Documentation

Singular Value Decomposition

Factor matrix using singular value decomposition

Library

Math Functions / Matrices and Linear Algebra / Matrix Factorizations

dspfactors

Description

The Singular Value Decomposition block factors the M-by-N input matrix A such that

A=Udiag(S)V*

where

  • U is an M-by-P matrix

  • V is an N-by-P matrix

  • S is a length-P vector

  • P is defined as min(M,N)

When

  • M = N, U and V are both M-by-M unitary matrices

  • M > N, V is an N-by-N unitary matrix, and U is an M-by-N matrix whose columns are the first N columns of a unitary matrix

  • N > M, U is an M-by-M unitary matrix, and V is an N-by-M matrix whose columns are the first M columns of a unitary matrix

In all cases, S is an unoriented vector of positive singular values having length P.

Length-N row inputs are treated as length-N columns.

Note that the first (maximum) element of output S is equal to the 2-norm of the matrix A.

Dialog Box

Show singular vector ports

Select to enable the U and V output ports.

Show error status port

Select to enable the E output port, which reports a failure to converge. The possible values you can receive on the port are:

  • 0 — The singular value decomposition calculation converges.

  • 1 — The singular value decomposition calculation does not converge.

If the singular value decomposition calculation fails to converge, the output at ports U, S, and V are undefined matrices of the correct size.

References

Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Data Types

PortSupported Data Types

A

  • Double-precision floating point

  • Single-precision floating point

U

  • Double-precision floating point

  • Single-precision floating point

S

  • Double-precision floating point

  • Single-precision floating point

V

  • Double-precision floating point

  • Single-precision floating point

E

  • Boolean

See Also

Autocorrelation LPCDSP System Toolbox
Cholesky FactorizationDSP System Toolbox
LDL FactorizationDSP System Toolbox
LU InverseDSP System Toolbox
PseudoinverseDSP System Toolbox
QR FactorizationDSP System Toolbox
SVD SolverDSP System Toolbox
svdMATLAB

See Matrix Factorizations for related information.

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