chbmv (l) - Linux Manuals
chbmv: performs the matrix-vector operation y := alpha*A*x + beta*y,
NAME
CHBMV - performs the matrix-vector operation y := alpha*A*x + beta*y,SYNOPSIS
- SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
- COMPLEX ALPHA,BETA
- INTEGER INCX,INCY,K,LDA,N
- CHARACTER UPLO
- COMPLEX A(LDA,*),X(*),Y(*)
PURPOSE
CHBMV performs the matrix-vector operationwhere 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.
ARGUMENTS
- UPLO - CHARACTER*1.
-
On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being supplied as
follows:
UPLO = aqUaq or aquaq The upper triangular part of A is being supplied.
UPLO = aqLaq or aqlaq The lower triangular part of A is being supplied.
Unchanged on exit.
- N - INTEGER.
- On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
- K - INTEGER.
- On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit.
- ALPHA - COMPLEX .
- On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
- A - COMPLEX array of DIMENSION ( LDA, n ).
-
Before entry with UPLO = aqUaq or aquaq, 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 = aqLaq or aqlaq, 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. Unchanged on exit.
- LDA - INTEGER.
- On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ). Unchanged on exit.
- X - COMPLEX array of DIMENSION at least
- ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x. Unchanged on exit.
- INCX - INTEGER.
- On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
- BETA - COMPLEX .
- On entry, BETA specifies the scalar beta. Unchanged on exit.
- Y - COMPLEX array of DIMENSION at least
- ( 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 - INTEGER.
- On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.
FURTHER DETAILS
Level 2 Blas routine.
-- 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.