선형 대수

선형 연립방정식 풀기, 행렬 분해 및 역행렬 구하기

DSP System Toolbox™ 시스템 선형 대수 블록을 사용하면 Simulink^®에서 행렬로 작업할 수 있습니다. 예를 들어 Levinson-Durbin 방법과 촐레스키 방법을 통해 선형 방정식 세트를 풀려면 Levinson-Durbin 및 Cholesky Solver 블록을 사용합니다. 이러한 기법은 Yule-Walker AR 문제 및 선형 예측 코딩 등의 응용 분야에서 일반적으로 사용됩니다. 정사각 행렬을 상부 및 하부 성분으로 분해하려면 LDL 분해, LU 분해와 같은 방법을 사용하십시오. 행렬의 역행렬을 구하려면 촐레스키 분해, LDL 분해, LU 분해와 같은 방법을 사용하십시오. 모든 지원되는 기법과 이러한 기법을 구현하는 DSP System Toolbox의 해당 블록에 대한 요약은 Linear Algebra and Least Squares 항목을 참조하십시오.

블록

모두 확장

행렬 분해

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

선형 시스템 솔버

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

역행렬

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 분해를 사용하여 정사각 행렬의 역행렬 계산
Pseudoinverse	Compute Moore-Penrose pseudoinverse of matrix

도움말 항목

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.