Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?sbmv
Computes a matrix-vector product with a symmetric band matrix.
Syntax
call ssbmv(uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
call dsbmv(uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)call sbmv(a, x, y [, uplo] [, alpha] [, beta])Include Files
mkl.fi, mkl_blas.f90
Description
The ?sbmv 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 symmetric band matrix, with k super-diagonals.
Input Parameters
- Layout
-
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
uplo
CHARACTER*1 . Specifies whether the upper or lower triangular part of the band matrix A is used:
if uplo = 'U' or ‘u’ uplo = CblasUpper - upper triangular part;
if uplo = 'L' or ‘l’ - low triangular part.
n
INTEGER . Specifies the order of the matrix A . The value of n must be at least zero.
k
INTEGER . Specifies the number of super-diagonals of the matrix A .
The value of k must satisfy 0 ≤ k .
- alpha
-
REAL for ssbmv DOUBLE PRECISION for dsbmv Specifies the scalar alpha .
- a
-
REAL for ssbmv DOUBLE PRECISION for dsbmv
Array, size (lda, n)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 symmetric matrix, 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 symmetric band matrix from conventional full matrix storage ( matrix ) to band storage ( a ):
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 symmetric 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 symmetric band matrix from conventional full matrix storage ( matrix ) to band storage ( a ):
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 symmetric 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 symmetric 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 symmetric 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 symmetric 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 ):
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
-
REAL for ssbmv DOUBLE PRECISION for dsbmv 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
-
REAL for ssbmv DOUBLE PRECISION for dsbmv Specifies the scalar beta .
- y
-
REAL for ssbmv DOUBLE PRECISION for dsbmv 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 sbmv 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.