a*d*PolyLog(2, d*x) - c*x*PolyLog(2, d*x) + (a - c/d^2)*d*log(1 - d*x)*PolyLog(2, d*x) - (a/x - c*x)*log(1 - d*x)*PolyLog(2, d*x) - (1/2)*b*PolyLog(2, d*x)^2 + 2*(a - c/d^2)*d*log(1 - d*x)*PolyLog(2, 1 - d*x) - a*d*PolyLog(3, d*x) - 2*(a - c/d^2)*d*PolyLog(3, 1 - d*x)]
@test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^3, x, 32, (-a)*d^2*log(x) + a*d^2*log(1 - d*x) - (a*d*log(1 - d*x))/x - (1/4)*a*d^2*log(1 - d*x)^2 + (a*log(1 - d*x)^2)/(4*x^2) + (b*(1 - d*x)*log(1 - d*x)^2)/x - (b^2*log(d*x)*log(1 - d*x)^2)/(2*a) + ((b + a*d)^2*log(d*x)*log(1 - d*x)^2)/(2*a) - 2*b*d*PolyLog(2, d*x) - (1/2)*a*d^2*PolyLog(2, d*x) + (a*d*PolyLog(2, d*x))/(2*x) + ((b + a*d)^2*log(1 - d*x)*PolyLog(2, d*x))/(2*a) - ((a + b*x)^2*log(1 - d*x)*PolyLog(2, d*x))/(2*a*x^2) - (1/2)*c*PolyLog(2, d*x)^2 - (b^2*log(1 - d*x)*PolyLog(2, 1 - d*x))/a + ((b + a*d)^2*log(1 - d*x)*PolyLog(2, 1 - d*x))/a - (1/2)*d*(2*b + a*d)*PolyLog(3, d*x) + (b^2*PolyLog(3, 1 - d*x))/a - ((b + a*d)^2*PolyLog(3, 1 - d*x))/a]
@test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^4, x, 43, (7*a*d^2)/(36*x) - (1/2)*b*d^2*log(x) - (5/12)*a*d^3*log(x) - (1/6)*d^2*(3*b + 2*a*d)*log(x) + (1/2)*b*d^2*log(1 - d*x) + (5/12)*a*d^3*log(1 - d*x) + (1/6)*d^2*(3*b + 2*a*d)*log(1 - d*x) - (7*a*d*log(1 - d*x))/(36*x^2) - (b*d*log(1 - d*x))/(2*x) - (2*a*d^2*log(1 - d*x))/(9*x) - (d*(3*b + 2*a*d)*log(1 - d*x))/(6*x) - (1/4)*b*d^2*log(1 - d*x)^2 - (1/9)*a*d^3*log(1 - d*x)^2 + (a*log(1 - d*x)^2)/(9*x^3) + (b*log(1 - d*x)^2)/(4*x^2) + (c*(1 - d*x)*log(1 - d*x)^2)/x + (1/6)*d*(6*c + d*(3*b + 2*a*d))*log(d*x)*log(1 - d*x)^2 - 2*c*d*PolyLog(2, d*x) - (1/2)*b*d^2*PolyLog(2, d*x) - (2/9)*a*d^3*PolyLog(2, d*x) + (a*d*PolyLog(2, d*x))/(6*x^2) + (d*(3*b + 2*a*d)*PolyLog(2, d*x))/(6*x) + (1/6)*d*(6*c + d*(3*b + 2*a*d))*log(1 - d*x)*PolyLog(2, d*x) - (1/6)*((2*a)/x^3 + (3*b)/x^2 + (6*c)/x)*log(1 - d*x)*PolyLog(2, d*x) + (1/3)*d*(6*c + d*(3*b + 2*a*d))*log(1 - d*x)*PolyLog(2, 1 - d*x) - (1/6)*d*(6*c + d*(3*b + 2*a*d))*PolyLog(3, d*x) - (1/3)*d*(6*c + d*(3*b + 2*a*d))*PolyLog(3, 1 - d*x)]
@test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^5, x, 61, (5*a*d^2)/(144*x^2) + (b*d^2)/(9*x) + (19*a*d^3)/(144*x) + (d^2*(4*b + 3*a*d))/(48*x) - (1/2)*c*d^2*log(x) - (1/3)*b*d^3*log(x) - (37/144)*a*d^4*log(x) - (1/48)*d^3*(4*b + 3*a*d)*log(x) - (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(x) + (1/2)*c*d^2*log(1 - d*x) + (1/3)*b*d^3*log(1 - d*x) + (37/144)*a*d^4*log(1 - d*x) + (1/48)*d^3*(4*b + 3*a*d)*log(1 - d*x) + (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(1 - d*x) - (5*a*d*log(1 - d*x))/(72*x^3) - (b*d*log(1 - d*x))/(9*x^2) - (a*d^2*log(1 - d*x))/(16*x^2) - (d*(4*b + 3*a*d)*log(1 - d*x))/(48*x^2) - (c*d*log(1 - d*x))/(2*x) - (2*b*d^2*log(1 - d*x))/(9*x) - (a*d^3*log(1 - d*x))/(8*x) - (d*(6*c + d*(4*b + 3*a*d))*log(1 - d*x))/(12*x) - (1/4)*c*d^2*log(1 - d*x)^2 - (1/9)*b*d^3*log(1 - d*x)^2 - (1/16)*a*d^4*log(1 - d*x)^2 + (a*log(1 - d*x)^2)/(16*x^4) + (b*log(1 - d*x)^2)/(9*x^3) + (c*log(1 - d*x)^2)/(4*x^2) + (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(d*x)*log(1 - d*x)^2 - (1/2)*c*d^2*PolyLog(2, d*x) - (2/9)*b*d^3*PolyLog(2, d*x) - (1/8)*a*d^4*PolyLog(2, d*x) + (a*d*PolyLog(2, d*x))/(12*x^3) + (d*(4*b + 3*a*d)*PolyLog(2, d*x))/(24*x^2) + (d*(6*c + d*(4*b + 3*a*d))*PolyLog(2, d*x))/(12*x) + (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(1 - d*x)*PolyLog(2, d*x) - (1/12)*((3*a)/x^4 + (4*b)/x^3 + (6*c)/x^2)*log(1 - d*x)*PolyLog(2, d*x) + (1/6)*d^2*(6*c + d*(4*b + 3*a*d))*log(1 - d*x)*PolyLog(2, 1 - d*x) - (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*PolyLog(3, d*x) - (1/6)*d^2*(6*c + d*(4*b + 3*a*d))*PolyLog(3, 1 - d*x)]
end
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] | 1.464519 | 63,541 |
import MixedModels: LinearMixedModel,
setθ!,
updateL!
import RCall: rcopy,
RClass,
rcopytype,
reval,
S4Sxp,
sexp,
protect,
unprotect,
sexpclass,
@rput,
@rget,
@R_str
# if RCall is available, then so is DataFrames
import DataFrames: DataFrame
import Tables: ColumnTable
# from R
# note that weights are not extracted
# TODO: document weights issue and warn
function rcopy(::Type{LinearMixedModel}, s::Ptr{S4Sxp})
# these try blocks should probably be changed to an examination of the indices
# this only extracts the name within the call, not the actual weights
try
wts = rcopy(s[:call][:weights])
@error "weights are not supported"
catch err
if !isa(err, BoundsError) # this is the error we were expecting
rethrow(err)
end
# no weights defined, we continue on our way
end
try
contrasts = rcopy(s[:call][:contrasts])
@error "Contrasts must be specified in the dataframe, not the lmer() call"
catch err
if !isa(err, BoundsError) # this is the error we were expecting
rethrow(err)
end
# no extra contrasts defined, we continue on our way
end
# for some reason this doesn't always give a formula with lmerTest
#f = rcopy(s[:call][:formula])
f = rcopy(R"as.formula($(s)@call$formula)")
data = rcopy(s[:frame])
contrasts = get_r_contrasts(s[:frame])
θ = rcopyarray(s[:theta])
reml = rcopy(s[:devcomp][:dims][:REML]) ≠ 0
m = LinearMixedModel(f, data, contrasts=contrasts)
if length(θ) != length(m.θ)
@error """You're probably using || in R with a categorical variable,
whose translation is currently unsupported with MixedModels 3.0."""
throw(ArgumentError("Parameter vectors in R and Julia are different sizes."))
end
θ = _reorder_theta_from_lme4(θ, m)
m.optsum.REML = reml
m.optsum.feval = rcopy(s[:optinfo][:feval])
# I'm wondering if this be filled in from the Julia side
m.optsum.final = rcopyarray(s[:optinfo][:val])
m.optsum.optimizer = Symbol("$(rcopy(s[:optinfo][:optimizer])) (lme4)")
m.optsum.returnvalue = rcopy(s[:optinfo][:conv][:opt]) == 0 ? :FAILURE : :SUCCESS
m.optsum.fmin = reml ? rcopy(s[:devcomp][:cmp][:REML]) : rcopy(s[:devcomp][:cmp][:dev])
updateL!(setθ!(m, θ))
end
rcopytype(::Type{RClass{:lmerMod}}, s::Ptr{S4Sxp}) = LinearMixedModel
# add lmerTest::lmer and afex::lmer_alt support
rcopytype(::Type{RClass{:lmerModLmerTest}}, s::Ptr{S4Sxp}) = LinearMixedModel
# TODO: fix some conversions -- Julia->R->Julia roundtrip currently due to
# ERROR: REvalError: Error in function (x, value, pos = -1, envir = as.environment(pos), inherits = FALSE, :
# SET_VECTOR_ELT() can only be applied to a 'list', not a 'character'
function sexp(::Type{RClass{:lmerMod}}, x::Tuple{LinearMixedModel{T}, DataFrame}) where T
m, tbl = x
if !isempty(m.sqrtwts)
@error "weights are not currently supported"
end
m.optsum.feval > 0 || throw(ArgumentError("Model must be fitted"))
jellyme4_data = tbl
formula = convert_julia_to_r(m.formula)
θ = m.θ
rsteps = 1
REML = m.optsum.REML ? "TRUE" : "FALSE"
jellyme4_theta = _reorder_theta_to_lme4(m)
fval = m.optsum.fmin
feval = m.optsum.feval
conv = m.optsum.returnvalue == :SUCCESS ? 0 : 1
optimizer = String(m.optsum.optimizer)
message = "fit with MixedModels.jl"
@rput jellyme4_data
@rput jellyme4_theta
set_r_contrasts!("jellyme4_data", m.formula)
r = """
jellyme4_mod <- $LMER(formula = $(formula),
data=jellyme4_data,
REML=$(REML),
control=lme4::lmerControl(optimizer="nloptwrap",
optCtrl=list(maxeval=$(rsteps)),
calc.derivs=FALSE,
check.nobs.vs.nRE= "warning"),
start=list(theta=jellyme4_theta))
jellyme4_mod@optinfo\$feval <- $(feval)
jellyme4_mod@optinfo\$message <- "$(message)"
jellyme4_mod@optinfo\$optimizer <- "$(optimizer)"
jellyme4_mod
"""
r = reval(r)
r = protect(sexp(r))
unprotect(1)
r
end
sexpclass(x::Tuple{LinearMixedModel{T}, DataFrame}) where T = LMER in ("afex::lmer_alt", "lmer_alt") ? RClass{:lmerModLmerTest} : RClass{:lmerMod}
sexp(::Type{RClass{:lmerModLmerTest}}, x::Tuple{LinearMixedModel{T}, DataFrame}) where T = sexp(RClass{:lmerMod}, x)
# generalize to ColumnTable, which is what MixedModels actually requires
function sexp(ss::Type{RClass{:lmerMod}}, x::Tuple{LinearMixedModel{T}, ColumnTable}) where T
m, t = x
sexp(ss, (m, DataFrame(t)))
end
sexpclass(x::Tuple{LinearMixedModel{T}, ColumnTable}) where T = RClass{:lmerMod}
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] | 2.123685 | 2,377 |
# Raytracer.jl
# Raytracing for the generation of photorealistic images in Julia
# Copyright (c) 2021 Samuele Colombo, Paolo Galli
# Point light sources used by point-light tracer
@doc raw"""
PointLight
A point light (used by [`PointLightRenderer`](@ref)).
This type holds information about a point light.
# Fields
- `position::Point`: a [`Point`](@ref) object holding the position of the point light in 3D space.
- `color::RGB{Float32}`: the color of the point light.
- `linear_radius::Float32`: radius of the source, used to compute solid angle subtended by the light.
If `linear_radius` is non-zero, it is used to compute the solid angle subtended by the light at a given
distance `d` through the formula:
```math
\left(\frac{\mathrm{linear\_radius}}{d}\right)^2
```
"""
Base.@kwdef struct PointLight
position::Point = ORIGIN
color::RGB{Float32} = WHITE
linear_radius::Float32 = 0f0
end
@doc """
PointLight(position::Point, color::RGB{Float32}, linear_radius::Float32)
Constructor for a [`PointLight`](@ref) instance.
""" PointLight(::Point, ::RGB{Float32}, ::Float32)
@doc """
PointLight(; position::Point = ORIGIN,
color::RGB{Float32} = WHITE,
linear_radius::Float32 = 0f0)
Constructor for a [`PointLight`](@ref) instance.
If no parameter is specified, it return a white point light in the origin with no radius.
""" PointLight(; ::Point, ::RGB{Float32}, ::Float32)
"""
Lights
Alias of `Vector{PointLight}`, to store a list of [`PointLight`](@ref) sources.
"""
const Lights = Vector{PointLight}
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] | 2.945896 | 536 |
using MagneticLocSuchowiak
using Test
@testset "MagneticLocSuchowiak.jl" begin
# Write your tests here.
end
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# syntax: proto3
using ProtoBuf
import ProtoBuf.meta
mutable struct MultilineChartContent <: ProtoType
__protobuf_jl_internal_meta::ProtoMeta
__protobuf_jl_internal_values::Dict{Symbol,Any}
__protobuf_jl_internal_defaultset::Set{Symbol}
function MultilineChartContent(; kwargs...)
obj = new(meta(MultilineChartContent), Dict{Symbol,Any}(), Set{Symbol}())
values = obj.__protobuf_jl_internal_values
symdict = obj.__protobuf_jl_internal_meta.symdict
for nv in kwargs
fldname, fldval = nv
fldtype = symdict[fldname].jtyp
(fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname))
values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval)
end
obj
end
end # mutable struct MultilineChartContent
const __meta_MultilineChartContent = Ref{ProtoMeta}()
function meta(::Type{MultilineChartContent})
ProtoBuf.metalock() do
if !isassigned(__meta_MultilineChartContent)
__meta_MultilineChartContent[] = target = ProtoMeta(MultilineChartContent)
allflds = Pair{Symbol,Union{Type,String}}[:tag => Base.Vector{AbstractString}]
meta(target, MultilineChartContent, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES)
end
__meta_MultilineChartContent[]
end
end
function Base.getproperty(obj::MultilineChartContent, name::Symbol)
if name === :tag
return (obj.__protobuf_jl_internal_values[name])::Base.Vector{AbstractString}
else
getfield(obj, name)
end
end
mutable struct MarginChartContent_Series <: ProtoType
__protobuf_jl_internal_meta::ProtoMeta
__protobuf_jl_internal_values::Dict{Symbol,Any}
__protobuf_jl_internal_defaultset::Set{Symbol}
function MarginChartContent_Series(; kwargs...)
obj = new(meta(MarginChartContent_Series), Dict{Symbol,Any}(), Set{Symbol}())
values = obj.__protobuf_jl_internal_values
symdict = obj.__protobuf_jl_internal_meta.symdict
for nv in kwargs
fldname, fldval = nv
fldtype = symdict[fldname].jtyp
(fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname))
values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval)
end
obj
end
end # mutable struct MarginChartContent_Series
const __meta_MarginChartContent_Series = Ref{ProtoMeta}()
function meta(::Type{MarginChartContent_Series})
ProtoBuf.metalock() do
if !isassigned(__meta_MarginChartContent_Series)
__meta_MarginChartContent_Series[] = target = ProtoMeta(MarginChartContent_Series)
allflds = Pair{Symbol,Union{Type,String}}[:value => AbstractString, :lower => AbstractString, :upper => AbstractString]
meta(target, MarginChartContent_Series, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES)
end
__meta_MarginChartContent_Series[]
end
end
function Base.getproperty(obj::MarginChartContent_Series, name::Symbol)
if name === :value
return (obj.__protobuf_jl_internal_values[name])::AbstractString
elseif name === :lower
return (obj.__protobuf_jl_internal_values[name])::AbstractString
elseif name === :upper
return (obj.__protobuf_jl_internal_values[name])::AbstractString
else
getfield(obj, name)
end
end
mutable struct MarginChartContent <: ProtoType
__protobuf_jl_internal_meta::ProtoMeta
__protobuf_jl_internal_values::Dict{Symbol,Any}
__protobuf_jl_internal_defaultset::Set{Symbol}
function MarginChartContent(; kwargs...)
obj = new(meta(MarginChartContent), Dict{Symbol,Any}(), Set{Symbol}())
values = obj.__protobuf_jl_internal_values
symdict = obj.__protobuf_jl_internal_meta.symdict
for nv in kwargs
fldname, fldval = nv
fldtype = symdict[fldname].jtyp
(fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname))
values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval)
end
obj
end
end # mutable struct MarginChartContent
const __meta_MarginChartContent = Ref{ProtoMeta}()
function meta(::Type{MarginChartContent})
ProtoBuf.metalock() do
if !isassigned(__meta_MarginChartContent)
__meta_MarginChartContent[] = target = ProtoMeta(MarginChartContent)
allflds = Pair{Symbol,Union{Type,String}}[:series => Base.Vector{MarginChartContent_Series}]
meta(target, MarginChartContent, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES)
end
__meta_MarginChartContent[]
end
end
function Base.getproperty(obj::MarginChartContent, name::Symbol)
if name === :series
return (obj.__protobuf_jl_internal_values[name])::Base.Vector{MarginChartContent_Series}
else
getfield(obj, name)
end
end
mutable struct Chart <: ProtoType
__protobuf_jl_internal_meta::ProtoMeta
__protobuf_jl_internal_values::Dict{Symbol,Any}
__protobuf_jl_internal_defaultset::Set{Symbol}
function Chart(; kwargs...)
