version 1.2, 2010/08/07 13:22:46
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version 1.8, 2011/11/21 22:19:59
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SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO ) |
*> \brief \b ZTRTTF |
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* |
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* =========== DOCUMENTATION =========== |
* |
* |
* -- LAPACK routine (version 3.2.1) -- |
* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
* |
* |
* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- |
*> \htmlonly |
* -- April 2009 -- |
*> Download ZTRTTF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrttf.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/ztrttf.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/ztrttf.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 ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER TRANSR, UPLO |
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* INTEGER INFO, N, LDA |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * ) |
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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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*> ZTRTTF copies a triangular matrix A from standard full format (TR) |
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*> to rectangular full packed format (TF) . |
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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] TRANSR |
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*> \verbatim |
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*> TRANSR is CHARACTER*1 |
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*> = 'N': ARF in Normal mode is wanted; |
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*> = 'C': ARF in Conjugate Transpose mode is wanted; |
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*> \endverbatim |
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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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*> = 'U': A is upper triangular; |
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*> = 'L': A is lower triangular. |
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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 order of the matrix A. N >= 0. |
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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 COMPLEX*16 array, dimension ( LDA, N ) |
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*> On entry, the triangular matrix A. If UPLO = 'U', the |
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*> leading N-by-N upper triangular part of the array A contains |
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*> the upper triangular matrix, and the strictly lower |
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*> triangular part of A is not referenced. If UPLO = 'L', the |
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*> leading N-by-N lower triangular part of the array A contains |
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*> the lower triangular matrix, and the strictly upper |
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*> triangular part of A is not referenced. |
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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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*> The leading dimension of the matrix A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] ARF |
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*> \verbatim |
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*> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ), |
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*> On exit, the upper or lower triangular matrix A stored in |
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*> RFP format. For a further discussion see Notes below. |
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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, 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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* ======== |
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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 complex16OTHERcomputational |
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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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*> We first consider Standard Packed Format when N is even. |
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*> We give an example where N = 6. |
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*> |
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*> AP is Upper AP is Lower |
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*> |
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*> 00 01 02 03 04 05 00 |
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*> 11 12 13 14 15 10 11 |
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*> 22 23 24 25 20 21 22 |
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*> 33 34 35 30 31 32 33 |
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*> 44 45 40 41 42 43 44 |
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*> 55 50 51 52 53 54 55 |
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*> |
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*> |
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*> Let TRANSR = 'N'. RFP holds AP as follows: |
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*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last |
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*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of |
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*> conjugate-transpose of the first three columns of AP upper. |
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*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first |
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*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of |
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*> conjugate-transpose of the last three columns of AP lower. |
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*> To denote conjugate we place -- above the element. This covers the |
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*> case N even and TRANSR = 'N'. |
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*> |
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*> RFP A RFP A |
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*> |
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*> -- -- -- |
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*> 03 04 05 33 43 53 |
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*> -- -- |
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*> 13 14 15 00 44 54 |
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*> -- |
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*> 23 24 25 10 11 55 |
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*> |
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*> 33 34 35 20 21 22 |
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*> -- |
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*> 00 44 45 30 31 32 |
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*> -- -- |
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*> 01 11 55 40 41 42 |
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*> -- -- -- |
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*> 02 12 22 50 51 52 |
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*> |
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*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- |
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*> transpose of RFP A above. One therefore gets: |
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*> |
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*> |
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*> RFP A RFP A |
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*> |
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*> -- -- -- -- -- -- -- -- -- -- |
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*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 |
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*> -- -- -- -- -- -- -- -- -- -- |
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*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 |
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*> -- -- -- -- -- -- -- -- -- -- |
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*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 |
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*> |
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*> |
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*> We next consider Standard Packed Format when N is odd. |
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*> We give an example where N = 5. |
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*> |
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*> AP is Upper AP is Lower |
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*> |
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*> 00 01 02 03 04 00 |
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*> 11 12 13 14 10 11 |
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*> 22 23 24 20 21 22 |
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*> 33 34 30 31 32 33 |
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*> 44 40 41 42 43 44 |
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*> |
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*> |
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*> Let TRANSR = 'N'. RFP holds AP as follows: |
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*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last |
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*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of |
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*> conjugate-transpose of the first two columns of AP upper. |
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*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first |
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*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of |
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*> conjugate-transpose of the last two columns of AP lower. |
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*> To denote conjugate we place -- above the element. This covers the |
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*> case N odd and TRANSR = 'N'. |
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*> |
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*> RFP A RFP A |
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*> |
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*> -- -- |
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*> 02 03 04 00 33 43 |
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*> -- |
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*> 12 13 14 10 11 44 |
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*> |
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*> 22 23 24 20 21 22 |
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*> -- |
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*> 00 33 34 30 31 32 |
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*> -- -- |
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*> 01 11 44 40 41 42 |
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*> |
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*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- |
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*> transpose of RFP A above. One therefore gets: |
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*> |
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*> |
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*> RFP A RFP A |
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*> |
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*> -- -- -- -- -- -- -- -- -- |
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*> 02 12 22 00 01 00 10 20 30 40 50 |
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*> -- -- -- -- -- -- -- -- -- |
