SGBMV, DGBMV, CGBMV, or ZGBMV Subroutine

Purpose

Performs matrix-vector operations with general banded matrices.

Library

BLAS Library (libblas.a)

FORTRAN Syntax

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(*)

Description

The SGBMV, DGBMV, CGBMV, or ZGBMV subroutine performs one of the following matrix-vector 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.

Parameters

Item Description
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 + (N-1) * abs( INCX ) ) when TRANS = 'N' or 'n', otherwise, at least (1 + (M-1) * 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 + (M-1) * abs( INCY ) ) when TRANS = 'N' or 'n' , otherwise, at least (1 + (N-1) * 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.