phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
e2428ec4cbbbfb86fb48a67a0696347f73aebc21
lapack/SRC/cpftrs.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

299 lines
8.9 KiB
FortranFixed
Raw Blame History

*> \brief \b CPFTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CPFTRS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpftrs.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cpftrs.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpftrs.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANSR, UPLO
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX A( 0: * ), B( LDB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CPFTRS 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 CPFTRF.
*> \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 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 CPFTRF.
*> See note below for more details about RFP A.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX 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.
*
*> \ingroup complexOTHERcomputational
*
*> \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 CPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER TRANSR, UPLO
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX A( 0: * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LOWER, NORMALTRANSR
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, CTFSM
* ..
* .. 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( 'CPFTRS', -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 CTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
$ LDB )
CALL CTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
$ LDB )
ELSE
CALL CTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
$ LDB )
CALL CTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
$ LDB )
END IF
*
RETURN
*
* End of CPFTRS
*
END
Reference in New Issue View Git Blame Copy Permalink