# Solving a Triangular System of Linear Equations (trs)

trs solves a triangular system of the form $$A X = B$$ or $$A^T X = B$$, where $$A$$ is a triangular matrix of order $$n$$, and $$B$$ is an $$n \times n_{\text{rhs}}$$ matrix. A check is made to verify that $$A$$ is nonsingular.

## 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 TrMatrix
The triangular matrix $$A$$.

B

(input/output) real or complex valued GeMatrix
On entry, the right hand side matrix $$B$$. On exit, if the return value equals zero, the solution matrix $$X$$.

Return value:

 i=0 Successful exit. i>0 $$A_{i,i}$$ is exactly zero, indicating that the matrix is singular and the solutions $$X$$ have not been computed.

## 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 TrMatrix
The triangular matrix $$A$$.

b

(input/output) real or complex valued DenseVector
On entry, the right hand side vector $$b$$. On exit, if the return value equals zero, the solution vector $$x$$.

Return value:

 i=0 Successful exit. i>0 $$A_{i,i}$$ is exactly zero, indicating that the matrix is singular and the solutions $$x$$ have not been computed.