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lapack/SRC/csptrs.f
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*> \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.
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CSPTRS( UPLO, N, NRHS, AP, IPIV, 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 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
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