Lineare Algebra
R2024bDie linearen Algebra-Blöcke der DSP System Toolbox™ ermöglichen es Ihnen, in Simulink® mit Matrizen zu arbeiten. Wenn Sie beispielsweise einen Satz linearer Gleichungen mithilfe der Levinson-Durbin- und Cholesky-Methoden lösen möchten, können Sie die Blöcke Levinson-Durbin und Cholesky Solver verwenden. Diese Techniken kommen oft in Anwendungen wie dem Yule-Walker-AR-Problem und linearer prädiktiver Codierung zum Einsatz. Um eine quadratische Matrix in obere und untere Bestandteile zu faktorisieren, verwenden Sie Methoden wie LDL-Faktorisierung und LU-Faktorisierung. Um Matrizen zu invertieren, verwenden Sie Methoden wie Cholesky-Faktorisierung, LDL-Faktorisierung und LU-Faktorisierung. Eine Zusammenfassung aller unterstützten Techniken und der entsprechenden Blöcke in DSP System Toolbox, die die Technik implementieren, finden Sie unter Linear Algebra and Least Squares.
Blöcke
 | 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 |
Themen
- 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.
