451 lines
12 KiB
Fortran
451 lines
12 KiB
Fortran
*> \brief \b CSPTRS
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download CSPTRS + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csptrs.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csptrs.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csptrs.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IPIV( * )
|
|
* COMPLEX AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CSPTRS solves a system of linear equations A*X = B with a complex
|
|
*> symmetric matrix A stored in packed format using the factorization
|
|
*> A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> Specifies whether the details of the factorization are stored
|
|
*> as an upper or lower triangular matrix.
|
|
*> = 'U': Upper triangular, form is A = U*D*U**T;
|
|
*> = 'L': Lower triangular, form is A = L*D*L**T.
|
|
*> \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] AP
|
|
*> \verbatim
|
|
*> AP is COMPLEX array, dimension (N*(N+1)/2)
|
|
*> The block diagonal matrix D and the multipliers used to
|
|
*> obtain the factor U or L as computed by CSPTRF, stored as a
|
|
*> packed triangular matrix.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] IPIV
|
|
*> \verbatim
|
|
*> IPIV is INTEGER array, dimension (N)
|
|
*> Details of the interchanges and the block structure of D
|
|
*> as determined by CSPTRF.
|
|
*> \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.
|
|
*
|
|
*> \date December 2016
|
|
*
|
|
*> \ingroup complexOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CSPTRS( UPLO, N, NRHS, AP, IPIV, 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 UPLO
|
|
INTEGER INFO, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
COMPLEX AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX ONE
|
|
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL UPPER
|
|
INTEGER J, K, KC, KP
|
|
COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CGEMV, CGERU, CSCAL, CSWAP, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
INFO = 0
|
|
UPPER = LSAME( UPLO, 'U' )
|
|
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
|
|
INFO = -1
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -2
|
|
ELSE IF( NRHS.LT.0 ) THEN
|
|
INFO = -3
|
|
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
|
|
INFO = -7
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CSPTRS', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 .OR. NRHS.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
IF( UPPER ) THEN
|
|
*
|
|
* Solve A*X = B, where A = U*D*U**T.
|
|
*
|
|
* First solve U*D*X = B, overwriting B with X.
|
|
*
|
|
* K is the main loop index, decreasing from N to 1 in steps of
|
|
* 1 or 2, depending on the size of the diagonal blocks.
|
|
*
|
|
K = N
|
|
KC = N*( N+1 ) / 2 + 1
|
|
10 CONTINUE
|
|
*
|
|
* If K < 1, exit from loop.
|
|
*
|
|
IF( K.LT.1 )
|
|
$ GO TO 30
|
|
*
|
|
KC = KC - K
|
|
IF( IPIV( K ).GT.0 ) THEN
|
|
*
|
|
* 1 x 1 diagonal block
|
|
*
|
|
* Interchange rows K and IPIV(K).
|
|
*
|
|
KP = IPIV( K )
|
|
IF( KP.NE.K )
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
*
|
|
* Multiply by inv(U(K)), where U(K) is the transformation
|
|
* stored in column K of A.
|
|
*
|
|
CALL CGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
|
|
$ B( 1, 1 ), LDB )
|
|
*
|
|
* Multiply by the inverse of the diagonal block.
|
|
*
|
|
CALL CSCAL( NRHS, ONE / AP( KC+K-1 ), B( K, 1 ), LDB )
|
|
K = K - 1
|
|
ELSE
|
|
*
|
|
* 2 x 2 diagonal block
|
|
*
|
|
* Interchange rows K-1 and -IPIV(K).
|
|
*
|
|
KP = -IPIV( K )
|
|
IF( KP.NE.K-1 )
|
|
$ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
|
|
*
|
|
* Multiply by inv(U(K)), where U(K) is the transformation
|
|
* stored in columns K-1 and K of A.
|
|
*
|
|
CALL CGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
|
|
$ B( 1, 1 ), LDB )
|
|
CALL CGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1,
|
|
$ B( K-1, 1 ), LDB, B( 1, 1 ), LDB )
|
|
*
|
|
* Multiply by the inverse of the diagonal block.
|
|
*
|
|
AKM1K = AP( KC+K-2 )
|
|
AKM1 = AP( KC-1 ) / AKM1K
|
|
AK = AP( KC+K-1 ) / AKM1K
|
|
DENOM = AKM1*AK - ONE
|
|
DO 20 J = 1, NRHS
|
|
BKM1 = B( K-1, J ) / AKM1K
|
|
BK = B( K, J ) / AKM1K
|
|
B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
|
|
B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
|
|
20 CONTINUE
|
|
KC = KC - K + 1
|
|
K = K - 2
|
|
END IF
|
|
*
|
|
GO TO 10
|
|
30 CONTINUE
|
|
*
|
|
* Next solve U**T*X = B, overwriting B with X.
|
|
*
|
|
* K is the main loop index, increasing from 1 to N in steps of
|
|
* 1 or 2, depending on the size of the diagonal blocks.
|
|
*
|
|
K = 1
|
|
KC = 1
|
|
40 CONTINUE
|
|
*
|
|
* If K > N, exit from loop.
|
|
*
|
|
IF( K.GT.N )
|
|
$ GO TO 50
|
|
*
|
|
IF( IPIV( K ).GT.0 ) THEN
|
|
*
|
|
* 1 x 1 diagonal block
|
|
*
|
|
* Multiply by inv(U**T(K)), where U(K) is the transformation
|
|
* stored in column K of A.
|
|
*
|
|
CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
|
|
$ 1, ONE, B( K, 1 ), LDB )
|
|
*
|
|
* Interchange rows K and IPIV(K).
