# ?tpmv

Computes a matrix-vector product using a triangular packed matrix.

## Syntax

FORTRAN 77:

call stpmv(uplo, trans, diag, n, ap, x, incx )

call dtpmv(uplo, trans, diag, n, ap, x, incx )

call ctpmv(uplo, trans, diag, n, ap, x, incx )

call ztpmv(uplo, trans, diag, n, ap, x, incx )

Fortran 95:

call tpmv(a, x [,uplo] [, trans] [,diag])

## Description

The ?tpmv routines perform one of the matrix-vector operations defined as

`x := A*x`, or `x := A'*x`, or `x := conjg(A')*x`,

where:

x is an n-element vector,

A is an n-by-n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.

## Input Parameters

uplo

  CHARACTER*1. Specifies whether the matrix A is upper or lower triangular:

  if `uplo = 'U'` or 'u', then the matrix is upper triangular;

  if `uplo = 'L'` or 'l', then the matrix is low triangular.

trans

  CHARACTER*1. Specifies the operation:

  if `trans = 'N'` or `'n'`, then `x := A*x`;

  if `trans = 'T'` or `'t'`, then `x := A'*x`;

  if `trans = 'C'` or `'c'`, then `x := conjg(A')*x`.

diag

  CHARACTER*1. Specifies whether the matrix A is unit triangular:

  if `diag = 'U'` or 'u' then the matrix is unit triangular;

  if `diag = 'N'` or 'n', then the matrix is not unit triangular.

n

  INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

ap

  REAL for stpmv

  DOUBLE PRECISION for dtpmv

  COMPLEX for ctpmv

  DOUBLE COMPLEX for ztpmv

  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. When `diag = 'U'` or 'u', the diagonal elements of a are not referenced, but are assumed to be unity.

x

  REAL for stpmv

  DOUBLE PRECISION for dtpmv

  COMPLEX for ctpmv

  DOUBLE COMPLEX for ztpmv

  Array, DIMENSION at least `(1 + (n - 1)*abs(incx))`. Before entry, the incremented array x must contain the n-element vector x.

incx

  INTEGER. Specifies the increment for the elements of x.

  The value of incx must not be zero.

## Output Parameters

x

  Overwritten with the transformed vector x.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine tpmv interface are the following:

a

  Holds the array a of size (n*(n+1)/2).

x

  Holds the vector of length (n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

trans

  Must be 'N', 'C', or 'T'.

  The default value is 'N'.

diag

  Must be 'N' or 'U'. The default value is 'N'.

Parent topic: BLAS Level 2 Routines