# ?trmv

Computes a matrix-vector product using a triangular matrix.

## Syntax

FORTRAN 77:

call strmv(uplo, trans, diag, n, a, lda, x, incx )

call dtrmv(uplo, trans, diag, n, a, lda, x, incx )

call ctrmv(uplo, trans, diag, n, a, lda, x, incx )

call ztrmv(uplo, trans, diag, n, a, lda, x, incx )

Fortran 95:

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

## Description

The ?trmv routines perform one of the following 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.

## 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.

a

  REAL for strmv

  DOUBLE PRECISION for dtrmv

  COMPLEX for ctrmv

  DOUBLE COMPLEX for ztrmv

  Array, DIMENSION `(lda,n)`. Before entry with `uplo = 'U'` or 'u', the leading n-by-n upper triangular part of the array a must contain the upper triangular matrix and the strictly lower triangular part of a is not referenced. Before entry with `uplo = 'L'` or 'l', the leading n-by-n lower triangular part of the array a must contain the lower triangular matrix and the strictly upper triangular part of a is not referenced.

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

lda

  INTEGER. Specifies the first dimension of a as declared in the calling (sub)program. The value of lda must be at least `max(1, n)`.

x

  REAL for strmv

  DOUBLE PRECISION for dtrmv

  COMPLEX for ctrmv

  DOUBLE COMPLEX for ztrmv

  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 trmv interface are the following:

a

  Holds the matrix A of size (n,n).

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