obj = new(meta(Chart), Dict{Symbol,Any}(), Set{Symbol}())
values = obj.__protobuf_jl_internal_values
symdict = obj.__protobuf_jl_internal_meta.symdict
for nv in kwargs
fldname, fldval = nv
fldtype = symdict[fldname].jtyp
(fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname))
values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval)
end
obj
end
end # mutable struct Chart
const __meta_Chart = Ref{ProtoMeta}()
function meta(::Type{Chart})
ProtoBuf.metalock() do
if !isassigned(__meta_Chart)
__meta_Chart[] = target = ProtoMeta(Chart)
allflds = Pair{Symbol,Union{Type,String}}[:title => AbstractString, :multiline => MultilineChartContent, :margin => MarginChartContent]
oneofs = Int[0,1,1]
oneof_names = Symbol[Symbol("content")]
meta(target, Chart, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, oneofs, oneof_names)
end
__meta_Chart[]
end
end
function Base.getproperty(obj::Chart, name::Symbol)
if name === :title
return (obj.__protobuf_jl_internal_values[name])::AbstractString
elseif name === :multiline
return (obj.__protobuf_jl_internal_values[name])::MultilineChartContent
elseif name === :margin
return (obj.__protobuf_jl_internal_values[name])::MarginChartContent
else
getfield(obj, name)
end
end
mutable struct Category <: ProtoType
__protobuf_jl_internal_meta::ProtoMeta
__protobuf_jl_internal_values::Dict{Symbol,Any}
__protobuf_jl_internal_defaultset::Set{Symbol}
function Category(; kwargs...)
obj = new(meta(Category), Dict{Symbol,Any}(), Set{Symbol}())
values = obj.__protobuf_jl_internal_values
symdict = obj.__protobuf_jl_internal_meta.symdict
for nv in kwargs
fldname, fldval = nv
fldtype = symdict[fldname].jtyp
(fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname))
values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval)
end
obj
end
end # mutable struct Category
const __meta_Category = Ref{ProtoMeta}()
function meta(::Type{Category})
ProtoBuf.metalock() do
if !isassigned(__meta_Category)
__meta_Category[] = target = ProtoMeta(Category)
allflds = Pair{Symbol,Union{Type,String}}[:title => AbstractString, :chart => Base.Vector{Chart}, :closed => Bool]
meta(target, Category, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES)
end
__meta_Category[]
end
end
function Base.getproperty(obj::Category, name::Symbol)
if name === :title
return (obj.__protobuf_jl_internal_values[name])::AbstractString
elseif name === :chart
return (obj.__protobuf_jl_internal_values[name])::Base.Vector{Chart}
elseif name === :closed
return (obj.__protobuf_jl_internal_values[name])::Bool
else
getfield(obj, name)
end
end
mutable struct Layout <: ProtoType
__protobuf_jl_internal_meta::ProtoMeta
__protobuf_jl_internal_values::Dict{Symbol,Any}
__protobuf_jl_internal_defaultset::Set{Symbol}
function Layout(; kwargs...)
obj = new(meta(Layout), Dict{Symbol,Any}(), Set{Symbol}())
values = obj.__protobuf_jl_internal_values
symdict = obj.__protobuf_jl_internal_meta.symdict
for nv in kwargs
fldname, fldval = nv
fldtype = symdict[fldname].jtyp
(fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname))
values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval)
end
obj
end
end # mutable struct Layout
const __meta_Layout = Ref{ProtoMeta}()
function meta(::Type{Layout})
ProtoBuf.metalock() do
if !isassigned(__meta_Layout)
__meta_Layout[] = target = ProtoMeta(Layout)
allflds = Pair{Symbol,Union{Type,String}}[:version => Int32, :category => Base.Vector{Category}]
meta(target, Layout, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES)
end
__meta_Layout[]
end
end
function Base.getproperty(obj::Layout, name::Symbol)
if name === :version
return (obj.__protobuf_jl_internal_values[name])::Int32
elseif name === :category
return (obj.__protobuf_jl_internal_values[name])::Base.Vector{Category}
else
getfield(obj, name)
end
end
export Chart, MultilineChartContent, MarginChartContent_Series, MarginChartContent, Category, Layout
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] | 2.290506 | 4,561 |
include("model.jl")
# particle marginal metropolis-hastings
@compiled @gen function var_proposal(prev)
var_x::Float64 = get_assignment(prev)[:var_x]
var_y::Float64 = get_assignment(prev)[:var_y]
#@addr(normal(var_x, sqrt(0.15)), :var_x)
#@addr(normal(var_y, sqrt(0.08)), :var_y)
@addr(normal(var_x, sqrt(0.5)), :var_x)
@addr(normal(var_y, sqrt(0.5)), :var_y)
end
@gen function observer(ys)
for (i, y) in enumerate(ys)
@addr(dirac(y), :hmm => :y => i)
end
end
load_generated_functions()
##########
function strip_lineinfo(expr::Expr)
@assert !(expr.head == :line)
new_args = []
for arg in expr.args
if (isa(arg, Expr) && arg.head == :line) || isa(arg, LineNumberNode)
elseif isa(arg, Expr) && arg.head == :block
stripped = strip_lineinfo(arg)
append!(new_args, stripped.args)
else
push!(new_args, strip_lineinfo(arg))
end
end
Expr(expr.head, new_args...)
end
function strip_lineinfo(expr)
expr
end
println("\n######################################################################\n")
obs = get_assignment(simulate(obs_sub, (1.2,)))
#println(strip_lineinfo(
#Gen.codegen_generate(typeof(kernel), Tuple{Int,State,Params}, typeof(obs), Nothing)))
import InteractiveUtils
InteractiveUtils.code_warntype(
generate,
(typeof(kernel), Tuple{Int,State,Params}, typeof(obs), Nothing))
println("\n######################################################################\n")
function initial_collapsed_trace(ys)
T = length(ys)
constraints = get_assignment(simulate(observer, (ys,)))
(trace, weight) = generate(model_collapsed, (T,), constraints)
trace
end
import Random
Random.seed!(1)
# generate synthetic dataset
T = 100 # was 500
(xs_sim, ys_sim) = hmm(10., 1., T)
# do inference
function do_inference(n)
trace = initial_collapsed_trace(ys_sim)
for iter=1:n
score = get_call_record(trace).score
println("score: $score")
trace = mh(model_collapsed, var_proposal, (), trace)
choices = get_assignment(trace)
println("var_x: $(choices[:var_x]), var_y: $(choices[:var_y])")
end
end
import Profile
@time do_inference(2)
@time do_inference(100)
#Profile.@profile do_inference(17)
#Profile.print(format=:flat, sortedby=:count)
#Profile.print(mincount=10)
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] | 2.414213 | 985 |
module TestDistance
using ParallelKMeans: pairwise!, SingleThread, MultiThread
using Test
@testset "naive singlethread pairwise" begin
X = [1.0 2.0; 3.0 5.0; 4.0 6.0]
y = [1.0 2.0; ]
r = Array{Float64, 2}(undef, 3, 1)
pairwise!(r, X, y)
@test all(r .≈ [0.0, 13.0, 25.0])
end
@testset "multithread pairwise" begin
X = [1.0 2.0; 3.0 5.0; 4.0 6.0]
y = [1.0 2.0; ]
r = Array{Float64, 2}(undef, 3, 1)
pairwise!(r, X, y, MultiThread())
@test all(r .≈ [0.0, 13.0, 25.0])
end
end # module
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] | 1.973783 | 267 |
# ------------------------------------------------------------------------------------------
# # Condicionales
#
# En Julia, la sintaxis
#
# ```julia
# if *condición 1*
# *opción 1*
# elseif *condición 2*
# *opción 2*
# else
# *opción 3*
# end
# ```
#
# Nos permite eventualmente evaluar una de nuestras opciones.
# <br><br>
# Por ejemplo, tal vez queremos implementar la prueba de FizzBuzz: Dado un número N, imprime
# "Fizz" si N es divisible entre 3, "Buzz" si N es divisible entre 5, y "FizzBuzz" si N es
# divisible entre ambos 3 y 5. En cualquier otro caso, imprimo el número mismo.
# ------------------------------------------------------------------------------------------
N =
if (N % 3 == 0) & (N % 5 == 0)
println("FizzBuzz")
elseif N % 3 == 0
println("Fizz")
elseif N % 5 == 0
println("Buzz")
else
println(N)
end
# ------------------------------------------------------------------------------------------
# Ahora digamos que queremos regresar el mayor número de ambos. Escoge tus propios x y y
# ------------------------------------------------------------------------------------------
x =
y =
if x > y
x
else
y
end
# ------------------------------------------------------------------------------------------
# Para el último bloque, podemos usar el operador ternario, con la sintaxis
#
# ```julia
# a ? b : c
# ```
#
# que equivale a
#
# ```julia
# if a
# b
# else
# c
# end
# ```
# ------------------------------------------------------------------------------------------
(x > y) ? x : y
# ------------------------------------------------------------------------------------------
# Un truco relacionado es la evaluación de corto-circuito
#
# ```julia
# a && b
# ```
# ------------------------------------------------------------------------------------------
(x > y) && println(x)
(x < y) && println(y)
# ------------------------------------------------------------------------------------------
# Cuando escribimos `a && b`, `b` se ejecuta sólo si `a` se evalúa a `true`.
# <br>
# Si `a` se evalúa a `false`, la expresión `a && b` regresa `false`
# ------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------
# ### Ejercicios
#
# 5.1 Reescribe FizzBuzz sin usar `elseif`.
# ------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------
# 5.2 Reescribe FizzBuzz usando el operador ternario.
# ------------------------------------------------------------------------------------------
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] | 3.709986 | 731 |
module RandomVariates
export
# SEED, A, C, MOD,
bernoulli_rng,
beta_rng,
binomial_rng,
erlang_rng,
expon_rng,
gamma_rng,
geometric_rng,
neg_binomial_rng,
conv_neg_binomial_rng,
normal_rng,
lognormal_rng,
mv_normal_rng,
poisson_rng,
uniform_rng,
weibull_rng,
tausworthe_rng,
triag_rng
include("uniform.jl")
include("exponential.jl")
include("erlang.jl")
include("weibull.jl")
include("bernoulli.jl")
include("geometric.jl")
include("poisson.jl")
include("binomial.jl")
include("neg_binomial.jl")
include("normal.jl")
include("gamma.jl")
include("beta.jl")
include("tausworthe.jl")
include("triangular.jl")
using Dates
global SEED = Dates.value(Dates.now()) # Use current epoch time as default seed
# using POSIX params for LCG
# https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use
const A = 25214903917
const C = 11
const MOD = 2^48
"""
set_seed(seed::Int)
Set the global `SEED` variable.
"""
function set_seed(seed::Int)
global SEED = seed
end
"""
set_user_seed(seed::Int)
Set a user-defined seed as global `SEED` variable.
"""
function set_user_seed(seed::Int)
global SEED = seed * 7856209
end
"""
seed_setter(seed::Union{Int, Nothing}=nothing)
Set a user defined seed, if given.
"""
function seed_setter(seed::Union{Int, Nothing}=nothing)
if !isnothing(seed)
set_user_seed(seed) # only set user seed once so we get new seed in subsequent calls
end
end
"""
get_seed()
Get the global `SEED` variable.
"""
function get_seed()
return SEED
end
"""
check_p(p::Real)
Check that parameter `p` falls between 0 and 1.
"""
function check_p(p::Real)
if (p > 1) || (p < 0)
throw(ArgumentError("Parameter `p` must fall between 0 and 1."))
end
end
# End of Module
end
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2,
5268,
286,
19937,
198,
437,
198
] | 2.517781 | 703 |
# Don't modify this, it's just there to make the tests work.
module MLJTutorials
end
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2,
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] | 3.269231 | 26 |
### Generic MUSE code
abstract type AbstractMuseProblem end
## interface to be implemented by specific problem types
function ∇θ_logLike end
function logLike_and_∇z_logLike end
function sample_x_z end
logPriorθ(prob::AbstractMuseProblem, θ) = 0
standardizeθ(prob::AbstractMuseProblem, θ) = θ
# this can also be overriden by specific problems
# the default does LBFGS using the provided logLike_and_∇z_logLike
function ẑ_at_θ(prob::AbstractMuseProblem, x, z₀, θ; ∇z_logLike_atol)
soln = optimize(Optim.only_fg(z -> .-logLike_and_∇z_logLike(prob, x, z, θ)), z₀, Optim.LBFGS(), Optim.Options(g_tol=∇z_logLike_atol))
soln.minimizer, soln
end
### MUSE result
@doc doc"""
Stores the result of a MUSE run. Can be constructed by-hand as
`MuseResult()` and passed to any of the inplace `muse!`, `get_J!`, or
`get_H!`.
Fields:
* `θ` — The estimate of the $\theta$ parameters.
* `Σ, Σ⁻¹` — The approximate covariance of $\theta$ and its inverse.
* `H, J` — The $H$ and $J$ matrices which form the covariance (see
[Millea & Seljak, 2021](https://arxiv.org/abs/2112.09354))
* `gs` — The MAP gradient sims used to compute `J`.
* `Hs` — The jacobian sims used to compute `H`.
* `dist` — A `Normal` or `MvNormal` built from `θ` and `Σ`, for
convenience.
* `history` — Internal diagnostic info from the run.
* `rng` — RNG used to generate sims for this run (so the same sims can
be reused if resuming later).
* `time` — Total `Millisecond` wall-time spent computing the result.
"""
Base.@kwdef mutable struct MuseResult
θ = nothing
H = nothing
J = nothing
Σ⁻¹ = nothing
Σ = nothing
dist = nothing
history = []
gs = []
Hs = []
rng = nothing
time = Millisecond(0)
end
### MUSE solver
@doc doc"""
muse(prob::AbstractMuseProblem, θ₀; kwargs...)
muse!(result::MuseResult, prob::AbstractMuseProblem, [θ₀=nothing]; kwargs...)
Run the MUSE estimate. The `muse!` form resumes an existing result. If the
`muse` form is used instead, `θ₀` must give a starting guess for $\theta$.
See [`MuseResult`](@ref) for description of return value.
Optional keyword arguments:
* `rng` — Random number generator to use. Taken from `result.rng` or `Random.default_rng()` if not passed.
* `z₀` — Starting guess for the latent space MAP.
* `maxsteps = 50` — Maximum number of iterations.
* `θ_rtol = 1e-1` — Error tolerance on $\theta$ relative to its standard deviation.
* `∇z_logLike_atol = 1e-2` — Absolute tolerance on the $z$-gradient at the MAP solution.
* `nsims = 100` — Number of simulations.
* `α = 0.7` — Step size for root-finder.
* `progress = false` — Show progress bar.
* `pmap` — Parallel map function.
* `regularize = identity` — Apply some regularization after each step.
* `H⁻¹_like = nothing` — Initial guess for the inverse Jacobian of $s^{\rm MUSE}(\theta)$
* `H⁻¹_update` — How to update `H⁻¹_like`. Should be `:sims`, `:broyden`, or `:diagonal_broyden`.
* `broyden_memory = Inf` — How many past steps to keep for Broyden updates.
* `checkpoint_filename = nothing` — Save result to a file after each iteration.
* `get_covariance = false` — Also call `get_H` and `get_J` to get the full covariance.
"""
muse(args...; kwargs...) = muse!(MuseResult(), args...; kwargs...)
function muse!(
result :: MuseResult,
prob :: AbstractMuseProblem,
θ₀ = nothing;
rng = nothing,
z₀ = nothing,
maxsteps = 50,
θ_rtol = 1e-1,
∇z_logLike_atol = 1e-2,
nsims = 100,
α = 0.7,
progress = false,
pmap = _map,
batch_size = 1,
regularize = identity,
H⁻¹_like = nothing,
H⁻¹_update = :sims,
broyden_memory = Inf,
checkpoint_filename = nothing,
get_covariance = false
)
rng = @something(rng, result.rng, copy(Random.default_rng()))
θunreg = θ = θ₀ = standardizeθ(prob, @something(result.θ, θ₀))
z₀ = @something(z₀, sample_x_z(prob, copy(rng), θ₀).z)
local H⁻¹_post, g_like_sims
history = result.history
result.rng = _rng = copy(rng)
xz_sims = [sample_x_z(prob, _rng, θ) for i=1:nsims]
xs = [[prob.x]; getindex.(xz_sims, :x)]
ẑs = [[z₀]; getindex.(xz_sims, :z)]
# set up progress bar
pbar = progress ? RemoteProgress((maxsteps-length(result.history))*(nsims+1)÷batch_size, 0.1, "MUSE: ") : nothing
try
for i = (length(result.history)+1):maxsteps
t₀ = now()
if i > 1
_rng = copy(rng)
xs = [[prob.x]; [sample_x_z(prob, _rng, θ).x for i=1:nsims]]
end
if i > 2
Δθ = history[end].θ - history[end-1].θ
norm(Δθ ./ θ) < θ_rtol && break
end
# MUSE gradient
gẑs = pmap(xs, ẑs, fill(θ,length(xs)); batch_size) do x, ẑ_prev, θ
local ẑ, history = ẑ_at_θ(prob, x, ẑ_prev, θ; ∇z_logLike_atol)
g = ∇θ_logLike(prob, x, ẑ, θ)
progress && ProgressMeter.next!(pbar)
(;g, ẑ, history)
end
ẑs = getindex.(gẑs, :ẑ)
ẑ_history_dat, ẑ_history_sims = peel(getindex.(gẑs, :history))
g_like_dat, g_like_sims = peel(getindex.(gẑs, :g))
g_like = g_like_dat .- mean(g_like_sims)
g_prior = AD.gradient(AD.ForwardDiffBackend(), θ -> logPriorθ(prob, θ), θ)[1]
g_post = g_like .+ g_prior
# Jacobian
h⁻¹_like_sims = -1 ./ var(collect(g_like_sims))
H⁻¹_like_sims = h⁻¹_like_sims isa Number ? h⁻¹_like_sims : Diagonal(h⁻¹_like_sims)
if (H⁻¹_like == nothing) || (H⁻¹_update == :sims)
H⁻¹_like = H⁻¹_like_sims
elseif i > 2 && (H⁻¹_update in [:broyden, :diagonal_broyden])
# on subsequent steps, do a Broyden's update using at
# most the previous `broyden_memory` steps
j₀ = Int(max(2, i - broyden_memory))
H⁻¹_like = history[j₀-1].H⁻¹_like_sims
for j = j₀:i-1
Δθ = history[j].θ - history[j-1].θ
Δg_like = history[j].g_like - history[j-1].g_like
H⁻¹_like = H⁻¹_like + ((Δθ - H⁻¹_like * Δg_like) / (Δθ' * H⁻¹_like * Δg_like)) * Δθ' * H⁻¹_like
if H⁻¹_update == :diagonal_broyden
H⁻¹_like = Diagonal(H⁻¹_like)
end
end
end
H_prior = AD.hessian(AD.ForwardDiffBackend(), θ -> logPriorθ(prob, θ), θ)[1]
H⁻¹_post = inv(inv(H⁻¹_like) + H_prior)
t = now() - t₀
push!(
history,
(;θ, θunreg,
g_like_dat, g_like_sims, g_like, g_prior, g_post,
H⁻¹_post, H_prior, H⁻¹_like, H⁻¹_like_sims,
ẑ_history_dat, ẑ_history_sims, t)
)
# Newton-Rhapson step
θunreg = θ .- α .* (H⁻¹_post * g_post)
θ = regularize(θunreg)
(checkpoint_filename != nothing) && save(checkpoint_filename, "result", result)
end
finally
progress && ProgressMeter.finish!(pbar)
end
result.time += sum(getindex.(history,:t))
result.θ = θunreg
result.gs = collect(g_like_sims)
if get_covariance
get_J!(result, prob)
get_H!(result, prob)
end
result
end
function get_H!(
result :: MuseResult,
prob :: AbstractMuseProblem,
θ₀ = result.θ;
fdm :: FiniteDifferenceMethod = central_fdm(3,1),
∇z_logLike_atol = 1e-8,
rng = Random.default_rng(),
nsims = 10,
step = nothing,
pmap = _map,
batch_size = 1,
pmap_over = :auto,
progress = false,
skip_errors = false,
)
θ₀ = standardizeθ(prob, @something(θ₀, result.θ))
nsims_remaining = nsims - length(result.Hs)
(nsims_remaining <= 0) && return
pbar = progress ? RemoteProgress(nsims_remaining*(1+length(θ₀))÷batch_size, 0.1, "get_H: ") : nothing
t₀ = now()
# generate simulation locally, advancing rng, and saving rng state to be reused remotely
xs_zs_rngs = map(1:nsims_remaining) do i
_rng = copy(rng)
(x, z) = sample_x_z(prob, rng, θ₀)
(x, z, _rng)
end
# initial fit at fiducial, used at starting points for finite difference below
ẑ₀s_rngs = pmap(xs_zs_rngs; batch_size) do (x, z, rng)
ẑ, = ẑ_at_θ(prob, x, z, θ₀; ∇z_logLike_atol)
progress && ProgressMeter.next!(pbar)
(ẑ, rng)
end
# finite difference Jacobian
pmap_sims, pmap_jac = (pmap_over == :jac || (pmap_over == :auto && length(θ₀) > nsims_remaining)) ? (_map, pmap) : (pmap, _map)
append!(result.Hs, skipmissing(pmap_sims(ẑ₀s_rngs; batch_size) do (ẑ₀, rng)
try
return first(pjacobian(fdm, θ₀, step; pmap=pmap_jac, batch_size, pbar) do θ
x, = sample_x_z(prob, copy(rng), θ)
ẑ, = ẑ_at_θ(prob, x, ẑ₀, θ₀; ∇z_logLike_atol)
∇θ_logLike(prob, x, ẑ, θ₀)
end)
catch err
if skip_errors && !(err isa InterruptException)
@warn err
return missing
else
rethrow(err)
end
end
end))
result.H = (θ₀ isa Number) ? mean(first.(result.Hs)) : mean(result.Hs)
result.time += now() - t₀
finalize_result!(result, prob)
end
function get_J!(
result :: MuseResult,
prob :: AbstractMuseProblem,
θ₀ = nothing;
∇z_logLike_atol = 1e-1,
rng = Random.default_rng(),
nsims = 100,
pmap = _map,
batch_size = 1,
progress = false,
skip_errors = false,
covariance_method = LinearShrinkage(target=DiagonalCommonVariance(), shrinkage=:rblw),
)
θ₀ = standardizeθ(prob, @something(θ₀, result.θ))
nsims_remaining = nsims - length(result.gs)
if nsims_remaining > 0
pbar = progress ? RemoteProgress(nsims_remaining÷batch_size, 0.1, "get_J: ") : nothing
(xs, zs) = map(Base.vect, map(1:nsims_remaining) do i
sample_x_z(prob, rng, θ₀)
end...)
append!(result.gs, skipmissing(pmap(xs, zs, fill(θ₀,length(xs)); batch_size) do x, z, θ₀
try
ẑ, = ẑ_at_θ(prob, x, z, θ₀; ∇z_logLike_atol)
g = ∇θ_logLike(prob, x, ẑ, θ₀)
progress && ProgressMeter.next!(pbar)
return g
catch err
if skip_errors && !(err isa InterruptException)
@warn err
return missing
else
rethrow(err)
end
end
end))
end
result.J = (θ₀ isa Number) ? var(result.gs) : cov(covariance_method, identity.(result.gs))
finalize_result!(result, prob)
end
function finalize_result!(result::MuseResult, prob::AbstractMuseProblem)
@unpack H, J = result
if H != nothing && J != nothing
H_prior = -AD.hessian(AD.ForwardDiffBackend(), θ -> logPriorθ(prob, θ), result.θ)[1]
result.Σ⁻¹ = H' * inv(J) * H + H_prior
result.Σ = inv(result.Σ⁻¹)
if length(result.θ) == 1
result.dist = Normal(result.θ[1], sqrt(result.Σ[1]))
else
result.dist = MvNormal(result.θ, result.Σ)
end
end
result
end
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] | 1.931469 | 5,866 |
using GeometricBase
using Test
dt = Float64
nt = 10
@testset "$(rpad("Dataseries 1d (scalar data)",80))" begin
nd = 1
ni = 1
ds = DataSeries(rand(dt), nt)
@test typeof(ds) == typeof(DataSeries{dt,1}(nt, ni))
@test typeof(ds) <: AbstractArray{dt,1}
@test firstindex(ds) == 0
@test firstindex(ds,1) == firstindex(ds.d,1) - 1
@test firstindex(ds,2) == 1
@test lastindex(ds) == nt
@test lastindex(ds,1) == lastindex(ds.d,1) - 1
@test lastindex(ds,2) == 1
@test strides(ds) == (1,)
@test stride(ds,1) == 1
@test axes(ds) == (0:nt,)
@test axes(ds,1) == 0:nt
@test axes(ds,2) == 1:1
@test size(ds.d) == (nt+1,)
@test size(ds.d) == size(ds)
@test size(ds.d,1) == nt+1
@test ndims(ds) == 1
@test eltype(ds) == dt
@test parent(ds) == ds.d
@test eachindex(ds) == 0:nt
@test eachindex(IndexLinear(), ds) == 0:nt
@test eachindex(IndexCartesian(), ds) == CartesianIndices((0:nt,))
for i in 0:nt
ds[i] = i
end
@test ds.d[1] == ds[0]
@test ds.d[end] == ds[nt]
@test ds.d[end] == ds[end]
@test ds.d == collect(0:nt)
@test parent(ds)[:] == parent(ds[:])
reset!(ds)
@test ds[0] == ds[end]
d = rand(nt+1)
ds = DataSeries(d)
@test ds.d == d
@test similar(ds).d == zero(d)
for i in 0:nt
set_data!(ds, dt(i), i)
end
@test ds.d == collect(0:nt)
end
@testset "$(rpad("Dataseries 1d (vector-valued data)",80))" begin
nd = 2
ni = 1
ds = DataSeries(rand(dt, nd), nt)
@test typeof(ds) == typeof(DataSeries{Vector{dt},1}(nt, ni))
@test typeof(ds) <: AbstractArray{Vector{dt},1}
@test firstindex(ds) == 0
@test firstindex(ds,1) == firstindex(ds.d,1) - 1
@test firstindex(ds,2) == 1
@test lastindex(ds) == nt
@test lastindex(ds,1) == lastindex(ds.d,1) - 1
@test lastindex(ds,2) == 1
@test strides(ds) == (1,)
@test stride(ds,1) == 1
@test axes(ds) == (0:nt,)
@test axes(ds,1) == 0:nt
@test axes(ds,2) == 1:1
@test size(ds.d) == (nt+1,)
@test size(ds.d) == size(ds)
@test size(ds.d,1) == nt+1
@test ndims(ds) == 1
@test eltype(ds) == Vector{dt}
@test parent(ds) == ds.d
@test eachindex(ds) == 0:nt
@test eachindex(IndexLinear(), ds) == 0:nt
@test eachindex(IndexCartesian(), ds) == CartesianIndices((0:nt,))
for i in 0:nt
ds[i] = [i, i^2]
end
@test ds.d[1] == ds[0]
@test ds.d[end] == ds[nt]
@test ds.d[end] == ds[end]
@test ds.d == [Vector{dt}([i, i^2]) for i in 0:nt]
@test parent(ds)[:] == parent(ds[:])
reset!(ds)
@test ds[0] == ds[end]
d = rand(nt+1)
ds = DataSeries(d)
@test ds.d == d
@test similar(ds).d == zero(d)
for i in 0:nt
set_data!(ds, dt(i), i)
end
@test ds.d == collect(0:nt)
end
@testset "$(rpad("Dataseries 2d (scalar data)",80))" begin
ni = 2
ds = DataSeries(rand(dt, ni), nt, ni)
@test typeof(ds) == typeof(DataSeries{dt,2}(nt, ni))
@test typeof(ds) <: AbstractArray{dt,2}
@test firstindex(ds) == firstindex(ds.d)
@test firstindex(ds,1) == firstindex(ds.d,1) - 1
@test firstindex(ds,2) == 1
@test lastindex(ds) == lastindex(ds.d)
@test lastindex(ds,1) == lastindex(ds.d,1) - 1
@test lastindex(ds,2) == lastindex(ds.d,2)
@test strides(ds) == (1,nt+1)
@test stride(ds,1) == 1
@test stride(ds,2) == nt+1
@test axes(ds) == (0:nt, 1:ni)
@test axes(ds,1) == 0:nt
@test axes(ds,2) == 1:2
@test size(ds.d) == (nt+1, ni)
@test size(ds.d) == size(ds)
@test size(ds.d,1) == nt+1
@test size(ds.d,2) == ni
@test ndims(ds) == 2
@test eltype(ds) == dt
@test parent(ds) == ds.d
for i in 0:nt
set_data!(ds, dt(i), i, 1)
set_data!(ds, dt(i)^2, i, 2)
end
@test ds.d[:,1] == collect(0:nt)
@test ds.d[:,2] == collect(0:nt) .^ 2
@test ds.d[1,1] == ds[0,1]
@test ds.d[1,1:ni] == ds[0,1:nsamples(ds)]
@test ds[end,1] == ds.d[end,1]
@test ds[end,1] == ds[nt,1]
@test ds[end,1:nsamples(ds)] == ds[nt,1:ni]
@test ds.d[1,:] == ds[0,:]
@test ds.d[:,1] == parent(ds[:,1])
@test ds.d[:,:] == parent(ds[:,:])
reset!(ds)
@test ds[0,1] == ds[end,1]
# tx = rand(nd)
# ds[:,0] .= tx
# @test ds.d[:,1] == tx
d = rand(nt+1,ni)
ds = DataSeries(d)
@test ds.d == d
@test similar(ds).d == zero(d)
end
@testset "$(rpad("Dataseries 2d (vector-valued data)",80))" begin
nd = 2
ni = 5
ds = DataSeries([rand(dt, nd) for i in 1:ni], nt)
@test typeof(ds) == typeof(DataSeries{Vector{dt},2}(nt, ni))
@test typeof(ds) <: AbstractArray{Vector{dt},2}
@test firstindex(ds) == firstindex(ds.d)
@test firstindex(ds,1) == firstindex(ds.d,1) - 1
@test firstindex(ds,2) == 1
@test lastindex(ds) == lastindex(ds.d)
@test lastindex(ds,1) == lastindex(ds.d,1) - 1
@test lastindex(ds,2) == lastindex(ds.d,2)
@test strides(ds) == (1,nt+1)
@test stride(ds,1) == 1
@test stride(ds,2) == nt+1
@test axes(ds) == (0:nt, 1:ni)
@test axes(ds,1) == 0:nt
@test axes(ds,2) == 1:ni
@test size(ds.d) == (nt+1, ni)
@test size(ds.d) == size(ds)
@test size(ds.d,1) == nt+1
@test size(ds.d,2) == ni
@test ndims(ds) == 2
@test eltype(ds) == Vector{dt}
@test parent(ds) == ds.d
for k in 1:ni
for i in 0:nt
ds[i,k][1] = k*i
ds[i,k][2] = k*i^2
end
end
tx = zeros(dt, nd)
for k in 1:ni
for i in 0:nt
get_data!(ds, tx, i, k)
@test tx == Array{eltype(tx)}(k .* [i, i^2])
end
end
@test ds.d[1,1] == ds[0,1]
@test ds.d[1,1:ni] == ds[0,1:nsamples(ds)]
@test ds[end,1] == ds.d[end,1]
@test ds[end,1] == ds[nt,1]
@test ds[end,1:nsamples(ds)] == ds[nt,1:ni]
@test ds.d[1,:] == ds[0,:]
@test ds.d[:,1] == parent(ds[:,1])
@test ds.d[:,:] == parent(ds[:,:])
reset!(ds)
@test ds[0,1] == ds[end,1]
# tx = rand(nd)
# ds[:,0] .= tx
# @test ds.d[:,1] == tx
d = rand(nt+1,ni)
ds = DataSeries(d)
@test ds.d == d
@test similar(ds).d == zero(d)
end
# TODO: Add tests for array-valued data
# @testset "$(rpad("Dataseries 3d",80))" begin
# nd = 2
# ni = 2
# ds = DataSeries(dt, nd, nt, ni)
# @test typeof(ds) <: AbstractArray{dt,3}
# @test firstindex(ds) == firstindex(ds.d)
# @test firstindex(ds,1) == firstindex(ds.d,1)
# @test firstindex(ds,2) == firstindex(ds.d,2) - 1
# @test firstindex(ds,3) == firstindex(ds.d,3)
# @test firstindex(ds,4) == 1
# @test lastindex(ds) == lastindex(ds.d)
# @test lastindex(ds,1) == lastindex(ds.d,1)
# @test lastindex(ds,2) == lastindex(ds.d,2) - 1
# @test lastindex(ds,3) == lastindex(ds.d,3)
# @test lastindex(ds,4) == 1
# @test strides(ds) == (1,nd,nd*(nt+1))
# @test stride(ds,1) == 1
# @test stride(ds,2) == nd
# @test axes(ds) == (1:nd, 0:nt, 1:ni)
# @test axes(ds,1) == 1:nd
# @test axes(ds,2) == 0:nt
# @test axes(ds,3) == 1:ni
# @test axes(ds,4) == 1:1
# @test size(ds.d) == (nd, nt+1, ni)
# @test size(ds.d) == size(ds)
# @test size(ds.d,1) == nd
# @test size(ds.d,2) == nt+1
# @test size(ds.d,3) == ni
# @test ndims(ds) == 3
# @test eltype(ds) == dt
# @test parent(ds) == ds.d
# for j in 1:ni
# for i in 1:nt
# ds[1,i,j] = j*i
# ds[2,i,j] = j*i^2
# end
# end
# tx = zeros(nd)
# ty = zeros(nd,ni)
# tz = zeros(nd,ni)
# for i in 1:nt
# for j in 1:ni
# get_data!(ds, tx, i, j)
# @test tx == Array{eltype(tx)}([j*i, j*i^2])
# tz[1,j] = j*i
# tz[2,j] = j*i^2
# end
# get_data!(ds, ty, i)
# @test ty == tz
# end
# @test ds.d[1,1,1] == ds[1,0,1]
# @test ds.d[1:ds.nd,1,1] == ds[1:ds.nd,0,1]
# @test ds[1,end,1] == ds.d[1,end,1]
# @test ds[1,nt,1] == ds[1,end,1]
# @test ds[1:ds.nd,nt,1] == ds[1:ds.nd,end,1]
# @test ds.d[:,1,1] == ds[:,0,1]
# @test ds.d[:,1,:] == ds[:,0,:]
# reset!(ds)
# @test ds[1,0,1] == ds[1,end,1]
# tx = rand(nd)
# ds[:,0,1] .= tx
# @test ds.d[:,1,1] == tx
# d = rand(nd,nt+1,ni)
# ds = DataSeries(d)
# @test ds.d == d
# @test similar(ds).d == zero(d)
# end
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] | 1.788502 | 4,766 |
module COFF
using StructIO
# Bring in ObjectFile definitions
using ObjectFile
import ObjectFile: DynamicLink, DynamicLinks, RPath, ObjectHandle, Section, Sections, SectionRef,
Segment, Segments, SegmentRef, StrTab, Symbols, SymtabEntry, SymbolRef,
getindex, length, lastindex, iterate, keys, eltype, handle, header, path,
rpaths, canonical_rpaths, find_library, readmeta, seek, seekstart, skip,
iostream, position, read, readuntil, eof, endianness, is64bit, isrelocatable,
isexecutable, islibrary, isdynamic, mangle_section_name, mangle_symbol_name,
format_string, section_header_offset, section_header_size, section_header_type,
segment_header_offset, segment_header_size, segment_header_type, startaddr,
symtab_entry_offset, symtab_entry_size, symtab_entry_type, find_libraries,
findfirst, deref, section_name, section_size,
section_offset, section_address, section_number, segment_name, segment_offset,
segment_file_size, segment_memory_size, segment_address, strtab_lookup,
symbol_name, symbol_value, isundef, isglobal, islocal, isweak, symbol_number
# Load in imported C #define constants
include("constants.jl")
# Start to bring in concrete types, in the order they're needed
include("COFFHeader.jl")
include("COFFOptionalHeader.jl")
include("COFFHandle.jl")
include("COFFSection.jl")
include("COFFStrTab.jl")
include("COFFSymbol.jl")
include("COFFDynamicLink.jl")
end # module COFF
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] | 2.490015 | 651 |
# Test Interpolation
@testset "lagrange order 1" begin
order = 1
ip = Lagrange{1,RefLine,order}()
bf = getnbasefunctions(ip)
nv = CGMethod1D.nvertexdofs(ip)
@test isapprox(bf, order+1, atol=1e-8)
@test isapprox(nv, 1, atol=1e-8)
end
@testset "lagrange order 2" begin
order = 2
ip = Lagrange{1,RefLine,order}()
bf = getnbasefunctions(ip)
nv = CGMethod1D.nvertexdofs(ip)
@test isapprox(bf, order+1, atol=1e-8)
@test isapprox(nv, 1, atol=1e-8)
end
@testset "value order 1" begin
order = 1
ip = Lagrange{1,RefLine,order}()
i1 = 1
i2 = 2
ξ = Vec{1}((-1.0,))
N1 = value(ip, i1, ξ)
N2 = value(ip, i2, ξ)
println("N1:$N1; N2:$N2")
@test isapprox(N1+N2, 1, atol=1e-8)
end
@testset "value order 2" begin
order = 2
ip = Lagrange{1,RefLine,order}()
i1 = 1
i2 = 2
i3 = 3
ξ = Vec{1}((-1.0,))
N1 = value(ip, i1, ξ)
N2 = value(ip, i2, ξ)
N3 = value(ip, i3, ξ)
println("N1:$N1; N2:$N2; N3:$N3")
@test isapprox(N1+N2+N3, 1, atol=1e-8)
end
@testset "reference_coordinates order 1" begin
order = 1; n = order+1;
ip = Lagrange{1,RefLine,order}()
coords = reference_coordinates(ip)
println(coords)
ξ_vec = collect(range(-1, stop=1, length=n))
for (idx,val) in enumerate(ξ_vec)
@test coords[idx][1] in ξ_vec
end
@test coords[1][1] == -1.0
@test coords[2][1] == 1.0
@test issorted(coords[3:end-1])
end
@testset "reference_coordinates order 2" begin
order = 20; n = order+1;
ip = Lagrange{1,RefLine,order}()
coords = reference_coordinates(ip)
println(coords)
ξ_vec = collect(range(-1, stop=1, length=n))
for (idx,val) in enumerate(ξ_vec)
@test coords[idx][1] in ξ_vec
end
@test coords[1][1] == -1.0
@test coords[2][1] == 1.0
@test issorted(coords[3:end-1])
end
@testset "Ferrite 1D order 1" begin
order = 1
i1 = 1
i2 = 2
ξ = Vec{1}((0.25,))
ip_F = Lagrange{1,RefCube,order}()
bf_F = getnbasefunctions(ip_F)
ip_C = Lagrange{1,RefLine,order}()
bf_C = getnbasefunctions(ip_C)
N1_F = value(ip_F, i1, ξ)
N2_F = value(ip_F, i2, ξ)
N1_C = value(ip_C, i1, ξ)
N2_C = value(ip_C, i2, ξ)
@test isapprox(bf_F, bf_C, atol=1e-8)
@test isapprox(N1_F, N1_C, atol=1e-8)
@test isapprox(N2_F, N2_C, atol=1e-8)
end
@testset "Ferrite 1D order 2" begin
order = 2
i1 = 1
i2 = 2
i3 = 3
ξ = Vec{1}((0.25,))
ip_F = Lagrange{1,RefCube,order}()
bf_F = getnbasefunctions(ip_F)
ip_C = Lagrange{1,RefLine,order}()
bf_C = getnbasefunctions(ip_C)
N1_F = value(ip_F, i1, ξ)
N2_F = value(ip_F, i2, ξ)
N3_F = value(ip_F, i3, ξ)
N1_C = value(ip_C, i1, ξ)
N2_C = value(ip_C, i2, ξ)
N3_C = value(ip_C, i3, ξ)
@test isapprox(bf_F, bf_C, atol=1e-8)
@test isapprox(N1_F, N1_C, atol=1e-8)
@test isapprox(N2_F, N2_C, atol=1e-8)
@test isapprox(N3_F, N3_C, atol=1e-8)
end | [
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] | 1.803021 | 1,655 |
using MicroCoverage
using Test
module MicroCoverageTestSuite
using MicroCoverage
using Test
function get_test_directory()::String
return dirname(@__FILE__)
end
function get_filename(parts...)::String
return joinpath(get_test_directory(), parts...)
