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version 1.11, 2014/01/27 09:28:18
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*> \brief \b DLA_GBAMV performs a matrix-vector operation to calculate error bounds. |
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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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*> \htmlonly |
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*> Download DLA_GBAMV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbamv.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbamv.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbamv.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, |
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* 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, LDAB, M, N, KL, KU, TRANS |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), 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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*> DLA_GBAMV performs one of the matrix-vector operations |
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*> |
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*> y := alpha*abs(A)*abs(x) + beta*abs(y), |
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*> or y := alpha*abs(A)**T*abs(x) + beta*abs(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 matrix. |
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*> |
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*> This function is primarily used in calculating error bounds. |
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*> To protect against underflow during evaluation, components in |
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*> the resulting vector are perturbed away from zero by (N+1) |
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*> times the underflow threshold. To prevent unnecessarily large |
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*> errors for block-structure embedded in general matrices, |
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*> "symbolically" zero components are not perturbed. A zero |
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*> entry is considered "symbolic" if all multiplications involved |
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*> in computing that entry have at least one zero multiplicand. |
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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 INTEGER |
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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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*> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) |
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*> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) |
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*> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) |
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*> |
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*> Unchanged on exit. |
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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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*> Unchanged on exit. |
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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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*> Unchanged on exit. |
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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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*> The number of subdiagonals within the band of A. KL >= 0. |
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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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*> The number of superdiagonals within the band of A. KU >= 0. |
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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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*> Unchanged on exit. |
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*> \endverbatim |
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*> |
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*> \param[in] AB |
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*> \verbatim |
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*> AB is DOUBLE PRECISION array of DIMENSION ( LDAB, n ) |
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*> Before entry, the leading m by n part of the array AB must |
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*> contain the matrix of coefficients. |
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*> Unchanged on exit. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> On entry, LDA specifies the first dimension of AB as declared |
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*> in the calling (sub) program. LDAB must be at least |
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*> max( 1, m ). |
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*> Unchanged on exit. |
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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, dimension |
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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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*> Unchanged on exit. |
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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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*> Unchanged on exit. |
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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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*> Unchanged on exit. |
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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, dimension |
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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 with BETA non-zero, the incremented array Y |
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*> must contain the vector y. On exit, Y is overwritten by the |
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*> 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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*> Unchanged on exit. |
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*> |
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*> Level 2 Blas routine. |
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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 September 2012 |
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* |
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*> \ingroup doubleGBcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, |
SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, |
$ INCX, BETA, Y, INCY ) |
$ INCX, BETA, Y, INCY ) |
* |
* |
* -- LAPACK routine (version 3.3.1) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Jason Riedy of Univ. of California Berkeley. -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- June 2010 -- |
* September 2012 |
* |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley and NAG Ltd. -- |
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* |
* |
IMPLICIT NONE |
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* .. |
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* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION ALPHA, BETA |
DOUBLE PRECISION ALPHA, BETA |
INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS |
INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS |
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DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * ) |
DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
|
* |
|
* DLA_GBAMV performs one of the matrix-vector operations |
|
* |
|
* y := alpha*abs(A)*abs(x) + beta*abs(y), |
|
* or y := alpha*abs(A)**T*abs(x) + beta*abs(y), |
|
* |
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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 matrix. |
|
* |
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* This function is primarily used in calculating error bounds. |
|
* To protect against underflow during evaluation, components in |
|
* the resulting vector are perturbed away from zero by (N+1) |
|
* times the underflow threshold. To prevent unnecessarily large |
|
* errors for block-structure embedded in general matrices, |
|
* "symbolically" zero components are not perturbed. A zero |
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* entry is considered "symbolic" if all multiplications involved |
|
* in computing that entry have at least one zero multiplicand. |
|
* |
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* Arguments |
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* ========== |
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* |
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* TRANS (input) INTEGER |
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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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* BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) |
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* BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) |
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* BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) |
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* |
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* Unchanged on exit. |
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* |
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* M (input) 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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* Unchanged on exit. |
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* |
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* N (input) 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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* Unchanged on exit. |
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* |
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* KL (input) INTEGER |
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* The number of subdiagonals within the band of A. KL >= 0. |
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* |
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* KU (input) INTEGER |
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* The number of superdiagonals within the band of A. KU >= 0. |
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* |
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* ALPHA (input) 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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* AB (input) DOUBLE PRECISION array of DIMENSION ( LDAB, n ) |
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* Before entry, the leading m by n part of the array AB must |
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* contain the matrix of coefficients. |
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* Unchanged on exit. |
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* |
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* LDAB (input) INTEGER |
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* On entry, LDA specifies the first dimension of AB as declared |
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* in the calling (sub) program. LDAB must be at least |
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* max( 1, m ). |
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* Unchanged on exit. |
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* |
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* X (input) DOUBLE PRECISION array, dimension |
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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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* Unchanged on exit. |
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* |
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* INCX (input) 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 (input) 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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* Unchanged on exit. |
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* |
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* Y (input/output) DOUBLE PRECISION array, dimension |
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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 with BETA non-zero, the incremented array Y |
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* must contain the vector y. On exit, Y is overwritten by the |
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* updated vector y. |
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* |
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* INCY (input) 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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* |
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* Level 2 Blas routine. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |