svd

Syntax

svd(obj, [fullMatrices=true], [computeUV=true])

Arguments

obj is a matrix.

fullMatrices is a Boolean value. The default value is true.

computeUV is a Boolean value. The default value is true.

Details

Perform the singular decomposition of a matrix.

Given an m-by-n matrix A:

• If fullMatrices=true, return an m-by-m matrix U (unitary matrix having left singular vectors as columns), an n-by-n matrix V (unitary matrix having right singular vectors as rows) and a vector s (singular values sorted in descending order) such that A=U*S*V. S is an m-by-n matrix with s as the diagonal elements.

• If fullMatrices=false, remove the extra rows or columns of zeros from matrix S, along with the columns/rows in U and V that multiply those zeros in the expression A = U*S*V. Removing these zeros and columns/rows can improve execution time and reduce storage requirements without compromising the accuracy of the decomposition. The resulting matrix U is m-by-k, matrix V is k-by-n and matrix S is k-by-k with k=min(m,n).

• If computeUV=false, only return vector s.

Examples

$ m=matrix([[2,1,0],[1,3,1],[0,1,4],[1,2,3]]);
$ U,s,V=svd(m);
$ U;

#0	#1	#2
-0.233976	0.57735	-0.782254
-0.560464	0.57735	0.593756
-0.79444	-0.57735	-0.188498

$ s;
[6.029042,3,1.284776]

$ V;

#0	#1	#2	#3
-0.170577	-0.449459	-0.620036	-0.620036
0.57735	0.57735	-0.57735	0
-0.755582	0.630862	-0.12472	-0.12472
-0.258199	-0.258199	-0.516398	0.774597

$ U,s,V=svd(m,fullMatrices=false);
$ V;

#0	#1	#2	#3
-0.170577	-0.449459	-0.620036	-0.620036
0.57735	0.57735	-0.57735	0
-0.755582	0.630862	-0.12472	-0.12472