*> \brief \b DSYGST * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYGST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYGST reduces a real symmetric-definite generalized eigenproblem *> to standard form. *> *> If ITYPE = 1, the problem is A*x = lambda*B*x, *> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) *> *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or *> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. *> *> B must have been previously factorized as U**T*U or L*L**T by DPOTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); *> = 2 or 3: compute U*A*U**T or L**T*A*L. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored and B is factored as *> U**T*U; *> = 'L': Lower triangle of A is stored and B is factored as *> L*L**T. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION 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 transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,N) *> The triangular factor from the Cholesky factorization of B, *> as returned by DPOTRF. *> \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 doubleSYcomputational * * ===================================================================== SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, 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, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER K, KB, NB * .. * .. External Subroutines .. EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYGST', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 ) * IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) ELSE * * Use blocked code * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**T)*A*inv(U) * DO 10 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the upper triangle of A(k:n,k:n) * CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, \$ B( K, K ), LDB, INFO ) IF( K+KB.LE.N ) THEN CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit', \$ KB, N-K-KB+1, ONE, B( K, K ), LDB, \$ A( K, K+KB ), LDA ) CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, \$ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, \$ A( K, K+KB ), LDA ) CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE, \$ A( K, K+KB ), LDA, B( K, K+KB ), LDB, \$ ONE, A( K+KB, K+KB ), LDA ) CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, \$ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, \$ A( K, K+KB ), LDA ) CALL DTRSM( 'Right', UPLO, 'No transpose', \$ 'Non-unit', KB, N-K-KB+1, ONE, \$ B( K+KB, K+KB ), LDB, A( K, K+KB ), \$ LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**T) * DO 20 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the lower triangle of A(k:n,k:n) * CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, \$ B( K, K ), LDB, INFO ) IF( K+KB.LE.N ) THEN CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit', \$ N-K-KB+1, KB, ONE, B( K, K ), LDB, \$ A( K+KB, K ), LDA ) CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, \$ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, \$ A( K+KB, K ), LDA ) CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB, \$ -ONE, A( K+KB, K ), LDA, B( K+KB, K ), \$ LDB, ONE, A( K+KB, K+KB ), LDA ) CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, \$ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, \$ A( K+KB, K ), LDA ) CALL DTRSM( 'Left', UPLO, 'No transpose', \$ 'Non-unit', N-K-KB+1, KB, ONE, \$ B( K+KB, K+KB ), LDB, A( K+KB, K ), \$ LDA ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**T * DO 30 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the upper triangle of A(1:k+kb-1,1:k+kb-1) * CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', \$ K-1, KB, ONE, B, LDB, A( 1, K ), LDA ) CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), \$ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE, \$ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, \$ LDA ) CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), \$ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit', \$ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ), \$ LDA ) CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, \$ B( K, K ), LDB, INFO ) 30 CONTINUE ELSE * * Compute L**T*A*L * DO 40 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the lower triangle of A(1:k+kb-1,1:k+kb-1) * CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', \$ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA ) CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), \$ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE, \$ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, \$ LDA ) CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), \$ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB, \$ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA ) CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, \$ B( K, K ), LDB, INFO ) 40 CONTINUE END IF END IF END IF RETURN * * End of DSYGST * END