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# -*- coding: utf-8 -*-
"""
Cython linker with C solver
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
cimport numpy as np
from ..utils import dist
cimport cython
cimport libc.math as math
import warnings
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 maxIter)
cdef enum ProblemType: INFEASIBLE, OPTIMAL, UNBOUNDED, MAX_ITER_REACHED
def check_result(result_code):
if result_code == OPTIMAL:
return None
if result_code == INFEASIBLE:
message = "Problem infeasible. Check that a and b are in the simplex"
elif result_code == UNBOUNDED:
message = "Problem unbounded"
elif result_code == MAX_ITER_REACHED:
message = "numItermax reached before optimality. Try to increase numItermax."
warnings.warn(message)
return message
@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 max_iter):
"""
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
.. warning::
Note that the M matrix needs to be a C-order :py.cls:`numpy.array`
Parameters
----------
a : (ns,) numpy.ndarray, float64
source histogram
b : (nt,) numpy.ndarray, float64
target histogram
M : (ns,nt) numpy.ndarray, float64
loss matrix
max_iter : int
The maximum number of iterations before stopping the optimization
algorithm if it has not converged.
Returns
-------
gamma: (ns x nt) numpy.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 result_code = EMD_wrap(n1, n2, <double*> a.data, <double*> b.data, <double*> M.data, <double*> G.data, <double*> alpha.data, <double*> beta.data, <double*> &cost, max_iter)
return G, cost, alpha, beta, result_code
@cython.boundscheck(False)
@cython.wraparound(False)
def emd_1d_sorted(np.ndarray[double, ndim=1, mode="c"] u_weights,
np.ndarray[double, ndim=1, mode="c"] v_weights,
np.ndarray[double, ndim=1, mode="c"] u,
np.ndarray[double, ndim=1, mode="c"] v,
str metric='sqeuclidean',
double p=1.):
r"""
Solves the Earth Movers distance problem between sorted 1d measures and
returns the OT matrix and the associated cost
Parameters
----------
u_weights : (ns,) ndarray, float64
Source histogram
v_weights : (nt,) ndarray, float64
Target histogram
u : (ns,) ndarray, float64
Source dirac locations (on the real line)
v : (nt,) ndarray, float64
Target dirac locations (on the real line)
metric: str, optional (default='sqeuclidean')
Metric to be used. Only strings listed in :func:`ot.dist` are accepted.
Due to implementation details, this function runs faster when
`'sqeuclidean'`, `'minkowski'`, `'cityblock'`, or `'euclidean'` metrics
are used.
p: float, optional (default=1.0)
The p-norm to apply for if metric='minkowski'
Returns
-------
gamma: (n, ) ndarray, float64
Values in the Optimal transportation matrix
indices: (n, 2) ndarray, int64
Indices of the values stored in gamma for the Optimal transportation
matrix
cost
cost associated to the optimal transportation
"""
cdef double cost = 0.
cdef int n = u_weights.shape[0]
cdef int m = v_weights.shape[0]
cdef int i = 0
cdef double w_i = u_weights[0]
cdef int j = 0
cdef double w_j = v_weights[0]
cdef double m_ij = 0.
cdef np.ndarray[double, ndim=1, mode="c"] G = np.zeros((n + m - 1, ),
dtype=np.float64)
cdef np.ndarray[long, ndim=2, mode="c"] indices = np.zeros((n + m - 1, 2),
dtype=np.int)
cdef int cur_idx = 0
while i < n and j < m:
if metric == 'sqeuclidean':
m_ij = (u[i] - v[j]) * (u[i] - v[j])
elif metric == 'cityblock' or metric == 'euclidean':
m_ij = math.fabs(u[i] - v[j])
elif metric == 'minkowski':
m_ij = math.pow(math.fabs(u[i] - v[j]), p)
else:
m_ij = dist(u[i].reshape((1, 1)), v[j].reshape((1, 1)),
metric=metric)[0, 0]
if w_i < w_j or j == m - 1:
cost += m_ij * w_i
G[cur_idx] = w_i
indices[cur_idx, 0] = i
indices[cur_idx, 1] = j
i += 1
w_j -= w_i
w_i = u_weights[i]
else:
cost += m_ij * w_j
G[cur_idx] = w_j
indices[cur_idx, 0] = i
indices[cur_idx, 1] = j
j += 1
w_i -= w_j
w_j = v_weights[j]
cur_idx += 1
return G[:cur_idx], indices[:cur_idx], cost
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