Main Content

LU Solver

Solve AX = B when A is a square matrix

expand all in page
  • LU Solver block

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

Solve Matrix Equation Using LU Solver

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

Ports

Input

expand all

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

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

expand all

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 (Ap) of the square input matrix A as

Ap=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 Ap in

ApX=Bp

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

LUX=Bp

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

LY=BpUX=Y

Extended Capabilities

Version History

Introduced before R2006a

See Also

| | | | | |