version 1.7, 2011/07/22 07:38:01
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version 1.11, 2014/01/27 09:28:12
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*> \brief \b DSBMV |
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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 DSBMV(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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* DOUBLE PRECISION 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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* 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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*> DSBMV 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 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 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 DOUBLE PRECISION array of 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 DOUBLE PRECISION. |
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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 DOUBLE PRECISION array of 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 November 2011 |
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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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* ===================================================================== |
SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) |
SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) |
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* |
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* -- Reference BLAS level2 routine (version 3.4.0) -- |
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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 2011 |
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* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION ALPHA,BETA |
DOUBLE PRECISION ALPHA,BETA |
INTEGER INCX,INCY,K,LDA,N |
INTEGER INCX,INCY,K,LDA,N |
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DOUBLE PRECISION A(LDA,*),X(*),Y(*) |
DOUBLE PRECISION A(LDA,*),X(*),Y(*) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSBMV 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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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - 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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* |
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* Unchanged on exit. |
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* |
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* N - 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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* Unchanged on exit. |
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* |
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* K - 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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* Unchanged on exit. |
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* |
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* ALPHA - DOUBLE PRECISION. |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* A - DOUBLE PRECISION array of 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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* |
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* Unchanged on exit. |
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* |
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* LDA - 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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* Unchanged on exit. |
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* |
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* X - DOUBLE PRECISION array of 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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* Unchanged on exit. |
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* |
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* INCX - 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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* Unchanged on exit. |
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* |
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* BETA - DOUBLE PRECISION. |
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* On entry, BETA specifies the scalar beta. |
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* Unchanged on exit. |
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* |
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* Y - DOUBLE PRECISION array of 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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* |
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* INCY - 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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* Unchanged on exit. |
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* |
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* Further Details |
|
* =============== |
|
* |
|
* Level 2 Blas routine. |
|
* The vector and matrix arguments are not referenced when N = 0, or M = 0 |
|
* |
|
* -- 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. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |