# Generalized SVD Decomposition (G Dataflow)

Computes the generalized singular value decomposition (GSVD) of a matrix pair.

## matrix A

A matrix with m rows and p columns.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

## matrix B

A matrix with n rows and p columns.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

## singular values only?

A Boolean specifying whether the node computes only the generalized singular values.

 True Computes only the generalized singular values of the matrix pair. False Computes all matrices in the generalized SVD decomposition.

Default: False

## SVD option

Value specifying how the node performs the decomposition.

Name Value Description
Thin 0

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).

Full 1

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).

Default: Thin

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## singular values

Generalized singular values of the input matrix pair (matrix A, matrix B).

## matrix U

The U matrix of the GSVD results.

## matrix V

The V matrix of the GSVD results.

## matrix C

The C matrix of the GSVD results.

## matrix S

The S matrix of the GSVD results.

## error out

Error information. The node produces this output according to standard error behavior.

## matrix R

The R matrix of the GSVD results.

## Algorithm for Calculating Generalized SVD Decomposition

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 k is the rank of matrix $\left(\begin{array}{c}A\\ B\end{array}\right)$, then the first k diagonal elements of matrix CC + SS are ones and all of the other elements are zeros. The square roots of the first k diagonal elements of CC and SS determine the numerators and denominators of the generalized singular values, respectively.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported