ztpmv

```ZTPMV(1)                         BLAS routine                         ZTPMV(1)

NAME
ZTPMV - performs one of the matrix-vector operations   x := A*x, or x
:= A'*x, or x := conjg( A' )*x,

SYNOPSIS
SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)

INTEGER                                   INCX,N

CHARACTER                                 DIAG,TRANS,UPLO

DOUBLE                                    COMPLEX AP(*),X(*)

PURPOSE
ZTPMV  performs one of the matrix-vector operations

where x is an n element vector and  A is an n by n unit, or non-unit,
upper or lower triangular matrix, supplied in packed form.

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 operation to be performed as
follows:

TRANS = 'N' or 'n'   x := A*x.

TRANS = 'T' or 't'   x := A'*x.

TRANS = 'C' or 'c'   x := conjg( A' )*x.

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*16       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*16       array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
array X must contain the n element vector x. On exit, X is
overwritten with the tranformed vector x.

INCX   - INTEGER.
On entry, INCX specifies the increment for the elements of X.
INCX must not be zero.  Unchanged on exit.

FURTHER DETAILS
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                        ZTPMV(1)```