# dtrsv

```DTRSV(1)                         BLAS routine                         DTRSV(1)

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.

BLAS routine                     November 2008                        DTRSV(1)```