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# Technical Reference: Base Operating System and Extensions , Volume 2

## STRSV, DTRSV, CTRSV, or ZTRSV Subroutine

### Purpose

Solves system of equations.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE STRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
REAL A(LDA,*), X(*)

```SUBROUTINE DTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
DOUBLE PRECISION A(LDA,*), X(*)
```

```SUBROUTINE CTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX A(LDA,*), X(*)
```

```SUBROUTINE ZTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX*16 A(LDA,*), X(*)
```

### Description

The STRSV, DTRSV, CTRSV, or ZTRSV subroutine solves one of the systems of equations:

A * x = b

OR

A' * x = b

where b and x are N element vectors and A is an N by N unit, or non-unit, upper or lower triangular matrix.

### Parameters

 UPLO On entry, UPLO specifies whether the matrix 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. TRANS On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A * x = b TRANS = 'T' or 't' A' * x = b TRANS = 'C' or 'c' A' * x = b 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. N On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit. A An array of dimension ( LDA, N ); on entry with UPLO = 'U' or 'u', the leading N by N 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 N by N 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; LDA must be at least max( 1, N ); unchanged on exit. X A vector of dimension at least (1 + (N-1) * abs(INCX) ); on entry, the incremented array X must contain the N element right-hand side vector b; on exit, X is overwritten with the solution vector x. INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.

### Implementation Specifics

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

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