*> \brief \b ZPFTRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZPFTRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER TRANSR, UPLO * INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. * COMPLEX*16 A( 0: * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANSR *> \verbatim *> TRANSR is CHARACTER*1 *> = 'N': The Normal TRANSR of RFP A is stored; *> = 'C': The Conjugate-transpose TRANSR of RFP A is stored. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of RFP A is stored; *> = 'L': Lower triangle of RFP A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); *> The triangular factor U or L from the Cholesky factorization *> of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF. *> See note below for more details about RFP A. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> We first consider Standard Packed Format when N is even. *> We give an example where N = 6. *> *> AP is Upper AP is Lower *> *> 00 01 02 03 04 05 00 *> 11 12 13 14 15 10 11 *> 22 23 24 25 20 21 22 *> 33 34 35 30 31 32 33 *> 44 45 40 41 42 43 44 *> 55 50 51 52 53 54 55 *> *> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of *> conjugate-transpose of the first three columns of AP upper. *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of *> conjugate-transpose of the last three columns of AP lower. *> To denote conjugate we place -- above the element. This covers the *> case N even and TRANSR = 'N'. *> *> RFP A RFP A *> *> -- -- -- *> 03 04 05 33 43 53 *> -- -- *> 13 14 15 00 44 54 *> -- *> 23 24 25 10 11 55 *> *> 33 34 35 20 21 22 *> -- *> 00 44 45 30 31 32 *> -- -- *> 01 11 55 40 41 42 *> -- -- -- *> 02 12 22 50 51 52 *> *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- *> transpose of RFP A above. One therefore gets: *> *> *> RFP A RFP A *> *> -- -- -- -- -- -- -- -- -- -- *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 *> -- -- -- -- -- -- -- -- -- -- *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 *> -- -- -- -- -- -- -- -- -- -- *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 *> *> *> We next consider Standard Packed Format when N is odd. *> We give an example where N = 5. *> *> AP is Upper AP is Lower *> *> 00 01 02 03 04 00 *> 11 12 13 14 10 11 *> 22 23 24 20 21 22 *> 33 34 30 31 32 33 *> 44 40 41 42 43 44 *> *> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of *> conjugate-transpose of the first two columns of AP upper. *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of *> conjugate-transpose of the last two columns of AP lower. *> To denote conjugate we place -- above the element. This covers the *> case N odd and TRANSR = 'N'. *> *> RFP A RFP A *> *> -- -- *> 02 03 04 00 33 43 *> -- *> 12 13 14 10 11 44 *> *> 22 23 24 20 21 22 *> -- *> 00 33 34 30 31 32 *> -- -- *> 01 11 44 40 41 42 *> *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- *> transpose of RFP A above. One therefore gets: *> *> *> RFP A RFP A *> *> -- -- -- -- -- -- -- -- -- *> 02 12 22 00 01 00 10 20 30 40 50 *> -- -- -- -- -- -- -- -- -- *> 03 13 23 33 11 33 11 21 31 41 51 *> -- -- -- -- -- -- -- -- -- *> 04 14 24 34 44 43 44 22 32 42 52 *> \endverbatim *> * ===================================================================== SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER TRANSR, UPLO INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. COMPLEX*16 A( 0: * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LOWER, NORMALTRANSR * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZTFSM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NORMALTRANSR = LSAME( TRANSR, 'N' ) LOWER = LSAME( UPLO, 'L' ) IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN INFO = -1 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( NRHS.LT.0 ) THEN INFO = -4 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZPFTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * * start execution: there are two triangular solves * IF( LOWER ) THEN CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, $ LDB ) CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, $ LDB ) ELSE CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, $ LDB ) CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, $ LDB ) END IF * RETURN * * End of ZPFTRS * END