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NAME
ZGBMV - perform one of the matrix-vector operations y :=
alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y :=
alpha*conjg( A' )*x + beta*y,
SYNOPSIS
SUBROUTINE ZGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X,
INCX, BETA, Y, INCY )
COMPLEX*16 ALPHA, BETA
INTEGER INCX, INCY, KL, KU, LDA, M, N
CHARACTER*1 TRANS
COMPLEX*16 A( LDA, * ), X( * ), Y( * )
PURPOSE
ZGBMV performs one of the matrix-vector operations
where 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.
PARAMETERS
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be per-
formed as follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*conjg( A' )*x +
beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the
matrix A. M must be at least zero. Unchanged on
exit.
N - INTEGER.
On entry, N specifies the number of columns of the
matrix A. N must be at least zero. Unchanged on
exit.
KL - INTEGER.
On entry, KL specifies the number of sub-diagonals of
the matrix A. KL must satisfy 0 .le. KL. Unchanged
on exit.
KU - INTEGER.
On entry, KU specifies the number of super-diagonals
of the matrix A. KU must satisfy 0 .le. KU.
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, the leading ( kl + ku + 1 ) by n part
of the array A must contain the matrix of coeffi-
cients, 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 posi-
tion 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
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 ( kl + ku + 1 ). Unchanged on exit.
X - COMPLEX*16 array of 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. 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. When BETA
is supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - COMPLEX*16 array of 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 - 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.