*> \brief \b SSYTRS2
*
* =========== DOCUMENTATION ===========
*
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*
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*
* Definition:
* ===========
*
* SUBROUTINE SSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
* WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, LDB, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SSYTRS2 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 SSYTRF and converted by SSYCONV.
*> \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 REAL array, dimension (LDA,N)
*> The block diagonal matrix D and the multipliers used to
*> obtain the factor U or L as computed by SSYTRF.
*> 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 SSYTRF.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL 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 REAL 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 November 2015
*
*> \ingroup realSYcomputational
*
* =====================================================================
SUBROUTINE SSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
$ WORK, INFO )
*
* -- LAPACK computational routine (version 3.6.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2015
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IINFO, J, K, KP
REAL AK, AKM1, AKM1K, BK, BKM1, DENOM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, SSYCONV, SSWAP, STRSM, 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( 'SSYTRS2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Convert A
*
CALL SSYCONV( 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 SSWAP( 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 SSWAP( 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 STRSM('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 SSCAL( 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 STRSM('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 SSWAP( 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 SSWAP( 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 SSWAP( 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 SSWAP( 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 STRSM('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 SSCAL( 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 STRSM('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 SSWAP( 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 SSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
K=K-2
ENDIF
END DO
*
END IF
*
* Revert A
*
CALL SSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
*
RETURN
*
* End of SSYTRS2
*
END