lapsvdusv

Purpose

Computes the singular value decomposition a real or complex rectangular matrix.

Format

{ u, s, v } = lapsvdusv(x)

Parameters:

x (MxN matrix) – real or complex rectangular matrix.

Returns:

• u (MxM matrix) – left singular vectors.

• s (MxN matrix) – singular values.

• v (NxN matrix) – right singular vectors.

Examples

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

{ u, s, v } = lapsvdusv(x);

print u;

-0.5553  0.0490  0.8302
-0.4309  0.8368 -0.3377
-0.7113 -0.5452 -0.4436

print s;

13.8959 0.0000 0.0000
 0.0000 2.1894 0.0000
 0.0000 0.0000 1.4344

print v;

-0.1362  0.4650  0.8748
 0.6221  0.6470 -0.4408
-0.7710 -0.6043  0.2011

Remarks

lapsvdusv() computes the singular value decomposition of a real or complex rectangular matrix. The SVD is

x = usv'

where v is the matrix of right singular vectors. lapsvdusv() is based on the LAPACK drivers DGESVD and ZGESVD. Further documentation of these functions may be found in the LAPACK User’s Guide.

See also

Functions lapsvds(), lapsvdcusv()