Developer Reference for Intel® oneAPI Math Kernel Library for C
?hbmv
Computes a matrix-vector product using a Hermitian band matrix.
Syntax
void cblas_chbmv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const MKL_INT n,
const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda,
const void *x, const MKL_INT incx, const void *beta, void *y,
const MKL_INT incy);
void cblas_zhbmv(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const MKL_INT n,
const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda,
const void *x, const MKL_INT incx, const void *beta, void *y,
const MKL_INT incy);Include Files
mkl.h
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
- Layout
-
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
uplo
Specifies whether the upper or lower triangular part of the Hermitian band matrix A is used:
If uplo = CblasUpper , then the upper triangular part of the matrix A is used.
If uplo = CblasLower , then the low triangular part of the matrix A is used.
n
Specifies the order of the matrix A . The value of n must be at least zero.
k
For uplo = CblasUpper : Specifies the number of super-diagonals of the matrix A .
For uplo = CblasLower : 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)lda*n .
Layout = CblasColMajor :
Before entry with uplo = CblasUpper , 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 of the array, the first super-diagonal starting at position 1 in row (k - 1) , 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 , with leading dimension ldm ) to band storage ( a , with leading dimension lda ):
Before entry with uplo = CblasLower , 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 0 of the array, the first sub-diagonal starting at position 0 in row 1 , 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 , with leading dimension ldm ) to band storage ( a , with leading dimension lda ):
Layout = CblasRowMajor: Before entry with uplo = CblasUpper , the leading ( k + 1)-by- n part of array a must contain the upper triangular band part of the Hermitian matrix. The matrix must be supplied row-by-row, with the leading diagonal of the matrix in column 0 of the array, the first super-diagonal starting at position 0 in column 1, and so on. The bottom right k -by- k triangle of array a is not referenced. The following program segment transfers the upper triangular part of a Hermitian band matrix from row-major full matrix storage ( matrix with leading dimension ldm ) to row-major band storage ( a , with leading dimension lda ): Before entry with uplo = CblasLower , the leading ( k + 1)-by- n part of array a must contain the lower triangular band part of the Hermitian matrix, supplied row-by-row, with the leading diagonal of the matrix in column k of the array, the first sub-diagonal starting at position 1 in column k -1, and so on. The top left k -by- k triangle of array a is not referenced. The following program segment transfers the lower triangular part of a Hermitian row-major band matrix from row-major full matrix storage ( matrix , with leading dimension ldm ) to row-major band storage ( a , with leading dimension lda ): The imaginary parts of the diagonal elements need not be set and are assumed to be zero.
lda
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
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
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
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.