Lineare Algebra

Lösen Sie ein System linearer Gleichungen und faktorisieren und invertieren Sie Matrizen

Die 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

alle erweitern

Matrizen-Faktorisierung

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

Solver für lineare Systeme

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

Matrizen-Invertierung

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.