end
function readstring_filename(parts...)::String
_filename = get_filename(parts...)
return read(_filename, String)
end
@testset "MicroCoverage.jl" begin
@testset "assert.jl" begin
@test MicroCoverage.always_assert(true, "") == nothing
@test_throws MicroCoverage.AlwaysAssertionError MicroCoverage.always_assert(false, "")
end
@testset "instrument.jl" begin
MicroCoverage.instrument("", Expr(:block), Val(:block)) == Expr(:block)
end
@testset "public_interface.jl" begin
MicroCoverage.with_temp_dir() do tmp_depot
MicroCoverage.with_temp_dir() do tmp_src_directory
nonexistent_filename = joinpath(tmp_src_directory, "nonexistent.jl")
foo_jl_filename = joinpath(tmp_src_directory, "foo.jl")
test_foo_jl_filename = joinpath(tmp_src_directory, "test_foo.jl")
foo_jl_microcov_filename = joinpath(tmp_src_directory, "foo.jl.microcov")
bar_jl_filename = joinpath(tmp_src_directory, "bar.jl")
test_bar_jl_filename = joinpath(tmp_src_directory, "test_bar.jl")
bar_jl_microcov_filename = joinpath(tmp_src_directory, "bar.jl.microcov")
open(foo_jl_filename, "w") do io
print(io, readstring_filename("inputs", "foo.jl"))
end
open(test_foo_jl_filename, "w") do io
print(io, readstring_filename("inputs", "test_foo.jl"))
end
open(bar_jl_filename, "w") do io
print(io, readstring_filename("inputs", "bar.jl"))
end
open(test_bar_jl_filename, "w") do io
print(io, readstring_filename("inputs", "test_bar.jl"))
end
@test_throws ArgumentError MicroCoverage.start(nonexistent_filename)
@test_throws ArgumentError MicroCoverage.clean(nonexistent_filename)
MicroCoverage.start(strip(foo_jl_filename))
MicroCoverage.start(bar_jl_filename)
MicroCoverage.preview_coverage(; dump_coverage_io = devnull)
include(foo_jl_filename)
MicroCoverage.preview_coverage(; dump_coverage_io = devnull)
include(bar_jl_filename)
MicroCoverage.preview_coverage(; dump_coverage_io = devnull)
include(test_foo_jl_filename)
MicroCoverage.preview_coverage(; dump_coverage_io = devnull)
include(test_bar_jl_filename)
MicroCoverage.preview_coverage(; dump_coverage_io = devnull)
@test !isfile(foo_jl_microcov_filename)
@test !ispath(foo_jl_microcov_filename)
@test !isfile(bar_jl_microcov_filename)
@test !ispath(bar_jl_microcov_filename)
MicroCoverage.stop(; dump_coverage = true, dump_coverage_io = devnull)
@test isfile(foo_jl_microcov_filename)
@test ispath(foo_jl_microcov_filename)
@test isfile(bar_jl_microcov_filename)
@test ispath(bar_jl_microcov_filename)
if Sys.iswindows()
@test chomp(read(foo_jl_microcov_filename, String)) == chomp(readstring_filename("expected_outputs", "foo.jl.microcov.expected"))
@test chomp(read(bar_jl_microcov_filename, String)) == chomp(readstring_filename("expected_outputs", "bar.jl.microcov.expected"))
else
@test read(foo_jl_microcov_filename, String) == readstring_filename("expected_outputs", "foo.jl.microcov.expected")
@test read(bar_jl_microcov_filename, String) == readstring_filename("expected_outputs", "bar.jl.microcov.expected")
end
touch(foo_jl_microcov_filename)
MicroCoverage.clean(foo_jl_filename)
touch(foo_jl_microcov_filename)
MicroCoverage.clean(tmp_src_directory)
end
end
end
end
end # end module MicroCoverageTestSuite
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] | 2.075095 | 2,104 |
@testset "wiener" begin
k_1 = WienerKernel(i=-1)
@test typeof(k_1) <: WhiteKernel
k0 = WienerKernel()
@test typeof(k0) <: WienerKernel{0}
k1 = WienerKernel(i=1)
@test typeof(k1) <: WienerKernel{1}
k2 = WienerKernel(i=2)
@test typeof(k2) <: WienerKernel{2}
k3 = WienerKernel(i=3)
@test typeof(k3) <: WienerKernel{3}
@test_throws AssertionError WienerKernel(i=4)
@test_throws AssertionError WienerKernel(i=-2)
v1 = rand(4)
v2 = rand(4)
X = sqrt(sum(abs2, v1))
Y = sqrt(sum(abs2, v2))
minXY = min(X, Y)
@test k0(v1, v2) ≈ minXY
@test k1(v1, v2) ≈ 1 / 3 * minXY^3 + 1 / 2 * minXY^2 * euclidean(v1, v2)
@test k2(v1, v2) ≈ 1 / 20 * minXY^5 + 1 / 12 * minXY^3 * euclidean(v1, v2) *
( X + Y - 1 / 2 * minXY )
@test k3(v1, v2) ≈ 1 / 252 * minXY^7 + 1 / 720 * minXY^4 * euclidean(v1, v2) *
( 5 * max(X, Y)^2 + 2 * X * Y + 3 * minXY^2 )
# kernelmatrix tests
m1 = rand(3,4)
m2 = rand(3,4)
@test kernelmatrix(k0, m1, m1) ≈ kernelmatrix(k0, m1) atol=1e-5
K = zeros(4,4)
kernelmatrix!(K,k0,m1,m2)
@test K ≈ kernelmatrix(k0, m1, m2) atol=1e-5
V = zeros(4)
kerneldiagmatrix!(V,k0,m1)
@test V ≈ kerneldiagmatrix(k0,m1) atol=1e-5
x1 = rand()
x2 = rand()
@test kernelmatrix(k0, x1*ones(1,1), x2*ones(1,1))[1] ≈ k0(x1, x2) atol=1e-5
@test kernelmatrix(k1, x1*ones(1,1), x2*ones(1,1))[1] ≈ k1(x1, x2) atol=1e-5
@test kernelmatrix(k2, x1*ones(1,1), x2*ones(1,1))[1] ≈ k2(x1, x2) atol=1e-5
@test kernelmatrix(k3, x1*ones(1,1), x2*ones(1,1))[1] ≈ k3(x1, x2) atol=1e-5
# test_ADs(()->WienerKernel(i=1))
@test_broken "No tests passing"
end
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62,
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366,
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437,
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] | 1.746914 | 972 |
module Data
export List, Fun
include("TypedFn.jl")
@info TypedFn
using MLStyle.Data.TypedFn
include("List.jl")
end
| [
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] | 2.468085 | 47 |
#*****************************************************************************
# Written by Ritchie Lee, ritchie.lee@sv.cmu.edu
# *****************************************************************************
# Copyright ã 2015, United States Government, as represented by the
# Administrator of the National Aeronautics and Space Administration. All
# rights reserved. The Reinforcement Learning Encounter Simulator (RLES)
# platform is licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License. You
# may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0. Unless required by applicable
# law or agreed to in writing, software distributed under the License is
# distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied. See the License for the specific language
# governing permissions and limitations under the License.
# _____________________________________________________________________________
# Reinforcement Learning Encounter Simulator (RLES) includes the following
# third party software. The SISLES.jl package is licensed under the MIT Expat
# License: Copyright (c) 2014: Youngjun Kim.
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to
# deal in the Software without restriction, including without limitation the
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
# sell copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED
# "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
# NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
# PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
# *****************************************************************************
using TensorFlow
import TensorFlow.API: shape, gather, concat, expand_dims, div_
type Normalizer{T<:AbstractFloat}
ndim::Int64
maxes::Array{T}
mins::Array{T}
end
function Normalizer(data::TFDataset; converttype::Union{Type,Void}=nothing)
N = ndims(data.X)
rmdims = collect(1:N-1)
#find max/mins per column over entire dataset
maxes = maximum(data.X, rmdims)
mins = minimum(data.X, rmdims)
if converttype != nothing
maxes = convert(Array{converttype}, maxes)
mins = convert(Array{converttype}, mins)
end
norm = Normalizer(N, maxes, mins)
norm
end
#"""
#"""
function normalize01(norm::Normalizer, Xin::Tensor)
N = norm.ndim
maxes = constant(norm.maxes)
mins = constant(norm.mins)
tileshape = concat(Tensor(0), Tensor([gather(shape(Xin), Tensor(collect(0:N-2))); Tensor([1])]))
tiledmaxes = tile(maxes, tileshape)
tiledmins = tile(mins, tileshape)
Xout = div_((Xin - tiledmins), (tiledmaxes - tiledmins))
Xout
end
function normalize(norm::Normalizer, Xin::Tensor, minval::AbstractFloat=-1.0,
maxval::AbstractFloat=1.0)
X01 = normalize(Xin)
max = constant(maxval)
min = constant(minval)
shape = get_shape(Xin)
tiledmax = tile(max, Tensor(shape))
tiledmin = tile(min, Tensor(shape))
Xout = X01 * (tiledmax - tiledmin) + tiledmin
Xout
end
| [
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2,
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] | 3.349688 | 1,121 |
"""
Contains some functions for calculating cross-correlations, autocorrelations,
and Pearson correlations among rate units in a rate network
"""
using Statistics
import DSP.xcorr
"""
xcorr_unbiased(x::Vector, y::Vector, maxlag::Int64)
Returns the cross-correlation of two signals normalized by the length of the
available convolution window.
Written by Rainer Engelken (re2365@columbia.edu).
"""
function xcorr_unbiased(x, y, maxlag)
l = length(x) # we assume same length for x and y
lags = -maxlag:maxlag
scale = l .- abs.(lags)
scale[scale .<= 0] .= 1 # avoid zero division
xcorr(x, y)[l .+ lags] ./ scale
end
"""
avg_autocorrs(A::Matrix{T}, maxlag::Int64, wait::Int64=0) where T <: AbstractFloat
Returns the average autocorrelation for the activity of each unit described in
the `N x NT` matrix `A`.
Note the autocorrelations are not mean-subtracted. The `maxlag` parameter
gives the maximum shift of the signal, and the `wait` parameter gives the number
of timesteps in the beginning to disregard.
"""
function avg_autocorrs(A::Matrix{T}, maxlag::Int64, wait::Int64=0) where T <: AbstractFloat
(N, NT) = size(A)
unit_autocorrs = mapslices(view(A, :, (wait + 1):NT), dims=2) do x
return xcorr_unbiased(x, x, maxlag)
end
return vec(mean(unit_autocorrs, dims=1))
end
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] | 2.878049 | 451 |
function mnistgrid(images, nrow, filename=nothing)
yy = reshape(images, 28, 28, size(images)[end])
yy = permutedims(yy, (2,1,3))
yy = Images.imresize(yy, 40, 40)
yy = Gray.(mosaicview(yy, 0.5f0, nrow=nrow, npad=1, rowmajor=true))
if filename == nothing
display(yy)
else
save(filename, yy)
end
end
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] | 2.104938 | 162 |
using Random, LightGraphs, SimpleWeightedGraphs
@testset "Testing local_search.jl" begin
@testset "Testing pearson_correlation" begin
# Check equal
b1 = [i/6 for i in 1:6]
b2 = [i/6 for i in 1:6]
@test AbrkgaObop.pearson_correlation(b1,b2,6) == 1.0
# Check reverse
b3 = reverse(b1)
@test AbrkgaObop.pearson_correlation(b1,b3,6) ≈ -1.0
end;
@testset "Testing weighted_label_propagation" begin
Random.seed!(0)
keys = [0.16666666666666666 0.159 0.84;
0.3333333333333333 0.32 0.82;
0.5 0.49 0.65;
0.6666666666666666 0.65 0.49;
0.8333333333333334 0.82 0.32;
1.0 0.84 0.159]
# Create weighted graph
sigma = 0.7 # Used to make graph sparse
n_itens = size(keys,1)
n_voters = size(keys,2)
graph = SimpleWeightedGraph(n_voters)
for i in 1:n_voters-1
for j in i+1:n_voters
weight = AbrkgaObop.pearson_correlation(keys[:,i],keys[:,j],n_itens)
if weight >= sigma
add_edge!(graph, i, j, weight)
end
end
end
# Return the index of the chromosomes that the LS will be applied
index_local_search = AbrkgaObop.weighted_label_propagation(graph)
@test index_local_search == [1,3]
end
@testset "Testing objective_partial" begin
instance = read_dataset("datasets/movie.toi")
bucket = [0 0;
0 0;
0 0;
0 0;
0 0;
0 0]
keys = [0.16666666666666666 0.159;
0.3333333333333333 0.32;
0.5 0.49;
0.6666666666666666 0.65;
0.8333333333333334 0.82;
1.0 0.84]
fitness = [0,0]
AbrkgaObop.decoder!(1,bucket,keys)
AbrkgaObop.objective!(1,bucket,fitness,instance)
# Check i -> j
fitness_from_i_j = AbrkgaObop.objective_partial(bucket[:,1], fitness[1], 1, 1, 6, instance)
@test fitness_from_i_j == 32
# Check j -> i
fitness_from_j_i = AbrkgaObop.objective_partial(bucket[:,1], fitness_from_i_j, 1, 6, 1, instance)
@test fitness_from_j_i == fitness[1]
# Compare with another bucket with same bucket order
AbrkgaObop.decoder!(2,bucket,keys)
AbrkgaObop.objective!(2,bucket,fitness,instance)
@test fitness_from_i_j == AbrkgaObop.objective_partial(bucket[:,2], fitness[2], 1, 1, 6, instance)
end
@testset "Testing local_search" begin
Random.seed!(0)
instance = read_dataset("datasets/movie.toi")
bucket = [0 0;
0 0;
0 0;
0 0;
0 0;
0 0]
keys = [0.16666666666666666 0.159;
0.3333333333333333 0.32;
0.5 0.49;
0.6666666666666666 0.65;
0.8333333333333334 0.82;
1.0 0.84]
fitness = [0,0]
statistics = AbrkgaObop.OBOPStatistics([],[],[],[],[],[],0.0,0.0,0,0)
AbrkgaObop.decoder!(1,bucket,keys)
AbrkgaObop.objective!(1,bucket,fitness,instance)
best_solution = AbrkgaObop.OBOPSolution(instance.total_itens,time())
AbrkgaObop.local_search!(1,keys,bucket,fitness,instance,best_solution,1,statistics)
@test best_solution.objective == 72
@test best_solution.bucket == [1,1,1,2,2,3]
end
@testset "Testing local_search_parallel" begin
Random.seed!(0)
instance = read_dataset("datasets/movie.toi")
bucket = [0 0;
0 0;
0 0;
0 0;
0 0;
0 0]
keys = [0.16666666666666666 0.159;
0.3333333333333333 0.32;
0.5 0.49;
0.6666666666666666 0.65;
0.8333333333333334 0.82;
1.0 0.84]
fitness = [0,0]
statistics = AbrkgaObop.OBOPStatistics([],[],[],[],[],[],0.0,0.0,0,0)
AbrkgaObop.decoder!(1,bucket,keys)
AbrkgaObop.objective!(1,bucket,fitness,instance)
best_solution = AbrkgaObop.OBOPSolution(instance.total_itens,time())
AbrkgaObop.local_search_parallel!(1,keys,bucket,fitness,instance,best_solution,1,statistics)
@test best_solution.objective == 72
@test best_solution.bucket == [1,1,1,2,2,3]
end
#=
@testset "Testing clustering_search" begin
Random.seed!(0)
instance = read_dataset("datasets/movie.toi")
bucket = [0 0;
0 0;
0 0;
0 0;
0 0;
0 0]
keys = [0.16666666666666666 0.159;
0.3333333333333333 0.32;
0.5 0.49;
0.6666666666666666 0.65;
0.8333333333333334 0.82;
1.0 0.84]
fitness = [0,0]
AbrkgaObop.decoder!(1,bucket,keys)
AbrkgaObop.objective!(1,bucket,fitness,instance)
AbrkgaObop.decoder!(2,bucket,keys)
AbrkgaObop.objective!(2,bucket,fitness,instance)
best_solution = AbrkgaObop.OBOPSolution(instance.total_itens,time())
statistics = AbrkgaObop.OBOPStatistics([],[],[],[],[],[],0.0,0.0,0,0)
AbrkgaObop.clustering_search(2,
[1,2],
keys,
bucket,
fitness,
instance,
best_solution,
1,
statistics)
@test best_solution.objective == 72
@test best_solution.bucket == [1,1,1,2,2,3]
end
=#
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] | 1.672326 | 3,711 |
@testset "utilities.jl" begin
f_test(x, a, b) = a .* x .+ b
@test EasyPhys.number_of_arguments(f_test) == 3
@test EasyPhys.argument_names(f_test) == [:x, :a, :b]
EasyPhys.@partially_applicable g_test(x, a, b; kwargs...) = (a * x + b)
for x in 1:5, a in 6:10, b in 1:10
@test g_test(x, a, b; test=true) == x |> g_test(a, b; test=false) == a * x + b
end
EasyPhys.@partially_applicable g_test(x; kwargs...) = (println(kwargs); 5*x)
@test g_test(2; test=:somearg) == (2::Int) |> g_test(test=:someotherarg) == 10
end
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] | 2.104418 | 249 |
abstract AbstractNoiseModel
noise(s::Symbol,args...) = _noise(Val{s},args...)
