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version 1.2, 2010/08/07 13:22:15
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version 1.22, 2023/08/07 08:38:51
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| SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
*> \brief \b DGSVJ1 pre-processor for the routine dgesvj, applies Jacobi rotations targeting only particular pivots. |
| + EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* |
| |
* =========== DOCUMENTATION =========== |
| |
* |
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* Online html documentation available at |
| |
* http://www.netlib.org/lapack/explore-html/ |
| * |
* |
| * -- LAPACK routine (version 3.2.2) -- |
*> \htmlonly |
| |
*> Download DGSVJ1 + dependencies |
| |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj1.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/dgsvj1.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/dgsvj1.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 DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
| |
* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
| |
* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION EPS, SFMIN, TOL |
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* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP |
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* CHARACTER*1 JOBV |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), |
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* $ WORK( LWORK ) |
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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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*> DGSVJ1 is called from DGESVJ as a pre-processor and that is its main |
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*> purpose. It applies Jacobi rotations in the same way as DGESVJ does, but |
| |
*> it targets only particular pivots and it does not check convergence |
| |
*> (stopping criterion). Few tuning parameters (marked by [TP]) are |
| |
*> available for the implementer. |
| |
*> |
| |
*> Further Details |
| |
*> ~~~~~~~~~~~~~~~ |
| |
*> DGSVJ1 applies few sweeps of Jacobi rotations in the column space of |
| |
*> the input M-by-N matrix A. The pivot pairs are taken from the (1,2) |
| |
*> off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The |
| |
*> block-entries (tiles) of the (1,2) off-diagonal block are marked by the |
| |
*> [x]'s in the following scheme: |
| |
*> |
| |
*> | * * * [x] [x] [x]| |
| |
*> | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. |
| |
*> | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. |
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*> |[x] [x] [x] * * * | |
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*> |[x] [x] [x] * * * | |
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*> |[x] [x] [x] * * * | |
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*> |
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*> In terms of the columns of A, the first N1 columns are rotated 'against' |
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*> the remaining N-N1 columns, trying to increase the angle between the |
| |
*> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is |
| |
*> tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter. |
| |
*> The number of sweeps is given in NSWEEP and the orthogonality threshold |
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*> is given in TOL. |
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*> \endverbatim |
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* |
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* Arguments: |
| |
* ========== |
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* |
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*> \param[in] JOBV |
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*> \verbatim |
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*> JOBV is CHARACTER*1 |
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*> Specifies whether the output from this procedure is used |
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*> to compute the matrix V: |
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*> = 'V': the product of the Jacobi rotations is accumulated |
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*> by postmulyiplying the N-by-N array V. |
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*> (See the description of V.) |
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*> = 'A': the product of the Jacobi rotations is accumulated |
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*> by postmulyiplying the MV-by-N array V. |
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*> (See the descriptions of MV and V.) |
