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Technical Reference: Base Operating System and Extensions , Volume 2
Performs matrixvector operations
with general banded matrices.
BLAS Library
(libblas.a)
SUBROUTINE SGBMV(TRANS, M, N, KL, KU, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
REAL ALPHA, BETA
INTEGER INCX, INCY, KL, KU, LDA, M, N
CHARACTER*1 TRANS
REAL A(LDA,*), X(*), Y(*)
SUBROUTINE DGBMV(TRANS, M, N, KL, KU, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
DOUBLE PRECISION ALPHA,BETA
INTEGER INCX,INCY,KL,KU,LDA,M,N
CHARACTER*1 TRANS
DOUBLE PRECISION A(LDA,*), X(*), Y(*)
SUBROUTINE CGBMV(TRANS, M, N, KL, KU, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
COMPLEX ALPHA,BETA
INTEGER INCX,INCY,KL,KU,LDA,M,N
CHARACTER*1 TRANS
COMPLEX A(LDA,*), X(*), Y(*)
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(*)
The SGBMV,
DGBMV, CGBMV, or ZGBMV subroutine performs
one of the following matrixvector operations:
y := alpha
* A * x + beta * y
OR
y := alpha
* A' * x + beta * y
where alpha and beta are scalars,
x and y are vectors and A is an M by N band
matrix, with KL subdiagonals and KU
superdiagonals.
TRANS
 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' * x + beta * y
 TRANS = 'C'
or 'c'
 y := alpha * A' * x + beta * y
Unchanged on exit.

M
 On entry, M specifies the number of rows of the matrix
A; M must be at least 0; unchanged on
exit.

N
 On entry, N specifies the number of columns of the matrix
A; N must be at least 0; unchanged on
exit.

KL
 On entry, KL specifies the number of subdiagonals of the
matrix A; KL must satisfy 0 .le.
KL; unchanged on exit.

KU
 On entry, KU specifies the number of superdiagonals of the
matrix A; KU must satisfy 0 .le.
KU; unchanged on exit.

ALPHA
 On entry, ALPHA specifies the scalar alpha; unchanged on
exit.

A
 A vector of dimension ( LDA, N ); on 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 superdiagonal starting at position 2 in row
KU, the first subdiagonal 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 transfers 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
 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
 A vector of dimension at least (1 + (N1) * abs(
INCX ) ) when TRANS = 'N' or 'n',
otherwise, at least (1 + (M1) * abs( INCX ) ); on
entry, the incremented array X must contain the vector x;
unchanged on exit.

INCX
 On entry, INCX specifies the increment for the elements of
X; INCX must not be 0; unchanged on
exit.

BETA
 On entry, BETA specifies the scalar beta; when
BETA is supplied as 0 then Y need not be set on input;
unchanged on exit.

Y
 A vector of dimension at least (1 + (M1) * abs(
INCY ) ) when TRANS = 'N' or 'n' ,
otherwise, at least (1 + (N1) * abs( INCY ) ); on
entry, the incremented array Y must contain the vector y; on
exit, Y is overwritten by the updated vector y.

INCY
 On entry, INCY specifies the increment for the elements of
Y; INCY must not be 0; unchanged on
exit.

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