NAME¶

DTRSV - solves one of the systems of equations A*x = b, or A'*x = b,

SYNOPSIS¶

SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)

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

PURPOSE¶

DTRSV solves one of the systems of equations

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

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

ARGUMENTS¶

UPLO - CHARACTER*1.

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 - CHARACTER*1.

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 - CHARACTER*1.

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 - INTEGER.

On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.

A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).

Before 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. Before 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. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit.

LDA - INTEGER.

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 - DOUBLE PRECISION array of dimension at least

( 1 + ( n - 1 )*abs( INCX ) ). Before 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 - INTEGER.

On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

Level 2 Blas routine.

-- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.