*> \brief \b DSPGST * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSPGST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, N * .. * .. Array Arguments .. * DOUBLE PRECISION AP( * ), BP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSPGST reduces a real symmetric-definite generalized eigenproblem *> to standard form, using packed storage. *> *> 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 DPPTRF. *> \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] AP *> \verbatim *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the symmetric matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] BP *> \verbatim *> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2) *> The triangular factor from the Cholesky factorization of B, *> stored in the same format as A, as returned by DPPTRF. *> \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 doubleOTHERcomputational * * ===================================================================== SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, 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, N * .. * .. Array Arguments .. DOUBLE PRECISION AP( * ), BP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK DOUBLE PRECISION AJJ, AKK, BJJ, BKK, CT * .. * .. External Subroutines .. EXTERNAL DAXPY, DSCAL, DSPMV, DSPR2, DTPMV, DTPSV, \$ XERBLA * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DDOT EXTERNAL LSAME, DDOT * .. * .. 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 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSPGST', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**T)*A*inv(U) * * J1 and JJ are the indices of A(1,j) and A(j,j) * JJ = 0 DO 10 J = 1, N J1 = JJ + 1 JJ = JJ + J * * Compute the j-th column of the upper triangle of A * BJJ = BP( JJ ) CALL DTPSV( UPLO, 'Transpose', 'Nonunit', J, BP, \$ AP( J1 ), 1 ) CALL DSPMV( UPLO, J-1, -ONE, AP, BP( J1 ), 1, ONE, \$ AP( J1 ), 1 ) CALL DSCAL( J-1, ONE / BJJ, AP( J1 ), 1 ) AP( JJ ) = ( AP( JJ )-DDOT( J-1, AP( J1 ), 1, BP( J1 ), \$ 1 ) ) / BJJ 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**T) * * KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) * KK = 1 DO 20 K = 1, N K1K1 = KK + N - K + 1 * * Update the lower triangle of A(k:n,k:n) * AKK = AP( KK ) BKK = BP( KK ) AKK = AKK / BKK**2 AP( KK ) = AKK IF( K.LT.N ) THEN CALL DSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 ) CT = -HALF*AKK CALL DAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL DSPR2( UPLO, N-K, -ONE, AP( KK+1 ), 1, \$ BP( KK+1 ), 1, AP( K1K1 ) ) CALL DAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL DTPSV( UPLO, 'No transpose', 'Non-unit', N-K, \$ BP( K1K1 ), AP( KK+1 ), 1 ) END IF KK = K1K1 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**T * * K1 and KK are the indices of A(1,k) and A(k,k) * KK = 0 DO 30 K = 1, N K1 = KK + 1 KK = KK + K * * Update the upper triangle of A(1:k,1:k) * AKK = AP( KK ) BKK = BP( KK ) CALL DTPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP, \$ AP( K1 ), 1 ) CT = HALF*AKK CALL DAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL DSPR2( UPLO, K-1, ONE, AP( K1 ), 1, BP( K1 ), 1, \$ AP ) CALL DAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL DSCAL( K-1, BKK, AP( K1 ), 1 ) AP( KK ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**T *A*L * * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) * JJ = 1 DO 40 J = 1, N J1J1 = JJ + N - J + 1 * * Compute the j-th column of the lower triangle of A * AJJ = AP( JJ ) BJJ = BP( JJ ) AP( JJ ) = AJJ*BJJ + DDOT( N-J, AP( JJ+1 ), 1, \$ BP( JJ+1 ), 1 ) CALL DSCAL( N-J, BJJ, AP( JJ+1 ), 1 ) CALL DSPMV( UPLO, N-J, ONE, AP( J1J1 ), BP( JJ+1 ), 1, \$ ONE, AP( JJ+1 ), 1 ) CALL DTPMV( UPLO, 'Transpose', 'Non-unit', N-J+1, \$ BP( JJ ), AP( JJ ), 1 ) JJ = J1J1 40 CONTINUE END IF END IF RETURN * * End of DSPGST * END