Algebra lineare
R2024bI blocchi di algebra lineare del sistema DSP System Toolbox™ consentono di lavorare con le matrici in Simulink®. Ad esempio, per risolvere un insieme di equazioni lineari con i metodi Levinson-Durbin e Cholesky, utilizzare i blocchi Levinson-Durbin e Cholesky Solver. Queste tecniche sono comunemente utilizzate in applicazioni come il problema di Yule-Walker AR e la codifica predittiva lineare. Per fattorizzare una matrice quadrata in componenti superiori e inferiori, si utilizzano metodi come la fattorizzazione LDL e la fattorizzazione LU. Per invertire le matrici, si utilizzano metodi come la fattorizzazione di Cholesky, la fattorizzazione LDL e la fattorizzazione LU. Per un riepilogo di tutte le tecniche supportate e dei blocchi corrispondenti in DSP System Toolbox che implementano tali tecniche, vedere Linear Algebra and Least Squares.
Blocchi
 | 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 |
 | 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 |
 | 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 |
Argomenti
- 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.
