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299 lines
8.9 KiB
299 lines
8.9 KiB
2 years ago
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*> \brief \b ZPFTRS
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download 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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*> \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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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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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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*
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* .. Parameters ..
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COMPLEX*16 CONE
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PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LOWER, NORMALTRANSR
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZTFSM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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NORMALTRANSR = LSAME( TRANSR, 'N' )
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LOWER = LSAME( UPLO, 'L' )
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IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZPFTRS', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 .OR. NRHS.EQ.0 )
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$ RETURN
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*
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* start execution: there are two triangular solves
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*
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IF( LOWER ) THEN
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CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
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$ LDB )
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CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
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$ LDB )
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ELSE
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CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
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$ LDB )
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CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
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$ LDB )
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END IF
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*
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RETURN
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*
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* End of ZPFTRS
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*
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END
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