SVD Solver

Solve AX = B using singular value decomposition

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Libraries:
DSP System Toolbox / Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description

The SVD Solver block solves the linear system AX = B. The linear system can be overdetermined, underdetermined, or exactly determined. The block solves the system by applying singular value decomposition (SVD) factorization to the input matrix at the A port.

Examples

Solve Matrix Equation Using Singular Value Decomposition

Use SVD Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.

• Open Model

Ports

Input

A — Input A matrix

M-by-N matrix

Specify the input matrix A as an M-by-N matrix through this port. Inputs A and B must have the same number of rows.

Data Types: single | double
Complex Number Support: Yes

B — B matrix

M-by-L matrix | M-by-1 vector

Specify the matrix B in the AX = B equation as an M-by-L matrix or an M-by-1 vector.

When you specify an M-by-1 vector, the block treats the length-M unoriented vector input at port B as an M-by-1 matrix. Inputs A and B must have the same number of rows.

Data Types: single | double
Complex Number Support: Yes

Output

X — Solution to system of equations

N-by-L matrix

The output at the X port is the N-by-L matrix X. The block computes X to minimize the sum of the squares of the elements of B − AX (the residual).

When B is a vector, this solution minimizes the vector 2-norm of the residual. When B is a matrix, this solution minimizes the matrix Frobenius norm of the residual. In this case, the columns of X are the solutions to the L corresponding systems AX_k = B_k, where B_k is the kth column of B, and X_k is the kth column of X.

X is known as the minimum-norm-residual solution to AX = B. The minimum-norm-residual solution is unique for overdetermined and exactly determined linear systems, but the solution is not unique for underdetermined linear systems. Thus when you apply the SVD Solver block to an underdetermined system, the block computes X to minimize the number of nonzero entries in X.

Data Types: single | double
Complex Number Support: Yes

E — Show error status report

logical scalar

The block returns a logical scalar value of 0 if the singular value decomposition calculation converges, and a logical scalar value of 1 if the singular value decomposition calculation does not converge.

Data Types: Boolean

Parameters

Show error status port (E) — Select to report failure to converge

off (default) | on

Select to enable the E output port, which reports the failure to converge as one of the following:

• 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 port X is an undefined matrix of the expected size.

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Version History

Introduced before R2006a