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## 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 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.
```