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# -*- coding: utf-8 -*-
"""
Cython linker with C solver
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import warnings
import numpy as np
cimport numpy as np
cimport cython
cdef extern from "EMD.h":
int EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double* alpha, double* beta, double *cost, int numItermax)
cdef enum ProblemType: INFEASIBLE, OPTIMAL, UNBOUNDED, MAX_ITER_REACHED
@cython.boundscheck(False)
@cython.wraparound(False)
def emd_c( np.ndarray[double, ndim=1, mode="c"] a,np.ndarray[double, ndim=1, mode="c"] b,np.ndarray[double, ndim=2, mode="c"] M, int numItermax):
"""
Solves the Earth Movers distance problem and returns the optimal transport matrix
gamm=emd(a,b,M)
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the metric cost matrix
- a and b are the sample weights
Parameters
----------
a : (ns,) ndarray, float64
source histogram
b : (nt,) ndarray, float64
target histogram
M : (ns,nt) ndarray, float64
loss matrix
numItermax : int
The maximum number of iterations before stopping the optimization
algorithm if it has not converged.
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
"""
cdef int n1= M.shape[0]
cdef int n2= M.shape[1]
cdef double cost=0
cdef np.ndarray[double, ndim=2, mode="c"] G=np.zeros([n1, n2])
cdef np.ndarray[double, ndim=1, mode="c"] alpha=np.zeros(n1)
cdef np.ndarray[double, ndim=1, mode="c"] beta=np.zeros(n2)
if not len(a):
a=np.ones((n1,))/n1
if not len(b):
b=np.ones((n2,))/n2
# calling the function
cdef int resultSolver = EMD_wrap(n1,n2,<double*> a.data,<double*> b.data,<double*> M.data,<double*> G.data, <double*> alpha.data, <double*> beta.data, <double*> &cost, numItermax)
if resultSolver != OPTIMAL:
if resultSolver == INFEASIBLE:
warnings.warn("Problem infeasible. Check that a and b are in the simplex")
elif resultSolver == UNBOUNDED:
warnings.warn("Problem unbounded")
elif resultSolver == MAX_ITER_REACHED:
warnings.warn("numItermax reached before optimality. Try to increase numItermax.")
return G, cost, alpha, beta
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