--- rpl/lapack/lapack/dsbgst.f 2010/12/21 13:53:37 1.7 +++ rpl/lapack/lapack/dsbgst.f 2011/11/21 20:43:03 1.8 @@ -1,10 +1,168 @@ +*> \brief \b DSBGST +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSBGST + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, +* LDX, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO, VECT +* INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), +* $ X( LDX, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSBGST reduces a real symmetric-definite banded generalized +*> eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, +*> such that C has the same bandwidth as A. +*> +*> B must have been previously factorized as S**T*S by DPBSTF, using a +*> split Cholesky factorization. A is overwritten by C = X**T*A*X, where +*> X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the +*> bandwidth of A. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] VECT +*> \verbatim +*> VECT is CHARACTER*1 +*> = 'N': do not form the transformation matrix X; +*> = 'V': form X. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrices A and B. N >= 0. +*> \endverbatim +*> +*> \param[in] KA +*> \verbatim +*> KA is INTEGER +*> The number of superdiagonals of the matrix A if UPLO = 'U', +*> or the number of subdiagonals if UPLO = 'L'. KA >= 0. +*> \endverbatim +*> +*> \param[in] KB +*> \verbatim +*> KB is INTEGER +*> The number of superdiagonals of the matrix B if UPLO = 'U', +*> or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. +*> \endverbatim +*> +*> \param[in,out] AB +*> \verbatim +*> AB is DOUBLE PRECISION array, dimension (LDAB,N) +*> On entry, the upper or lower triangle of the symmetric band +*> matrix A, stored in the first ka+1 rows of the array. The +*> j-th column of A is stored in the j-th column of the array AB +*> as follows: +*> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; +*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). +*> +*> On exit, the transformed matrix X**T*A*X, stored in the same +*> format as A. +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= KA+1. +*> \endverbatim +*> +*> \param[in] BB +*> \verbatim +*> BB is DOUBLE PRECISION array, dimension (LDBB,N) +*> The banded factor S from the split Cholesky factorization of +*> B, as returned by DPBSTF, stored in the first KB+1 rows of +*> the array. +*> \endverbatim +*> +*> \param[in] LDBB +*> \verbatim +*> LDBB is INTEGER +*> The leading dimension of the array BB. LDBB >= KB+1. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (LDX,N) +*> If VECT = 'V', the n-by-n matrix X. +*> If VECT = 'N', the array X is not referenced. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. +*> LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (2*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 November 2011 +* +*> \ingroup doubleOTHERcomputational +* +* ===================================================================== SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, $ LDX, WORK, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER UPLO, VECT @@ -15,76 +173,6 @@ $ X( LDX, * ) * .. * -* Purpose -* ======= -* -* DSBGST reduces a real symmetric-definite banded generalized -* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, -* such that C has the same bandwidth as A. -* -* B must have been previously factorized as S**T*S by DPBSTF, using a -* split Cholesky factorization. A is overwritten by C = X**T*A*X, where -* X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the -* bandwidth of A. -* -* Arguments -* ========= -* -* VECT (input) CHARACTER*1 -* = 'N': do not form the transformation matrix X; -* = 'V': form X. -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrices A and B. N >= 0. -* -* KA (input) INTEGER -* The number of superdiagonals of the matrix A if UPLO = 'U', -* or the number of subdiagonals if UPLO = 'L'. KA >= 0. -* -* KB (input) INTEGER -* The number of superdiagonals of the matrix B if UPLO = 'U', -* or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. -* -* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) -* On entry, the upper or lower triangle of the symmetric band -* matrix A, stored in the first ka+1 rows of the array. The -* j-th column of A is stored in the j-th column of the array AB -* as follows: -* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; -* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -* -* On exit, the transformed matrix X**T*A*X, stored in the same -* format as A. -* -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= KA+1. -* -* BB (input) DOUBLE PRECISION array, dimension (LDBB,N) -* The banded factor S from the split Cholesky factorization of -* B, as returned by DPBSTF, stored in the first KB+1 rows of -* the array. -* -* LDBB (input) INTEGER -* The leading dimension of the array BB. LDBB >= KB+1. -* -* X (output) DOUBLE PRECISION array, dimension (LDX,N) -* If VECT = 'V', the n-by-n matrix X. -* If VECT = 'N', the array X is not referenced. -* -* LDX (input) INTEGER -* The leading dimension of the array X. -* LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value. -* * ===================================================================== * * .. Parameters ..