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*> = 'N': the Jacobi rotations are not accumulated. |
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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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*> The number of rows of the input matrix A. M >= 0. |
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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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*> The number of columns of the input matrix A. |
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*> M >= N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] N1 |
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*> \verbatim |
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*> N1 is INTEGER |
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*> N1 specifies the 2 x 2 block partition, the first N1 columns are |
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*> rotated 'against' the remaining N-N1 columns of A. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, M-by-N matrix A, such that A*diag(D) represents |
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*> the input matrix. |
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*> On exit, |
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*> A_onexit * D_onexit represents the input matrix A*diag(D) |
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*> post-multiplied by a sequence of Jacobi rotations, where the |
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*> rotation threshold and the total number of sweeps are given in |
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*> TOL and NSWEEP, respectively. |
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*> (See the descriptions of N1, D, TOL and NSWEEP.) |
| |
*> \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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*> The leading dimension of the array A. LDA >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[in,out] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> The array D accumulates the scaling factors from the fast scaled |
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*> Jacobi rotations. |
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*> On entry, A*diag(D) represents the input matrix. |
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*> On exit, A_onexit*diag(D_onexit) represents the input matrix |
| |
*> post-multiplied by a sequence of Jacobi rotations, where the |
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*> rotation threshold and the total number of sweeps are given in |
| |
*> TOL and NSWEEP, respectively. |
| |
*> (See the descriptions of N1, A, TOL and NSWEEP.) |
| |
*> \endverbatim |
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*> |
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*> \param[in,out] SVA |
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*> \verbatim |
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*> SVA is DOUBLE PRECISION array, dimension (N) |
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*> On entry, SVA contains the Euclidean norms of the columns of |
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*> the matrix A*diag(D). |
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*> On exit, SVA contains the Euclidean norms of the columns of |
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*> the matrix onexit*diag(D_onexit). |
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*> \endverbatim |
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*> |
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*> \param[in] MV |
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*> \verbatim |
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*> MV is INTEGER |
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*> If JOBV = 'A', then MV rows of V are post-multipled by a |
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*> sequence of Jacobi rotations. |
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*> If JOBV = 'N', then MV is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in,out] V |
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*> \verbatim |
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*> V is DOUBLE PRECISION array, dimension (LDV,N) |
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*> If JOBV = 'V', then N rows of V are post-multipled by a |
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*> sequence of Jacobi rotations. |
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*> If JOBV = 'A', then MV rows of V are post-multipled by a |
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*> sequence of Jacobi rotations. |
