371 lines
10 KiB
Fortran
371 lines
10 KiB
Fortran
*> \brief \b DGBMV
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION ALPHA,BETA
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* INTEGER INCX,INCY,KL,KU,LDA,M,N
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* CHARACTER TRANS
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A(LDA,*),X(*),Y(*)
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DGBMV performs one of the matrix-vector operations
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*>
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*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
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*>
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*> where alpha and beta are scalars, x and y are vectors and A is an
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*> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> On entry, TRANS specifies the operation to be performed as
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*> follows:
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*>
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*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
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*>
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*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
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*>
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*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> On entry, M specifies the number of rows of the matrix A.
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*> M must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> On entry, N specifies the number of columns of the matrix A.
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*> N must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] KL
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*> \verbatim
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*> KL is INTEGER
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*> On entry, KL specifies the number of sub-diagonals of the
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*> matrix A. KL must satisfy 0 .le. KL.
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*> \endverbatim
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*>
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*> \param[in] KU
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*> \verbatim
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*> KU is INTEGER
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*> On entry, KU specifies the number of super-diagonals of the
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*> matrix A. KU must satisfy 0 .le. KU.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is DOUBLE PRECISION.
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*> On entry, ALPHA specifies the scalar alpha.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
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*> Before entry, the leading ( kl + ku + 1 ) by n part of the
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*> array A must contain the matrix of coefficients, supplied
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*> column by column, with the leading diagonal of the matrix in
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*> row ( ku + 1 ) of the array, the first super-diagonal
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*> starting at position 2 in row ku, the first sub-diagonal
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*> starting at position 1 in row ( ku + 2 ), and so on.
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*> Elements in the array A that do not correspond to elements
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*> in the band matrix (such as the top left ku by ku triangle)
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*> are not referenced.
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*> The following program segment will transfer a band matrix
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*> from conventional full matrix storage to band storage:
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*>
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*> DO 20, J = 1, N
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*> K = KU + 1 - J
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*> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
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*> A( K + I, J ) = matrix( I, J )
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*> 10 CONTINUE
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*> 20 CONTINUE
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> On entry, LDA specifies the first dimension of A as declared
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*> in the calling (sub) program. LDA must be at least
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*> ( kl + ku + 1 ).
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is DOUBLE PRECISION array of DIMENSION at least
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*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
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*> and at least
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*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
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*> Before entry, the incremented array X must contain the
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*> vector x.
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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is INTEGER
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*> On entry, INCX specifies the increment for the elements of
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*> X. INCX must not be zero.
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*> \endverbatim
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*>
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*> \param[in] BETA
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*> \verbatim
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*> BETA is DOUBLE PRECISION.
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*> On entry, BETA specifies the scalar beta. When BETA is
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*> supplied as zero then Y need not be set on input.
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*> \endverbatim
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*>
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*> \param[in,out] Y
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*> \verbatim
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*> Y is DOUBLE PRECISION array of DIMENSION at least
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*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
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*> and at least
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*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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*> Before entry, the incremented array Y must contain the
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*> vector y. On exit, Y is overwritten by the updated vector y.
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*> \endverbatim
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*>
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*> \param[in] INCY
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*> \verbatim
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*> INCY is INTEGER
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*> On entry, INCY specifies the increment for the elements of
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*> Y. INCY must not be zero.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2015
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*
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*> \ingroup double_blas_level2
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> Level 2 Blas routine.
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*> The vector and matrix arguments are not referenced when N = 0, or M = 0
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*>
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*> -- Written on 22-October-1986.
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*> Jack Dongarra, Argonne National Lab.
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*> Jeremy Du Croz, Nag Central Office.
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*> Sven Hammarling, Nag Central Office.
