svd1#

Purpose#

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

Format#

{ u, s, v } = svd1(x)#
Parameters:

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

Returns:

  • u (NxN matrix) – the left singular vectors of x.

  • s (NxP diagonal matrix) – contains the singular values of x arranged in descending order on the principal diagonal.

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

Examples#

// Create 6x3 matrix
x = { -9.35    15.67   -41.75,
     -13.55    40.97    15.55,
      -0.95   -17.03    40.15,
       8.15    -9.73    13.15,
       2.35   -36.73   -43.55,
      13.35     6.87    16.45  };

// Perform matrix decomposition
{ u, s, v } = svd1(x);

After the code above, the outputs will have the following values;

u =  0.44    -0.49    -0.06     0.36    -0.24     0.61
    -0.35    -0.60    -0.28     0.12     0.65    -0.08
    -0.41     0.46    -0.53     0.07     0.03     0.58
    -0.12     0.25     0.24     0.91     0.08    -0.18
     0.67     0.35    -0.13    -0.02     0.64     0.05
    -0.23     0.04     0.75    -0.17     0.33     0.50

s = 79.03     0.00     0.00
     0.00    60.19     0.00
     0.00     0.00    17.16
     0.00     0.00     0.00
     0.00     0.00     0.00
     0.00     0.00     0.00

v = -0.02     0.26     0.97
    -0.32    -0.91     0.24
    -0.95     0.31    -0.10

Remarks#

  1. svd1() is not thread-safe. New code should use svdusv() instead.

  2. Error handling is controlled with the low bit of the trap flag.

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(), svd2(), svdusv()

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