Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Group: Linear Algebra
See also: eigsm eiggn

Function: svd
Description: computes the singular value decomposition of an n x p matrix x (n >= p). The singular value decomposition finds matrices u, l, v such that x = u*l*v', where u and v are orthogonal matrices and l is a diagonal matrix.

Usage: y = svd(x)
Input:
x n x p matrix to be decomposed
Output:
y.u n x p matrix, the left matrix u
y.l p x 1 vector, elements of the diagonal of matrix l
y.v p x p matrix, the right matrix v

Example:
x = #(1:5)~#(6:10)~#(11:15)
y = svd(x)
y.u
y.l
y.v
r = x - y.u *(y.l .* y.v')
r

Result:
Contents of u
[1,] -0.35456 -0.68869  0.61103
[2,]  -0.3987 -0.37555 -0.53304
[3,] -0.44284 -0.062422 -0.32161
[4,] -0.48697  0.25071 -0.20176
[5,] -0.53111  0.56384  0.44539

Contents of l
[1,]   35.127
[2,]   2.4654
[3,]  2.0468e-15

Contents of v
[1,] -0.20166  0.89032 -0.40825
[2,] -0.51683  0.25733   0.8165
[3,]   -0.832 -0.37565 -0.40825

		Contents of r
[1,] -8.8818e-16 -2.6645e-15        0
[2,] -8.8818e-16 -1.7764e-15 -3.5527e-15
[3,] -1.3323e-15 -1.7764e-15 -3.5527e-15
[4,] -8.8818e-16 -3.5527e-15 -5.3291e-15
[5,] -1.7764e-15 -7.1054e-15 -1.0658e-14



(C) MD*TECH Method and Data Technologies, 05.02.2006