362 lines
10 KiB
Fortran
362 lines
10 KiB
Fortran
*> \brief \b DSYTRS2
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download DSYTRS2 + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs2.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs2.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs2.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
|
|
* WORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, LDA, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IPIV( * )
|
|
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DSYTRS2 solves a system of linear equations A*X = B with a real
|
|
*> symmetric matrix A using the factorization A = U*D*U**T or
|
|
*> A = L*D*L**T computed by DSYTRF and converted by DSYCONV.
|
|
*> \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,out] A
|
|
*> \verbatim
|
|
*> A is DOUBLE PRECISION array, dimension (LDA,N)
|
|
*> The block diagonal matrix D and the multipliers used to
|
|
*> obtain the factor U or L as computed by DSYTRF.
|
|
*> Note that A is input / output. This might be counter-intuitive,
|
|
*> and one may think that A is input only. A is input / output. This
|
|
*> is because, at the start of the subroutine, we permute A in a
|
|
*> "better" form and then we permute A back to its original form at
|
|
*> the end.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,N).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] IPIV
|
|
*> \verbatim
|
|
*> IPIV is INTEGER array, dimension (N)
|
|
*> Details of the interchanges and the block structure of D
|
|
*> as determined by DSYTRF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] B
|
|
*> \verbatim
|
|
*> B is DOUBLE PRECISION 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] WORK
|
|
*> \verbatim
|
|
*> WORK is DOUBLE PRECISION array, dimension (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 June 2016
|
|
*
|
|
*> \ingroup doubleSYcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
|
|
$ WORK, 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..--
|
|
* June 2016
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INFO, LDA, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ONE
|
|
PARAMETER ( ONE = 1.0D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL UPPER
|
|
INTEGER I, IINFO, J, K, KP
|
|
DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DSCAL, DSYCONV, DSWAP, DTRSM, 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( LDA.LT.MAX( 1, N ) ) THEN
|
|
INFO = -5
|
|
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
|
|
INFO = -8
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'DSYTRS2', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 .OR. NRHS.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* Convert A
|
|
*
|
|
CALL DSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
|
|
*
|
|
IF( UPPER ) THEN
|
|
*
|
|
* Solve A*X = B, where A = U*D*U**T.
|
|
*
|
|
* P**T * B
|
|
K=N
|
|
DO WHILE ( K .GE. 1 )
|
|
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 DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K-1
|
|
ELSE
|
|
* 2 x 2 diagonal block
|
|
* Interchange rows K-1 and -IPIV(K).
|
|
KP = -IPIV( K )
|
|
IF( KP.EQ.-IPIV( K-1 ) )
|
|
$ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K-2
|
|
END IF
|
|
END DO
|
|
*
|
|
* Compute (U \P**T * B) -> B [ (U \P**T * B) ]
|
|
*
|
|
CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
|
|
*
|
|
* Compute D \ B -> B [ D \ (U \P**T * B) ]
|
|
*
|
|
I=N
|
|
DO WHILE ( I .GE. 1 )
|
|
IF( IPIV(I) .GT. 0 ) THEN
|
|
CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
|
|
ELSEIF ( I .GT. 1) THEN
|
|
IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
|
|
AKM1K = WORK(I)
|
|
AKM1 = A( I-1, I-1 ) / AKM1K
|
|
AK = A( I, I ) / AKM1K
|
|
DENOM = AKM1*AK - ONE
|
|
DO 15 J = 1, NRHS
|
|
BKM1 = B( I-1, J ) / AKM1K
|
|
BK = B( I, J ) / AKM1K
|
|
B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
|
|
B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
|
|
15 CONTINUE
|
|
I = I - 1
|
|
ENDIF
|
|
ENDIF
|
|
I = I - 1
|
|
END DO
|
|
*
|
|
* Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ]
|
|
*
|
|
CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
|
|
*
|
|
* P * B [ P * (U**T \ (D \ (U \P**T * B) )) ]
|
|
*
|
|
K=1
|
|
DO WHILE ( K .LE. N )
|
|
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 DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K+1
|
|
ELSE
|
|
* 2 x 2 diagonal block
|
|
* Interchange rows K-1 and -IPIV(K).
|
|
KP = -IPIV( K )
|
|
IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
|
|
$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K+2
|
|
ENDIF
|
|
END DO
|
|
*
|
|
ELSE
|
|
*
|
|
* Solve A*X = B, where A = L*D*L**T.
|
|
*
|
|
* P**T * B
|
|
K=1
|
|
DO WHILE ( K .LE. N )
|
|
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 DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K+1
|
|
ELSE
|
|
* 2 x 2 diagonal block
|
|
* Interchange rows K and -IPIV(K+1).
|
|
KP = -IPIV( K+1 )
|
|
IF( KP.EQ.-IPIV( K ) )
|
|
$ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K+2
|
|
ENDIF
|
|
END DO
|
|
*
|
|
* Compute (L \P**T * B) -> B [ (L \P**T * B) ]
|
|
*
|
|
CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
|
|
*
|
|
* Compute D \ B -> B [ D \ (L \P**T * B) ]
|
|
*
|
|
I=1
|
|
DO WHILE ( I .LE. N )
|
|
IF( IPIV(I) .GT. 0 ) THEN
|
|
CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
|
|
ELSE
|
|
AKM1K = WORK(I)
|
|
AKM1 = A( I, I ) / AKM1K
|
|
AK = A( I+1, I+1 ) / AKM1K
|
|
DENOM = AKM1*AK - ONE
|
|
DO 25 J = 1, NRHS
|
|
BKM1 = B( I, J ) / AKM1K
|
|
BK = B( I+1, J ) / AKM1K
|
|
B( I, J ) = ( AK*BKM1-BK ) / DENOM
|
|
B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
|
|
25 CONTINUE
|
|
I = I + 1
|
|
ENDIF
|
|
I = I + 1
|
|
END DO
|
|
*
|
|
* Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ]
|
|
*
|
|
CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
|
|
*
|
|
* P * B [ P * (L**T \ (D \ (L \P**T * B) )) ]
|
|
*
|
|
K=N
|
|
DO WHILE ( K .GE. 1 )
|
|
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 DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K-1
|
|
ELSE
|
|
* 2 x 2 diagonal block
|
|
* Interchange rows K-1 and -IPIV(K).
|
|
KP = -IPIV( K )
|
|
IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
|
|
$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
|
|
K=K-2
|
|
ENDIF
|
|
END DO
|
|
*
|
|
END IF
|
|
*
|
|
* Revert A
|
|
*
|
|
CALL DSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DSYTRS2
|
|
*
|
|
END
|