281 lines
8.6 KiB
Fortran
281 lines
8.6 KiB
Fortran
*> \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DSYGS2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygs2.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygs2.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygs2.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, ITYPE, LDA, LDB, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DSYGS2 reduces a real symmetric-definite generalized eigenproblem
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*> to standard form.
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*>
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*> If ITYPE = 1, the problem is A*x = lambda*B*x,
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*> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
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*>
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*> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
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*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
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*>
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*> B must have been previously factorized as U**T *U or L*L**T by DPOTRF.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] ITYPE
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*> \verbatim
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*> ITYPE is INTEGER
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*> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
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*> = 2 or 3: compute U*A*U**T or L**T *A*L.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> symmetric matrix A is stored, and how B has been factorized.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrices A and B. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
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*> n by n upper triangular part of A contains the upper
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*> triangular part of the matrix A, and the strictly lower
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*> triangular part of A is not referenced. If UPLO = 'L', the
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*> leading n by n lower triangular part of A contains the lower
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*> triangular part of the matrix A, and the strictly upper
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*> triangular part of A is not referenced.
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*>
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*> On exit, if INFO = 0, the transformed matrix, stored in the
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*> same format as A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (LDB,N)
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*> The triangular factor from the Cholesky factorization of B,
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*> as returned by DPOTRF.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit.
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*> < 0: if INFO = -i, the i-th argument had an illegal value.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doubleSYcomputational
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*
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* =====================================================================
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SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, ITYPE, LDA, LDB, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), B( LDB, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, HALF
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PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER K
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DOUBLE PRECISION AKK, BKK, CT
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
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INFO = -1
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ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DSYGS2', -INFO )
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RETURN
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END IF
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*
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IF( ITYPE.EQ.1 ) THEN
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IF( UPPER ) THEN
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*
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* Compute inv(U**T)*A*inv(U)
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*
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DO 10 K = 1, N
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*
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* Update the upper triangle of A(k:n,k:n)
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*
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AKK = A( K, K )
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BKK = B( K, K )
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AKK = AKK / BKK**2
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A( K, K ) = AKK
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IF( K.LT.N ) THEN
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CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA )
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CT = -HALF*AKK
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CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ),
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$ LDA )
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CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA,
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$ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA )
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CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ),
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$ LDA )
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CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K,
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$ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA )
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END IF
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10 CONTINUE
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ELSE
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*
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* Compute inv(L)*A*inv(L**T)
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*
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DO 20 K = 1, N
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*
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* Update the lower triangle of A(k:n,k:n)
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*
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AKK = A( K, K )
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BKK = B( K, K )
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AKK = AKK / BKK**2
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A( K, K ) = AKK
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IF( K.LT.N ) THEN
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CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 )
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CT = -HALF*AKK
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CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 )
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CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1,
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$ B( K+1, K ), 1, A( K+1, K+1 ), LDA )
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CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 )
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CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K,
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$ B( K+1, K+1 ), LDB, A( K+1, K ), 1 )
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END IF
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20 CONTINUE
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END IF
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ELSE
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IF( UPPER ) THEN
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*
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* Compute U*A*U**T
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*
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DO 30 K = 1, N
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*
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* Update the upper triangle of A(1:k,1:k)
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*
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AKK = A( K, K )
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BKK = B( K, K )
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CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
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$ LDB, A( 1, K ), 1 )
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CT = HALF*AKK
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CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 )
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CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1,
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$ A, LDA )
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CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 )
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CALL DSCAL( K-1, BKK, A( 1, K ), 1 )
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A( K, K ) = AKK*BKK**2
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30 CONTINUE
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ELSE
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*
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* Compute L**T *A*L
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*
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DO 40 K = 1, N
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*
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* Update the lower triangle of A(1:k,1:k)
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*
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AKK = A( K, K )
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BKK = B( K, K )
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CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB,
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$ A( K, 1 ), LDA )
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CT = HALF*AKK
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CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA )
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CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ),
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$ LDB, A, LDA )
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CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA )
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CALL DSCAL( K-1, BKK, A( K, 1 ), LDA )
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A( K, K ) = AKK*BKK**2
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40 CONTINUE
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END IF
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END IF
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RETURN
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*
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* End of DSYGS2
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*
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END
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