DSP Blockset

Singular Value Decomposition

Factor a matrix using singular value decomposition

Library

Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description

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

where U is an M-by-P matrix, V is an N-by-P matrix, S is a length-P vector, and P is defined as min(M,N).

When M = N, U and V are both M-by-M unitary matrices. When 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. When N > M, U is an M-by-M unitary matrix, and V is an M-by-N matrix whose columns are the first N columns of a unitary matrix. In all cases, S is a 1-D vector of positive singular values having length P. The output is always sample based.

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

• [U,S,V] = svd(A,0)       % Equivalent MATLAB code for M > N
  

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

You can enable the U and V output ports by selecting the Output the singular vectors parameter.

Dialog Box

Output the singular vectors

Enables the U and V output ports when selected.

References

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

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert your data types to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Autocorrelation LPC	DSP Blockset
Cholesky Factorization	DSP Blockset
LDL Factorization	DSP Blockset
LU Inverse	DSP Blockset
Pseudoinverse	DSP Blockset
QR Factorization	DSP Blockset
SVD Solver	DSP Blockset
svd	MATLAB

See Factoring Matrices for related information.

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