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*> If JOBV = 'N', then V is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDV |
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*> \verbatim |
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*> LDV is INTEGER |
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*> The leading dimension of the array V, LDV >= 1. |
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*> If JOBV = 'V', LDV >= N. |
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*> If JOBV = 'A', LDV >= MV. |
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*> \endverbatim |
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*> |
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*> \param[in] EPS |
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*> \verbatim |
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*> EPS is DOUBLE PRECISION |
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*> EPS = DLAMCH('Epsilon') |
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*> \endverbatim |
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*> |
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*> \param[in] SFMIN |
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*> \verbatim |
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*> SFMIN is DOUBLE PRECISION |
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*> SFMIN = DLAMCH('Safe Minimum') |
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*> \endverbatim |
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*> |
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*> \param[in] TOL |
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*> \verbatim |
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*> TOL is DOUBLE PRECISION |
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*> TOL is the threshold for Jacobi rotations. For a pair |
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*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is |
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*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL. |
| |
*> \endverbatim |
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*> |
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*> \param[in] NSWEEP |
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*> \verbatim |
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*> NSWEEP is INTEGER |
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*> NSWEEP is the number of sweeps of Jacobi rotations to be |
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*> performed. |
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*> \endverbatim |
| |
*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (LWORK) |
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*> \endverbatim |
| |
*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> LWORK is the dimension of WORK. LWORK >= M. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit. |
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*> < 0: if INFO = -i, then the i-th argument had an illegal value |
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*> \endverbatim |
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* |
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* Authors: |
| |
* ======== |
| |
* |
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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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*> \ingroup doubleOTHERcomputational |
| |
* |
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*> \par Contributors: |
| |
* ================== |
| |
*> |
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*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) |
| * |
* |
| * -- Contributed by Zlatko Drmac of the University of Zagreb and -- |
* ===================================================================== |
| * -- Kresimir Veselic of the Fernuniversitaet Hagen -- |
SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
| * -- June 2010 -- |
$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
| * |
* |
| |
* -- LAPACK computational routine -- |
| * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| * |
* |
| * This routine is also part of SIGMA (version 1.23, October 23. 2008.) |
|
| * SIGMA is a library of algorithms for highly accurate algorithms for |
|
| * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the |
|
| * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. |
|
| * |
|
| IMPLICIT NONE |
|
| * .. |
|
| * .. Scalar Arguments .. |
* .. Scalar Arguments .. |
| DOUBLE PRECISION EPS, SFMIN, TOL |
DOUBLE PRECISION EPS, SFMIN, TOL |
| INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP |
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP |
|
