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# dtrsv

```
NAME
DTRSV - solve 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*1  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.

PARAMETERS
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 tri-
angular.

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 con-
tain 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 tri-
angular 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 ele-
ments 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.
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