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# -*- coding: utf-8 -*-
"""
Various function that can be usefull
"""
import numpy as np
from scipy.spatial.distance import cdist
import time
__time_tic_toc=time.time()
def tic():
""" Python implementation of Matlab tic() function """
global __time_tic_toc
__time_tic_toc=time.time()
def toc(message='Elapsed time : {} s'):
""" Python implementation of Matlab toc() function """
t=time.time()
print(message.format(t-__time_tic_toc))
return t-__time_tic_toc
def toq():
""" Python implementation of Julia toc() function """
t=time.time()
return t-__time_tic_toc
def kernel(x1,x2,method='gaussian',sigma=1,**kwargs):
"""Compute kernel matrix"""
if method.lower() in ['gaussian','gauss','rbf']:
K=np.exp(-dist(x1,x2)/(2*sigma**2))
return K
def unif(n):
""" return a uniform histogram of length n (simplex)
Parameters
----------
n : int
number of bins in the histogram
Returns
-------
h : np.array (n,)
histogram of length n such that h_i=1/n for all i
"""
return np.ones((n,))/n
def dist(x1,x2=None,metric='sqeuclidean'):
"""Compute distance between samples in x1 and x2 using function scipy.spatial.distance.cdist
Parameters
----------
x1 : np.array (n1,d)
matrix with n1 samples of size d
x2 : np.array (n2,d), optional
matrix with n2 samples of size d (if None then x2=x1)
metric : str, fun, optional
name of the metric to be computed (full list in the doc of scipy), If a string,
the distance function can be ‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘cityblock’,
‘correlation’, ‘cosine’, ‘dice’, ‘euclidean’, ‘hamming’, ‘jaccard’, ‘kulsinski’,
‘mahalanobis’, ‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’,
‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘wminkowski’, ‘yule’.
Returns
-------
M : np.array (n1,n2)
distance matrix computed with given metric
"""
if x2 is None:
x2=x1
return cdist(x1,x2,metric=metric)
def dist0(n,method='lin_square'):
"""Compute standard cost matrices of size (n,n) for OT problems
Parameters
----------
n : int
size of the cost matrix
method : str, optional
Type of loss matrix chosen from:
* 'lin_square' : linear sampling between 0 and n-1, quadratic loss
Returns
-------
M : np.array (n1,n2)
distance matrix computed with given metric
"""
res=0
if method=='lin_square':
x=np.arange(n,dtype=np.float64).reshape((n,1))
res=dist(x,x)
return res
def dots(*args):
""" dots function for multiple matrix multiply """
return reduce(np.dot,args)
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