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| * .. |
* .. |
| * .. Array Arguments .. |
* .. Array Arguments .. |
| DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), |
DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), |
| + WORK( LWORK ) |
$ WORK( LWORK ) |
| * .. |
* .. |
| * |
* |
| * Purpose |
|
| * ======= |
|
| * |
|
| * DGSVJ1 is called from SGESVJ as a pre-processor and that is its main |
|
| * purpose. It applies Jacobi rotations in the same way as SGESVJ does, but |
|
| * it targets only particular pivots and it does not check convergence |
|
| * (stopping criterion). Few tunning parameters (marked by [TP]) are |
|
| * available for the implementer. |
|
| * |
|
| * Further Details |
|
| * ~~~~~~~~~~~~~~~ |
|
| * DGSVJ1 applies few sweeps of Jacobi rotations in the column space of |
|
| * the input M-by-N matrix A. The pivot pairs are taken from the (1,2) |
|
| * off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The |
|
| * block-entries (tiles) of the (1,2) off-diagonal block are marked by the |
|
| * [x]'s in the following scheme: |
|
| * |
|
| * | * * * [x] [x] [x]| |
|
| * | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. |
|
| * | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. |
|
| * |[x] [x] [x] * * * | |
|
| * |[x] [x] [x] * * * | |
|
| * |[x] [x] [x] * * * | |
|
| * |
|
| * In terms of the columns of A, the first N1 columns are rotated 'against' |
|
| * the remaining N-N1 columns, trying to increase the angle between the |
|
| * corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is |
|
| * tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter. |
|
| * The number of sweeps is given in NSWEEP and the orthogonality threshold |
|
| * is given in TOL. |
|
| * |
|
| * Contributors |
|
| * ~~~~~~~~~~~~ |
|
| * Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) |
|
| * |
|
| * Arguments |
|
| * ========= |
|
| * |
|
| * JOBV (input) CHARACTER*1 |
|
| * Specifies whether the output from this procedure is used |
|
| * to compute the matrix V: |
|
| * = 'V': the product of the Jacobi rotations is accumulated |
|
| * by postmulyiplying the N-by-N array V. |
|
| * (See the description of V.) |
|
| * = 'A': the product of the Jacobi rotations is accumulated |
|
| * by postmulyiplying the MV-by-N array V. |
|
| * (See the descriptions of MV and V.) |
|
| * = 'N': the Jacobi rotations are not accumulated. |
|
| * |
|
| * M (input) INTEGER |
|
| * The number of rows of the input matrix A. M >= 0. |
|
| * |
|
| * N (input) INTEGER |
|
| * The number of columns of the input matrix A. |
|
| * M >= N >= 0. |
|
| * |
|
| * N1 (input) INTEGER |
|
| * N1 specifies the 2 x 2 block partition, the first N1 columns are |
|
| * rotated 'against' the remaining N-N1 columns of A. |
|
| * |
|
| * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
|
| * On entry, M-by-N matrix A, such that A*diag(D) represents |
|
| * the input matrix. |
|
| * On exit, |
|
| * A_onexit * D_onexit represents the input matrix A*diag(D) |
|
| * post-multiplied by a sequence of Jacobi rotations, where the |
|
| * rotation threshold and the total number of sweeps are given in |
|
| * TOL and NSWEEP, respectively. |
|
| * (See the descriptions of N1, D, TOL and NSWEEP.) |
|
| * |
|
| * LDA (input) INTEGER |
|
| * The leading dimension of the array A. LDA >= max(1,M). |
|
| * |
|
| * D (input/workspace/output) DOUBLE PRECISION array, dimension (N) |
|
| * The array D accumulates the scaling factors from the fast scaled |
|
| * Jacobi rotations. |
|
| * On entry, A*diag(D) represents the input matrix. |
|
| * On exit, A_onexit*diag(D_onexit) represents the input matrix |
|
| * post-multiplied by a sequence of Jacobi rotations, where the |
|
| * rotation threshold and the total number of sweeps are given in |
|
| * TOL and NSWEEP, respectively. |
|
| * (See the descriptions of N1, A, TOL and NSWEEP.) |
|
| * |
|
| * SVA (input/workspace/output) DOUBLE PRECISION array, dimension (N) |
|
| * On entry, SVA contains the Euclidean norms of the columns of |
|
| * the matrix A*diag(D). |
|
| * On exit, SVA contains the Euclidean norms of the columns of |
|
| * the matrix onexit*diag(D_onexit). |
|
| * |
|
| * MV (input) INTEGER |
|
| * If JOBV .EQ. 'A', then MV rows of V are post-multipled by a |
|
| * sequence of Jacobi rotations. |
|
| * If JOBV = 'N', then MV is not referenced. |
|
| * |
|
| * V (input/output) DOUBLE PRECISION array, dimension (LDV,N) |
|
| * If JOBV .EQ. 'V' then N rows of V are post-multipled by a |
|
| * sequence of Jacobi rotations. |
|
| * If JOBV .EQ. 'A' then MV rows of V are post-multipled by a |
|
| * sequence of Jacobi rotations. |
|
| * If JOBV = 'N', then V is not referenced. |
|
| * |
|
| * LDV (input) INTEGER |
|
| * The leading dimension of the array V, LDV >= 1. |