noisemodelname(::AbstractNoiseModel) = "AbstractNoiseModel"
function show(io::IO,n::AbstractNoiseModel)
println(io,noisemodelname(n))
for f in fieldnames(n)
print(io," ",f,": ",typeof(getfield(n,f)))
println(io)
end
nothing
end
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] | 2.480916 | 131 |
# License for this file: MIT (expat)
# Copyright 2017-2018, DLR Institute of System Dynamics and Control
#
# This file is part of module
# ModiaMath.SimulationEngine(ModiaMath/SimulationEngine/_module.jl)
#
# Methods that involve IDA UserData
#=
"KLU sparse matrix type"
type SlsMat
M::Cint # number of rows
N::Cint # number of columns
NNZ::Cint # maximum number of nonzero entries in the matrix
data::Ptr{Sundials.realtype} # data[NNZ] - value of nonzero entries
rowvals::Ptr{Cint} # rowvals[NNZ] - row indices of data (index starts at zero)
colptrs::Ptr{Cint} # colptrs[N+1] - index of the first column entry into the
# data and rowvals arrays (index starts at zero)
# The last entry contains the total number of nonzero values
# in the matrix and hence points one past the end
# of the active data in the data and rowvals arrays.
end
const SlsMat_Ptr = Ptr{SlsMat}
"""
CSCtoSlsMat!(mat, matKLU)
Copy SparseMatrixCSC mat to SlsMat data structure matKLU
(storage for both objects are provided in the calling program)
"""
function CSCtoSlsMat!(mat::SparseMatrixCSC{Float64,Cint}, matKLU::SlsMat)
for i = 1:length(mat.nzval)
unsafe_store!(matKLU.data , mat.nzval[i], i)
unsafe_store!(matKLU.rowvals, mat.rowval[i]-1, i)
end
for i = 1:length(mat.colptr)
unsafe_store!(matKLU.colptrs, mat.colptr[i]-1, i)
end
end
=#
##################################################################
#
# Wrappers to IDA code
#
##################################################################
function sol_f!(simModel::IntegratorData, sim, t::Float64, _y::Vector{Float64}, _yp::Vector{Float64}, r::Vector{Float64}, hcur)
stat = simModel.statistics
stat.hMin = min(stat.hMin, simModel.hcur[1])
stat.hMax = max(stat.hMax, simModel.hcur[1])
stat.orderMax = max(stat.orderMax, simModel.order[1])
stat.nResidues += 1
sim = simModel.simulationState
sim.time = t
simModel.last_t = t
simModel.last_norm_y = norm(simModel.y, Inf)
ModiaMath.DAE.getResidues!(simModel.model, sim, t, _y, _yp, r, hcur)
#println(_y, _yp, t, r, hcur )
return nothing
end
#------- full jacobian
function sol_fulljac(t::Float64, cj::Float64, _y::Vector{Float64}, _yp::Vector{Float64}, _r::Vector{Float64},
_fulljac::Array{Float64}, simModel::IntegratorData,
tmp1::Vector{Float64}, tmp2::Vector{Float64}, tmp3::Vector{Float64})
# Compute full Jacobian
sim = simModel.simulationState
sim.time = t
simModel.hcur[1] = simModel.sol_data.hcur
simModel.eweight = simModel.sol_data.weights
simModel.y = _y
simModel.yp = _yp
r = _r
ModiaMath.DAE.computeJacobian!(simModel.model, sim, t, y, yp, r, simModel.fulljac, simModel.hcur[1], cj, simModel.eweight)
simModel.statistics += sim.nx
return 0 # indicates normal return
end
function find_roots(t::Array{Float64, 1}, ys::Array{Array{Float64, 1}, 1}, yps::Array{Array{Float64,1},1}, simModel::IntegratorData, resprob!, abstol::Float64, reltol::Array{Float64,1})
#solve again with better precision to be sure
FTOL=eps(Float64)^(1 / 3)
sim = simModel.simulationState
nsol_f!(r, y) = ModiaMath.DAE.getResidues!(simModel.model, sim, t[1], ys[1], yps[1], r, simModel.hcur[1])
nsol = nlsolve(nsol_f!, ys[1], ftol=FTOL)
y = nsol.zero
prob = DAEProblem{true}(resprob!, yps[1], y, (t[1], t[end]), differential_vars=[true,true,false])
sol = solve(prob, dassl(), reltol = reltol, abstol = abstol/100)
return sol.t[end], sol.u[end], sol.du[end]
end
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] | 2.226426 | 1,771 |
using Dash
using DashCoreComponents
using DashHtmlComponents
using PlotlyJS
include("IntegralUtils.jl")
include("GraphingUtils.jl")
using .IntegralUtils
using .GraphingUtils
mathjax = "https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_CHTML"
app = dash(external_stylesheets=["https://codepen.io/chriddyp/pen/bWLwgP.css"],
assets_folder="assets",
external_scripts=[mathjax])
options_ = ["S: r(u, v)", "S: z = f(x, y), y = g(x)"]
app.layout = html_div() do
html_div(children = [
html_h1("\$\$\\text{Surface integrals calculator}\$\$", style=Dict("textAlign" => "center", "margin" => "3%")),
html_div(id="header",
children=[
html_h3(id="header_h3", "\$\$ \\text{Hello, let the fun begin!}\$\$")
]
),
html_hr(style=Dict("borderTop" => "1px dashed #d69c2f")),
html_div(id="surface", children=[
html_label(id="surface_label", "\$\$\\text{Choose the way of defining the surface:}\$\$"),
dcc_dropdown(
id = "dropdown",
options = [(label = i, value = i) for i in options_],
value = options_[1],
),
]),
html_hr(style=Dict("borderTop" => "1px dashed #d69c2f")),
html_div(id="main", children=[
html_div(id="inputs", children=[
html_label(id="vector_field_l", "\$\$\\text{Enter your vector field formula}\$\$"),
html_div(id="field", children=[
html_label(id="mFx", "\$\$\\vec{F}\\cdot\\hat{i}\$\$"),
dcc_input(id="Fx", type="text", value="x"),
html_label(id="mFy", "\$\$\\vec{F}\\cdot\\hat{j}\$\$"),
dcc_input(id="Fy", type="text", value="y"),
html_label(id="mFz", "\$\$\\vec{F}\\cdot\\hat{k}\$\$"),
dcc_input(id="Fz", type="text", value="z"),
]
),
html_label(id="method_dropdown", "\$\$\\text{Choose method of numeric integration:}\$\$"),
dcc_dropdown(
id = "method",
options = [(label = i, value = i) for i in ("Simpson", "Monte Carlo")],
value = "Simpson"
),
html_label(id="accurary", "\$\$\\text{Choose the accuracy of numeric integration:}\$\$"),
dcc_slider(
id = "integral_accuracy",
min = 10,
max = 100,
marks = Dict([Symbol(v) => Symbol(v) for v in 10:10:100]),
value = 10,
step = 10,
),
html_div(id="parametric_bounds", children=[
html_label(id="r1lab", "\$\$\\vec{r}(u, v)\\cdot\\hat{i} =\$\$"),
dcc_input(id="r1", type="text", value="sqrt(1/4 + u^2) * cos(v)"),
html_label(id="r2lab", "\$\$\\vec{r}(u, v)\\cdot\\hat{j} =\$\$"),
dcc_input(id="r2", type="text", value="sqrt(1/4 + u^2) * sin(v)"),
html_label(id="r3lab", "\$\$\\vec{r}(u, v)\\cdot\\hat{k} =\$\$"),
dcc_input(id="r3", type="text", value="u"),
html_label(id="u_range1", "\$\$u_{min} =\$\$"),
dcc_input(id="u_range1i", type="text", value="-1"),
html_label(id="u_range2", "\$\$u_{max} =\$\$"),
dcc_input(id="u_range2i", type="text", value="1"),
html_label(id="v_range1", "\$\$\\phi(u) =\$\$"),
dcc_input(id="v_range1i", type="text", value="0"),
html_label(id="v_range2", "\$\$\\theta(u) =\$\$"),
dcc_input(id="v_range2i", type="text", value="2pi")
], style=Dict("display" => "grid")
),
html_div(id="fxy_bounds", children=[
html_label(id="x_range1", "\$\$x_{\\text{min}} =\$\$"),
dcc_input(id="x_range1i", type="text", value="-2"),
html_label(id="x_range2", "\$\$ x_{\\text{max}} =\$\$"),
dcc_input(id="x_range2i", type="text", value="3"),
html_label(id="y_range1", "\$\$ \\zeta(x) =\$\$"),
dcc_input(id="y_range1i", type="text", value="-2"),
html_label(id="y_range2", "\$\$ \\eta(x) =\$\$"),
dcc_input(id="y_range2i", type="text", value="2"),
html_label(id="z_range1", "\$\$ f(x, y) =\$\$"),
dcc_input(id="z_range1i", type="text", value="-(x^2 + y^2)"),
html_label(id="z_range2", "\$\$ g(x, y) =\$\$"),
dcc_input(id="z_range2i", type="text", value="x^2+y^2"),
], style=Dict("display" => "none")
), html_button(id = "submit-button-state", children = "submit", n_clicks = 0),
html_div(id="output_")
]),
html_div(id="graphing", children=[
dcc_graph(
id = "surface_plot",
figure = (
data = [
(x = [0],
y = [0],
z = [[0], [0]],
type = "surface")
],
layout = (
autosize=false,
width=600,
height=600
)
)
),
]
),
]),
html_div(id="plot_attributes",
children=[
html_label(id="field_density_lab", "\$\$\\text{Choose the density of the vector field.}\$\$"),
dcc_slider(
id = "field_density",
min = 0,
max = ,10
marks = Dict([Symbol(v) => Symbol(v) for v in 0:1:10]),
value = 5,
step = 1,
),
html_label(id="graph_accuracy_lab", "\$\$\\text{Choose the accuracy of plotting.}\$\$"),
dcc_slider(
id = "graph_accuracy",
min = 10,
max = 100,
marks = Dict([Symbol(v) => Symbol(v) for v in 10:10:100]),
value = 20,
step = 10,
)
]
), html_footer("\$\$\\text{MIT License}. \\ \\text{MM, ML, MK.}\$\$", style=Dict("marginTop" => "3em", "textAlign" => "center"))
])
end
callback!(app,
Output("parametric_bounds", "style"),
Output("fxy_bounds", "style"),
Input("dropdown", "value")
) do user_choice
if user_choice == options_[1]
return Dict("display" => "grid"), Dict("display" => "none")
else
return Dict("display" => "none"), Dict("display" => "grid")
end
end
callback!(app,
Output("output_", "children"),
Input("submit-button-state", "n_clicks"),
State("dropdown", "value"),
State("r1", "value"),
State("r2", "value"),
State("r3", "value"),
State("Fx", "value"),
State("Fy", "value"),
State("Fz", "value"),
State("method", "value"),
State("integral_accuracy", "value"),
State("u_range1i", "value"),
State("u_range2i", "value"),
State("v_range1i", "value"),
State("v_range2i", "value"),
State("x_range1i", "value"),
State("x_range2i", "value"),
State("y_range1i", "value"),
State("y_range2i", "value"),
State("z_range1i", "value"),
State("z_range2i", "value")
) do n_clicks, dropdown_value, r1, r2, r3, Fx, Fy, Fz, technique, n, u_min, u_max,
v_min, v_max, x_min, x_max, y_min, y_max, z_min, z_max
if dropdown_value == options_[1]
try
u_min, u_max = parse_num.([u_min, u_max])
p = parse_function(join(["[" * r1, r2, r3 *"]" ], ", "), :u, :v)
q = parse_function(join(["[" * Fx, Fy, Fz * "]"], ", "), :x, :y, :z)
ϕ = parse_function(v_min, :u)
ψ = parse_function(v_max, :u)
value(f, g, a, b) = round_float(Φ(f, g, (u_min, u_max), a, b; N = Int(n ÷ 2), technique = technique), 1e-3)
value_ = @eval abs(($value($q, $p, $ϕ, $ψ)))
return html_h5("|Φ| = $(value_).", style=Dict("textAlign" => "center"))
catch e
return html_h5("\$\$\\text{Wrong input. Try again.}\$\$", style=Dict("textAlign" => "center"))
end
else
try
x_min, x_max = parse_num.([x_min, x_max])
q = parse_function(join(["[" * Fx, Fy, Fz * "]"], ", "), :x, :y, :z)
ϕ = parse_function(y_min, :x)
ψ = parse_function(y_max, :x)
ρ = parse_function(z_min, :x, :y)
η = parse_function(z_max, :x, :y)
value(f, a, b, c, d) = round_float(Φ(f, (x_min, x_max), a, b, c, d; N = Int(n ÷ 2), technique = technique), 1e-3)
value_ = @eval abs(($value($q, $ρ, $η, $ϕ, $ψ)))
return html_h5("|Φ| = $(value_).", style=Dict("textAlign" => "center"))
catch e
return html_h5("\$\$ \\text{Wrong input. Try again.} \$\$", style=Dict("textAlign" => "center"))
end
end
end
callback!(app,
Output("surface_plot", "figure"),
Input("submit-button-state", "n_clicks"),
State("r1", "value"),
State("r2", "value"),
State("r3", "value"),
State("dropdown", "value"),
State("graph_accuracy", "value"),
State("u_range1i", "value"),
State("u_range2i", "value"),
State("v_range1i", "value"),
State("v_range2i", "value"),
State("x_range1i", "value"),
State("x_range2i", "value"),
State("y_range1i", "value"),
State("y_range2i", "value"),
State("z_range1i", "value"),
State("z_range2i", "value"),
State("Fx", "value"),
State("Fy", "value"),
State("Fz","value"),
State("field_density", "value")
) do n_clicks, r1, r2, r3, dropdown_value, N, u_min, u_max, v_min, v_max,
x_min, x_max, y_min, y_max, z_min, z_max, F1, F2, F3, density
if dropdown_value == options_[1] # _______________parametric
try
u_min = parse_num(u_min)
u_max = parse_num(u_max)
v_min = parse_function(v_min, :u)
v_max = parse_function(v_max, :u)
catch e
u_min = -1
u_max = 1
v_min = parse_function("0", :u)
v_max = parse_function("2pi", :u)
end
if false
return Plot(surface(;
x = [0],
y = [0],
z = [[0], [0]]))
else
Fx = Fy = Fz = "_"
X(u, v) = 0
Y(u, v) = 0
Z(u, v) = 0
try
X = parse_function(r1, :u, :v)
Y = parse_function(r2, :u, :v)
Z = parse_function(r3, :u, :v)
Fx = parse_function(F1, :x, :y, :z)
Fy = parse_function(F2, :x, :y, :z)
Fz = parse_function(F3, :x, :y, :z)
@eval ($X(-2, 3), $Y(-2, 3), $Z(-2, 3))
@eval (isa($X(-2, 3), Array{Float64, 1}))
@eval (isa($Y(-2, 3), Array{Float64, 1}))
@eval (isa($Z(-2, 3), Array{Float64, 1}))
@eval (isa($Fx(-2, -2, -2), Number))
@eval (isa($Fy(-2, -2, -2), Number))
@eval (isa($Fz(-2, -2, -2), Number))
catch e
X = parse_function("0", :u, :v)
Y = parse_function("0", :u, :v)
Z = parse_function("0", :u, :v)
Fx = parse_function("0", :x, :y, :z)
Fy = parse_function("0", :x, :y, :z)
Fz = parse_function("0", :x, :y, :z)
end
us = LinRange(u_min, u_max, N)
value_(g, u::LinRange) = g.(u)
value_(g, u::Number) = g(u)
vs = @eval (LinRange(minimum($value_($v_min, $us)), maximum($value_($v_max, $us)), $N))
check(u, v, f) = @eval($value_($v_min, $u) <= $v && $value_($v_max, $u) >= $v ? $f($u, $v) : NaN)
value(g) = check.(us', vs, g)
x1 = @eval ($value($X))
y1 = @eval ($value($Y))
z1 = @eval ($value($Z))
return @eval($graph_all($x1, $y1, $z1, $Fx, $Fy, $Fz,
minimum(filter(!isnan, $x1)), maximum(filter(!isnan, $x1)),
minimum(filter(!isnan, $y1)), maximum(filter(!isnan, $y1)),
minimum(filter(!isnan, $z1)), maximum(filter(!isnan, $z1)), $density))
end
else # ______________________________________________f(x,y)
Fx = Fy = Fz = "_"
try
x_min = parse_num(x_min)
x_max = parse_num(x_max)
y_min = parse_function(y_min, :x)
y_max = parse_function(y_max, :x)
z_min = parse_function(z_min, :x, :y)
z_max = parse_function(z_max, :x, :y)
Fx = parse_function(F1, :x, :y, :z)
Fy = parse_function(F2, :x, :y, :z)
Fz = parse_function(F3, :x, :y, :z)
@eval (isa($Fx(-2, -2, -2), Number))
@eval (isa($Fy(-2, -2, -2), Number))
@eval (isa($Fz(-2, -2, -2), Number))
catch e
x_min = -2
y_min = parse_function("-2", :x)
z_min = parse_function("-2", :x, :y)
x_max = 2
y_max = parse_function("2", :x)
z_max = parse_function("2", :x, :y)
Fx = parse_function("0", :x, :y, :z)
Fy = parse_function("0", :x, :y, :z)
Fz = parse_function("0", :x, :y, :z)
end
if false #(x_min > x_max) | (y_min > y_max) | (z_min > z_max)
return Plot(surface(;
x = [0],
y = [0],
z = [[0], [0]]))
else
xs = LinRange(x_min, x_max, N)
value2_(g::Function, x::LinRange{Float64}) = g.(x)
value2_(g::Function, x::Number) = g(x)
ys = @eval (LinRange(minimum($value2_($y_min, $xs)), maximum($value2_($y_max, $xs)), $N))
check2(x::Number, y::Number, h::Function)::Float64 = @eval($value2_($y_min, $x) <= $y && $value2_($y_max, $x) >= $y ? $h($x, $y) : NaN)
value2(g) = check2.(xs', ys, g)
zs = @eval($value2($z_max))
z₀ = @eval($value2($z_min))
temp = deepcopy(zs)
zs[zs .< z₀] .= NaN
z₀[z₀ .> temp] .= NaN
return @eval($graph_all($xs, $ys, $zs, $Fx, $Fy, $Fz,
minimum($xs), maximum($xs),
minimum(filter(!isnan, $ys)), maximum(filter(!isnan, $ys)),
minimum(filter(!isnan, $z₀)), maximum(filter(!isnan, $zs)), $density, $z₀))
end
end
end
run_server(app, "0.0.0.0")
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220,
220,
1812,
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24396,
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12340,
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220,
220,
220,
220,
220,
220,
1812,
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1373,
62,
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62,
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16,
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220,
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220,
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1812,
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62,
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220,
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220,
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1812,
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62,
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220,
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1812,
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62,
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220,
220,
220,
220,
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220,
1812,
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62,
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220,
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1812,
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62,
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62,
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220,
220,
220,
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62,
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220,
220,
220,
220,
220,
220,
1812,
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89,
62,
9521,
16,
72,
1600,
366,
8367,
12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
7203,
89,
62,
9521,
17,
72,
1600,
366,
8367,
4943,
198,
220,
220,
220,
220,
220,
220,
220,
1267,
466,
299,
62,
565,
3378,
11,
4268,
2902,
62,
8367,
11,
374,
16,
11,
374,
17,
11,
374,
18,
11,
376,
87,
11,
376,
88,
11,
376,
89,
11,
8173,
11,
299,
11,
334,
62,
1084,
11,
334,
62,
9806,
11,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
410,
62,
1084,
11,
410,
62,
9806,
11,
2124,
62,
1084,
11,
2124,
62,
9806,
11,
331,
62,
1084,
11,
331,
62,
9806,
11,
1976,
62,
1084,
11,
1976,
62,
9806,
198,
220,
220,
220,
220,
220,
220,
220,
611,
4268,
2902,
62,
8367,
6624,
3689,
62,
58,
16,
60,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1949,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
334,
62,
1084,
11,
334,
62,
9806,
796,
21136,
62,
22510,
12195,
58,
84,
62,
1084,
11,
334,
62,
9806,
12962,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
279,
796,
21136,
62,
8818,
7,
22179,
7,
14692,
14692,
1635,
374,
16,
11,
374,
17,
11,
374,
18,
1635,
8973,
1,
16589,
33172,
366,
828,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
10662,
796,
21136,
62,
8818,
7,
22179,
7,
14692,
14692,
1635,
376,
87,
11,
376,
88,
11,
376,
89,
1635,
366,
30866,
4357,
33172,
366,
828,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
18074,
243,
796,
21136,
62,
8818,
7,
85,
62,
1084,
11,
1058,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
18074,
230,
796,
21136,
62,
8818,
7,
85,
62,
9806,
11,
1058,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
7,
69,
11,
308,
11,
257,
11,
275,
8,
796,
2835,
62,
22468,
7,
138,
99,
7,
69,
11,
308,
11,
357,
84,
62,
1084,
11,
334,
62,
9806,
828,
257,
11,
275,
26,
399,
796,
2558,
7,
77,
6184,
115,
362,
828,
8173,
796,
8173,
828,
352,
68,
12,
18,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
62,
796,
2488,
18206,
2352,
7,
16763,
8367,
16763,
80,
11,
720,
79,
11,
720,
139,
243,
11,
720,
139,
230,
22305,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
27711,
62,
71,
20,
7203,
91,
138,
99,
91,
796,
29568,
8367,
62,
21387,
11,
3918,
28,
35,
713,
7203,
5239,
2348,
570,
1,
5218,
366,
16159,
48774,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
4929,
304,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
27711,
62,
71,
20,
7203,
59,
3,
59,
3,
6852,
5239,
90,
39213,
506,
5128,
13,
9993,
757,
13,
32239,
3,
59,
3,
1600,
3918,
28,
35,
713,
7203,
5239,
2348,
570,
1,
5218,
366,
16159,
48774,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
198,
220,
220,
220,
220,
220,
220,
220,
2073,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1949,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
62,
1084,
11,
2124,
62,
9806,
796,
21136,
62,
22510,
12195,
58,
87,
62,
1084,
11,
2124,
62,
9806,
12962,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
10662,
796,
21136,
62,
8818,
7,
22179,
7,
14692,
14692,
1635,
376,
87,
11,
376,
88,
11,
376,
89,
1635,
366,
30866,
4357,
33172,
366,
828,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
18074,
243,
796,
21136,
62,
8818,
7,
88,
62,
1084,
11,
1058,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
18074,
230,
796,
21136,
62,
8818,
7,
88,
62,
9806,
11,
1058,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
18074,
223,
796,
21136,
62,
8818,
7,
89,
62,
1084,
11,
1058,
87,
11,
1058,
88,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
7377,
115,
796,
21136,
62,
8818,
7,
89,
62,
9806,
11,
1058,
87,
11,
1058,
88,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
7,
69,
11,
257,
11,
275,
11,
269,
11,
288,
8,
796,
2835,
62,
22468,
7,
138,
99,
7,
69,
11,
357,
87,
62,
1084,
11,
2124,
62,
9806,
828,
257,
11,
275,
11,
269,
11,
288,
26,
399,
796,
2558,
7,
77,
6184,
115,
362,
828,
8173,
796,
8173,
828,
352,
68,
12,
18,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
62,
796,
2488,
18206,
2352,
7,
16763,
8367,
16763,
80,
11,
720,
33643,
11,
720,
138,
115,
