LU Solver
Solving a system of linear equations with a quadratic matrix of coefficients using the LU expansion usage.
blockType: SubSystem
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Path in the library: |
Description
Block LU Solver solves a system of linear equations using the usage of the LU decomposition of the input matrix , where
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— square matrix of coefficients on at the entrance A;
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— matrix of free terms on at the entrance B;
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— solution of a system of equations, a matrix on the output is X.
The algorithm
The LU-decomposition algorithm represents a square input matrix with rearranged lines How:
Where
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— the matrix with rearranged strings, the order of the permutations is determined by the permutation vector ;
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— lower triangular matrix with single diagonal elements (unit triangular matrix);
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— upper triangular matrix.
If we replace the matrix factors in the original equation by , then we get
Where — a variant of the matrix with rearranged lines.
The resulting equation will have the form:
When replacing on it turns out two systems of equations with triangular matrices:
Ports
Input
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A
—
matrix of coefficients
matrix M by M
Details
The Matrix in the equation size on . Input ports A and B must have the same number of lines.
| Data types |
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| Complex numbers support |
Yes |
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B
—
the matrix of free terms
matrix M by N | vector M by 1
Details
The Matrix in the equation , given as a matrix of size on or a vector of size on .
If a vector is given on , then the block processes the input vector of length on port B as a matrix on . The Inputs A and B must have the same number of lines.
| Data types |
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| Complex numbers support |
Yes |
Output
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X
—
solving a system of equations
matrix M by N | vector M by 1
Details
The solution of the system of equations returned in the form of a matrix on or vectors on . The size of the output matrix X is the same as the size of the input matrix B.
| Data types |
|
| Complex numbers support |
Yes |