# dtpmv.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dtpmv.f

## SYNOPSIS

### Functions/Subroutines

subroutine dtpmv (UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV

## Function/Subroutine Documentation

### subroutine dtpmv (character UPLO, character TRANS, character DIAG, integer N, double precision, dimension(*) AP, double precision, dimension(*) X, integer INCX)

DTPMV

Purpose:

``` DTPMV  performs one of the matrix-vector operations

x := A*x,   or   x := A**T*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**T*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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, 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
transformed 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:

December 2016

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 144 of file dtpmv.f.

## Author

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