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NAME

```       DTPSV - solve one of the systems of equations   A*x = b, or A’*x = b,

```

SYNOPSIS

```       SUBROUTINE DTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )

INTEGER      INCX, N

CHARACTER*1  DIAG, TRANS, UPLO

DOUBLE       PRECISION AP( * ), X( * )

```

PURPOSE

```       DTPSV  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, supplied in packed form.

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.

AP     - DOUBLE PRECISION array of DIMENSION at least
(  (  n*(  n + 1 ) )/2 ).  Before entry with  UPLO = ’U’ or ’u’,
the array AP must contain the  upper  triangular  matrix  packed
sequentially, column by column, so that AP( 1 ) contains a( 1, 1
), AP( 2 ) and AP( 3 )  contain  a(  1,  2  )  and  a(  2,  2  )
respectively,  and  so on.  Before entry with UPLO = ’L’ or ’l’,
the array AP must contain the  lower  triangular  matrix  packed
sequentially, column by column, so that AP( 1 ) contains a( 1, 1
), AP( 2 ) and AP( 3 )  contain  a(  2,  1  )  and  a(  3,  1  )
respectively, and so on.  Note that when  DIAG = ’U’ or ’u’, the
diagonal elements of A are not referenced, but are assumed to be
unity.  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.
```