376 lines
11 KiB
Fortran
376 lines
11 KiB
Fortran
*> \brief \b SSBMV
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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 SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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*
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* .. Scalar Arguments ..
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* REAL ALPHA,BETA
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* INTEGER INCX,INCY,K,LDA,N
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* CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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* REAL 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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*> SSBMV performs the matrix-vector operation
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*>
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*> y := alpha*A*x + beta*y,
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*>
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*> where alpha and beta are scalars, x and y are n element vectors and
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*> A is an n by n symmetric band matrix, with k 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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> On entry, UPLO specifies whether the upper or lower
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*> triangular part of the band matrix A is being supplied as
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*> follows:
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*>
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*> UPLO = 'U' or 'u' The upper triangular part of A is
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*> being supplied.
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*>
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*> UPLO = 'L' or 'l' The lower triangular part of A is
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*> being supplied.
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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 order 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] K
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*> \verbatim
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*> K is INTEGER
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*> On entry, K specifies the number of super-diagonals of the
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*> matrix A. K must satisfy 0 .le. K.
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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 REAL
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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 REAL array, dimension ( LDA, N )
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*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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*> by n part of the array A must contain the upper triangular
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*> band part of the symmetric matrix, supplied column by
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*> column, with the leading diagonal of the matrix in row
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*> ( k + 1 ) of the array, the first super-diagonal starting at
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*> position 2 in row k, and so on. The top left k by k triangle
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*> of the array A is not referenced.
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*> The following program segment will transfer the upper
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*> triangular part of a symmetric band matrix from conventional
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*> full matrix storage to band storage:
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*>
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*> DO 20, J = 1, N
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*> M = K + 1 - J
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*> DO 10, I = MAX( 1, J - K ), J
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*> A( M + I, J ) = matrix( I, J )
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*> 10 CONTINUE
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*> 20 CONTINUE
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*>
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*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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*> by n part of the array A must contain the lower triangular
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*> band part of the symmetric matrix, supplied column by
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*> column, with the leading diagonal of the matrix in row 1 of
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*> the array, the first sub-diagonal starting at position 1 in
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*> row 2, and so on. The bottom right k by k triangle of the
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*> array A is not referenced.
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*> The following program segment will transfer the lower
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*> triangular part of a symmetric band matrix from conventional
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*> full matrix storage to band storage:
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*>
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*> DO 20, J = 1, N
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*> M = 1 - J
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*> DO 10, I = J, MIN( N, J + K )
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*> A( M + 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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*> ( k + 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 REAL array, dimension at least
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*> ( 1 + ( n - 1 )*abs( INCX ) ).
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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 REAL
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*> On entry, BETA specifies the scalar beta.
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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 REAL array, dimension at least
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*> ( 1 + ( n - 1 )*abs( INCY ) ).
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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 December 2016
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*
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*> \ingroup single_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 SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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*
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* -- Reference BLAS level2 routine (version 3.7.0) --
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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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* December 2016
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*
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* .. Scalar Arguments ..
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REAL ALPHA,BETA
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INTEGER INCX,INCY,K,LDA,N
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CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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REAL 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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REAL ONE,ZERO
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PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
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* ..
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* .. Local Scalars ..
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REAL TEMP1,TEMP2
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INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
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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(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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INFO = 1
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ELSE IF (N.LT.0) THEN
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INFO = 2
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ELSE IF (K.LT.0) THEN
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INFO = 3
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ELSE IF (LDA.LT. (K+1)) THEN
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INFO = 6
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ELSE IF (INCX.EQ.0) THEN
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INFO = 8
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ELSE IF (INCY.EQ.0) THEN
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INFO = 11
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('SSBMV ',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 ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
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*
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* Set up the start points in X and Y.
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*
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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 - (N-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 - (N-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 the array A
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* are accessed sequentially with one pass through 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,N
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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,N
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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,N
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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,N
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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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IF (LSAME(UPLO,'U')) THEN
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*
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* Form y when upper triangle of A is stored.
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*
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KPLUS1 = K + 1
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
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DO 60 J = 1,N
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TEMP1 = ALPHA*X(J)
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TEMP2 = ZERO
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L = KPLUS1 - J
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DO 50 I = MAX(1,J-K),J - 1
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Y(I) = Y(I) + TEMP1*A(L+I,J)
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TEMP2 = TEMP2 + A(L+I,J)*X(I)
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50 CONTINUE
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Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
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60 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 80 J = 1,N
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TEMP1 = ALPHA*X(JX)
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TEMP2 = ZERO
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IX = KX
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IY = KY
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L = KPLUS1 - J
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DO 70 I = MAX(1,J-K),J - 1
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Y(IY) = Y(IY) + TEMP1*A(L+I,J)
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TEMP2 = TEMP2 + A(L+I,J)*X(IX)
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IX = IX + INCX
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IY = IY + INCY
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70 CONTINUE
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Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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IF (J.GT.K) THEN
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KX = KX + INCX
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KY = KY + INCY
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END IF
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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 when lower triangle of A is stored.
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*
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
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DO 100 J = 1,N
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TEMP1 = ALPHA*X(J)
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TEMP2 = ZERO
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Y(J) = Y(J) + TEMP1*A(1,J)
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L = 1 - J
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DO 90 I = J + 1,MIN(N,J+K)
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Y(I) = Y(I) + TEMP1*A(L+I,J)
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TEMP2 = TEMP2 + A(L+I,J)*X(I)
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90 CONTINUE
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Y(J) = Y(J) + ALPHA*TEMP2
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100 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 120 J = 1,N
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TEMP1 = ALPHA*X(JX)
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TEMP2 = ZERO
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Y(JY) = Y(JY) + TEMP1*A(1,J)
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L = 1 - J
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IX = JX
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IY = JY
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DO 110 I = J + 1,MIN(N,J+K)
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IX = IX + INCX
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IY = IY + INCY
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Y(IY) = Y(IY) + TEMP1*A(L+I,J)
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TEMP2 = TEMP2 + A(L+I,J)*X(IX)
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110 CONTINUE
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Y(JY) = Y(JY) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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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 SSBMV .
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*
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END
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