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*AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2*

## STRSM, DTRSM, CTRSM, or ZTRSM Subroutine

### Purpose

Solves certain matrix equations.

### Library

BLAS Library (**libblas.a**)

### FORTRAN Syntax

**SUBROUTINE** **STRSM(***SIDE***, ***UPLO***, ***TRANSA***, ***DIAG***,**
*M***, ***N***, ***ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***)**
**CHARACTER*1** *SIDE***,***UPLO***,***TRANSA***,***DIAG*
**INTEGER** *M***,***N***,***LDA***,***LDB*
**REAL** *ALPHA*
**REAL** *A***(***LDA***,*), ***B***(***LDB***,*)**

**SUBROUTINE** **DTRSM(***SIDE***, ***UPLO***, ***TRANSA***, ***DIAG***,**
*M***, ***N***, ***ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***)**
**CHARACTER*1** *SIDE***,***UPLO***,***TRANSA***,***DIAG*
**INTEGER** *M***,***N***,***LDA***,***LDB*
**DOUBLE PRECISION** *ALPHA*
**DOUBLE PRECISION** *A***(***LDA***,*), ***B***(***LDB***,*)**

**SUBROUTINE** **CTRSM(***SIDE***, ***UPLO***, ***TRANSA***, ***DIAG***,**
*M***, ***N***, ***ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***)**
**CHARACTER*1** *SIDE***,***UPLO***,***TRANSA***,***DIAG*
**INTEGER** *M***,***N***,***LDA***,***LDB*
**COMPLEX** *ALPHA*
**COMPLEX** *A***(***LDA***,*), ***B***(***LDB***,*)**

**SUBROUTINE** **ZTRSM(***SIDE***, ***UPLO***, ***TRANSA***, ***DIAG***,**
*M***, ***N***, ***ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***)**
**CHARACTER*1** *SIDE***,***UPLO***,***TRANSA***,***DIAG*
**INTEGER** *M***,***N***,***LDA***,***LDB*
**COMPLEX*16** *ALPHA*
**COMPLEX*16** *A***(***LDA***,*), ***B***(***LDB***,*)**

### Description

The **STRSM**, **DTRSM**, **CTRSM**, or **ZTRSM** subroutine solves one of the matrix equations:

`op( `
`A`
` ) * X = alpha * `
`B`
`X * op( `
`A`
` ) = alpha * `
`B`

where alpha is a scalar, X and *B* are *M* by *N* matrices, *A* is a unit, or non-unit, upper or lower triangular matrix, and op( *A* ) is either op( *A* ) = *A* or op( *A* ) = *A*'. The matrix X is overwritten on *B*.

### Parameters

*SIDE* |
On entry, *SIDE* specifies whether op( *A* ) appears on the left or right of X as follows:
*SIDE* = 'L' or 'l' |
op( *A* ) * X = alpha * *B* |
*SIDE* = 'R' or 'r' |
X * op( *A* ) = alpha * *B* |
Unchanged on exit. |

*UPLO* |
On entry, *UPLO* specifies whether the matrix *A* is an upper or lower triangular matrix as follows:
*UPLO* = 'U' or 'u' |
*A* is an upper triangular matrix. |
*UPLO* = 'L' or 'l' |
*A* is a lower triangular matrix. |
Unchanged on exit. |

*TRANSA* |
On entry, *TRANSA* specifies the form of op( *A* ) to be used in the matrix multiplication as follows:
*TRANSA* = 'N' or 'n' |
op( *A* ) = *A* |
*TRANSA* = 'T' or 't' |
op( *A* ) = *A*' |
*TRANSA* = 'C' or 'c' |
op( *A* ) = *A*' |
Unchanged on exit. |

*DIAG* |
On entry, *DIAG* specifies whether or not *A* is unit triangular as follows:
*DIAG* = 'U' or 'u' |
*A* is assumed to be unit triangular. |
*DIAG* = 'N' or 'n' |
*A* is not assumed to be unit triangular. |
Unchanged on exit. |

*M* |
On entry, *M* specifies the number of rows of *B*; *M* must be at least 0; unchanged on exit. |

*N* |
On entry, *N* specifies the number of columns of* B;* *N* must be at least 0; unchanged on exit. |

*ALPHA* |
On entry, *ALPHA* specifies the scalar alpha. When alpha is 0 then *A* is not referenced and *B* need not be set before entry; unchanged on exit. |

*A* |
An array of dimension ( *LDA*, k ), where k is *M* when *SIDE* = 'L' or 'l' and is *N* when *SIDE *= 'R' or 'r'. On entry with* UPLO* = 'U' or 'u', the leading k by k upper triangular part of the array *A* must contain the upper triangular matrix and the strictly lower triangular part of *A* is not referenced; on entry with *UPLO* = 'L' or 'l', the leading k by k lower triangular part of the array* A* must contain the lower triangular matrix and the strictly upper triangular part of *A* is not referenced. When *DIAG* = 'U' or 'u', the diagonal elements of *A* are not referenced, but are assumed to be unity; unchanged on exit. |

*LDA* |
On entry, *LDA* specifies the first dimension of *A* as declared in the calling (sub) program. When *SIDE* = 'L' or 'l', *LDA* must be at least max( 1, *M* ); when *SIDE* = 'R' or 'r', *LDA *must be at least max( 1, *N* ); unchanged on exit. |

*B* |
An array of dimension ( *LDB*, *N* ); on entry, the leading *M* by *N* part of the array *B* must contain the right-hand side matrix *B*, and on exit is overwritten by the solution matrix X. |

*LDB* |
On entry, *LDB* specifies the first dimension of *B* as declared in the calling (sub) program. *LDB* must be at least max( 1, *M* ); unchanged on exit. |

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