11,
720,
139,
243,
11,
720,
139,
230,
22305,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
27711,
62,
71,
20,
7203,
91,
138,
99,
91,
796,
29568,
8367,
62,
21387,
11,
3918,
28,
35,
713,
7203,
5239,
2348,
570,
1,
5218,
366,
16159,
48774,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
4929,
304,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
27711,
62,
71,
20,
7203,
59,
3,
59,
3,
26867,
5239,
90,
39213,
506,
5128,
13,
9993,
757,
44587,
3467,
3,
59,
3,
1600,
3918,
28,
35,
713,
7203,
5239,
2348,
570,
1,
5218,
366,
16159,
48774,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
198,
220,
220,
220,
220,
220,
220,
220,
886,
198,
437,
628,
198,
47423,
0,
7,
1324,
11,
198,
220,
220,
220,
220,
220,
220,
220,
25235,
7203,
42029,
62,
29487,
1600,
366,
26875,
12340,
198,
220,
220,
220,
220,
220,
220,
220,
23412,
7203,
46002,
12,
16539,
12,
5219,
1600,
366,
77,
62,
565,
3378,
12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
7203,
81,
16,
1600,
366,
8367,
12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
7203,
81,
17,
1600,
366,
8367,
12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
7203,
81,
18,
1600,
366,
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12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
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14781,
2902,
1600,
366,
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12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
7203,
34960,
62,
4134,
23843,
1600,
366,
8367,
12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
7203,
84,
62,
9521,
16,
72,
1600,
366,
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12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
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84,
62,
9521,
17,
72,
1600,
366,
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12340,
198,
220,
220,
220,
220,
220,
220,
220,
1812,
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85,
62,
9521,
16,
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366,
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12340,
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220,
220,
220,
220,
220,
220,
1812,
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62,
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12340,
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220,
220,
220,
220,
220,
220,
1812,
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87,
62,
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220,
220,
220,
220,
220,
1812,
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87,
62,
9521,
17,
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366,
8367,
12340,
198,
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220,
220,
220,
220,
220,
220,
1812,
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88,
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220,
220,
220,
220,
220,
1812,
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220,
1812,
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12340,
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220,
220,
220,
220,
220,
1812,
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9521,
17,
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12340,
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220,
220,
220,
220,
220,
220,
1812,
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37,
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12340,
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220,
220,
220,
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220,
1812,
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12340,
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220,
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220,
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1812,
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1812,
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3245,
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4943,
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220,
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220,
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220,
1267,
466,
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62,
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3378,
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16,
11,
374,
17,
11,
374,
18,
11,
4268,
2902,
62,
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399,
11,
334,
62,
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11,
334,
62,
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62,
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62,
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220,
220,
220,
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2124,
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11,
2124,
62,
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11,
331,
62,
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11,
331,
62,
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11,
1976,
62,
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11,
1976,
62,
9806,
11,
376,
16,
11,
376,
17,
11,
376,
18,
11,
12109,
628,
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220,
220,
220,
220,
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220,
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611,
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2902,
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6624,
3689,
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1303,
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2602,
37405,
17143,
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628,
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220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
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1949,
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220,
220,
220,
220,
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220,
220,
220,
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220,
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334,
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334,
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21136,
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220,
220,
220,
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21136,
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62,
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220,
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220,
220,
220,
220,
220,
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220,
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220,
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410,
62,
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21136,
62,
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7,
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62,
9806,
11,
1058,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
4929,
304,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
334,
62,
1084,
796,
532,
16,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
334,
62,
9806,
796,
352,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
410,
62,
1084,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
410,
62,
9806,
796,
21136,
62,
8818,
7203,
17,
14415,
1600,
1058,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
611,
3991,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
28114,
7,
42029,
7,
26,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
796,
685,
15,
4357,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
796,
685,
15,
4357,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
796,
16410,
15,
4357,
685,
15,
11907,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2073,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
87,
796,
376,
88,
796,
376,
89,
796,
45434,
1,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1395,
7,
84,
11,
410,
8,
796,
657,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
575,
7,
84,
11,
410,
8,
796,
657,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1168,
7,
84,
11,
410,
8,
796,
657,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1949,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1395,
796,
21136,
62,
8818,
7,
81,
16,
11,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
575,
796,
21136,
62,
8818,
7,
81,
17,
11,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1168,
796,
21136,
62,
8818,
7,
81,
18,
11,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
87,
796,
21136,
62,
8818,
7,
37,
16,
11,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
88,
796,
21136,
62,
8818,
7,
37,
17,
11,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
89,
796,
21136,
62,
8818,
7,
37,
18,
11,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
7198,
55,
32590,
17,
11,
513,
828,
720,
56,
32590,
17,
11,
513,
828,
720,
57,
32590,
17,
11,
513,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
55,
32590,
17,
11,
513,
828,
15690,
90,
43879,
2414,
11,
352,
92,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
56,
32590,
17,
11,
513,
828,
15690,
90,
43879,
2414,
11,
352,
92,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
57,
32590,
17,
11,
513,
828,
15690,
90,
43879,
2414,
11,
352,
92,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
37,
87,
32590,
17,
11,
532,
17,
11,
532,
17,
828,
7913,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
37,
88,
32590,
17,
11,
532,
17,
11,
532,
17,
828,
7913,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
37,
89,
32590,
17,
11,
532,
17,
11,
532,
17,
828,
7913,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
4929,
304,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1395,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
575,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1168,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
84,
11,
1058,
85,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
87,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
88,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
89,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
628,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
514,
796,
5164,
17257,
7,
84,
62,
1084,
11,
334,
62,
9806,
11,
399,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
41052,
70,
11,
334,
3712,
14993,
17257,
8,
796,
308,
12195,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
41052,
70,
11,
334,
3712,
15057,
8,
796,
308,
7,
84,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
3691,
796,
2488,
18206,
357,
14993,
17257,
7,
39504,
16763,
8367,
62,
16763,
85,
62,
1084,
11,
720,
385,
36911,
5415,
16763,
8367,
62,
16763,
85,
62,
9806,
11,
720,
385,
36911,
720,
45,
4008,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2198,
7,
84,
11,
410,
11,
277,
8,
796,
2488,
18206,
16763,
8367,
62,
16763,
85,
62,
1084,
11,
720,
84,
8,
19841,
720,
85,
11405,
720,
8367,
62,
16763,
85,
62,
9806,
11,
720,
84,
8,
18189,
720,
85,
5633,
720,
69,
16763,
84,
11,
720,
85,
8,
1058,
11013,
45,
8,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
7,
70,
8,
796,
2198,
12195,
385,
3256,
3691,
11,
308,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
16,
796,
2488,
18206,
7198,
8367,
16763,
55,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
16,
796,
2488,
18206,
7198,
8367,
16763,
56,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
16,
796,
2488,
18206,
7198,
8367,
16763,
57,
4008,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
2488,
18206,
16763,
34960,
62,
439,
16763,
87,
16,
11,
720,
88,
16,
11,
720,
89,
16,
11,
720,
37,
87,
11,
720,
37,
88,
11,
720,
37,
89,
11,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
5288,
7,
24455,
7,
0,
271,
12647,
11,
720,
87,
16,
36911,
5415,
7,
24455,
7,
0,
271,
12647,
11,
720,
87,
16,
36911,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
5288,
7,
24455,
7,
0,
271,
12647,
11,
720,
88,
16,
36911,
5415,
7,
24455,
7,
0,
271,
12647,
11,
720,
88,
16,
36911,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
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220,
220,
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220,
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220,
220,
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5288,
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220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2073,
220,
1303,
220,
10221,
2602,
25947,
69,
7,
87,
11,
88,
8,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
87,
796,
376,
88,
796,
376,
89,
796,
45434,
1,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1949,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
62,
1084,
796,
21136,
62,
22510,
7,
87,
62,
1084,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
62,
9806,
796,
21136,
62,
22510,
7,
87,
62,
9806,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
62,
1084,
796,
21136,
62,
8818,
7,
88,
62,
1084,
11,
1058,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
62,
9806,
796,
21136,
62,
8818,
7,
88,
62,
9806,
11,
1058,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
62,
1084,
796,
21136,
62,
8818,
7,
89,
62,
1084,
11,
1058,
87,
11,
1058,
88,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
62,
9806,
796,
21136,
62,
8818,
7,
89,
62,
9806,
11,
1058,
87,
11,
1058,
88,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
87,
796,
21136,
62,
8818,
7,
37,
16,
11,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
88,
796,
21136,
62,
8818,
7,
37,
17,
11,
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87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
89,
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21136,
62,
8818,
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37,
18,
11,
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87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
37,
87,
32590,
17,
11,
532,
17,
11,
532,
17,
828,
7913,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
37,
88,
32590,
17,
11,
532,
17,
11,
532,
17,
828,
7913,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2488,
18206,
357,
9160,
16763,
37,
89,
32590,
17,
11,
532,
17,
11,
532,
17,
828,
7913,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
4929,
304,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
62,
1084,
796,
532,
17,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
62,
1084,
796,
21136,
62,
8818,
7203,
12,
17,
1600,
1058,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
62,
1084,
796,
21136,
62,
8818,
7203,
12,
17,
1600,
1058,
87,
11,
1058,
88,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
62,
9806,
796,
362,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
62,
9806,
796,
21136,
62,
8818,
7203,
17,
1600,
1058,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
62,
9806,
796,
21136,
62,
8818,
7203,
17,
1600,
1058,
87,
11,
1058,
88,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
87,
796,
21136,
62,
8818,
7203,
15,
1600,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
88,
796,
21136,
62,
8818,
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15,
1600,
1058,
87,
11,
1058,
88,
11,
1058,
89,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
376,
89,
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21136,
62,
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15,
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11,
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88,
11,
1058,
89,
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198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
611,
3991,
220,
1303,
7,
87,
62,
1084,
1875,
2124,
62,
9806,
8,
930,
357,
88,
62,
1084,
1875,
331,
62,
9806,
8,
930,
357,
89,
62,
1084,
1875,
1976,
62,
9806,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
28114,
7,
42029,
7,
26,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
796,
685,
15,
4357,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
796,
685,
15,
4357,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
796,
16410,
15,
4357,
685,
15,
11907,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2073,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2124,
82,
796,
5164,
17257,
7,
87,
62,
1084,
11,
2124,
62,
9806,
11,
399,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
17,
41052,
70,
3712,
22203,
11,
2124,
3712,
14993,
17257,
90,
43879,
2414,
30072,
796,
308,
12195,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
17,
41052,
70,
3712,
22203,
11,
2124,
3712,
15057,
8,
796,
308,
7,
87,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
331,
82,
796,
2488,
18206,
357,
14993,
17257,
7,
39504,
16763,
8367,
17,
62,
16763,
88,
62,
1084,
11,
720,
34223,
36911,
5415,
16763,
8367,
17,
62,
16763,
88,
62,
9806,
11,
720,
34223,
36911,
720,
45,
4008,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
2198,
17,
7,
87,
3712,
15057,
11,
331,
3712,
15057,
11,
289,
3712,
22203,
2599,
25,
43879,
2414,
796,
2488,
18206,
16763,
8367,
17,
62,
16763,
88,
62,
1084,
11,
720,
87,
8,
19841,
720,
88,
11405,
720,
8367,
17,
62,
16763,
88,
62,
9806,
11,
720,
87,
8,
18189,
720,
88,
5633,
720,
71,
16763,
87,
11,
720,
88,
8,
1058,
11013,
45,
8,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1988,
17,
7,
70,
8,
796,
2198,
17,
12195,
34223,
3256,
331,
82,
11,
308,
8,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
82,
796,
2488,
18206,
16763,
8367,
17,
16763,
89,
62,
9806,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
158,
224,
222,
796,
2488,
18206,
16763,
8367,
17,
16763,
89,
62,
1084,
4008,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
20218,
796,
2769,
30073,
7,
89,
82,
8,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
82,
58,
89,
82,
764,
27,
1976,
158,
224,
222,
60,
764,
28,
11013,
45,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1976,
158,
224,
222,
58,
89,
158,
224,
222,
764,
29,
20218,
60,
764,
28,
11013,
45,
628,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
1441,
2488,
18206,
16763,
34960,
62,
439,
16763,
34223,
11,
720,
893,
11,
720,
89,
82,
11,
720,
37,
87,
11,
720,
37,
88,
11,
720,
37,
89,
11,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
5288,
16763,
34223,
828,
5415,
16763,
34223,
828,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
5288,
7,
24455,
7,
0,
271,
12647,
11,
720,
893,
36911,
5415,
7,
24455,
7,
0,
271,
12647,
11,
720,
893,
36911,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
5288,
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24455,
7,
0,
271,
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5415,
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82,
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720,
43337,
11,
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4008,
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220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
198,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
220,
886,
198,
220,
220,
220,
220,
220,
220,
220,
886,
628,
198,
5143,
62,
15388,
7,
1324,
11,
366,
15,
13,
15,
13,
15,
13,
15,
4943,
198
] | 1.663592 | 9,432 |
using SigmaRidgeRegression
using Test
using Random
import StatsBase
ar1_design = BlockCovarianceDesign([
AR1Design(;ρ=0.8),
AR1Design(;ρ=0.5)])
id_design = BlockCovarianceDesign([
IdentityCovarianceDesign(),
IdentityCovarianceDesign()])
grp1 = GroupedFeatures([2000,4000])
grp2 = GroupedFeatures([800,500])
for grp in [grp1; grp2]
for _design in [ar1_design; id_design]
_design = set_groups(_design, grp)
_n = 2000
_γs = grp.ps ./ _n
_λs = [2.0; 0.4]
_αs = [1.0; 7.0]
theory_risk = @show SigmaRidgeRegression.risk_formula(spectrum.(_design.blocks), _γs, _αs, _λs)
_ridge_sim = GroupRidgeSimulationSettings(;
groups=grp,
ntrain=_n,
ntest=20_000,
Σ=_design,
response_model=RandomLinearResponseModel(; αs=_αs, grp=grp),
)
Random.seed!(1)
_sim_res = simulate(_ridge_sim)
_X_train = _sim_res.X[_sim_res.resampling_idx[1][1],:]
_Y_train = _sim_res.Y[_sim_res.resampling_idx[1][1]]
_X_test = _sim_res.X[_sim_res.resampling_idx[1][2],:]
_Y_test = _sim_res.Y[_sim_res.resampling_idx[1][2]]
ridge_risk = mse_ridge(
StatsBase.fit(
MultiGroupRidgeRegressor(; groups=grp, λs=_λs, center=false, scale=false),
_X_train,
_Y_train,
grp,
),
_X_test,
_Y_test,
)
@test ridge_risk ≈ theory_risk atol =1.0
end
end
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] | 1.789354 | 883 |
"""
AbstractLattice
Contains information about a crystal lattice.
