Display largest and lowest singular values when iterating

src/beyn.py

 import solver as Solver
+import sys
 import numpy  as np
 import numpy.matlib
 
@@ -35,11 +36,15 @@ def simple(operator, origin, radius,
     # Search A0
     if(verbose): print "Searching A0..."
     while(not hasK and it != maxIt):
-        if(verbose): print " # Iteration: " + str(it+1)
+        if(verbose): print " # Iteration: " + str(it+1),
+        if(verbose): sys.stdout.flush()
 
-        vHat = randomMatrix(m ,l)                       # Take a random VHat
+        vHat = randomMatrix(m, l)                       # Take a random VHat
         A0   = integrate(operator, myPath, 0, vHat)     # Compute A0
-        k    = np.linalg.matrix_rank(A0, tol=rankTol)   # Rank test
+        k, sMax, sMin = rank(A0, rankTol)               # Rank
+
+        if(verbose): print "| " + format(sMax, ".2e"),
+        if(verbose): print "| " + format(sMin, ".2e")
 
         if(k == 0):                                     # Rank is zero?
             if(verbose): print " # Rank test is zero: keep A0 as is!"
@@ -92,10 +97,28 @@ def simple(operator, origin, radius,
 
 
 ## Import only simple (other functions are just helpers)
-__all__ = ['simple']
+__all__ = ["simple"]
 
 
 ## Helper functions
+def rank(A, tol):
+    """Returns the rank of a given matrix and its largest and lowest SVs
+
+    Keywords arguments:
+    A -- the matrix to use
+    tol -- the tolerance used to compute the rank
+    """
+
+    S   = np.linalg.svd(A, full_matrices=False, compute_uv=0)
+    nSV = len(S)
+    k   = 0
+
+    for i in range(nSV):
+        if(S[i] > tol): k = k + 1
+
+    return k, S[0].tolist(), S[nSV - 1].tolist()
+
+
 def path(nodes, origin, radius):
     """Returns a list with the coordinates of a circular contour
 
@@ -187,12 +210,12 @@ def display(nodes, maxIt, lStart, lStep, rankTol, origin, radius):
     print " # Initial size of col(A0):            " + " " + str(lStart)
     print " # Step size for increasing col(A0):   " + " " + str(lStep)
     print " # Rank test tolerance:                ",
-    print format(rankTol, '.2e')
+    print format(rankTol, ".2e")
     print "---------------------------------------"
     print " # Cirular path origin:                ",
-    print "(" + format(np.real(origin).tolist(), '+.2e') + ")",
+    print "(" + format(np.real(origin).tolist(), "+.2e") + ")",
     print "+",
-    print "(" + format(np.imag(origin).tolist(), '+.2e') + ")j"
+    print "(" + format(np.imag(origin).tolist(), "+.2e") + ")j"
     print " # Cirular path radius:                ",
-    print format(radius, '+.2e')
+    print format(radius, "+.2e")
     print "---------------------------------------"