lapsvds#

Purpose#

Computes the singular values of a real or complex rectangular matrix

Format#

s = lapsvds(x)#

Parameters:: x (MxN matrix) – real or complex rectangular matrix.
Returns:: s (min(M,N)x1 vector) – singular values.

Examples#

// Assign x matrix
x = { 2.143 4.345 6.124,
      1.244 5.124 3.412,
      0.235 5.657 8.214 };

// Compute the singular value decomposition
va = lapsvds(x);
print va';

13.895868 2.1893939 1.4344261

// Assign xi
xi = { 4+1 3+1 2+2,
       1+2 5+3 2+2,
       1+1 2+1 6+2 };

// Compute the singular value decomposition
ve = lapsvds(xi);
print ve';

10.352877 4.0190557 2.3801546

Note the transpose operator (') at the end of the print statements. This causes the output of these column vectors to be printed as a row vector.

Remarks#

lapsvds() computes the singular values of a real or complex rectangular matrix. The SVD is

x = usv'

where v is the matrix of right singular vectors. For the computation of the singular vectors, see lapsvdcusv() and lapsvdusv().

lapsvds() is based on the LAPACK drivers DGESVD and ZGESVD. Further documentation of these functions may be found in the LAPACK User’s Guide.