|
| * If JOBV = 'V', LDV .GE. N. |
|
| * If JOBV = 'A', LDV .GE. MV. |
|
| * |
|
| * EPS (input) DOUBLE PRECISION |
|
| * EPS = DLAMCH('Epsilon') |
|
| * |
|
| * SFMIN (input) DOUBLE PRECISION |
|
| * SFMIN = DLAMCH('Safe Minimum') |
|
| * |
|
| * TOL (input) DOUBLE PRECISION |
|
| * TOL is the threshold for Jacobi rotations. For a pair |
|
| * A(:,p), A(:,q) of pivot columns, the Jacobi rotation is |
|
| * applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. |
|
| * |
|
| * NSWEEP (input) INTEGER |
|
| * NSWEEP is the number of sweeps of Jacobi rotations to be |
|
| * performed. |
|
| * |
|
| * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) |
|
| * |
|
| * LWORK (input) INTEGER |
|
| * LWORK is the dimension of WORK. LWORK .GE. M. |
|
| * |
|
| * INFO (output) INTEGER |
|
| * = 0 : successful exit. |
|
| * < 0 : if INFO = -i, then the i-th argument had an illegal value |
|
| * |
|
| * ===================================================================== |
* ===================================================================== |
| * |
* |
| * .. Local Parameters .. |
* .. Local Parameters .. |
| DOUBLE PRECISION ZERO, HALF, ONE, TWO |
DOUBLE PRECISION ZERO, HALF, ONE |
| PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, |
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) |
| + TWO = 2.0D0 ) |
|
| * .. |
* .. |
| * .. Local Scalars .. |
* .. Local Scalars .. |
| DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, |
DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, |
| + BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, |
$ BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, |
| + ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T, |
$ ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T, |
| + TEMP1, THETA, THSIGN |
$ TEMP1, THETA, THSIGN |
| INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, |
INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, |
| + ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr, |
$ ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr, |
| + p, PSKIPPED, q, ROWSKIP, SWBAND |
$ p, PSKIPPED, q, ROWSKIP, SWBAND |
| LOGICAL APPLV, ROTOK, RSVEC |
LOGICAL APPLV, ROTOK, RSVEC |
| * .. |
* .. |
| * .. Local Arrays .. |
* .. Local Arrays .. |
| DOUBLE PRECISION FASTR( 5 ) |
DOUBLE PRECISION FASTR( 5 ) |
| * .. |
* .. |
| * .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
| INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT |
INTRINSIC DABS, MAX, DBLE, MIN, DSIGN, DSQRT |
| * .. |
* .. |
| * .. External Functions .. |
* .. External Functions .. |
| DOUBLE PRECISION DDOT, DNRM2 |
DOUBLE PRECISION DDOT, DNRM2 |
|
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|
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|
| EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 |
EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 |
| * .. |
* .. |
| * .. External Subroutines .. |
* .. External Subroutines .. |
| EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP |
EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP, |
| |
$ XERBLA |
| * .. |
* .. |
| * .. Executable Statements .. |
* .. Executable Statements .. |
| * |
* |
|
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|
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|
| INFO = -4 |
INFO = -4 |
| ELSE IF( LDA.LT.M ) THEN |
ELSE IF( LDA.LT.M ) THEN |
| INFO = -6 |
INFO = -6 |
| ELSE IF( MV.LT.0 ) THEN |
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN |
| INFO = -9 |
INFO = -9 |
| ELSE IF( LDV.LT.M ) THEN |
ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR. |
| |
$ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN |
| INFO = -11 |
INFO = -11 |
| ELSE IF( TOL.LE.EPS ) THEN |
ELSE IF( TOL.LE.EPS ) THEN |
| INFO = -14 |
INFO = -14 |
|
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|
Line 343
|
| * |
* |
| * .. Row-cyclic pivot strategy with de Rijk's pivoting .. |
* .. Row-cyclic pivot strategy with de Rijk's pivoting .. |
| * |
* |
| KBL = MIN0( 8, N ) |
KBL = MIN( 8, N ) |
| NBLR = N1 / KBL |
NBLR = N1 / KBL |
| IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 |
IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 |
| |
|
|
Line 262
|
Line 354
|
| BLSKIP = ( KBL**2 ) + 1 |
BLSKIP = ( KBL**2 ) + 1 |
| *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
| |
|
| ROWSKIP = MIN0( 5, KBL ) |
ROWSKIP = MIN( 5, KBL ) |
| *[TP] ROWSKIP is a tuning parameter. |
*[TP] ROWSKIP is a tuning parameter. |
| SWBAND = 0 |
SWBAND = 0 |
| *[TP] SWBAND is a tuning parameter. It is meaningful and effective |
*[TP] SWBAND is a tuning parameter. It is meaningful and effective |
|
Line 305
|
Line 397
|
| * doing the block at ( ibr, jbc ) |
* doing the block at ( ibr, jbc ) |
| |
|
| IJBLSK = 0 |
IJBLSK = 0 |
| DO 2100 p = igl, MIN0( igl+KBL-1, N1 ) |
DO 2100 p = igl, MIN( igl+KBL-1, N1 ) |
| |
|
| AAPP = SVA( p ) |
AAPP = SVA( p ) |
| |
|
|
Line 313
|
Line 405
|
| |
|
| PSKIPPED = 0 |
PSKIPPED = 0 |
| |
|
| DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) |
DO 2200 q = jgl, MIN( jgl+KBL-1, N ) |
| * |
* |
| AAQQ = SVA( q ) |
AAQQ = SVA( q ) |
| |
|
|
Line 332
|
Line 424
|
| END IF |
END IF |
| IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
| AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
| + q ), 1 )*D( p )*D( q ) / AAQQ ) |
$ q ), 1 )*D( p )*D( q ) / AAQQ ) |
| + / AAPP |
$ / AAPP |
| ELSE |
ELSE |
| CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
| CALL DLASCL( 'G', 0, 0, AAPP, D( p ), |
CALL DLASCL( 'G', 0, 0, AAPP, D( p ), |
| + M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
| AAPQ = DDOT( M, WORK, 1, A( 1, q ), |
AAPQ = DDOT( M, WORK, 1, A( 1, q ), |
| + 1 )*D( q ) / AAQQ |
$ 1 )*D( q ) / AAQQ |
| END IF |
END IF |
| ELSE |
ELSE |
| IF( AAPP.GE.AAQQ ) THEN |
IF( AAPP.GE.AAQQ ) THEN |
|
Line 349
|
Line 441
|
| END IF |
END IF |
| IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
| AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
| + q ), 1 )*D( p )*D( q ) / AAQQ ) |
$ q ), 1 )*D( p )*D( q ) / AAQQ ) |
| + / AAPP |
$ / AAPP |
| ELSE |
ELSE |
| CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) |
| CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), |
CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), |
| + M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
| AAPQ = DDOT( M, WORK, 1, A( 1, p ), |
AAPQ = DDOT( M, WORK, 1, A( 1, p ), |
| + 1 )*D( p ) / AAPP |
$ 1 )*D( p ) / AAPP |
| END IF |
END IF |
| END IF |
END IF |
| |
|
| MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) |
MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) ) |
| |
|
| * TO rotate or NOT to rotate, THAT is the question ... |
* TO rotate or NOT to rotate, THAT is the question ... |
| * |
* |
|
Line 374
|
Line 466
|
| * |
* |
| AQOAP = AAQQ / AAPP |
AQOAP = AAQQ / AAPP |
| APOAQ = AAPP / AAQQ |
APOAQ = AAPP / AAQQ |
| THETA = -HALF*DABS( AQOAP-APOAQ ) / |
THETA = -HALF*DABS(AQOAP-APOAQ) / AAPQ |
| + AAPQ |
|
| IF( AAQQ.GT.AAPP0 )THETA = -THETA |
IF( AAQQ.GT.AAPP0 )THETA = -THETA |
| |
|
| IF( DABS( THETA ).GT.BIGTHETA ) THEN |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
|
Line 383
|
Line 474
|
| FASTR( 3 ) = T*D( p ) / D( q ) |
FASTR( 3 ) = T*D( p ) / D( q ) |
| FASTR( 4 ) = -T*D( q ) / D( p ) |
FASTR( 4 ) = -T*D( q ) / D( p ) |
| CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
| + A( 1, q ), 1, FASTR ) |
$ A( 1, q ), 1, FASTR ) |
| IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
| + V( 1, p ), 1, |
$ V( 1, p ), 1, |
| + V( 1, q ), 1, |
$ V( 1, q ), 1, |
| + FASTR ) |
$ FASTR ) |
| SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
| + ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
| AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
| + ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
| MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = MAX( MXSINJ, DABS( T ) ) |
| ELSE |
ELSE |
| * |
* |
| * .. choose correct signum for THETA and rotate |
* .. choose correct signum for THETA and rotate |
|
Line 400
|
Line 491
|
| THSIGN = -DSIGN( ONE, AAPQ ) |
THSIGN = -DSIGN( ONE, AAPQ ) |
| IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
| T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
| + DSQRT( ONE+THETA*THETA ) ) |
$ DSQRT( ONE+THETA*THETA ) ) |
| CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
| SN = T*CS |
SN = T*CS |
| MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
MXSINJ = MAX( MXSINJ, DABS( SN ) ) |
| SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
| + ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
| AAPP = AAPP*DSQRT( ONE-T*AQOAP* |
AAPP = AAPP*DSQRT( MAX( ZERO, |
| + AAPQ ) |
$ ONE-T*AQOAP*AAPQ ) ) |
| |
|
| APOAQ = D( p ) / D( q ) |
APOAQ = D( p ) / D( q ) |
| AQOAP = D( q ) / D( p ) |
AQOAP = D( q ) / D( p ) |
|
Line 419
|
Line 510
|
| D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
| D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
| CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
| + A( 1, q ), 1, |
$ A( 1, q ), 1, |
| + FASTR ) |
$ FASTR ) |
| IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
| + V( 1, p ), 1, V( 1, q ), |
$ V( 1, p ), 1, V( 1, q ), |
| + 1, FASTR ) |
$ 1, FASTR ) |
| ELSE |
ELSE |
| CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
| + A( 1, q ), 1, |
$ A( 1, q ), 1, |
| + A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
| CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
| + A( 1, p ), 1, |
$ A( 1, p ), 1, |
| + A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
| IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
| CALL DAXPY( MVL, -T*AQOAP, |
CALL DAXPY( MVL, -T*AQOAP, |
| + V( 1, q ), 1, |
$ V( 1, q ), 1, |
| + V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
| CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
| + CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
| + V( 1, p ), 1, |
$ V( 1, p ), 1, |
| + V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
| END IF |
END IF |
| D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
| D( q ) = D( q ) / CS |
D( q ) = D( q ) / CS |
|
Line 446
|
Line 537
|
| ELSE |
ELSE |
| IF( D( q ).GE.ONE ) THEN |
IF( D( q ).GE.ONE ) THEN |
| CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
| + A( 1, p ), 1, |
$ A( 1, p ), 1, |
| + A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
| CALL DAXPY( M, -CS*SN*AQOAP, |
CALL DAXPY( M, -CS*SN*AQOAP, |
| + A( 1, q ), 1, |
$ A( 1, q ), 1, |
| + A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
| IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
| CALL DAXPY( MVL, T*APOAQ, |
CALL DAXPY( MVL, T*APOAQ, |
| + V( 1, p ), 1, |
$ V( 1, p ), 1, |
| + V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
| CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
| + -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
| + V( 1, q ), 1, |
$ V( 1, q ), 1, |
| + V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
| END IF |
END IF |
| D( p ) = D( p ) / CS |
D( p ) = D( p ) / CS |
| D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
| ELSE |
ELSE |
| IF( D( p ).GE.D( q ) ) THEN |
IF( D( p ).GE.D( q ) ) THEN |
| CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
| + A( 1, q ), 1, |
$ A( 1, q ), 1, |
| + A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
| CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
| + A( 1, p ), 1, |
$ A( 1, p ), 1, |
| + A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
| D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
| D( q ) = D( q ) / CS |
D( q ) = D( q ) / CS |
| IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
| CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
| + -T*AQOAP, |
$ -T*AQOAP, |
| + V( 1, q ), 1, |
$ V( 1, q ), 1, |
| + V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
| CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
| + CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
| + V( 1, p ), 1, |
$ V( 1, p ), 1, |
| + V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
| END IF |
END IF |
| ELSE |
ELSE |
| CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
| + A( 1, p ), 1, |
$ A( 1, p ), 1, |
| + A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
| CALL DAXPY( M, |
CALL DAXPY( M, |
| + -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
| + A( 1, q ), 1, |
$ A( 1, q ), 1, |
| + A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
| D( p ) = D( p ) / CS |
D( p ) = D( p ) / CS |
| D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
| IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
| CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
| + T*APOAQ, V( 1, p ), |
$ T*APOAQ, V( 1, p ), |
| + 1, V( 1, q ), 1 ) |
$ 1, V( 1, q ), 1 ) |
| CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
| + -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
| + V( 1, q ), 1, |
$ V( 1, q ), 1, |
| + V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
| END IF |
END IF |
| END IF |
END IF |
| END IF |
END IF |
|
Line 509
|
Line 600
|
| ELSE |
ELSE |
| IF( AAPP.GT.AAQQ ) THEN |
IF( AAPP.GT.AAQQ ) THEN |
| CALL DCOPY( M, A( 1, p ), 1, WORK, |
CALL DCOPY( M, A( 1, p ), 1, WORK, |
| + 1 ) |
$ 1 ) |
| CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
| + M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
| CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
| + M, 1, A( 1, q ), LDA, |
$ M, 1, A( 1, q ), LDA, |
| + IERR ) |
$ IERR ) |
| TEMP1 = -AAPQ*D( p ) / D( q ) |
TEMP1 = -AAPQ*D( p ) / D( q ) |
| CALL DAXPY( M, TEMP1, WORK, 1, |
CALL DAXPY( M, TEMP1, WORK, 1, |
| + A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
| CALL DLASCL( 'G', 0, 0, ONE, AAQQ, |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, |
| + M, 1, A( 1, q ), LDA, |
$ M, 1, A( 1, q ), LDA, |
| + IERR ) |
$ IERR ) |
| SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
| + ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
| MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
| ELSE |
ELSE |
| CALL DCOPY( M, A( 1, q ), 1, WORK, |
CALL DCOPY( M, A( 1, q ), 1, WORK, |
| + 1 ) |
$ 1 ) |
| CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
| + M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
| CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
| + M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
| + IERR ) |
$ IERR ) |
| TEMP1 = -AAPQ*D( q ) / D( p ) |
