*> \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYGS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYGS2( 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 *> *> DSYGS2 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 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored, and how B has been factorized. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \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. * *> \date December 2016 * *> \ingroup doubleSYcomputational * * ===================================================================== SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. 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 DOUBLE PRECISION AKK, BKK, CT * .. * .. External Subroutines .. EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. 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( 'DSYGS2', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**T)*A*inv(U) * DO 10 K = 1, N * * Update the upper triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) CT = -HALF*AKK CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), \$ LDA ) CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA, \$ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), \$ LDA ) CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K, \$ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**T) * DO 20 K = 1, N * * Update the lower triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) CT = -HALF*AKK CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1, \$ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K, \$ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**T * DO 30 K = 1, N * * Update the upper triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, \$ LDB, A( 1, K ), 1 ) CT = HALF*AKK CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1, \$ A, LDA ) CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL DSCAL( K-1, BKK, A( 1, K ), 1 ) A( K, K ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**T *A*L * DO 40 K = 1, N * * Update the lower triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB, \$ A( K, 1 ), LDA ) CT = HALF*AKK CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ), \$ LDB, A, LDA ) CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL DSCAL( K-1, BKK, A( K, 1 ), LDA ) A( K, K ) = AKK*BKK**2 40 CONTINUE END IF END IF RETURN * * End of DSYGS2 * END