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import numpy as np
from scipy import linalg
import torch
def calculate_mpjpe(gt_joints, pred_joints):
"""
gt_joints: num_poses x num_joints(22) x 3
pred_joints: num_poses x num_joints(22) x 3
(obtained from recover_from_ric())
"""
assert gt_joints.shape == pred_joints.shape, f"GT shape: {gt_joints.shape}, pred shape: {pred_joints.shape}"
# Align by root (pelvis)
pelvis = gt_joints[:, [0]].mean(1)
gt_joints = gt_joints - torch.unsqueeze(pelvis, dim=1)
pelvis = pred_joints[:, [0]].mean(1)
pred_joints = pred_joints - torch.unsqueeze(pelvis, dim=1)
# Compute MPJPE
mpjpe = torch.linalg.norm(pred_joints - gt_joints, dim=-1) # num_poses x num_joints=22
mpjpe_seq = mpjpe.mean(-1) # num_poses
return mpjpe_seq
# (X - X_train)*(X - X_train) = -2X*X_train + X*X + X_train*X_train
def euclidean_distance_matrix(matrix1, matrix2):
"""
Params:
-- matrix1: N1 x D
-- matrix2: N2 x D
Returns:
-- dist: N1 x N2
dist[i, j] == distance(matrix1[i], matrix2[j])
"""
assert matrix1.shape[1] == matrix2.shape[1]
d1 = -2 * np.dot(matrix1, matrix2.T) # shape (num_test, num_train)
d2 = np.sum(np.square(matrix1), axis=1, keepdims=True) # shape (num_test, 1)
d3 = np.sum(np.square(matrix2), axis=1) # shape (num_train, )
dists = np.sqrt(d1 + d2 + d3) # broadcasting
return dists
def calculate_top_k(mat, top_k):
size = mat.shape[0]
gt_mat = np.expand_dims(np.arange(size), 1).repeat(size, 1)
bool_mat = (mat == gt_mat)
correct_vec = False
top_k_list = []
for i in range(top_k):
# print(correct_vec, bool_mat[:, i])
correct_vec = (correct_vec | bool_mat[:, i])
# print(correct_vec)
top_k_list.append(correct_vec[:, None])
top_k_mat = np.concatenate(top_k_list, axis=1)
return top_k_mat
def calculate_R_precision(embedding1, embedding2, top_k, sum_all=False):
dist_mat = euclidean_distance_matrix(embedding1, embedding2)
argmax = np.argsort(dist_mat, axis=1)
top_k_mat = calculate_top_k(argmax, top_k)
if sum_all:
return top_k_mat.sum(axis=0)
else:
return top_k_mat
def calculate_matching_score(embedding1, embedding2, sum_all=False):
assert len(embedding1.shape) == 2
assert embedding1.shape[0] == embedding2.shape[0]
assert embedding1.shape[1] == embedding2.shape[1]
dist = linalg.norm(embedding1 - embedding2, axis=1)
if sum_all:
return dist.sum(axis=0)
else:
return dist
def calculate_activation_statistics(activations):
"""
Params:
-- activation: num_samples x dim_feat
Returns:
-- mu: dim_feat
-- sigma: dim_feat x dim_feat
"""
mu = np.mean(activations, axis=0)
cov = np.cov(activations, rowvar=False)
return mu, cov
def calculate_diversity(activation, diversity_times):
assert len(activation.shape) == 2
assert activation.shape[0] > diversity_times
num_samples = activation.shape[0]
first_indices = np.random.choice(num_samples, diversity_times, replace=False)
second_indices = np.random.choice(num_samples, diversity_times, replace=False)
dist = linalg.norm(activation[first_indices] - activation[second_indices], axis=1)
return dist.mean()
def calculate_multimodality(activation, multimodality_times):
assert len(activation.shape) == 3
assert activation.shape[1] > multimodality_times
num_per_sent = activation.shape[1]
first_dices = np.random.choice(num_per_sent, multimodality_times, replace=False)
second_dices = np.random.choice(num_per_sent, multimodality_times, replace=False)
dist = linalg.norm(activation[:, first_dices] - activation[:, second_dices], axis=2)
return dist.mean()
def calculate_frechet_distance(mu1, sigma1, mu2, sigma2, eps=1e-6):
"""Numpy implementation of the Frechet Distance.
The Frechet distance between two multivariate Gaussians X_1 ~ N(mu_1, C_1)
and X_2 ~ N(mu_2, C_2) is
d^2 = ||mu_1 - mu_2||^2 + Tr(C_1 + C_2 - 2*sqrt(C_1*C_2)).
Stable version by Dougal J. Sutherland.
Params:
-- mu1 : Numpy array containing the activations of a layer of the
inception net (like returned by the function 'get_predictions')
for generated samples.
-- mu2 : The sample mean over activations, precalculated on an
representative data set.
-- sigma1: The covariance matrix over activations for generated samples.
-- sigma2: The covariance matrix over activations, precalculated on an
representative data set.
Returns:
-- : The Frechet Distance.
"""
mu1 = np.atleast_1d(mu1)
mu2 = np.atleast_1d(mu2)
sigma1 = np.atleast_2d(sigma1)
sigma2 = np.atleast_2d(sigma2)
assert mu1.shape == mu2.shape, \
'Training and test mean vectors have different lengths'
assert sigma1.shape == sigma2.shape, \
'Training and test covariances have different dimensions'
diff = mu1 - mu2
# Product might be almost singular
covmean, _ = linalg.sqrtm(sigma1.dot(sigma2), disp=False)
if not np.isfinite(covmean).all():
msg = ('fid calculation produces singular product; '
'adding %s to diagonal of cov estimates') % eps
print(msg)
offset = np.eye(sigma1.shape[0]) * eps
covmean = linalg.sqrtm((sigma1 + offset).dot(sigma2 + offset))
# Numerical error might give slight imaginary component
if np.iscomplexobj(covmean):
if not np.allclose(np.diagonal(covmean).imag, 0, atol=1e-3):
m = np.max(np.abs(covmean.imag))
raise ValueError('Imaginary component {}'.format(m))
covmean = covmean.real
tr_covmean = np.trace(covmean)
return (diff.dot(diff) + np.trace(sigma1) +
np.trace(sigma2) - 2 * tr_covmean)
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