--- rpl/lapack/lapack/dlaed9.f 2010/12/21 13:53:29 1.7 +++ rpl/lapack/lapack/dlaed9.f 2011/11/21 20:42:55 1.8 @@ -1,10 +1,165 @@ +*> \brief \b DLAED9 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAED9 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, +* S, LDS, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N +* DOUBLE PRECISION RHO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), +* $ W( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAED9 finds the roots of the secular equation, as defined by the +*> values in D, Z, and RHO, between KSTART and KSTOP. It makes the +*> appropriate calls to DLAED4 and then stores the new matrix of +*> eigenvectors for use in calculating the next level of Z vectors. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of terms in the rational function to be solved by +*> DLAED4. K >= 0. +*> \endverbatim +*> +*> \param[in] KSTART +*> \verbatim +*> KSTART is INTEGER +*> \endverbatim +*> +*> \param[in] KSTOP +*> \verbatim +*> KSTOP is INTEGER +*> The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP +*> are to be computed. 1 <= KSTART <= KSTOP <= K. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of rows and columns in the Q matrix. +*> N >= K (delation may result in N > K). +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> D(I) contains the updated eigenvalues +*> for KSTART <= I <= KSTOP. +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is DOUBLE PRECISION array, dimension (LDQ,N) +*> \endverbatim +*> +*> \param[in] LDQ +*> \verbatim +*> LDQ is INTEGER +*> The leading dimension of the array Q. LDQ >= max( 1, N ). +*> \endverbatim +*> +*> \param[in] RHO +*> \verbatim +*> RHO is DOUBLE PRECISION +*> The value of the parameter in the rank one update equation. +*> RHO >= 0 required. +*> \endverbatim +*> +*> \param[in] DLAMDA +*> \verbatim +*> DLAMDA is DOUBLE PRECISION array, dimension (K) +*> The first K elements of this array contain the old roots +*> of the deflated updating problem. These are the poles +*> of the secular equation. +*> \endverbatim +*> +*> \param[in] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (K) +*> The first K elements of this array contain the components +*> of the deflation-adjusted updating vector. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (LDS, K) +*> Will contain the eigenvectors of the repaired matrix which +*> will be stored for subsequent Z vector calculation and +*> multiplied by the previously accumulated eigenvectors +*> to update the system. +*> \endverbatim +*> +*> \param[in] LDS +*> \verbatim +*> LDS is INTEGER +*> The leading dimension of S. LDS >= max( 1, K ). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit. +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> > 0: if INFO = 1, an eigenvalue did not converge +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +*> \par Contributors: +* ================== +*> +*> Jeff Rutter, Computer Science Division, University of California +*> at Berkeley, USA +* +* ===================================================================== SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, $ S, LDS, 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 .. INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N @@ -15,73 +170,6 @@ $ W( * ) * .. * -* Purpose -* ======= -* -* DLAED9 finds the roots of the secular equation, as defined by the -* values in D, Z, and RHO, between KSTART and KSTOP. It makes the -* appropriate calls to DLAED4 and then stores the new matrix of -* eigenvectors for use in calculating the next level of Z vectors. -* -* Arguments -* ========= -* -* K (input) INTEGER -* The number of terms in the rational function to be solved by -* DLAED4. K >= 0. -* -* KSTART (input) INTEGER -* KSTOP (input) INTEGER -* The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP -* are to be computed. 1 <= KSTART <= KSTOP <= K. -* -* N (input) INTEGER -* The number of rows and columns in the Q matrix. -* N >= K (delation may result in N > K). -* -* D (output) DOUBLE PRECISION array, dimension (N) -* D(I) contains the updated eigenvalues -* for KSTART <= I <= KSTOP. -* -* Q (workspace) DOUBLE PRECISION array, dimension (LDQ,N) -* -* LDQ (input) INTEGER -* The leading dimension of the array Q. LDQ >= max( 1, N ). -* -* RHO (input) DOUBLE PRECISION -* The value of the parameter in the rank one update equation. -* RHO >= 0 required. -* -* DLAMDA (input) DOUBLE PRECISION array, dimension (K) -* The first K elements of this array contain the old roots -* of the deflated updating problem. These are the poles -* of the secular equation. -* -* W (input) DOUBLE PRECISION array, dimension (K) -* The first K elements of this array contain the components -* of the deflation-adjusted updating vector. -* -* S (output) DOUBLE PRECISION array, dimension (LDS, K) -* Will contain the eigenvectors of the repaired matrix which -* will be stored for subsequent Z vector calculation and -* multiplied by the previously accumulated eigenvectors -* to update the system. -* -* LDS (input) INTEGER -* The leading dimension of S. LDS >= max( 1, K ). -* -* INFO (output) INTEGER -* = 0: successful exit. -* < 0: if INFO = -i, the i-th argument had an illegal value. -* > 0: if INFO = 1, an eigenvalue did not converge -* -* Further Details -* =============== -* -* Based on contributions by -* Jeff Rutter, Computer Science Division, University of California -* at Berkeley, USA -* * ===================================================================== * * .. Local Scalars ..