*> \brief \b SSYTRS2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SSYTRS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * 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. * *> \ingroup realSYcomputational * * ===================================================================== SUBROUTINE SSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, \$ WORK, 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, 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