svd2

Purpose

Computes the singular value decomposition of a matrix so that: \(x = u * s * v'\) (compact u).

Format

{ u, s, v } = svd2(x)

Parameters:

x (NxP matrix) – matrix whose singular values are to be computed

Returns:

• u (NxN or NxP matrix) – the left singular vectors of x. If \(N > P\), then u will be \(NxP\), containing only the \(P\) left singular vectors of x.

• s (NxP or PxP diagonal matrix) – contains the singular values of x arranged in descending order on the principal diagonal. If \(N > P\), then s will be \(PxP\).

• v (PxP matrix) – the right singular vectors of x.

Examples

// Create a 10x3 matrix
x = {  -0.60     3.50     0.47,
        8.40    16.50     0.27,
       11.40     6.50     0.17,
        7.40    -0.50    -2.43,
       -9.60   -10.50     0.57,
      -17.60    -5.50     0.67,
      -12.60   -14.50     0.87,
       18.40    12.50    -1.43,
      -11.60   -19.50     0.77,
        6.40    11.50     0.07 };

// Calculate the singular values
{ u, s, v } = svd2(x);

After the code above, u, s and v will be equal to:

u =  0.04     0.20    -0.11
     0.36     0.38    -0.14
     0.25    -0.23    -0.44
     0.10    -0.39     0.75
    -0.29    -0.04    -0.06
    -0.33     0.57     0.35
    -0.39    -0.08    -0.14
     0.44    -0.29     0.10
    -0.44    -0.37    -0.25
     0.26     0.24    -0.07

s = 49.58     0.00     0.00
     0.00    14.96     0.00
     0.00     0.00     2.24

v =  0.70    -0.70    -0.10
     0.71     0.70     0.05
    -0.04     0.10    -0.99

Remarks

1. svd2() is not thread-safe. New code should use svdcusv() instead.

2. Error handling is controlled with the low bit of the trap flag. If the singular values cannot be computed, _svderr will be set to a non-zero value.

   trap 0	set _svderr to a non-zero value and terminate with message
   trap 1	set _svderr to a non-zero value and continue execution

Source

svd.src

See also

Functions svd(), svd1(), svdcusv()