# ztpmv.f(3) [centos man page]

```ztpmv.f(3)							      LAPACK								ztpmv.f(3)

NAME
ztpmv.f -

SYNOPSIS
Functions/Subroutines
subroutine ztpmv (UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV

Function/Subroutine Documentation
subroutine ztpmv (characterUPLO, characterTRANS, characterDIAG, integerN, complex*16, dimension(*)AP, complex*16, dimension(*)X, integerINCX)
ZTPMV Purpose:

ZTPMV  performs one of the matrix-vector operations

x := A*x,   or	x := A**T*x,   or   x := A**H*x,

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.

Parameters:
UPLO

UPLO is 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.

TRANS

TRANS is 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**T*x.

TRANS = 'C' or 'c'   x := A**H*x.

DIAG

DIAG is 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.

N

N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.

AP

AP is 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.

X

X is (input/output) 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

INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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.

Definition at line 143 of file ztpmv.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012							ztpmv.f(3)```

## Check Out this Related Man Page

```ZTPMV(3)							   BLAS routine 							  ZTPMV(3)

NAME
ZTPMV - perform 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*1	DIAG, TRANS, UPLO

COMPLEX*16	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.

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 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 sequen-
tially, 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.

Level 2 Blas routine.

-- Written on 22-October-1986.  Jack Dongarra, Argonne National Lab.  Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag Cen-
tral Office.  Richard Hanson, Sandia National Labs.

BLAS routine							  16 October 1992							  ZTPMV(3)```
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