CXML
ssbmv, dsbmv, chbmv, zhbmv
Matrix-vector product for a symmetric or
hermitian band matrix
FORMAT
{S,D}SBMV (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy) {C,Z}HBMV
(uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
Arguments
uplo character*1
On entry, specifies whether the upper- or lower-
triangular part of the array A is referenced:
If uplo = 'U' or 'u', the upper-triangular part of A is referenced.
If uplo = 'L' or 'l', the lower-triangular part of A is referenced.
On exit, uplo is unchanged.
n integer*4
On entry, the order of the matrix A; n >= 0.
On exit, n is unchanged.
k integer*4
On entry, if uplo specifies the upper portion of matrix
A, k represents the number of super-diagonals of the
matrix. If uplo specifies the lower portion, k is the
number of subdiagonals; k >= 0.
On exit, k is unchanged.
alpha real*4 | real*8 | complex*8 | complex*16
On entry, the scalar alpha*.
On exit, alpha is unchanged.
a real*4 | real*8 | complex*8 | complex*16
On entry, a two-dimensional array with dimensions lda
by n.
When uplo specifies the upper portion of the matrix, the leading (k + 1) by
n part of the array must contain the upper-triangular band part of the
matrix, supplied column by column. The main diagonal of the matrix is
stored in row (k + 1) of the array, the first super-diagonal is stored in
row k starting at position 2, and so on. The top left k by k triangle of
the array A is not referenced.
When uplo specifies the lower portion of the matrix, the leading (k + 1) by
n part of the array must contain the lower-triangular band part of the
matrix, supplied column by column. The main diagonal of the matrix is
stored in row 1 of the array, the first sub-diagonal is stored in row 2,
starting at position 1, and so on. The bottom right k by k triangle of the
array A is not referenced.
For CHBMV and ZHBMV routines, the imaginary parts of the diagonal elements
are not accessed, need not be set, and are assumed to be zero.
On exit, a is unchanged.
lda integer*4
On entry, the first dimension of array A; lda >= (k+1).
On exit, lda is unchanged.
x real*4 | real*8 | complex*8 | complex*16
On entry, a one-dimensional array X of length at least
(1+(n-1)*|incx|). Array X contains the vector x.
On exit, x is unchanged.
incx integer*4
On entry, the increment for the elements of X; incx
must not equal zero.
On exit, incx is unchanged.
beta real*4 | real*8 | complex*8 | complex*16
On entry, the scalar beta.
On exit, beta is unchanged.
y real*4 | real*8 | complex*8 | complex*16
On entry, a one-dimensional array Y of length at least
(1+(n-1)*|incy|).
If beta= 0, y need not be set. If betais not equal to zero, the
incremented array Y must contain the vector y.
On exit, y is overwritten by the updated vector y.
incy integer*4
On entry, the increment for the elements of Y; incy
must not equal zero.
On exit, incy is unchanged.
Description
SSBMV and DSBMV compute a matrix-vector product for a real symmetric band
matrix. CHBMV and ZHBMV compute a matrix-vector product for a complex
Hermitian band matrix. Both products are described by the following
operation: y = alpha*Ax + beta*y
alphaand betaare scalars, and x and y are vectors with n elements. In the
case of SSBMV and DSBMV, A is a symmetric matrix and in the case of CHBMV
and ZHBMV, A is a Hermitian matrix.
Example
REAL*8 A(2,10), X(10), Y(10), alpha, beta
N = 10
K = 1
alpha = 2.0D0
LDA = 2
INCX = 1
beta = 1.0D0
INCY = 1
CALL DSBMV('U',N,K,alpha,A,LDA,X,INCX,beta,Y,INCY)
This FORTRAN code computes the product y = alpha*Ax + y) where A is a
symmetric tridiagonal matrix, with A stored in upper-triangular form.
COMPLEX*8 A(2,10), X(10), Y(10), alpha, beta
N = 10
K = 1
alpha = (2.0, 2.2)
LDA = 2
INCX = 1
beta = (1.0, 0.0)
This FORTRAN code computes the product y = alpha*Ax + y) where A is a
Hermitian tridiagonal matrix, with the upper diagonal of A stored.
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