ZHBMV - perform the matrix-vector operation y :=
alpha*A*x + beta*y,
SYNOPSIS
SUBROUTINE ZHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX,
BETA, Y, INCY )
COMPLEX*16 ALPHA, BETA
INTEGER INCX, INCY, K, LDA, N
CHARACTER*1 UPLO
COMPLEX*16 A( LDA, * ), X( * ), Y( * )
PURPOSE
ZHBMV performs the matrix-vector operation
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 - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being sup
plied 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.
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*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading (
k + 1 ) by n part of the array A must contain the
supplied column by column, with the leading diago
nal 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 pro
gram 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 CON
TINUE 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 diago
nal 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 ele
ments 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*16 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 ele
ments of X. INCX must not be zero. Unchanged on
exit.
BETA - COMPLEX*16 .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
( 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 ele
ments of Y. INCY must not be zero. Unchanged on
exit.
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.
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