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Member of the linalgebra class.

Syntax

x = gsvd(A, B)

[U, V, R, C, S] = gsvd(A, B)

[U, V, R, C, S] = gsvd(A, B, 0)

Description

Performs generalized singular value decomposition (SVD) of a matrix pair.

Details

Examples

Inputs

Name	Description
A	Specifies a matrix.
B	Specifies a matrix. A and B must have the same number of columns.
0	Directs LabVIEW to perform generalized SVD in the economy size format.

Outputs

Name	Description
x	Returns the generalized singular values. x is a vector.
U	Returns an orthogonal matrix of the generalized SVD.
V	Returns an orthogonal matrix of the generalized SVD.
R	Returns a square matrix of the generalized SVD.
C	Returns a diagonal matrix of the generalized SVD.
S	Returns a diagonal matrix of the generalized SVD.

Details

The following equations define the generalized singular value decomposition of a matrix pair (A, B):

A = UCR'
B = VSR'

where U and V are orthogonal matrices, and R is a square matrix.

Let k be the rank of the matrix [A; B]. Then the first k diagonal elements of matrix C'C + S'S are ones and all other elements are zeros. The square roots of the first k diagonal elements of C'C and S'S determine the numerators and denominators, respectively, of the generalized singular values.

If A is an m-by-p matrix, and B is an n-by-p matrix, then [U, V, R, C, S] = gsvd(A, B) returns U as an m-by-m matrix, V as an n-by-n matrix, R as a p-by-p matrix, C as an m-by-p matrix, and S as an n-by-p matrix. If you specify 0, LabVIEW performs generalized SVD in the economy size format. In other words, [U, V, R, C, S] = gsvd(A, B, 0) returns U as an m-by-min(m, p) matrix, V as an n-by-min(n, p) matrix, R as a p-by-p matrix, C as a min(m, p)-by-p matrix, and S as a min(n, p)-by-p matrix.

Examples

A = reshape(1:12, 4, 3);
B = magic(3);
X = gsvd(A, B)

Related Topics

magic
reshape
svd