Visible to Intel only — GUID: GUID-2FB74140-ADF9-4D82-8644-FD32025F6B71
Visible to Intel only — GUID: GUID-2FB74140-ADF9-4D82-8644-FD32025F6B71
?gbmv
Computes a matrix-vector product with a general band matrix.
Syntax
call sgbmv(trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
call dgbmv(trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
call cgbmv(trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
call zgbmv(trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
call gbmv(a, x, y [,kl] [,m] [,alpha] [,beta] [,trans])
Include Files
- mkl.fi, blas.f90
Description
The ?gbmv routines perform a matrix-vector operation defined as
y := alpha*A*x + beta*y,
or
y := alpha*A'*x + beta*y,
or
y := alpha *conjg(A')*x + beta*y,
where:
alpha and beta are scalars,
x and y are vectors,
A is an m-by-n band matrix, with kl sub-diagonals and ku super-diagonals.
Input Parameters
- trans
-
CHARACTER*1. Specifies the operation:
If trans= 'N' or 'n', then y := alpha*A*x + beta*y
If trans= 'T' or 't', then y := alpha*A'*x + beta*y
If trans= 'C' or 'c', then y := alpha *conjg(A')*x + beta*y
- m
-
INTEGER. Specifies the number of rows of the matrix A.
The value of m must be at least zero.
- n
-
INTEGER. Specifies the number of columns of the matrix A.
The value of n must be at least zero.
- kl
-
INTEGER. Specifies the number of sub-diagonals of the matrix A.
The value of kl must satisfy 0≤kl.
- ku
-
INTEGER. Specifies the number of super-diagonals of the matrix A.
The value of ku must satisfy 0≤ku.
- alpha
-
REAL for sgbmv
DOUBLE PRECISION for dgbmv
COMPLEX for cgbmv
DOUBLE COMPLEX for zgbmv
Specifies the scalar alpha.
- a
-
REAL for sgbmv
DOUBLE PRECISION for dgbmv
COMPLEX for cgbmv
DOUBLE COMPLEX for zgbmv
Array, size (lda, n).
Before entry, the leading (kl + ku + 1) by n part of the array a must contain the matrix of coefficients. This matrix must be supplied column-by-column, with the leading diagonal of the matrix in row (ku + 1) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row (ku + 2), and so on. Elements in the array a that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced.
The following program segment transfers a band matrix from conventional full matrix storage (matrix) to band storage (a):
do 20, j = 1, n k = ku + 1 - j do 10, i = max(1, j-ku), min(m, j+kl) a(k+i, j) = matrix(i,j) 10 continue 20 continue
- lda
-
INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least (kl + ku + 1).
- x
-
REAL for sgbmv
DOUBLE PRECISION for dgbmv
COMPLEX for cgbmv
DOUBLE COMPLEX for zgbmv
Array, size at least (1 + (n - 1)*abs(incx)) when trans= 'N' or 'n', and at least (1 + (m - 1)*abs(incx)) otherwise. Before entry, the array x must contain the vector x.
- incx
-
INTEGER. Specifies the increment for the elements of x. incx must not be zero.
- beta
-
REAL for sgbmv
DOUBLE PRECISION for dgbmv
COMPLEX for cgbmv
DOUBLE COMPLEX for zgbmv
Specifies the scalar beta. When beta is equal to zero, then y need not be set on input.
- y
-
REAL for sgbmv
DOUBLE PRECISION for dgbmv
COMPLEX for cgbmv
DOUBLE COMPLEX for zgbmv
Array, size at least (1 +(m - 1)*abs(incy)) when trans= 'N' or 'n' and at least (1 +(n - 1)*abs(incy)) otherwise. 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
-
Buffer holding 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 gbmv interface are the following:
- a
-
Holds the array a of size (kl+ku+1, n). Contains a banded matrix m*nwith kl lower diagonal and ku upper diagonal.
- x
-
Holds the vector with the number of elements rx, where rx = n if trans = 'N',rx = m otherwise.
- y
-
Holds the vector with the number of elements ry, where ry = m if trans = 'N',ry = n otherwise.
- trans
-
Must be 'N', 'C', or 'T'.
The default value is 'N'.
- kl
-
If omitted, assumed kl = ku, that is, the number of lower diagonals equals the number of the upper diagonals.
- ku
-
Restored as ku = lda-kl-1, where lda is the leading dimension of matrix A.
- m
-
If omitted, assumed m = n, that is, a square matrix.
- alpha
-
The default value is 1.
- beta
-
The default value is 0.