*> \brief CSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CSYSV_ROOK + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, * LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LDB, LWORK, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CSYSV_ROOK computes the solution to a complex system of linear *> equations *> A * X = B, *> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS *> matrices. *> *> The diagonal pivoting method is used to factor A as *> A = U * D * U**T, if UPLO = 'U', or *> A = L * D * L**T, if UPLO = 'L', *> where U (or L) is a product of permutation and unit upper (lower) *> triangular matrices, and D is symmetric and block diagonal with *> 1-by-1 and 2-by-2 diagonal blocks. *> *> CSYTRF_ROOK is called to compute the factorization of a complex *> symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal *> pivoting method. *> *> The factored form of A is then used to solve the system *> of equations A * X = B by calling CSYTRS_ROOK. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of linear equations, i.e., 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 COMPLEX array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**T or A = L*D*L**T as computed by *> CSYTRF_ROOK. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges and the block structure of D, *> as determined by CSYTRF_ROOK. *> *> If UPLO = 'U': *> If IPIV(k) > 0, then rows and columns k and IPIV(k) *> were interchanged and D(k,k) is a 1-by-1 diagonal block. *> *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and *> columns k and -IPIV(k) were interchanged and rows and *> columns k-1 and -IPIV(k-1) were inerchaged, *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. *> *> If UPLO = 'L': *> If IPIV(k) > 0, then rows and columns k and IPIV(k) *> were interchanged and D(k,k) is a 1-by-1 diagonal block. *> *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and *> columns k and -IPIV(k) were interchanged and rows and *> columns k+1 and -IPIV(k+1) were inerchaged, *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX array, dimension (LDB,NRHS) *> On entry, the N-by-NRHS right hand side matrix B. *> On exit, if INFO = 0, the N-by-NRHS 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 COMPLEX array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of WORK. LWORK >= 1, and for best performance *> LWORK >= max(1,N*NB), where NB is the optimal blocksize for *> CSYTRF_ROOK. *> *> TRS will be done with Level 2 BLAS *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization *> has been completed, but the block diagonal matrix D is *> exactly singular, so the solution could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complexSYsolve * *> \par Contributors: * ================== *> *> \verbatim *> *> April 2012, 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 CSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, \$ LWORK, INFO ) * * -- LAPACK driver 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, LWORK, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LQUERY INTEGER LWKOPT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, CSYTRF_ROOK, CSYTRS_ROOK * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.LSAME( UPLO, 'U' ) .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 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN INFO = -10 END IF * IF( INFO.EQ.0 ) THEN IF( N.EQ.0 ) THEN LWKOPT = 1 ELSE CALL CSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, -1, INFO ) LWKOPT = INT( WORK( 1 ) ) END IF WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CSYSV_ROOK ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Compute the factorization A = U*D*U**T or A = L*D*L**T. * CALL CSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * * Solve with TRS_ROOK ( Use Level 2 BLAS) * CALL CSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * END IF * WORK( 1 ) = LWKOPT * RETURN * * End of CSYSV_ROOK * END