"""
abstract type AbstractLattice
end
"""
RealLattice{N}
Describes an N-dimensional real space crystal lattice, with an associated primitive and
conventional lattice. These lattices may be the same depending on the lattice type.
"""
struct RealLattice{N} <: AbstractLattice
# Primitive and conventional lattice vectors are stored together
prim::SVector{N,SVector{N,Float64}}
conv::SVector{N,SVector{N,Float64}}
end
# TODO: Implement lattice checking and conversion
# Some of this functionality might already be present in Crystalline.jl
# However, we need to be able to recognize primitive lattices with their own unique conditions
"""
nuniqlen(basis::AbstractVector{<:AbstractVector{<:Real}}) -> Int
Returns the number of vectors that are the same length.
"""
function nuniqlen(basis::AbstractVector{<:AbstractVector{<:Real}})
# unique!() does better than unique() here (per @btime)
return length(unique!(norm.(basis)))
end
# Same thing for matrices
nuniqlen(basis::AbstractMatrix{<:Real}) = nuniqlen(_tovectors(basis))
"""
northog(basis::AbstractVector{<:AbstractVector{<:Real}}) -> Int
Returns the number of pairs of orthogonal vectors.
"""
function northog(basis::AbstractVector{<:AbstractVector{<:Real}})
# FIXME: This doesn't work for arbitrary dimensions
# It needs to use the upper portion of the dot product matrix
return count(iszero, dot.(basis, basis[circshift(1:length(basis), 1)]))
end
northog(basis::AbstractMatrix{<:Real}) = northog(_tovectors(basis))
# TODO: Write a number of tests for checking if lattices meet certain criteria
#=
Criteria for primitive unit cells in 3 dimensions:
aP: 6 parameters (a, b, c, α, β, γ)
mP: 4 parameters (a, b, c, β), α = γ = 90°
mS: 4 parameters (a, c, α, γ), a = b, α = β
oP: 3 parameters (a, b, c), α = β = γ = 90°
oS: 3 parameters (a, c, γ), a = b, α = β = 90°
oI: 3 parameters (a, α, γ), a = b = c, |cos(α)| + |cos(β)| + |cos(γ)| = 1
oF: 3 parameters (a, b, c), sin(α)/a = sin(β)/b = sin(γ)/c, α + β + γ = 180°
3 parameters (a, c, γ), [forgot the rest of this alternate test]
tP: 2 parameters (a, c), a = b, α = β = γ = 90°
tI: 2 parameters (a, α), a = b = c, |cos(α)| + |cos(β)| + |cos(γ)| = 1
hP: 2 parameters (a, c), a = b, α = β = 90°, γ = 120°
hR: 2 parameters (a, α), a = b = c, α = β = γ
cP: 1 parameter (a), a = b = c, α = β = γ = 90°
cI: 1 parameter (a), a = b = c, α = β = γ = arccos(-1/3)°
cF: 1 parameter (a), a = b = c, α = β = γ = 60°
Rules that need to be checked:
Number of unique lengths
Number of orthogonal vectors
Number of unique angles
Cosine rule: |cos(α)| + |cos(β)| + |cos(γ)| = 1
Sine rule: sin(α)/a = sin(β)/b = sin(γ)/c, α + β + γ = 180°
The last three are probably going to be trickier to implement, or at the very least there
might be some unintuitive linear algebra tricks to make those checks happen faster.
=#
# TODO: what are the crtieria for a "good" lattice basis?
# Potentially worth looking at the Niggli reduction algorithm to do this
# TODO: Tools for working with reciprocal space lattices | [
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] | 2.726039 | 1,179 |
# # Singular Integrals
# This example shows how to use the `Integration` module for computing
# quadrature rules for functions with point singularities (such as those
# appearing in the numerical discretization of boundary integral equations).
# ## Change of variables
# The first set of *tricks* revolve a round a simple change of variables. We
# focus first on the one-dimensional case, where we wish to integrate
```math
\int_0^1 f(x) dx,
```
# and where the function ``f`` can have an integrable singularity at
using WaveProp.Geometry
using WaveProp.Integration
using WaveProp.Integration
using QuadGK
f = (x) -> x==0 ? 0.0 : log(abs(x))*cos(x)
I,_ = quadgk(f,0,1,rtol=1e-16)
rows = GaussLegendre.([5,10,20,40,80])
cols = [identity,IMT{1,2}(),Kress{8}(), Window{1,1,7}()]
ee = []
for qstd in rows
for shandler in cols
q = SingularQuadratureRule(qstd,shandler)
Is = integrate(f,q)
er = abs(I-Is)
push!(ee,er)
end
end
using NamedArrays
ee = reshape(ee,length(cols),length(rows)) |> transpose |> NamedArray
setnames!(ee,string.(rows),1)
setnames!(ee,string.(cols),2)
setdimnames!(ee,["Base quadrature","Singularity handler"])
show(ee)
# ##
# using Plots
# qstd = GaussLegendre(10)
# x̂,ŵ = qstd()
# cols = [IMT{1,2}(),Kress{8}(), Window{0.5,1,7}()]
# fig = plot()
# for shandler in cols
# phi = shandler.(x̂)
# phip = [jacobian(shandler,x)[1] for x in x̂]
# plot!(fig,x̂,f.(phi) .* phip,label=string(shandler),m=:x)
# end
# display(fig)
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] | 2.278665 | 689 |
struct Acronym
word::String
components::Vector{Union{String, Nothing}}
nvals::Vector{Int}
end
struct AcronymFamily
word::String
n_max::Int
components::Matrix{Vector{String}}
end
Base.show(io::IO, af::AcronymFamily) = print(io, typeof(af), "(\"", af.word, "\", ", af.n_max, ", ...)")
function _family_traces(af::AcronymFamily)
max_n, l = size(af.components)
a = [Vector{Tuple{Int, Int}}[] for _ in af.components]
for i in l:-1:1, n in 1:max_n
n > 1 && isempty(af.components[n, i]) && continue # No components
ind = (i, n)
next = i + n
if next == l + 1 # Last
push!(a[n, i], [ind])
elseif next <= l
for nexttraces in a[:, next]
for nexttrace in nexttraces
push!(a[n, i], vcat(ind, nexttrace))
end
end
end
end
return vcat(a[:, 1]...)
end
function acronyms(af::AcronymFamily, trace::AbstractVector{NTuple{2, Int}})
comp_lists = [af.components[n, i] for (i, n) in trace]
nvals = last.(trace)
comps_iter = Iterators.product((isempty(c) ? [nothing] : c for c in comp_lists)...)
return (Acronym(af.word, collect(comp), nvals) for comp in comps_iter)
end
acronyms(af::AcronymFamily) = Iterators.flatten(acronyms(af, trace) for trace in _family_traces(af))
function generate_acronyms(word::String, max_n::Int, prefix_map::Dict)
word = lowercase(word)
l = length(word)
components = Matrix{Vector{String}}(undef, max_n, l)
for i in 1:l
for j in 1:max_n
if i + j - 1 > l
components[j, i] = String[]
else
prefix = word[i:(i + j - 1)]
components[j, i] = get(prefix_map, prefix, String[])
end
end
end
return AcronymFamily(word, max_n, components)
end
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7,
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62,
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8,
198,
437,
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] | 2.015528 | 966 |
module VoronoiCells
# We do not compile
# 1. VoronoiDelaunay is not compiled.
# 2. VoronoiCells itself loads in about 100ms
include("voronoi_cells.jl")
include("store_cells.jl")
end # module
| [
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# breadth first search
function bfs(goal, start)
reset_timer!(to::TimerOutput)
node = createtree(start)
if node.state == goal
return node
end
frontier = [node]
reached = [node.state]
while !isempty(frontier)
@timeit to "Moves" acts = moves(node.state)
@timeit to "Pop" node = popfirst!(frontier)
@timeit to "Expand" states = expansion(node.state)
for (currentstate, currentaction) in zip(states, acts)
if currentstate == goal
sovle = addnode(currentaction, node, currentstate)
displaysolution(sovle)
return sovle
end
if !in(currentstate, reached)
@timeit to "Node Creation" currentnode = addnode(currentaction, node, currentstate)
@timeit to "Push" push!(frontier, currentnode)
end
end
end
println("No solutions found!"^10)
return nothing
end | [
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] | 2.205479 | 438 |
push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch2.dat")
include("../../Basin.jl")
pop!(ARGS)
#=
push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch3.dat")
include("../../Basin.jl")
pop!(ARGS)
push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch3.dat")
include("../../Basin.jl")
pop!(ARGS)
push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch4.dat")
include("../../Basin.jl")
pop!(ARGS)
push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch5.dat")
include("../../Basin.jl")
pop!(ARGS)
=#
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] | 2.244 | 250 |
using Base: Broadcast.DefaultArrayStyle, AbstractUnitRange
_broadcasted(style, f, x, r::AbstractRange) = invoke(Base.Broadcast.broadcasted, Tuple{typeof(style),typeof(f),Any,typeof(r)}, style, f, x, r)
_broadcasted(style, f, r::AbstractRange, x) = invoke(Base.Broadcast.broadcasted, Tuple{typeof(style),typeof(f),typeof(r),Any}, style, f, r, x)
for f in (+, -, *, /, \), R in (AbstractRange, AbstractUnitRange, StepRangeLen)
@eval begin
Base.Broadcast.broadcasted(style::DefaultArrayStyle{1}, ::typeof($f), x::Measurement, r::$R) = _broadcasted(style, $f, x, r)
Base.Broadcast.broadcasted(style::DefaultArrayStyle{1}, ::typeof($f), r::$R, x::Measurement) = _broadcasted(style, $f, r, x)
end
end
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] | 2.538732 | 284 |
# Testing the Small Demo
# Copyright (c) 2015 Harold Soh
# based on MATLAB code by Mark Schmidt
# For more details, see: http://www.cs.ubc.ca/~schmidtm/Software/UGM/small.html
include("../src/UGM.jl")
using UGM
using Base.Test
include("testUtils.jl")
# ======================================
# Simple Independent Node Test
# ======================================
srand(0)
nodepot = [ 1 3;
9 1;
1 3;
9 1 ]
nsamples = 100;
samples = zeros(4, nsamples)
for i = 1:4
for s = 1:nsamples
samples[i,s] = sampleDiscrete(nodepot[i,:]/sum(nodepot[i,:]));
end
end
sum_samples = sum(samples,2)
println("Sum Samples: ", sum_samples')
gold_result = [172; 107; 168; 110] # at seed 0
@test all(sum_samples .== gold_result)
print("Independent Nodes Test: ")
printPassed()
# ======================================
# Set up Dependent Nodes
# ======================================
nnodes = 4
nstates = 2
edgelist = [ 1 2;
2 1;
2 3;
3 2;
3 4;
4 3]
# Make Edge Structure
es = EdgeStruct(edgelist = edgelist, nstates = nstates, maxiter = 25)
# edgestruct tests
@test es.edgeends == [1 2; 2 3; 3 4]
@test es.edgedict[1] == Set([2])
@test es.edgedict[2] == Set([1,3])
@test es.edgedict[3] == Set([2,4])
@test es.edgedict[4] == Set([3])
@test es.nnodes == 4
@test es.nedges == 3
@test all(es.nstates .== [2.0; 2.0; 2.0; 2.0])
@test es.maxiter == 25
print("Edge Structure Test: ")
printPassed()
# Node potentials
nodepot = [1 3;
9 1;
1 3;
9 1]
# Edge potentials
maxstate = maximum(es.nstates);
edgepot = zeros( int(maxstate), int(maxstate), int(es.nedges));
for e = 1:es.nedges
edgepot[:,:,e] = [2 1 ; 1 2];
end
# ======================================
# Decoding
# ======================================
optdecoding = decodeExact(nodepot,edgepot,es)
println("Optimal Decoding: ", optdecoding')
@test all(optdecoding .== [2.0; 1.0; 1.0; 1.0])
print("Exact Decoding Test: ")
printPassed()
# ======================================
# Inference
# ======================================
nodebel,edgebel,logZ,Z = inferExact(nodepot,edgepot,es)
@test nodebel == [0.3596306068601583 0.6403693931398416
0.8430079155672823 0.15699208443271767
0.4862796833773087 0.5137203166226912
0.8810026385224274 0.11899736147757256]
@test edgebel[:,:,1] == [0.33720316622691293 0.022427440633245383
0.5058047493403693 0.1345646437994723]
@test edgebel[:,:,2] == [0.45118733509234826 0.391820580474934
0.03509234828496042 0.12189973614775726]
@test edgebel[:,:,3] == [0.46068601583113455 0.02559366754617414
0.4203166226912929 0.09340369393139841]
@test_approx_eq_eps(logZ, 8.240121298, 1e-8)
print("Exact Inference Test: ")
printPassed()
# ======================================
# Sampling Test
# ======================================
es.maxiter = 100
samples = sampleExact(nodepot,edgepot,es)
@test all(samples[1,:] .== [2.0 1.0 2.0 2.0])
@test all(samples[4,:] .== [2.0 2.0 2.0 1.0])
@test all(samples[100,:] .== [2.0 1.0 2.0 1.0])
print("Exact Sampling Test: ")
printPassed()
# println(samples)
# using Gadfly
# spy(samples)
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8,
198
] | 2.24846 | 1,461 |
using DelimitedFiles
function solve(input)
raw = vcat(readdlm(input,Int16)...)
p1 = process(copy(raw),aggregate)
@show p1
p2 = process(copy(raw),findRootValue)
@show p2
end
function process(list, f)
numChildren = popfirst!(list)
numMeta = popfirst!(list)
return f(ntimes(numChildren,list,f), splice!(list,1:numMeta))
end
function ntimes(n,list, f)
result = Int16[]
for i in 1:n
push!(result,process(list,f))
end
return result
end
function aggregate(child,metadata)
return sum(child) + sum(metadata)
end
function childValue((child,value),index)
if length(child)>index
value+=child[index+1]
else
value+= 0
end
return (child,value)
end
function findRootValue(child,metadata)
pushfirst!(child,0)
if length(child) == 1
return sum(metadata)
else
return reduce(childValue,metadata,init=(child,0))[2]
end
end
solve("input.txt")
| [
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] | 2.367246 | 403 |
function runSimulation(p::precipParam)
doInitialPrinting(p)
if p.runID == 1
mainDriver(p::precipParam)
elseif p.runID == 2
pureDiffusionOneChemicalTestDriver(p)
elseif p.runID == 3
pureAdvectionOneChemicalTestDriver(p)
elseif p.runID == 4
AdvectionDiffusionOneChemicalTestDriver(p)
elseif p.runID == 5
MultiphaseBrinkmanTestDriver(p)
elseif p.runID == 6
DiffusionAndReactionTwoChemicalTestDriver(p)
elseif p.runID == 7
pureReactionTestDriver(p)
else
println("runID of ",p.runID," not recognized.")