|
|
*
|
|
KP = IPIV( K )
|
|
IF( KP.NE.K )
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
KC = KC + K
|
|
K = K + 1
|
|
ELSE
|
|
*
|
|
* 2 x 2 diagonal block
|
|
*
|
|
* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
|
|
* stored in columns K and K+1 of A.
|
|
*
|
|
CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
|
|
$ 1, ONE, B( K, 1 ), LDB )
|
|
CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
|
|
$ AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB )
|
|
*
|
|
* Interchange rows K and -IPIV(K).
|
|
*
|
|
KP = -IPIV( K )
|
|
IF( KP.NE.K )
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
KC = KC + 2*K + 1
|
|
K = K + 2
|
|
END IF
|
|
*
|
|
GO TO 40
|
|
50 CONTINUE
|
|
*
|
|
ELSE
|
|
*
|
|
* Solve A*X = B, where A = L*D*L**T.
|
|
*
|
|
* First solve L*D*X = B, overwriting B with X.
|
|
*
|
|
* K is the main loop index, increasing from 1 to N in steps of
|
|
* 1 or 2, depending on the size of the diagonal blocks.
|
|
*
|
|
K = 1
|
|
KC = 1
|
|
60 CONTINUE
|
|
*
|
|
* If K > N, exit from loop.
|
|
*
|
|
IF( K.GT.N )
|
|
$ GO TO 80
|
|
*
|
|
IF( IPIV( K ).GT.0 ) THEN
|
|
*
|
|
* 1 x 1 diagonal block
|
|
*
|
|
* Interchange rows K and IPIV(K).
|
|
*
|
|
KP = IPIV( K )
|
|
IF( KP.NE.K )
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
*
|
|
* Multiply by inv(L(K)), where L(K) is the transformation
|
|
* stored in column K of A.
|
|
*
|
|
IF( K.LT.N )
|
|
$ CALL CGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ),
|
|
$ LDB, B( K+1, 1 ), LDB )
|
|
*
|
|
* Multiply by the inverse of the diagonal block.
|
|
*
|
|
CALL CSCAL( NRHS, ONE / AP( KC ), B( K, 1 ), LDB )
|
|
KC = KC + N - K + 1
|
|
K = K + 1
|
|
ELSE
|
|
*
|
|
* 2 x 2 diagonal block
|
|
*
|
|
* Interchange rows K+1 and -IPIV(K).
|
|
*
|
|
KP = -IPIV( K )
|
|
IF( KP.NE.K+1 )
|
|
$ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
|
|
*
|
|
* Multiply by inv(L(K)), where L(K) is the transformation
|
|
* stored in columns K and K+1 of A.
|
|
*
|
|
IF( K.LT.N-1 ) THEN
|
|
CALL CGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ),
|
|
$ LDB, B( K+2, 1 ), LDB )
|
|
CALL CGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1,
|
|
$ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
|
|
END IF
|
|
*
|
|
* Multiply by the inverse of the diagonal block.
|
|
*
|
|
AKM1K = AP( KC+1 )
|
|
AKM1 = AP( KC ) / AKM1K
|
|
AK = AP( KC+N-K+1 ) / AKM1K
|
|
DENOM = AKM1*AK - ONE
|
|
DO 70 J = 1, NRHS
|
|
BKM1 = B( K, J ) / AKM1K
|
|
BK = B( K+1, J ) / AKM1K
|
|
B( K, J ) = ( AK*BKM1-BK ) / DENOM
|
|
B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
|
|
70 CONTINUE
|
|
KC = KC + 2*( N-K ) + 1
|
|
K = K + 2
|
|
END IF
|
|
*
|
|
GO TO 60
|
|
80 CONTINUE
|
|
*
|
|
* Next solve L**T*X = B, overwriting B with X.
|
|
*
|
|
* K is the main loop index, decreasing from N to 1 in steps of
|
|
* 1 or 2, depending on the size of the diagonal blocks.
|
|
*
|
|
K = N
|
|
KC = N*( N+1 ) / 2 + 1
|
|
90 CONTINUE
|
|
*
|
|
* If K < 1, exit from loop.
|
|
*
|
|
IF( K.LT.1 )
|
|
$ GO TO 100
|
|
*
|
|
KC = KC - ( N-K+1 )
|
|
IF( IPIV( K ).GT.0 ) THEN
|
|
*
|
|
* 1 x 1 diagonal block
|
|
*
|
|
* Multiply by inv(L**T(K)), where L(K) is the transformation
|
|
* stored in column K of A.
|
|
*
|
|
IF( K.LT.N )
|
|
$ CALL CGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
|
|
$ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
|
|
*
|
|
* Interchange rows K and IPIV(K).
|
|
*
|
|
KP = IPIV( K )
|
|
IF( KP.NE.K )
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K = K - 1
|
|
ELSE
|
|
*
|
|
* 2 x 2 diagonal block
|
|
*
|
|
* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
|
|
* stored in columns K-1 and K of A.
|
|
*
|
|
IF( K.LT.N ) THEN
|
|
CALL CGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
|
|
$ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
|
|
CALL CGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
|
|
$ LDB, AP( KC-( N-K ) ), 1, ONE, B( K-1, 1 ),
|
|
$ LDB )
|
|
END IF
|
|
*
|
|
* Interchange rows K and -IPIV(K).
|
|
*
|
|
KP = -IPIV( K )
|
|
IF( KP.NE.K )
|
|
$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
KC = KC - ( N-K+2 )
|
|
K = K - 2
|
|
END IF
|
|
*
|
|
GO TO 90
|
|
100 CONTINUE
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CSPTRS
|
|
*
|
|
END
|