3.5 KiB
3.5 KiB
Linear Equations
This section provides functions for solving systems of linear equations of the form A·X = B, where A is a square coefficient matrix, B is the right-hand side, and X is the solution matrix or vector. The methods support various data types (double, float, complex, complexf) and are based on LAPACK functions to ensure high precision and performance.
The functions are categorized based on the type of the coefficient matrix A. Each function is overloaded to support both matrix and vector forms for the right-hand side (B) and the solution (X).
| Function | Action |
|---|---|
| LinearEquationsSolution | Computes the solution to the system of linear equations with a square coefficient matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n general matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK function GESV . |
| LinearEquationsSolutionTriangular | Computes the solution to the system of linear equations with a square triangular coefficient matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n general matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK function TRTRS . |
| InverseTriangular | Computes the inverse of a upper or lower triangular matrix A. LAPACK function TRTRI . |
| CondNumReciprocalTriangular | Estimates the reciprocal of the condition number of a upper or lower triangular matrix A in either the one-norm or infinity-norm. LAPACK function TRCON . |
| LinearEquationsSolutionSy | Computes the solution to the system of linear equations with a symmetric or Hermitian conjugated matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n symmetric or Hermitian conjugated matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK functions SYSV , HESV . |
| LinearEquationsSolutionComplexSy | Computes the solution to the system of linear equations with a complex symmetric (not Hermitian conjugated!) matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n complex symmetric matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK function SYSV . |
| LinearEquationsSolutionSyPD | Computes the solution to the system of linear equations with a symmetric or Hermitian conjugated positive-definite matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n symmetric or Hermitian conjugated positive-definite matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK function POSV . |
| LinearEquationsSolutionGeTrid | Computes the solution to the system of linear equations with a general (nonsymmetric) tridiagonal coefficient matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n general tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK function GTSV . |
| LinearEquationsSolutionSyTridPD | Computes the solution to the system of linear equations with a symmetric tridiagonal positive-definite coefficient matrix A and multiple right-hand sides. A*X = B, where A is an n-by-n symmetric tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. LAPACK function PTSV . |