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*> 03 13 23 33 11 33 11 21 31 41 51 |
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*> -- -- -- -- -- -- -- -- -- |
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*> 04 14 24 34 44 43 44 22 32 42 52 |
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*> \endverbatim |
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*> |
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* ===================================================================== |
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SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO ) |
* |
* |
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* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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..-- |
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* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER TRANSR, UPLO |
CHARACTER TRANSR, UPLO |
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COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * ) |
COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
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* ZTRTTF copies a triangular matrix A from standard full format (TR) |
|
* to rectangular full packed format (TF) . |
|
* |
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* Arguments |
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* ========= |
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* |
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* TRANSR (input) CHARACTER |
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* = 'N': ARF in Normal mode is wanted; |
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* = 'C': ARF in Conjugate Transpose mode is wanted; |
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* |
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* UPLO (input) CHARACTER |
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* = 'U': A is upper triangular; |
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* = 'L': A is lower triangular. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* A (input) COMPLEX*16 array, dimension ( LDA, N ) |
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* On entry, the triangular matrix A. If UPLO = 'U', the |
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* leading N-by-N upper triangular part of the array A contains |
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* the upper triangular matrix, and the strictly lower |
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* triangular part of A is not referenced. If UPLO = 'L', the |
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* leading N-by-N lower triangular part of the array A contains |
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* the lower triangular matrix, and the strictly upper |
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* triangular part of A is not referenced. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the matrix A. LDA >= max(1,N). |
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* |
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* ARF (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ), |
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* On exit, the upper or lower triangular matrix A stored in |
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* RFP format. For a further discussion see Notes below. |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* |
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* Further Details |
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* =============== |
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* |
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* We first consider Standard Packed Format when N is even. |
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* We give an example where N = 6. |
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* |
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* AP is Upper AP is Lower |
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* |
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* 00 01 02 03 04 05 00 |
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* 11 12 13 14 15 10 11 |
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* 22 23 24 25 20 21 22 |
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* 33 34 35 30 31 32 33 |
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* 44 45 40 41 42 43 44 |
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* 55 50 51 52 53 54 55 |
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* |
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* |
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* Let TRANSR = `N'. RFP holds AP as follows: |
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* For UPLO = `U' the upper trapezoid A(0:5,0:2) consists of the last |
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* three columns of AP upper. The lower triangle A(4:6,0:2) consists of |
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* conjugate-transpose of the first three columns of AP upper. |
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* For UPLO = `L' the lower trapezoid A(1:6,0:2) consists of the first |
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* three columns of AP lower. The upper triangle A(0:2,0:2) consists of |
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* conjugate-transpose of the last three columns of AP lower. |
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* To denote conjugate we place -- above the element. This covers the |
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* case N even and TRANSR = `N'. |
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* |
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* RFP A RFP A |
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* |
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* -- -- -- |
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* 03 04 05 33 43 53 |
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* -- -- |
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* 13 14 15 00 44 54 |
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* -- |
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* 23 24 25 10 11 55 |
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* |
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* 33 34 35 20 21 22 |
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* -- |
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* 00 44 45 30 31 32 |
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* -- -- |
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* 01 11 55 40 41 42 |
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* -- -- -- |
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* 02 12 22 50 51 52 |
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* |
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* Now let TRANSR = `C'. RFP A in both UPLO cases is just the conjugate- |
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* transpose of RFP A above. One therefore gets: |
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* |
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* |
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* RFP A RFP A |
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* |
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* -- -- -- -- -- -- -- -- -- -- |
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* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 |
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* -- -- -- -- -- -- -- -- -- -- |
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* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 |
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* -- -- -- -- -- -- -- -- -- -- |
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* 05 15 25 35 45 55 22 53 54 55 22 32 42 52 |
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* |
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* |
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* We next consider Standard Packed Format when N is odd. |
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* We give an example where N = 5. |
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* |
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* AP is Upper AP is Lower |
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* |
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* 00 01 02 03 04 00 |
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* 11 12 13 14 10 11 |
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* 22 23 24 20 21 22 |
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* 33 34 30 31 32 33 |
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* 44 40 41 42 43 44 |
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* |
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* |
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* Let TRANSR = `N'. RFP holds AP as follows: |
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* For UPLO = `U' the upper trapezoid A(0:4,0:2) consists of the last |
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* three columns of AP upper. The lower triangle A(3:4,0:1) consists of |
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* conjugate-transpose of the first two columns of AP upper. |
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* For UPLO = `L' the lower trapezoid A(0:4,0:2) consists of the first |
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* three columns of AP lower. The upper triangle A(0:1,1:2) consists of |
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* conjugate-transpose of the last two columns of AP lower. |
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* To denote conjugate we place -- above the element. This covers the |
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* case N odd and TRANSR = `N'. |
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* |
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* RFP A RFP A |
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* |
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* -- -- |
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* 02 03 04 00 33 43 |
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* -- |
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* 12 13 14 10 11 44 |
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* |
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* 22 23 24 20 21 22 |
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* -- |
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* 00 33 34 30 31 32 |
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* -- -- |
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* 01 11 44 40 41 42 |
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* |
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* Now let TRANSR = `C'. RFP A in both UPLO cases is just the conjugate- |
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* transpose of RFP A above. One therefore gets: |
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* |
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* |
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* RFP A RFP A |
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* |
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* -- -- -- -- -- -- -- -- -- |
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* 02 12 22 00 01 00 10 20 30 40 50 |
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* -- -- -- -- -- -- -- -- -- |
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* 03 13 23 33 11 33 11 21 31 41 51 |
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* -- -- -- -- -- -- -- -- -- |
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* 04 14 24 34 44 43 44 22 32 42 52 |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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K = N / 2 |
K = N / 2 |
NISODD = .FALSE. |
NISODD = .FALSE. |
IF( .NOT.LOWER ) |
IF( .NOT.LOWER ) |
+ NP1X2 = N + N + 2 |
$ NP1X2 = N + N + 2 |
ELSE |
ELSE |
NISODD = .TRUE. |
NISODD = .TRUE. |
IF( .NOT.LOWER ) |
IF( .NOT.LOWER ) |
+ NX2 = N + N |
$ NX2 = N + N |
END IF |
END IF |
* |
* |
IF( NISODD ) THEN |
IF( NISODD ) THEN |