Solving a General System of Linear Equations (trs)

trs solves a system of linear equations \( A X = B \) or \( A^T X = B \) with a general \( n \times n \) matrix \( A \) using the \( LU \) factorization computed trf.

Multiple Right-Hand Sides

trans

(input)
Specifies the form of the system of equations:

NoTrans

\( A X = B \)

Trans

\( A^T X = B \)

ConjTrans

\( A^H X = B \)

A

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

piv

(output) integer valued DenseVector
The pivot indices from trf. For \( 1 \leq i \leq \min\{m, n\} \), row \( i \) of the matrix was interchanged with row \( piv_i \).

B

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

Single Right-Hand Side

trans

(input)
Specifies the form of the system of equations:

NoTrans

\( A X = B \)

Trans

\( A^T X = B \)

ConjTrans

\( A^H X = B \)

A

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

piv

(output) integer valued DenseVector
The pivot indices from trf. For \( 1 \leq i \leq \min\{m, n\} \), row \( i \) of the matrix was interchanged with row \( piv_i \).

b

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