version 1.3, 2010/08/13 21:04:12
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version 1.13, 2017/06/17 10:54:25
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SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO ) |
*> \brief \b ZPFTRS |
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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 ZPFTRS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpftrs.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/zpftrs.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/zpftrs.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 ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER TRANSR, UPLO |
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* INTEGER INFO, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( 0: * ), B( LDB, * ) |
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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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*> ZPFTRS solves a system of linear equations A*X = B with a Hermitian |
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*> positive definite matrix A using the Cholesky factorization |
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*> A = U**H*U or A = L*L**H computed by ZPFTRF. |
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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': The Normal TRANSR of RFP A is stored; |
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*> = 'C': The Conjugate-transpose TRANSR of RFP A is stored. |
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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': Upper triangle of RFP A is stored; |
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*> = 'L': Lower triangle of RFP A is stored. |
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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] NRHS |
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*> \verbatim |
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*> NRHS is INTEGER |
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*> The number of right hand sides, i.e., the number of columns |
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*> of the matrix B. NRHS >= 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 ( N*(N+1)/2 ); |
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*> The triangular factor U or L from the Cholesky factorization |
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*> of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF. |
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*> See note below for more details about RFP A. |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is COMPLEX*16 array, dimension (LDB,NRHS) |
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*> On entry, the right hand side matrix B. |
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*> On exit, the solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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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 December 2016 |
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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 ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO ) |
* |
* |
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* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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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* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER TRANSR, UPLO |
CHARACTER TRANSR, UPLO |
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COMPLEX*16 A( 0: * ), B( LDB, * ) |
COMPLEX*16 A( 0: * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZPFTRS solves a system of linear equations A*X = B with a Hermitian |
|
* positive definite matrix A using the Cholesky factorization |
|
* A = U**H*U or A = L*L**H computed by ZPFTRF. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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* TRANSR (input) CHARACTER |
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* = 'N': The Normal TRANSR of RFP A is stored; |
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* = 'C': The Conjugate-transpose TRANSR of RFP A is stored. |
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* |
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* UPLO (input) CHARACTER |
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* = 'U': Upper triangle of RFP A is stored; |
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* = 'L': Lower triangle of RFP A is stored. |
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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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* NRHS (input) INTEGER |
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* The number of right hand sides, i.e., the number of columns |
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* of the matrix B. NRHS >= 0. |
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* |
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* A (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ); |
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* The triangular factor U or L from the Cholesky factorization |
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* of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF. |
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* See note below for more details about RFP A. |
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* |
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* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) |
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* On entry, the right hand side matrix B. |
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* On exit, the solution matrix X. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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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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* Quick return if possible |
* Quick return if possible |
* |
* |
IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
+ RETURN |
$ RETURN |
* |
* |
* start execution: there are two triangular solves |
* start execution: there are two triangular solves |
* |
* |
IF( LOWER ) THEN |
IF( LOWER ) THEN |
CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, |
CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, |
+ LDB ) |
$ LDB ) |
CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, |
CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, |
+ LDB ) |
$ LDB ) |
ELSE |
ELSE |
CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, |
CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, |
+ LDB ) |
$ LDB ) |
CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, |
CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, |
+ LDB ) |
$ LDB ) |
END IF |
END IF |
* |
* |
RETURN |
RETURN |