From 05905acdbf2e22bc4b3dc7556d0c6faba0786d23 Mon Sep 17 00:00:00 2001
From: Rémi Flamary <remi.flamary@gmail.com>
Date: Mon, 24 Oct 2016 16:08:55 +0200
Subject: add barycenter and unmixing

---
 ot/bregman.py | 89 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 89 insertions(+)

(limited to 'ot')

diff --git a/ot/bregman.py b/ot/bregman.py
index 8b97e1e..1761029 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -89,3 +89,92 @@ def sinkhorn(a,b, M, reg,numItermax = 1000,stopThr=1e-9):
     return np.dot(np.diag(u),np.dot(K,np.diag(v)))
 
 
+def geometricBar(weights,alldistribT):
+    assert(len(weights)==alldistribT.shape[1])       
+    return np.exp(np.dot(np.log(alldistribT),weights.T))    
+
+def geometricMean(alldistribT):     
+    return np.exp(np.mean(np.log(alldistribT),axis=1))    
+
+def projR(gamma,p):
+    #return np.dot(np.diag(p/np.maximum(np.sum(gamma,axis=1),1e-10)),gamma)
+    return np.multiply(gamma.T,p/np.maximum(np.sum(gamma,axis=1),1e-10)).T
+
+def projC(gamma,q):
+    #return (np.dot(np.diag(q/np.maximum(np.sum(gamma,axis=0),1e-10)),gamma.T)).T
+    return np.multiply(gamma,q/np.maximum(np.sum(gamma,axis=0),1e-10))
+    
+
+def barycenter(A,M,reg, weights=None, numItermax = 1000, tol_error=1e-4,log=dict()):
+    """Compute the Regularizzed wassersteien barycenter of distributions A"""
+    
+    
+    if weights is None:
+        weights=np.ones(A.shape[1])/A.shape[1]
+    else:
+        assert(len(weights)==A.shape[1])
+
+    #compute Mmax once for all
+    #M = M/np.median(M) # suggested by G. Peyre
+    K = np.exp(-reg*M)
+
+    cpt = 0
+    err=1
+
+    UKv=np.dot(K,np.divide(A.T,np.sum(K,axis=0)).T)
+    u = (geometricMean(UKv)/UKv.T).T
+    
+    log = {'niter':0, 'all_err':[]}
+    
+    while (err>tol_error and cpt<numItermax):
+        cpt = cpt +1
+        UKv=u*np.dot(K,np.divide(A,np.dot(K,u)))
+        u = (u.T*geometricBar(weights,UKv)).T/UKv
+        if cpt%10==1:
+            err=np.sum(np.std(UKv,axis=1))
+            log['all_err'].append(err)
+        
+    log['niter']=cpt
+    return geometricBar(weights,UKv)
+    
+
+def unmixBregman(distrib,D,M,M0,h0,reg,reg0,alpha,numItermax = 1000, tol_error=1e-3,log=dict()):
+    """
+        distrib : distribution to unmix
+        D : Dictionnary 
+        M : Metric matrix in the space of the distributions to unmix
+        M0 : Metric matrix in the space of the 'abundance values' to solve for
+        h0 : prior on solution (generally uniform distribution)
+        reg,reg0 : transport regularizations
+        alpha : how much should we trust the prior ? ([0,1])
+    """
+        
+    M = M/np.median(M) 
+    K = np.exp(-reg*M)
+ 
+    M0 = M0/np.median(M0)  
+    K0 = np.exp(-reg0*M0)
+    old = h0
+
+    err=1
+    cpt=0    
+    log = {'niter':0, 'all_err':[]}
+    
+    while (err>tol_error and cpt<numItermax):
+        K = projC(K,distrib)  
+        K0 = projC(K0,h0)  
+        new  = np.sum(K0,axis=1)
+        inv_new = np.dot(D,new) # we recombine the current selection from dictionnary
+        other = np.sum(K,axis=1)
+        delta = np.exp(alpha*np.log(other)+(1-alpha)*np.log(inv_new)) # geometric interpolation
+        K = projR(K,delta)
+        K0 =  np.dot(np.diag(np.dot(D.T,delta/inv_new)),K0)
+        
+        err=np.linalg.norm(np.sum(K0,axis=1)-old)
+        old = new
+        log['all_err'].append(err)
+        cpt = cpt+1
+        
+        
+    log['niter']=cpt
+    return np.sum(K0,axis=1)
-- 
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