comparison tests/l1eq_test.py @ 62:e684f76c1969

Added l1eq_pd(), l1 minimizer with equality constraints from l1-magic

+# -*- coding: utf-8 -*-
+"""
+Created on Fri Oct 21 14:28:08 2011
+
+@author: Nic
+
+Test l1-magic l1eq_pd() algorithm
+"""
+
+import numpy as np
+import numpy.linalg
+import scipy.io
+import unittest
+from pyCSalgos.BP.l1eq_pd import l1eq_pd
+#from l1qc import l1qc_logbarrier
+
+class l1eq_results(unittest.TestCase):
+  def testResults(self):
+    mdict = scipy.io.loadmat('l1eq_testdata.mat')
+    
+    # A = system matrix
+    # Y = matrix with measurements (on columns)
+    # X0 = matrix with initial solutions (on columns)
+    # Xr = matrix with correct solutions (on columns)
+    for A,Y,X0,Xr in zip(mdict['cellA'].squeeze(),mdict['cellY'].squeeze(),mdict['X0'].squeeze(),mdict['Xr'].squeeze()):
+      for i in np.arange(Y.shape[1]):
+        xr = l1eq_pd(X0[:,i], A, np.array([]), Y[:,i])
+        
+        # check if found solution is the same as the correct cslution
+        diff = numpy.linalg.norm(xr - Xr[:,i])
+        err1 = numpy.linalg.norm(Y[:,i] - np.dot(A,xr))
+        err2 = numpy.linalg.norm(Y[:,i] - np.dot(A,Xr[:,i]))
+        norm1 = numpy.linalg.norm(xr,1)
+        norm2 = numpy.linalg.norm(Xr[:,i],1)
+        print 'diff = ',diff
+        print 'err1 = ',err1
+        print 'err2 = ',err2
+        print 'norm1 = ',norm1
+        print 'norm2 = ',norm2
+        
+        # It seems Matlab's linsolve and scipy solve are slightly different
+        # Therefore make a more robust condition:
+        #  OK;    if   solutions are close enough (diff < 1e-6)
+        #              or
+        #              (
+        #               they fulfill the constraint close enough (differr < 1e-6)
+        #                 and
+        #               Python solution has l1 norm no more than 1e-6 larger as the reference solution
+        #                 (i.e. either norm1 < norm2   or   norm1>norm2 not by more than 1e-6)
+        #              )
+        #        
+        #  ERROR: else
+        differr  = abs((err1 - err2))
+        diffnorm = norm1 - norm2  # intentionately no abs(), since norm1 < norm2 is good
+        if diff < 1e-6 or (differr < 1e-6 and (diffnorm < 1e-6)):
+          isok = True
+        else:
+          isok = False
+
+        #if not isok:
+        #  print "should raise"
+        #  #self.assertTrue(isok)
+        self.assertTrue(isok)
+  
+if __name__ == "__main__":
+    unittest.main(verbosity=2)    
+    #suite = unittest.TestLoader().loadTestsFromTestCase(CompareResults)
+    #unittest.TextTestRunner(verbosity=2).run(suite)