LU Solver

Solve AX = B when A is a square matrix

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

Description

The LU Solver block solves the linear system AX = B by applying LU factorization, where:

• A is an M-by-M square matrix input through the A port.

• B is an M-by-N matrix input through the B port.

• X is the M-by-N output matrix and is the unique solution to the equations.

Examples

Solve Matrix Equation Using LU Solver

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

• Open Model

Ports

Input

A — Input A matrix

M-by-M matrix

Specify the input M-by-M square matrix A 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-N matrix | M-by-1 vector

Specify the B matrix in the AX = B equation as an M-by-N 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

M-by-N matrix | M-by-1 matrix

The block returns the output as an M-by-N matrix or a M-by-1 matrix. The size of X matrix is same as the size of the B matrix.

Data Types: single | double
Complex Number Support: Yes

Block Characteristics

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

Algorithms

The LU algorithm factors a row-permuted variant (A_p) of the square input matrix A as

$$A_p=LU$$

where L is a lower triangular square matrix with unity diagonal elements, and U is an upper triangular square matrix.

The matrix factors are substituted for A_p in

$$A_{p}X=B_p$$

where B_p is the row-permuted variant of B, and the resulting equation

$$LUX=B_p$$

is solved for X by substituting Y = UX, and solving two triangular systems.

$$\begin{array}{l}LY=B_p\hfill \\ UX=Y\hfill \end{array}$$

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