CHBMV (3) Linux Manual Page
chbmv.f –
Synopsis
Functions/Subroutines
subroutine chbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)CHBMV
Function/Subroutine Documentation
subroutine chbmv (characterUPLO, integerN, integerK, complexALPHA, complex, dimension(lda,*)A, integerLDA, complex, dimension(*)X, integerINCX, complexBETA, complex, dimension(*)Y, integerINCY)
CHBMV Purpose:CHBMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian band matrix, with k super-diagonals.
Parameters:
- UPLO
UPLO is CHARACTER*1
N
On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being supplied as
follows:
UPLO = ‘U’ or ‘u’ The upper triangular part of A is
being supplied.
UPLO = ‘L’ or ‘l’ The lower triangular part of A is
being supplied.N is INTEGER
K
On entry, N specifies the order of the matrix A.
N must be at least zero.K is INTEGER
ALPHA
On entry, K specifies the number of super-diagonals of the
matrix A. K must satisfy 0 .le. K.ALPHA is COMPLEX
A
On entry, ALPHA specifies the scalar alpha.A is COMPLEX array of DIMENSION ( LDA, n ).
LDA
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 hermitian 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 will transfer the upper
triangular part of a hermitian band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
M = K + 1 – J
DO 10, I = MAX( 1, J – K ), J
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
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 hermitian 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 will transfer the lower
triangular part of a hermitian band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
M = 1 – J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.LDA is INTEGER
X
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
( k + 1 ).X is COMPLEX array of DIMENSION at least
INCX
( 1 + ( n – 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the
vector x.INCX is INTEGER
BETA
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.BETA is COMPLEX
Y
On entry, BETA specifies the scalar beta.Y is COMPLEX array of DIMENSION at least
INCY
( 1 + ( n – 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the
vector y. On exit, Y is overwritten by the updated vector y.INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Author:
- Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- November 2011
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.
Definition at line 188 of file chbmv.f.