TEMP1 = -AAPQ*D( q ) / D( p ) |
| CALL DAXPY( M, TEMP1, WORK, 1, |
CALL DAXPY( M, TEMP1, WORK, 1, |
| + A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
| CALL DLASCL( 'G', 0, 0, ONE, AAPP, |
CALL DLASCL( 'G', 0, 0, ONE, AAPP, |
| + M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
| + IERR ) |
$ IERR ) |
| SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, |
SVA( p ) = AAPP*DSQRT( MAX( ZERO, |
| + ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
| MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
| END IF |
END IF |
| END IF |
END IF |
| * END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
|
Line 548
|
Line 639
|
| * In the case of cancellation in updating SVA(q) |
* In the case of cancellation in updating SVA(q) |
| * .. recompute SVA(q) |
* .. recompute SVA(q) |
| IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
| + THEN |
$ THEN |
| IF( ( AAQQ.LT.ROOTBIG ) .AND. |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
| + ( AAQQ.GT.ROOTSFMIN ) ) THEN |
$ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
| SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
| + D( q ) |
$ D( q ) |
| ELSE |
ELSE |
| T = ZERO |
T = ZERO |
| AAQQ = ZERO |
AAQQ = ONE |
| CALL DLASSQ( M, A( 1, q ), 1, T, |
CALL DLASSQ( M, A( 1, q ), 1, T, |
| + AAQQ ) |
$ AAQQ ) |
| SVA( q ) = T*DSQRT( AAQQ )*D( q ) |
SVA( q ) = T*DSQRT( AAQQ )*D( q ) |
| END IF |
END IF |
| END IF |
END IF |
| IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
| IF( ( AAPP.LT.ROOTBIG ) .AND. |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
| + ( AAPP.GT.ROOTSFMIN ) ) THEN |
$ ( AAPP.GT.ROOTSFMIN ) ) THEN |
| AAPP = DNRM2( M, A( 1, p ), 1 )* |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
| + D( p ) |
$ D( p ) |
| ELSE |
ELSE |
| T = ZERO |
T = ZERO |
| AAPP = ZERO |
AAPP = ONE |
| CALL DLASSQ( M, A( 1, p ), 1, T, |
CALL DLASSQ( M, A( 1, p ), 1, T, |
| + AAPP ) |
$ AAPP ) |
| AAPP = T*DSQRT( AAPP )*D( p ) |
AAPP = T*DSQRT( AAPP )*D( p ) |
| END IF |
END IF |
| SVA( p ) = AAPP |
SVA( p ) = AAPP |
|
Line 590
|
Line 681
|
| |
|
| * IF ( NOTROT .GE. EMPTSW ) GO TO 2011 |
* IF ( NOTROT .GE. EMPTSW ) GO TO 2011 |
| IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) |
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) |
| + THEN |
$ THEN |
| SVA( p ) = AAPP |
SVA( p ) = AAPP |
| NOTROT = 0 |
NOTROT = 0 |
| GO TO 2011 |
GO TO 2011 |
| END IF |
END IF |
| IF( ( i.LE.SWBAND ) .AND. |
IF( ( i.LE.SWBAND ) .AND. |
| + ( PSKIPPED.GT.ROWSKIP ) ) THEN |
$ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
| AAPP = -AAPP |
AAPP = -AAPP |
| NOTROT = 0 |
NOTROT = 0 |
| GO TO 2203 |
GO TO 2203 |
|
Line 611
|
Line 702
|
| * |
* |
| ELSE |
ELSE |
| IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
| + MIN0( jgl+KBL-1, N ) - jgl + 1 |
$ MIN( jgl+KBL-1, N ) - jgl + 1 |
| IF( AAPP.LT.ZERO )NOTROT = 0 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
| *** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 |
*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 |
| END IF |
END IF |
|
Line 622
|
Line 713
|
| * end of the jbc-loop |
* end of the jbc-loop |
| 2011 CONTINUE |
2011 CONTINUE |
| *2011 bailed out of the jbc-loop |
*2011 bailed out of the jbc-loop |
| DO 2012 p = igl, MIN0( igl+KBL-1, N ) |
DO 2012 p = igl, MIN( igl+KBL-1, N ) |
| SVA( p ) = DABS( SVA( p ) ) |
SVA( p ) = DABS( SVA( p ) ) |
| 2012 CONTINUE |
2012 CONTINUE |
| *** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 |
*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 |
|
Line 631
|
Line 722
|
| * |
* |
| * .. update SVA(N) |
* .. update SVA(N) |
| IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) |
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) |
| + THEN |
$ THEN |
| SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N ) |
SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N ) |
| ELSE |
ELSE |
| T = ZERO |
T = ZERO |
| AAPP = ZERO |
AAPP = ONE |
| CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) |
CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) |
| SVA( N ) = T*DSQRT( AAPP )*D( N ) |
SVA( N ) = T*DSQRT( AAPP )*D( N ) |
| END IF |
END IF |
|
Line 643
|
Line 734
|
| * Additional steering devices |
* Additional steering devices |
| * |
* |
| IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. |
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. |
| + ( ISWROT.LE.N ) ) )SWBAND = i |
$ ( ISWROT.LE.N ) ) )SWBAND = i |
| |
|
| IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND. |
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND. |
| + ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
$ ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
| GO TO 1994 |
GO TO 1994 |
| END IF |
END IF |
| |
|
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