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## NAME

```       CTPSV  -  solve one of the systems of equations   A*x = b, or A’*x = b,
or conjg( A’ )*x = b,

```

## SYNOPSIS

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

INTEGER      INCX, N

CHARACTER*1  DIAG, TRANS, UPLO

COMPLEX      AP( * ), X( * )

```

## PURPOSE

```       CTPSV  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’   conjg( 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     - COMPLEX          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      - COMPLEX          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.
```