C Library Functions - zgbmv (3)
NAME
zgbmv(3f) - [BLAS:COMPLEX_16_BLAS_LEVEL2]
CONTENTS
Synopsis
Definition
Options
Y
Authors
Further Details
See Also
SYNOPSIS
subroutine zgbmv(trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy)
.. Scalar Arguments .. complex(kind=real64),intent(in) :: alpha,beta integer,intent(in) :: incx,incy,kl,ku,lda,m,n character,intent(in) :: trans .. .. Array Arguments .. complex(kind=real64),intent(in) :: a(lda,*),x(*) complex(kind=real64),intent(inout) :: y(*) ..
DEFINITION
ZGBMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, orwhere alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.y := alpha*A**H*x + beta*y,
OPTIONS
TRANS
TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows:
TRANS = ’N’ or ’n’ y := alpha*A*x + beta*y.TRANS = ’T’ or ’t’ y := alpha*A**T*x + beta*y.
TRANS = ’C’ or ’c’ y := alpha*A**H*x + beta*y.
M
M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero.
N
N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero.
KL
KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL.
KU
KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.
ALPHA
ALPHA is complex(kind=real64) On entry, ALPHA specifies the scalar alpha.
A
A is complex(kind=real64) array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, 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 will transfer a band matrix from conventional full matrix storage to band storage:
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
LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ).
X
X is complex(kind=real64) array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = ’N’ or ’n’ and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.
INCX
INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
BETA
BETA is complex(kind=real64) On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
Y
Y is complex(kind=real64) array, dimension 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. On exit, Y is overwritten by the updated vector y.
INCY
INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
AUTHORS
o Univ. of Tennessee o Univ. of California Berkeley o Univ. of Colorado Denver o NAG Ltd. date:December 2016
FURTHER DETAILS
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0
-- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
SEE ALSO
Online html documentation available at http://www.netlib.org/lapack/explore-html/
| Nemo Release 3.1 | zgbmv (3) | July 22, 2023 |