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*> Richard Hanson, Sandia National Labs.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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*
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* -- Reference BLAS level2 routine (version 3.6.0) --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2015
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA,BETA
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INTEGER INCX,INCY,KL,KU,LDA,M,N
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CHARACTER TRANS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*),X(*),Y(*)
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE,ZERO
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PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION TEMP
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INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX,MIN
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* ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
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+ .NOT.LSAME(TRANS,'C')) THEN
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INFO = 1
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ELSE IF (M.LT.0) THEN
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INFO = 2
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ELSE IF (N.LT.0) THEN
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INFO = 3
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ELSE IF (KL.LT.0) THEN
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INFO = 4
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ELSE IF (KU.LT.0) THEN
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INFO = 5
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ELSE IF (LDA.LT. (KL+KU+1)) THEN
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INFO = 8
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ELSE IF (INCX.EQ.0) THEN
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INFO = 10
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ELSE IF (INCY.EQ.0) THEN
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INFO = 13
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('DGBMV ',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
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+ ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
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*
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* Set LENX and LENY, the lengths of the vectors x and y, and set
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* up the start points in X and Y.
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*
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IF (LSAME(TRANS,'N')) THEN
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LENX = N
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LENY = M
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ELSE
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LENX = M
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LENY = N
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END IF
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IF (INCX.GT.0) THEN
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KX = 1
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ELSE
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KX = 1 - (LENX-1)*INCX
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END IF
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IF (INCY.GT.0) THEN
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KY = 1
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ELSE
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KY = 1 - (LENY-1)*INCY
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END IF
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*
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* Start the operations. In this version the elements of A are
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* accessed sequentially with one pass through the band part of A.
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*
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* First form y := beta*y.
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*
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IF (BETA.NE.ONE) THEN
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IF (INCY.EQ.1) THEN
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IF (BETA.EQ.ZERO) THEN
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DO 10 I = 1,LENY
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Y(I) = ZERO
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10 CONTINUE
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ELSE
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DO 20 I = 1,LENY
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Y(I) = BETA*Y(I)
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20 CONTINUE
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END IF
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ELSE
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IY = KY
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IF (BETA.EQ.ZERO) THEN
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DO 30 I = 1,LENY
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Y(IY) = ZERO
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IY = IY + INCY
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30 CONTINUE
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ELSE
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DO 40 I = 1,LENY
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Y(IY) = BETA*Y(IY)
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IY = IY + INCY
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40 CONTINUE
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END IF
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END IF
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END IF
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IF (ALPHA.EQ.ZERO) RETURN
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KUP1 = KU + 1
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form y := alpha*A*x + y.
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*
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JX = KX
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IF (INCY.EQ.1) THEN
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DO 60 J = 1,N
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TEMP = ALPHA*X(JX)
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K = KUP1 - J
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DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
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Y(I) = Y(I) + TEMP*A(K+I,J)
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50 CONTINUE
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JX = JX + INCX
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60 CONTINUE
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ELSE
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DO 80 J = 1,N
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TEMP = ALPHA*X(JX)
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IY = KY
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K = KUP1 - J
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DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
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Y(IY) = Y(IY) + TEMP*A(K+I,J)
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IY = IY + INCY
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70 CONTINUE
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JX = JX + INCX
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IF (J.GT.KU) KY = KY + INCY
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80 CONTINUE
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END IF
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ELSE
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*
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* Form y := alpha*A**T*x + y.
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*
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JY = KY
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IF (INCX.EQ.1) THEN
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DO 100 J = 1,N
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TEMP = ZERO
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K = KUP1 - J
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DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
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TEMP = TEMP + A(K+I,J)*X(I)
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90 CONTINUE
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Y(JY) = Y(JY) + ALPHA*TEMP
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JY = JY + INCY
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100 CONTINUE
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ELSE
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DO 120 J = 1,N
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TEMP = ZERO
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IX = KX
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K = KUP1 - J
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DO 110 I = MAX(1,J-KU),MIN(M,J+KL)
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TEMP = TEMP + A(K+I,J)*X(IX)
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IX = IX + INCX
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110 CONTINUE
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Y(JY) = Y(JY) + ALPHA*TEMP
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JY = JY + INCY
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IF (J.GT.KU) KX = KX + INCX
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120 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of DGBMV .
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*
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END
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