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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) nogil
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`
.. warning::
The C++ solver discards all samples in the distributions with
zeros weights. This means that while the primal variable (transport
matrix) is exact, the solver only returns feasible dual potentials
on the samples with weights different from zero.
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 int nmax=n1+n2-1
cdef int result_code = 0
cdef int nG=0
cdef double cost=0
cdef np.ndarray[double, ndim=1, mode="c"] alpha=np.zeros(n1)
cdef np.ndarray[double, ndim=1, mode="c"] beta=np.zeros(n2)
cdef np.ndarray[double, ndim=2, mode="c"] G=np.zeros([0, 0])
cdef np.ndarray[double, ndim=1, mode="c"] Gv=np.zeros(0)
cdef np.ndarray[long, ndim=1, mode="c"] iG=np.zeros(0,dtype=np.int)
cdef np.ndarray[long, ndim=1, mode="c"] jG=np.zeros(0,dtype=np.int)
if not len(a):
a=np.ones((n1,))/n1
if not len(b):
b=np.ones((n2,))/n2
# init OT matrix
G=np.zeros([n1, n2])
# calling the function
with nogil:
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
|
