272 lines
8.0 KiB
Fortran
272 lines
8.0 KiB
Fortran
*> \brief \b SSPGST
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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 SSPGST + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sspgst.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/sspgst.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/sspgst.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 SSPGST( ITYPE, UPLO, N, AP, BP, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, ITYPE, N
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* ..
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* .. Array Arguments ..
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* REAL AP( * ), BP( * )
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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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*> SSPGST reduces a real symmetric-definite generalized eigenproblem
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*> to standard form, using packed storage.
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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 SPPTRF.
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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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*> = 'U': Upper triangle of A is stored and B is factored as
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*> U**T*U;
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*> = 'L': Lower triangle of A is stored and B is factored as
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*> L*L**T.
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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] AP
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*> \verbatim
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*> AP is REAL array, dimension (N*(N+1)/2)
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*> On entry, the upper or lower triangle of the symmetric matrix
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*> A, packed columnwise in a linear array. The j-th column of A
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*> is stored in the array AP as follows:
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
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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] BP
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*> \verbatim
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*> BP is REAL array, dimension (N*(N+1)/2)
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*> The triangular factor from the Cholesky factorization of B,
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*> stored in the same format as A, as returned by SPPTRF.
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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 realOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE SSPGST( ITYPE, UPLO, N, AP, BP, 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, N
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* ..
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* .. Array Arguments ..
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REAL AP( * ), BP( * )
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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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REAL ONE, HALF
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PARAMETER ( ONE = 1.0, HALF = 0.5 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
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REAL AJJ, AKK, BJJ, BKK, CT
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SSCAL, SSPMV, SSPR2, STPMV, STPSV,
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$ XERBLA
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SDOT
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EXTERNAL LSAME, SDOT
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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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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSPGST', -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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* J1 and JJ are the indices of A(1,j) and A(j,j)
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*
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JJ = 0
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DO 10 J = 1, N
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J1 = JJ + 1
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JJ = JJ + J
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*
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* Compute the j-th column of the upper triangle of A
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*
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BJJ = BP( JJ )
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CALL STPSV( UPLO, 'Transpose', 'Nonunit', J, BP,
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$ AP( J1 ), 1 )
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CALL SSPMV( UPLO, J-1, -ONE, AP, BP( J1 ), 1, ONE,
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$ AP( J1 ), 1 )
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CALL SSCAL( J-1, ONE / BJJ, AP( J1 ), 1 )
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AP( JJ ) = ( AP( JJ )-SDOT( J-1, AP( J1 ), 1, BP( J1 ),
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$ 1 ) ) / BJJ
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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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* KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
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*
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KK = 1
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DO 20 K = 1, N
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K1K1 = KK + N - K + 1
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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 = AP( KK )
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BKK = BP( KK )
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AKK = AKK / BKK**2
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AP( KK ) = AKK
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IF( K.LT.N ) THEN
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CALL SSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 )
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CT = -HALF*AKK
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CALL SAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
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CALL SSPR2( UPLO, N-K, -ONE, AP( KK+1 ), 1,
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$ BP( KK+1 ), 1, AP( K1K1 ) )
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CALL SAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
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CALL STPSV( UPLO, 'No transpose', 'Non-unit', N-K,
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$ BP( K1K1 ), AP( KK+1 ), 1 )
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END IF
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KK = K1K1
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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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* K1 and KK are the indices of A(1,k) and A(k,k)
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*
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KK = 0
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DO 30 K = 1, N
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K1 = KK + 1
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KK = KK + K
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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 = AP( KK )
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BKK = BP( KK )
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CALL STPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP,
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$ AP( K1 ), 1 )
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CT = HALF*AKK
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CALL SAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
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CALL SSPR2( UPLO, K-1, ONE, AP( K1 ), 1, BP( K1 ), 1,
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$ AP )
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CALL SAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
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CALL SSCAL( K-1, BKK, AP( K1 ), 1 )
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AP( KK ) = 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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* JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
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*
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JJ = 1
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DO 40 J = 1, N
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J1J1 = JJ + N - J + 1
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*
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* Compute the j-th column of the lower triangle of A
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*
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AJJ = AP( JJ )
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BJJ = BP( JJ )
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AP( JJ ) = AJJ*BJJ + SDOT( N-J, AP( JJ+1 ), 1,
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$ BP( JJ+1 ), 1 )
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CALL SSCAL( N-J, BJJ, AP( JJ+1 ), 1 )
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CALL SSPMV( UPLO, N-J, ONE, AP( J1J1 ), BP( JJ+1 ), 1,
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$ ONE, AP( JJ+1 ), 1 )
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CALL STPMV( UPLO, 'Transpose', 'Non-unit', N-J+1,
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$ BP( JJ ), AP( JJ ), 1 )
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JJ = J1J1
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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 SSPGST
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*
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END
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