Generalized SVD Decomposition VI

Owning Palette: Linear Algebra VIs

Requires: Full Development System

Computes the generalized singular value decomposition (GSVD) of a matrix pair (A,B). The data types you wire to the A and B inputs determine the polymorphic instance to use.

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Real Generalized SVD Decomposition

	A is a matrix with m rows and p columns.
	B is a matrix with n rows and p columns.
	singular values only? specifies whether to compute only the generalized singular values. The default is FALSE. When singular values only? is TRUE, the VI computes only Singular Values.
	SVD Option specifies how the VI performs the decomposition. 0 Thin (default)—Decomposes matrix A as the multiplication of matrix U (m x min(m,p)), C (min(m,p) x p) and transpose of R (p x p). Decomposes matrix B as the multiplication of matrix V (n x min(n,p)), S (min(n,p) x p) and transpose of R (p x p). 1 Full—Decomposes matrix A as the multiplication of matrix U (m x m), C (m x p) and transpose of R (p x p). Decomposes matrix B as the multiplication of matrix V (n x n), S (n x p) and transpose of R (p x p).
	Singular Values returns the generalized singular values of matrix pair (A,B).
	Matrix U returns the U matrix of the GSVD results.
	Matrix V returns the V matrix of the GSVD results.
	Matrix C returns the C matrix of the GSVD results.
	Matrix S returns the S matrix of the GSVD results.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.
	Matrix R returns the R matrix of the GSVD results.

Complex Generalized SVD Decomposition

	A is a matrix with m rows and p columns.
	B is a matrix with n rows and p columns.
	singular values only? specifies whether to compute only the generalized singular values. The default is FALSE. When singular values only? is TRUE, the VI computes only Singular Values.
	SVD Option specifies how the VI performs the decomposition. 0 Thin (default)—Decomposes matrix A as the multiplication of matrix U (m x min(m,p)), C (min(m,p) x p) and transpose of R (p x p). Decomposes matrix B as the multiplication of matrix V (n x min(n,p)), S (min(n,p) x p) and transpose of R (p x p). 1 Full—Decomposes matrix A as the multiplication of matrix U (m x m), C (m x p) and transpose of R (p x p). Decomposes matrix B as the multiplication of matrix V (n x n), S (n x p) and transpose of R (p x p).
	Singular Values returns the generalized singular values of matrix pair (A,B).
	Matrix U returns the U matrix of the GSVD results.
	Matrix V returns the V matrix of the GSVD results.
	Matrix C returns the C matrix of the GSVD results.
	Matrix S returns the S matrix of the GSVD results.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.
	Matrix R returns the R matrix of the GSVD results.

Generalized SVD Decomposition Details

The following expressions 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.

When you let k be the rank of matrix , then the first k diagonal elements of matrix C’C + S’S are ones and all of the other elements are zeros. The square roots of the first k diagonal elements of C’C and S’S determine the numerators and denominators of the generalized singular values, respectively.