SVD in Python

Here's a small example of Singular Value Decomposition using Python:

from scipy import linalg, mat, dot;
matrix = mat( [[2,1,0,0], [4,3,0,0]] );
print "Original matrix:"
print matrix
U, s, V = linalg.svd( matrix )
print "U:"
print U
print "sigma:"
print s
print "VT:"
print V
dimensions = 1
rows,cols = matrix.shape
#Dimension reduction, build SIGMA'
for index in xrange(dimensions, rows):
 s[index]=0
print "reduced sigma:"
print s
#Reconstruct MATRIX'
reconstructedMatrix= dot(dot(U,linalg.diagsvd(s,len(matrix),len(V))),V)
#Print transform
print "reconstructed:"
print reconstructedMatrix

This code prints the following:

Original matrix:
[[2 1 0 0]
[4 3 0 0]]
U:
[[-0.40455358 -0.9145143 ]
[-0.9145143   0.40455358]]
sigma:
[ 5.4649857   0.36596619]
VT:
[[-0.81741556 -0.57604844  0.          0.        ]
[-0.57604844  0.81741556  0.          0.        ]
[ 0.          0.          1.          0.        ]
[ 0.          0.          0.          1.        ]]
reduced sigma:
[ 5.4649857  0.       ]
reconstructed:
[[ 1.80720735  1.27357371  0.          0.        ]
[ 4.08528566  2.87897923  0.          0.        ]]

And with one more dimension for sigma:

reduced sigma:
[ 5.4649857   0.36596619]
reconstructed:
[[ 2.  1.  0.  0.]
[ 4.  3.  0.  0.]]

This is how you can use Python for quick tests and experiments on SVD.