Algèbre linéaire

Résoudre un système d’équations linéaires, factoriser et inverser des matrices

Les blocs d’algèbre linéaire des systèmes de DSP System Toolbox™ permettent de travailler avec des matrices dans Simulink^®. Par exemple, vous pouvez résoudre un système d’équations linéaires avec les méthodes de Levinson-Durbin et de Cholesky en utilisant les blocs Levinson-Durbin et Cholesky Solver. Ces techniques sont couramment utilisées dans des applications comme le problème autorégressif de Yule-Walker et le codage prédictif linéaire. Pour factoriser une matrice carrée en composantes supérieures et inférieures, utilisez par exemple les méthodes de factorisation LDL et LU. Pour inverser des matrices, utilisez par exemple les méthodes de factorisation LDL, LU et de Cholesky. Pour un récapitulatif de toutes les techniques supportées et des blocs correspondants de DSP System Toolbox permettant de les implémenter, veuillez consulter Linear Algebra and Least Squares.

Blocs

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Factorisation de matrices

Cholesky Factorization	Factor square Hermitian positive definite matrix into triangular components
LDL Factorization	Factor square Hermitian positive definite matrices into lower, upper, and diagonal components
LU Factorization	Factor square matrix into lower and upper triangular components
QR Factorization	Factor arbitrary matrix into unitary and upper triangular components
Singular Value Decomposition	Factor matrix using singular value decomposition

Solveurs de systèmes linéaires

Backward Substitution	Solve UX = B for X when U is upper triangular matrix
Cholesky Solver	Solve SX = B for X when S is a square Hermitian positive definite matrix
Forward Substitution	Solve LX = B for X when L is lower triangular matrix
LDL Solver	Solve SX = B when S is square Hermitian positive definite matrix
Levinson-Durbin	Solve linear system of equations using Levinson-Durbin recursion
LU Solver	Solve AX = B when A is a square matrix
QR Solver	Find minimum-norm-residual solution to AX=B
SVD Solver	Solve AX = B using singular value decomposition

Inversions de matrices

Cholesky Inverse	Compute inverse of Hermitian positive definite matrix using Cholesky factorization
LDL Inverse	Compute inverse of Hermitian positive definite matrix using LDL factorization
LU Inverse	Compute inverse of square matrix using LU factorization
Pseudoinverse	Compute Moore-Penrose pseudoinverse of matrix

Rubriques

Linear Algebra and Least Squares
Solve systems of linear equations.
LDL Factorization of 3-by-3 Hermitian Positive Definite Matrix
Simulink model example that shows how to use the LDL Factorization block.
Solve Matrix Equation Using Backward Substitution
Use Backward Substitution block to solve a system of linear equations. Verify the solution using Matrix Multiply block.
Solve Matrix Equation Using Forward Substitution
Use Forward Substitution block to solve a system of linear equations. Verify the solution using Matrix Multiply block.
Find Inverse of Matrix Using the LU Inverse Block
Find inverse of a square matrix using the LU Inverse block.
Solve Matrix Equation Using LU Solver
Use LU Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.
Solve Matrix Equation Using Singular Value Decomposition
Use SVD Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.
Solve Matrix Equation Using Cholesky Solver
Use Cholesky Solver block to solve a matrix equation. Verify the solution using Matrix Multiply block.
Factorize Matrix Using LU Factorization Block
Factorize a matrix using the LU Factorization block.