println("runID 1-7 required")
end
nothing
end
function mainDriver(p::precipParam)
timer, mesh, soln, tsoln, prob = initializeData(p)
# initial brinkman
mpbparam = BrinkmanMPParam(1.0,mpbFriction(soln.θf.u),soln.θf.u)
sol = solve(prob.fluid,mesh.fMesh,mpbparam)
tsoln.fluid.u = sol.u
tsoln.fluid.v = sol.v
tsoln.fluid.p = sol.p
intializeTimeSteppingTimer!(timer)
doPrinting!(timer,p,mesh,tsoln)
while timer.simulationTime < timer.finalTime
#Ninterp = 80
#interpVals = zeros(Ninterp,6)
#surf = mySurface([0.5,0.37],[0.5,-0.37])
# reaction
computeReaction!(p,tsoln)
soln.θs.u = tsoln.θs.u
soln.θf.u = tsoln.θf.u
θfn = normalize_thetaf(tsoln.θf.u)
peAnormalized = p.PeA./(θfn .+ 0.0 .*(1 .- θfn)) # 0.0 -> 0.5
peBnormalized = p.PeB./(θfn .+ 0.0 .*(1 .- θfn)) # 0.0 -> 0.25
ψAParam = AdvDiffParam(tsoln.fluid.u,tsoln.fluid.v,peAnormalized)
ψBParam = AdvDiffParam(tsoln.fluid.u,tsoln.fluid.v,peBnormalized)
ψCParam = AdvDiffParam(tsoln.fluid.u,tsoln.fluid.v,p.PeC./θfn)
# advection-diffusion
M = generateMassMatrixWScalar(mesh.sMesh,θfn)
StiffA = GenerateSystem(mesh.sMesh,prob.ψA,ψAParam)
ApplyBC!(StiffA,mesh.sMesh,prob.ψA,ψAParam,prob.ψA.OperatorType)
StiffB = GenerateSystem(mesh.sMesh,prob.ψB,ψBParam)
ApplyBC!(StiffB,mesh.sMesh,prob.ψB,ψBParam,prob.ψB.OperatorType)
StiffC = GenerateSystem(mesh.sMesh,prob.ψC,ψCParam)
ApplyBC!(StiffC,mesh.sMesh,prob.ψC,ψCParam,prob.ψC.OperatorType)
if timer.stepIndex < 5
soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=:backwardeuler)
soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=:backwardeuler)
soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=:backwardeuler)
else
soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=p.integrator)
soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=p.integrator)
soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=p.integrator)
end
# scrub scalars so they don't go below zero.
for i=1:length(soln.ψA.u)
if soln.ψA.u[i] < 0
soln.ψA.u[i] = 0.0
end
if soln.ψB.u[i] < 0
soln.ψB.u[i] = 0.0
end
if soln.ψC.u[i] < 0
soln.ψC.u[i] = 0.0
end
end
# brinkman
# normalize thetaf
mpbparam = BrinkmanMPParam(1.0,mpbFriction(θfn),θfn)
sol = solve(prob.fluid,mesh.fMesh,mpbparam)
soln.fluid.u = sol.u
soln.fluid.v = sol.v
soln.fluid.p = sol.p
# inteprolate values
#xvals = zeros(length(mesh.sMesh.xy))
#yvals = zeros(length(mesh.sMesh.xy))
#for i=1:length(mesh.sMesh.xy)
# xvals[i] = mesh.sMesh.xy[i].x
# yvals[i] = mesh.sMesh.xy[i].y
#end
#vmag = sqrt.(soln.fluid.u.^2 + soln.fluid.v.^2)
#interpVals[:,1] = SurfaceInterp(mesh.sMesh,xvals,surf,Ninterp-1)
#interpVals[:,2] = SurfaceInterp(mesh.sMesh,yvals,surf,Ninterp-1)
#interpVals[:,3] = SurfaceInterp(mesh.sMesh,soln.ψA.u,surf,Ninterp-1)
#interpVals[:,4] = SurfaceInterp(mesh.sMesh,soln.ψB.u,surf,Ninterp-1)
#interpVals[:,5] = SurfaceInterp(mesh.sMesh,soln.θs.u,surf,Ninterp-1)
#interpVals[:,6] = SurfaceInterp(mesh.fMesh,vmag,surf,Ninterp-1)
tsoln = deepcopy(soln)
if isPrintIndex(timer)
# save interpolated values
#savefile = string(p.SaveFolder,"/interpVals_",timer.printIndex,".jld2")
#save(savefile, "time", timer.simulationTime, "interpVals", interpVals)
# ordinary printing
doPrinting!(timer,p,mesh,soln)
end
updateSimulationTime!(timer)
updateStepIndex!(timer)
end
printSimulationFinishedMessage(timer)
nothing
end
function normalize_thetaf(θf::Vector{T}) where T<:Real
N=length(θf)
θf_normalized = zeros(T,N)
TOL = 0.1
for i=1:N
if θf[i] < TOL
θf_normalized[i] = TOL
else
θf_normalized[i] = θf[i]
end
end
return θf_normalized
end
function pureDiffusionOneChemicalTestDriver(p::precipParam)
timer, mesh, soln, tsoln, prob = initializeData(p)
ψAParam = PoissonParam(p.κA)
for i=1:length(soln.θf.u)
soln.θf.u[i] = 0.1
end
M = generateMassMatrixWScalar(mesh.sMesh,soln.θf.u)
StiffA = GenerateSystem(mesh.sMesh,prob.ψA,ψAParam)
ApplyBC!(StiffA,mesh.sMesh,prob.ψA,ψAParam,prob.ψA.OperatorType)
intializeTimeSteppingTimer!(timer)
doPrinting!(timer,p,mesh,soln)
while timer.simulationTime < timer.finalTime
if timer.stepIndex < 5
soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=:backwardeuler)
else
soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=p.integrator)
end
tsoln = deepcopy(soln)
if isPrintIndex(timer)
doPrinting!(timer,p,mesh,soln)
end
updateSimulationTime!(timer)
updateStepIndex!(timer)
end
printSimulationFinishedMessage(timer)
nothing
end
function pureAdvectionOneChemicalTestDriver(p::precipParam)
println("pure advection test driver isn't programmed yet")
nothing
end
function AdvectionDiffusionOneChemicalTestDriver(p::precipParam)
println("advection-diffusion test driver isn't programmed yet")
nothing
end
function MultiphaseBrinkmanTestDriver(p::precipParam)
function computeNorms(N)
start = time()
# load mesh
mesh = squareMeshFluid([-2,2,-1,1],N)
α1(x,y) = 1.0
α2(x,y) = 0.5+0.4*cos(3*x*y)
α3(x,y) = 0.5+0.4*sin(7*x*y)
xm = [i.x for i in mesh.xy]
ym = [i.y for i in mesh.xy]
α1arr = [α1(xm[i],ym[i]) for i=1:length(mesh.xy)]
α2arr = [α2(xm[i],ym[i]) for i=1:length(mesh.xy)]
α3arr = [α3(xm[i],ym[i]) for i=1:length(mesh.xy)]
param = BrinkmanMPParam(α1arr,α2arr,α3arr)
OperatorType = :BrinkmanMP2D
dNodes = Dirichlet(:left,:top,:bottom,:right)
Nodes = [dNodes]
u(x,y) = -x^4*y^2
v(x,y) = 4x^3*y^3/3
dUBCf = Dirichlet( (x,y) -> u(x,y) )
dVBCf = Dirichlet( (x,y) -> v(x,y) )
d2dudx(x,y) = -12*x^2*y^2; d2dudy(x,y) = -2*x^4
d2dvdx(x,y) = 8*x*y^3; d2dvdy(x,y) = 8*x^3*y
lapu(x,y) = d2dudx(x,y) + d2dudy(x,y)
lapv(x,y) = d2dvdx(x,y) + d2dvdy(x,y)
dpdx(x,y) = 3*x^2*y^3; dpdy(x,y) = 3*x^3*y^2
Fx(x,y) = -α1(x,y)*lapu(x,y) + α2(x,y)*u(x,y) + α3(x,y)*dpdx(x,y)
Fy(x,y) = -α1(x,y)*lapv(x,y) + α2(x,y)*v(x,y) + α3(x,y)*dpdy(x,y)
ffx = Forcing(Fx)
ffy = Forcing(Fy)
bcfun = [dUBCf,dVBCf,ffx,ffy]
prob = Problem(mesh,Nodes,bcfun,OperatorType)
sol = solve(prob,mesh,param)
elapsed = time()-start
# compute condition number of operator matrix
#LinOp = GenerateSystem(mesh,prob,param)
#ApplyBC!(LinOp,mesh,prob,param,OperatorType)
#κ = cond(Array(LinOp.Op),2)
κ = 0.5
# compute mesh h
h = hCalc(mesh)
# generate exact solution
Uexact(x,y) = dUBCf.f(x,y)
Vexact(x,y) = dVBCf.f(x,y)
Pexact(x,y) = x^3*y^3
UexactArr = [Uexact.(mesh.xy[i].x,mesh.xy[i].y) for i=1:length(mesh.xy)]
VexactArr = [Vexact.(mesh.xy[i].x,mesh.xy[i].y) for i=1:length(mesh.xy)]
PexactArr = [Pexact.(mesh.xyp[i].x,mesh.xyp[i].y) for i=1:length(mesh.xyp)]
# compute difference
velErr = sqrt.((sol.u - UexactArr).^2 + (sol.v -VexactArr).^2)
presErr = sol.p - PexactArr
# compute Li norm
L1v = DomainNorm(mesh.xy,mesh.cm,velErr;normID="1")
L2v = DomainNorm(mesh.xy,mesh.cm,velErr;normID="2")
Linfv = DomainNorm(mesh.xy,mesh.cm,velErr;normID="Inf")
L1p = DomainNorm(mesh.xyp,mesh.cmp,presErr;normID="1")
L2p = DomainNorm(mesh.xyp,mesh.cmp,presErr;normID="2")
Linfp = DomainNorm(mesh.xyp,mesh.cmp,presErr;normID="Inf")
# plot solution
sD = ScalarData(sol.p,α1arr,α2arr,α3arr)
sN = ScalarNames("pressure","alpha_1","alpha_2","alpha_3")
vD = VectorData([sol.u,sol.v])
vN = VectorNames("velocity")
fn = Path("solution_var")
vtksave(mesh,sD,sN,vD,vN,fn)
# plot solution
sD = ScalarData(PexactArr)
sN = ScalarNames("pressure")
vD = VectorData([UexactArr,VexactArr])
vN = VectorNames("velocity")
fn = Path("exact_var")
vtksave(mesh,sD,sN,vD,vN,fn)
return κ,h,L1v,L2v,Linfv,L1p,L2p,Linfp,elapsed
end
Narr = [4,4,8,16,32,64]#,96]
N = length(Narr)
harr = zeros(N)
L1arrV = zeros(N)
L2arrV = zeros(N)
LInfarrV = zeros(N)
L1arrP = zeros(N)
L2arrP = zeros(N)
LInfarrP = zeros(N)
timearr = zeros(N)
κarr = zeros(N)
for i=1:N
n = Narr[i]
κarr[i],harr[i],L1arrV[i],L2arrV[i],LInfarrV[i],
L1arrP[i],L2arrP[i],LInfarrP[i],timearr[i] =
computeNorms(n)
println("completed N=$(n)")
end
κarr = κarr[2:end]
harr = harr[2:end]
L1arrV = L1arrV[2:end]
L2arrV = L2arrV[2:end]
LInfarrV = LInfarrV[2:end]
L1arrP = L1arrP[2:end]
L2arrP = L2arrP[2:end]
LInfarrP = LInfarrP[2:end]
timearr = timearr[2:end]
# export output to *.jld file
run(`mkdir -p data`)
save("data/TEMP_mpb2D_validation.jld", "harr",harr,
"VL1arr", L1arrV,
"VL2arr", L2arrV,
"VLInfarr",LInfarrV,
"PL1arr", L1arrP,
"PL2arr", L2arrP,
"PLInfarr",LInfarrP,
"timearr",timearr,
"κarr",κarr)
nothing
end
function DiffusionAndReactionTwoChemicalTestDriver(p::precipParam)
timer, mesh, soln, tsoln, prob = initializeData(p)
ψAParam = PoissonParam(p.κA)
ψBParam = PoissonParam(p.κB)
ψCParam = PoissonParam(p.κC)
M = generateMassMatrix(mesh.sMesh)
StiffA = GenerateSystem(mesh.sMesh,prob.ψA,ψAParam)
ApplyBC!(StiffA,mesh.sMesh,prob.ψA,ψAParam,prob.ψA.OperatorType)
StiffB = GenerateSystem(mesh.sMesh,prob.ψB,ψBParam)
ApplyBC!(StiffB,mesh.sMesh,prob.ψB,ψBParam,prob.ψB.OperatorType)
StiffC = GenerateSystem(mesh.sMesh,prob.ψC,ψCParam)
ApplyBC!(StiffC,mesh.sMesh,prob.ψC,ψCParam,prob.ψC.OperatorType)
intializeTimeSteppingTimer!(timer)
doPrinting!(timer,p,mesh,soln)
while timer.simulationTime < timer.finalTime
println("i1=",timer.stepIndex," ",computeTotalMass(p,mesh.sMesh,soln))
if timer.stepIndex < 5
soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=:backwardeuler)
soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=:backwardeuler)
soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=:backwardeuler)
else
soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=p.integrator)
soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=p.integrator)
soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=p.integrator)
end
println("i2=",timer.stepIndex," ",computeTotalMass(p,mesh.sMesh,soln))
computeReaction!(p,soln)
println("i3=",timer.stepIndex," ",computeTotalMass(p,mesh.sMesh,soln))
println()
tsoln = deepcopy(soln)
if isPrintIndex(timer)
doPrinting!(timer,p,mesh,soln)
end
updateSimulationTime!(timer)
updateStepIndex!(timer)
end
printSimulationFinishedMessage(timer)
nothing
end
function pureReactionTestDriver(p::precipParam)
timer, mesh, soln, tsoln, prob = initializeData(p)
randomizeScalarSolutions!(soln)
intializeTimeSteppingTimer!(timer)
doPrinting!(timer,p,mesh,soln)
while timer.simulationTime < timer.finalTime
computeReaction!(p,soln)
if isPrintIndex(timer)
doPrinting!(timer,p,mesh,soln)
end
tsoln = deepcopy(soln)
# step time
updateSimulationTime!(timer)
updateStepIndex!(timer)
end
printSimulationFinishedMessage(timer)
nothing
end
function initializeData(p::precipParam)
timer = initializeTimer(p)
mesh = initializeMeshes(p)
soln = initializeSolution(p)
tsoln = initializeSolution(p)
prob = defineProblems(p,mesh)
return timer, mesh, soln, tsoln, prob
end
function mpbFriction(θf::Vector{T}) where T<:Real
N = length(θf)
friction = zeros(N)
K=0.5
n=2
ξstar = 30.0
θstar = 0.5
h = 1000.0#computeH(ξstar,θstar,K,n)
for i=1:N
friction[i] = h*frictionKernel(θf[i],K,n)
end
return friction
end
function frictionKernel(θf,K,n)
θs = (1.0-θf)
return θs^n/(K^n + θs^n)
end
function computeH(ξstar,θstar,K,n)
return ξstar/frictionKernel(θstar,K,n)
end
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] | 1.887396 | 6,847 |
using Maker
using Base.Test
using Glob
x = [ 3.14159 6.28319 9.42478
12.5664 15.708 18.8496
21.9911 25.1327 28.2743 ]
writecsv("in1.csv", x)
writecsv("in2.csv", 3x)
inputs = glob("in*.csv")
outputs = ["$(splitext(f)[1])-out.csv" for f in inputs]
for i in eachindex(inputs)
inp = inputs[i]
Maker.file(inp)
dest = outputs[i]
Maker.file(dest, inp) do
out = 2 * readcsv(inp, skipstart = 1)
writecsv(dest, out)
end
end
Maker.task("default", outputs)
Maker.clean(outputs)
Maker.task("clean2") do # another way to clean
println("CLEAN2")
for fn in glob("in*-out.csv")
Maker.rm(fn)
end
end
Maker.task("cleanall") do # another way to clean
for fn in glob("in*.csv")
Maker.rm(fn)
end
end
make()
@test isfile(outputs[1])
@test isfile(outputs[2])
make("clean")
@test !isfile(outputs[1])
@test !isfile(outputs[2])
make([]) # the [] are to test this call method
@test isfile(outputs[1])
@test isfile(outputs[2])
make("clean2")
@test !isfile(outputs[1])
@test !isfile(outputs[2])
make("cleanall")
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] | 2.136015 | 522 |
@safetestset gray_code_symmetry = "Gray code symmetry" begin
using BijectiveHilbert
# for i in 0:10
# println(lpad(i, 3, " "), " ", lpad(string(BijectiveHilbert.brgc(i), base = 2), 8, "0"))
# end
# Here's a test of the gray code.
n = 5
for i in 0x0:(0x1 << n - 0x1)
# println(BijectiveHilbert.brgc(1<<n - 1 - i), " ", BijectiveHilbert.brgc(i) ⊻ (1 << (n-1)))
@test(BijectiveHilbert.brgc(1<<n - 1 - i) == BijectiveHilbert.brgc(i) ⊻ (1 << (n - 1)))
end
end
@safetestset gray_code_single = "Gray code changes one bit" begin
using BijectiveHilbert: brgc, is_power_of_two
for i in 0x1:0x1000
@test is_power_of_two(brgc(i) ⊻ brgc(i + 1))
end
end
@safetestset brgc_own_inverse = "Gray code is own inverse" begin
using BijectiveHilbert
for i in 0x0:0x1000
@test(BijectiveHilbert.brgc_inv(BijectiveHilbert.brgc(i)) == i)
end
end
@safetestset brgc_equals_naive = "Gray code matches paper description" begin
using BijectiveHilbert: brgc_inv
using Random
rng = MersenneTwister(9719742)
for T in [UInt8, UInt16, UInt32, UInt64]
for trial in 1:10000
v = rand(rng, T)
n = brgc_inv(Int128(v)) # The paper version is used for integers.
i = brgc_inv(v)
@test n == i
end
end
end
@safetestset brgc_ranks_equal = "the rank calculation is the same as the paper" begin
using BijectiveHilbert: brgc_rank, brgc_rank2
using Random
rng = MersenneTwister(974073242)
for trial in 1:1000
n = rand(rng, 2:7)
w = UInt8(rand(rng, 0:(1<<n - 1)))
mask = UInt8(rand(rng, 0:(1<<n - 1)))
a = brgc_rank(mask, w, n)
b = brgc_rank2(mask, w, n)
@test a == b
end
end
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] | 2.141935 | 775 |
# TemplateName
isNull(x::TemplateName) = clang_TemplateName_isNull(x)
getKind(x::TemplateName) = clang_TemplateName_getKind(x)
getUnderlying(x::TemplateName) = TemplateName(clang_TemplateName_getUnderlying(x))
getNameToSubstitute(x::TemplateName) = TemplateName(clang_TemplateName_getNameToSubstitute(x))
isDependent(x::TemplateName) = clang_TemplateName_isDependent(x)
isInstantiationDependent(x::TemplateName) = clang_TemplateName_isInstantiationDependent(x)
containsUnexpandedParameterPack(x::TemplateName) = clang_TemplateName_containsUnexpandedParameterPack(x)
dump(x::TemplateName) = clang_TemplateName_dump(x)
function getTemplateName(x::TemplateSpecializationType)
return TemplateName(clang_TemplateSpecializationType_getTemplateName(get_type_ptr(x)))
end
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] | 3.019455 | 257 |
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] | 2.360313 | 383 |
import ..UncertainValues.TheoreticalDistributionScalarValue
import ..UncertainValues.UncertainScalarBinomialDistributed
import ..UncertainValues.UncertainScalarBetaBinomialDistributed
import ..UncertainValues: AbstractUncertainValue
import Distributions.pdf
import ..SamplingConstraints:
SamplingConstraint,
constrain
function get_density(uv::AbstractUncertainValue)
some_sample = resample(uv, 10000)
xmin = minimum(some_sample) * 0.97
xmax = maximum(some_sample) * 1.03
step = (xmax-xmin)/300
xvals = xmin:step:xmax+step
density = pdf.(uv.distribution, xvals)
xvals, density ./ sum(density)
end
function get_density(uv::UncertainScalarBinomialDistributed)
some_sample = resample(uv, 10000)
xmin = minimum(some_sample)
xmax = maximum(some_sample)
xvals = xmin:1:xmax
density = pdf.(uv.distribution, xvals)
xvals, density ./ sum(density)
end
function get_density(uv::UncertainScalarBetaBinomialDistributed)
some_sample = resample(uv, 10000)
xmin = minimum(some_sample)
xmax = maximum(some_sample)
xvals = xmin:1:xmax
density = pdf.(uv.distribution, xvals)
xvals, density ./ sum(density)
end
@recipe function plot_theoretical(uv::TheoreticalDistributionScalarValue,
density = true, n_samples = 1000)
if density
@series begin
get_density(uv)
end
else
@series begin
label --> ""
resample(uv, n_samples)
end
end
end
@recipe function plot_theoretical(uv::TheoreticalDistributionScalarValue,
constraint::SamplingConstraint, density = true, n_samples = 1000)
cuv = constrain(uv, constraint)
if density
@series begin
get_density(cuv)
end
else
@series begin
label --> ""
resample(cuv, n_samples)
end
end
end
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