?hbmv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?hbmv

Computes a matrix-vector product using a Hermitian band matrix.

Syntax

call chbmv(uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)

call zhbmv(uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)

call hbmv(a, x, y [,uplo][,alpha] [,beta])

Include Files

mkl.fi, blas.f90

Description

The ?hbmv routines perform a matrix-vector operation defined as y := alpha*A*x + beta*y,

where:

alpha and beta are scalars,

x and y are n-element vectors,

A is an n-by-n Hermitian band matrix, with k super-diagonals.

Input Parameters

uplo

CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian band matrix A is used:

If uplo = 'U' or 'u', then the upper triangular part of the matrix A is used.

If uplo = 'L' or 'l', then the low triangular part of the matrix A is used.

n

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

k

INTEGER. For uplo = 'U' or 'u'Specifies the number of super-diagonals of the matrix A.

For uplo = 'L' or 'l': Specifies the number of sub-diagonals of the matrix A.

The value of k must satisfy 0≤k.

alpha

COMPLEX for chbmv

DOUBLE COMPLEX for zhbmv

Specifies the scalar alpha.

a

COMPLEX for chbmv

DOUBLE COMPLEX for zhbmv

Array, size (lda, n).

Before entry with uplo = 'U' or 'u', the leading (k + 1) by n part of the array a must contain the upper triangular band part of the Hermitian matrix. The matrix must be supplied column-by-column, with the leading diagonal of the matrix in row (k + 1) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array a is not referenced.

The following program segment transfers the upper triangular part of a Hermitian band matrix from conventional full matrix storage (matrix) to band storage (a):

       do 20, j = 1, n
          m = k + 1 - j
          do 10, i = max( 1, j - k ), j
             a( m + i, j ) = matrix( i, j )
10        continue
20     continue

Before entry with uplo = 'L' or 'l', the leading (k + 1) by n part of the array a must contain the lower triangular band part of the Hermitian matrix, supplied column-by-column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array a is not referenced.

The following program segment transfers the lower triangular part of a Hermitian band matrix from conventional full matrix storage (matrix) to band storage (a):

       do 20, j = 1, n
          m = 1 - j
          do 10, i = j, min( n, j + k )
             a( m + i, j ) = matrix( i, j )
10        continue
20     continue

The imaginary parts of the diagonal elements need not be set and are assumed to be zero.

lda

INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least (k + 1).

x

COMPLEX for chbmv

DOUBLE COMPLEX for zhbmv

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

incx

INTEGER. Specifies the increment for the elements of x.

The value of incx must not be zero.

beta

COMPLEX for chbmv

DOUBLE COMPLEX for zhbmv

Specifies the scalar beta.

y

COMPLEX for chbmv

DOUBLE COMPLEX for zhbmv

Array, size at least (1 + (n - 1)*abs(incy)). Before entry, the incremented array y must contain the vector y.

incy

INTEGER. Specifies the increment for the elements of y.

The value of incy must not be zero.

Output Parameters

y: Overwritten by the updated vector y.

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 hbmv interface are the following:

a: Holds the array a of size (k+1,n).
x: Holds the vector with the number of elements n.
y: Holds the vector with the number of elements n.
uplo: Must be 'U' or 'L'. The default value is 'U'.
alpha: The default value is 1.
beta: The default value is 0.

Parent topic: BLAS Level 2 Routines

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