*> \brief \b CHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CHETRS_ROOK + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CHETRS_ROOK solves a system of linear equations A*X = B with a complex *> Hermitian matrix A using the factorization A = U*D*U**H or *> A = L*D*L**H computed by CHETRF_ROOK. *> \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**H; *> = 'L': Lower triangular, form is A = L*D*L**H. *> \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] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The block diagonal matrix D and the multipliers used to *> obtain the factor U or L as computed by CHETRF_ROOK. *> \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 CHETRF_ROOK. *> \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 complexHEcomputational * *> \par Contributors: * ================== *> *> \verbatim *> *> November 2013, Igor Kozachenko, *> Computer Science Division, *> University of California, Berkeley *> *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, *> School of Mathematics, *> University of Manchester *> *> \endverbatim * * ===================================================================== SUBROUTINE CHETRS_ROOK( UPLO, N, NRHS, A, LDA, 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, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, K, KP REAL S COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CGEMV, CGERU, CLACGV, CSSCAL, CSWAP, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, REAL * .. * .. 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( 'CHETRS_ROOK', -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**H. * * 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 10 CONTINUE * * If K < 1, exit from loop. * IF( K.LT.1 ) \$ GO TO 30 * 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, A( 1, K ), 1, B( K, 1 ), LDB, \$ B( 1, 1 ), LDB ) * * Multiply by the inverse of the diagonal block. * S = REAL( ONE ) / REAL( A( K, K ) ) CALL CSSCAL( NRHS, S, B( K, 1 ), LDB ) K = K - 1 ELSE * * 2 x 2 diagonal block * * Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1) * KP = -IPIV( K ) IF( KP.NE.K ) \$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * KP = -IPIV( K-1) 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, A( 1, K ), 1, B( K, 1 ), LDB, \$ B( 1, 1 ), LDB ) CALL CGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ), \$ LDB, B( 1, 1 ), LDB ) * * Multiply by the inverse of the diagonal block. * AKM1K = A( K-1, K ) AKM1 = A( K-1, K-1 ) / AKM1K AK = A( K, K ) / CONJG( AKM1K ) DENOM = AKM1*AK - ONE DO 20 J = 1, NRHS BKM1 = B( K-1, J ) / AKM1K BK = B( K, J ) / CONJG( AKM1K ) B( K-1, J ) = ( AK*BKM1-BK ) / DENOM B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM 20 CONTINUE K = K - 2 END IF * GO TO 10 30 CONTINUE * * Next solve U**H *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 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**H(K)), where U(K) is the transformation * stored in column K of A. * IF( K.GT.1 ) THEN CALL CLACGV( NRHS, B( K, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, \$ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB ) CALL CLACGV( NRHS, B( K, 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 ) K = K + 1 ELSE * * 2 x 2 diagonal block * * Multiply by inv(U**H(K+1)), where U(K+1) is the transformation * stored in columns K and K+1 of A. * IF( K.GT.1 ) THEN CALL CLACGV( NRHS, B( K, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, \$ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB ) CALL CLACGV( NRHS, B( K, 1 ), LDB ) * CALL CLACGV( NRHS, B( K+1, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B, \$ LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB ) CALL CLACGV( NRHS, B( K+1, 1 ), LDB ) END IF * * Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1) * KP = -IPIV( K ) IF( KP.NE.K ) \$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * KP = -IPIV( K+1 ) IF( KP.NE.K+1 ) \$ CALL CSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) * K = K + 2 END IF * GO TO 40 50 CONTINUE * ELSE * * Solve A*X = B, where A = L*D*L**H. * * 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 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, A( K+1, K ), 1, B( K, 1 ), \$ LDB, B( K+1, 1 ), LDB ) * * Multiply by the inverse of the diagonal block. * S = REAL( ONE ) / REAL( A( K, K ) ) CALL CSSCAL( NRHS, S, B( K, 1 ), LDB ) K = K + 1 ELSE * * 2 x 2 diagonal block * * Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1) * KP = -IPIV( K ) IF( KP.NE.K ) \$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * KP = -IPIV( K+1 ) 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, A( K+2, K ), 1, B( K, 1 ), \$ LDB, B( K+2, 1 ), LDB ) CALL CGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1, \$ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB ) END IF * * Multiply by the inverse of the diagonal block. * AKM1K = A( K+1, K ) AKM1 = A( K, K ) / CONJG( AKM1K ) AK = A( K+1, K+1 ) / AKM1K DENOM = AKM1*AK - ONE DO 70 J = 1, NRHS BKM1 = B( K, J ) / CONJG( AKM1K ) BK = B( K+1, J ) / AKM1K B( K, J ) = ( AK*BKM1-BK ) / DENOM B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 70 CONTINUE K = K + 2 END IF * GO TO 60 80 CONTINUE * * Next solve L**H *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 90 CONTINUE * * If K < 1, exit from loop. * IF( K.LT.1 ) \$ GO TO 100 * IF( IPIV( K ).GT.0 ) THEN * * 1 x 1 diagonal block * * Multiply by inv(L**H(K)), where L(K) is the transformation * stored in column K of A. * IF( K.LT.N ) THEN CALL CLACGV( NRHS, B( K, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, \$ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE, \$ B( K, 1 ), LDB ) CALL CLACGV( NRHS, B( K, 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 ) K = K - 1 ELSE * * 2 x 2 diagonal block * * Multiply by inv(L**H(K-1)), where L(K-1) is the transformation * stored in columns K-1 and K of A. * IF( K.LT.N ) THEN CALL CLACGV( NRHS, B( K, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, \$ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE, \$ B( K, 1 ), LDB ) CALL CLACGV( NRHS, B( K, 1 ), LDB ) * CALL CLACGV( NRHS, B( K-1, 1 ), LDB ) CALL CGEMV( 'Conjugate transpose', N-K, NRHS, -ONE, \$ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE, \$ B( K-1, 1 ), LDB ) CALL CLACGV( NRHS, B( K-1, 1 ), LDB ) END IF * * Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1) * KP = -IPIV( K ) IF( KP.NE.K ) \$ CALL CSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * KP = -IPIV( K-1 ) IF( KP.NE.K-1 ) \$ CALL CSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) * K = K - 2 END IF * GO TO 90 100 CONTINUE END IF * RETURN * * End of CHETRS_ROOK * END