Content

Triangular Solver (trs)

trs (defined in namespace flens::lapack) solves a system of linear equations

\[ A X = B \quad\text{or}\quad A^T X = B \]

Two variants are provided:

Further subvariants are provided for cases where the right hand side \(B\) is a matrix or vector.

Variant: System of Linear Equations

Multiple Right-Hand Sides

trans

(input) bool
Solve \(AX=B\), \(A^T X=B\) or \(A^H X = B\)

A

(input) real or complex valued GeMatrix
The factors \(L\) and \(U\) from the factorization \(A = PLU\) as computed trf.

piv

(input) integer valued DenseVector
The pivot indices as returned from trf.

B

(input/output) real or complex valued GeMatrix
On entry, the \(n \times n_{rhs}\) right hand side matrix \(B\).
On exit, the solution matrix \(X\).

Single Right-Hand Side

trans

(input) bool
Solve \(AX=B\), \(A^T X=B\) or \(A^H X = B\)

A

(input) real or complex valued GeMatrix
The factors \(L\) and \(U\) from the factorization \(A = PLU\) as computed trf.

piv

(input) integer valued DenseVector
The pivot indices as returned from trf.

b

(input/output) real or complex valued DenseVector
On entry, the right hand side vector \(b\).
On exit, the solution vector \(x\).

Variant: Triangular System

Multiple Right-Hand Sides

trans

(input) bool
Solve \(AX=B\), \(A^T X=B\) or \(A^H X = B\)

A

(input) real or complex valued TrMatrix
The \(n \times n\) triangular matrix.

B

(input/output) real or complex valued GeMatrix
On entry, the \(n \times n_{rhs}\) right hand side matrix \(B\).
On exit, the solution matrix \(X\).

Single Right-Hand Side

trans

(input) bool
Solve \(AX=B\), \(A^T X=B\) or \(A^H X = B\)

A

(input) real or complex valued TrMatrix
The \(n \times n\) triangular matrix.

b

(input/output) real or complex valued DenseVector
On entry, the \(n \times n_{rhs}\) right hand side vector \(b\).
On exit, the solution vector \(x\).

Notes