Computes a matrix-vector product using a triangular matrix.

## Syntax

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)

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

## Include Files

• mkl.fi, blas.f90

## 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:

uplo = 'U' or 'u'

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, size (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 leading 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, size 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.

## BLAS 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 BLAS 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 with the number of elements 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'.

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