Visible to Intel only — GUID: GUID-B6F7D890-8959-4EA0-8252-004E4BF9C93D
Visible to Intel only — GUID: GUID-B6F7D890-8959-4EA0-8252-004E4BF9C93D
?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.