線形代数
R2026bDSP System Toolbox™ システムの各種線形代数ブロックを使用すると、Simulink® で行列を操作できます。たとえば、レビンソン・ダービン手法やコレスキー手法を使って一連の線形方程式を解く場合、Levinson-Durbin ブロックや Cholesky Solver ブロックを使用します。これらの手法は通常、ユール・ウォーカー AR 問題や線形予測符号化などのアプリケーションで使用されます。正方行列を上位と下位の成分に因子分解するには、LDL 分解や LU 分解などの手法を使用します。逆行列を求めるには、コレスキー分解、LDL 分解、LU 分解などの手法を使用します。サポートされているすべての手法と、その手法を実装する DSP System Toolbox の対応するブロックの概要については、Linear Algebra and Least Squaresを参照してください。
ブロック
 | 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 | LU 分解による正方行列の逆行列の計算 |
 | Pseudoinverse | Moore-Penrose 疑似逆行列の計算 |
トピック
- 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.
