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from .emd import emd_c
import numpy as np
def emd(a,b,M):
"""
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 (uniform weigth if empty list)
b : (nt,) ndarray, float64
Target histogram (uniform weigth if empty list)
M : (ns,nt) ndarray, float64
loss matrix
Examples
--------
Simple example with obvious solution. The function :func:emd accepts lists and
perform automatic conversion tu numpy arrays
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.emd(a,b,M)
array([[ 0.5, 0. ],
[ 0. , 0.5]])
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
"""
a=np.asarray(a,dtype=np.float64)
b=np.asarray(b,dtype=np.float64)
if len(a)==0:
a=np.ones((M.shape[0],),dtype=np.float64)/M.shape[0]
if len(b)==0:
b=np.ones((M.shape[1],),dtype=np.float64)/M.shape[1]
return emd_c(a,b,M)
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