--- rpl/lapack/lapack/dlaed3.f 2010/12/21 13:53:29 1.7 +++ rpl/lapack/lapack/dlaed3.f 2011/11/21 20:42:54 1.8 @@ -1,10 +1,194 @@ +*> \brief \b DLAED3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAED3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, +* CTOT, W, S, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDQ, N, N1 +* DOUBLE PRECISION RHO +* .. +* .. Array Arguments .. +* INTEGER CTOT( * ), INDX( * ) +* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), +* $ S( * ), W( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAED3 finds the roots of the secular equation, as defined by the +*> values in D, W, and RHO, between 1 and K. It makes the +*> appropriate calls to DLAED4 and then updates the eigenvectors by +*> multiplying the matrix of eigenvectors of the pair of eigensystems +*> being combined by the matrix of eigenvectors of the K-by-K system +*> which is solved here. +*> +*> This code makes very mild assumptions about floating point +*> arithmetic. It will work on machines with a guard digit in +*> add/subtract, or on those binary machines without guard digits +*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. +*> It could conceivably fail on hexadecimal or decimal machines +*> without guard digits, but we know of none. +*> \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] N +*> \verbatim +*> N is INTEGER +*> The number of rows and columns in the Q matrix. +*> N >= K (deflation may result in N>K). +*> \endverbatim +*> +*> \param[in] N1 +*> \verbatim +*> N1 is INTEGER +*> The location of the last eigenvalue in the leading submatrix. +*> min(1,N) <= N1 <= N/2. +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> D(I) contains the updated eigenvalues for +*> 1 <= I <= K. +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is DOUBLE PRECISION array, dimension (LDQ,N) +*> Initially the first K columns are used as workspace. +*> On output the columns 1 to K contain +*> the updated eigenvectors. +*> \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,out] 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. May be changed on output by +*> having lowest order bit set to zero on Cray X-MP, Cray Y-MP, +*> Cray-2, or Cray C-90, as described above. +*> \endverbatim +*> +*> \param[in] Q2 +*> \verbatim +*> Q2 is DOUBLE PRECISION array, dimension (LDQ2, N) +*> The first K columns of this matrix contain the non-deflated +*> eigenvectors for the split problem. +*> \endverbatim +*> +*> \param[in] INDX +*> \verbatim +*> INDX is INTEGER array, dimension (N) +*> The permutation used to arrange the columns of the deflated +*> Q matrix into three groups (see DLAED2). +*> The rows of the eigenvectors found by DLAED4 must be likewise +*> permuted before the matrix multiply can take place. +*> \endverbatim +*> +*> \param[in] CTOT +*> \verbatim +*> CTOT is INTEGER array, dimension (4) +*> A count of the total number of the various types of columns +*> in Q, as described in INDX. The fourth column type is any +*> column which has been deflated. +*> \endverbatim +*> +*> \param[in,out] 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. Destroyed on +*> output. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (N1 + 1)*K +*> Will contain the eigenvectors of the repaired matrix which +*> will be multiplied by the previously accumulated eigenvectors +*> to update the system. +*> \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 \n +*> Modified by Francoise Tisseur, University of Tennessee +*> +* ===================================================================== SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, $ CTOT, W, S, 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, LDQ, N, N1 @@ -16,102 +200,6 @@ $ S( * ), W( * ) * .. * -* Purpose -* ======= -* -* DLAED3 finds the roots of the secular equation, as defined by the -* values in D, W, and RHO, between 1 and K. It makes the -* appropriate calls to DLAED4 and then updates the eigenvectors by -* multiplying the matrix of eigenvectors of the pair of eigensystems -* being combined by the matrix of eigenvectors of the K-by-K system -* which is solved here. -* -* This code makes very mild assumptions about floating point -* arithmetic. It will work on machines with a guard digit in -* add/subtract, or on those binary machines without guard digits -* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. -* It could conceivably fail on hexadecimal or decimal machines -* without guard digits, but we know of none. -* -* Arguments -* ========= -* -* K (input) INTEGER -* The number of terms in the rational function to be solved by -* DLAED4. K >= 0. -* -* N (input) INTEGER -* The number of rows and columns in the Q matrix. -* N >= K (deflation may result in N>K). -* -* N1 (input) INTEGER -* The location of the last eigenvalue in the leading submatrix. -* min(1,N) <= N1 <= N/2. -* -* D (output) DOUBLE PRECISION array, dimension (N) -* D(I) contains the updated eigenvalues for -* 1 <= I <= K. -* -* Q (output) DOUBLE PRECISION array, dimension (LDQ,N) -* Initially the first K columns are used as workspace. -* On output the columns 1 to K contain -* the updated eigenvectors. -* -* 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/output) 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. May be changed on output by -* having lowest order bit set to zero on Cray X-MP, Cray Y-MP, -* Cray-2, or Cray C-90, as described above. -* -* Q2 (input) DOUBLE PRECISION array, dimension (LDQ2, N) -* The first K columns of this matrix contain the non-deflated -* eigenvectors for the split problem. -* -* INDX (input) INTEGER array, dimension (N) -* The permutation used to arrange the columns of the deflated -* Q matrix into three groups (see DLAED2). -* The rows of the eigenvectors found by DLAED4 must be likewise -* permuted before the matrix multiply can take place. -* -* CTOT (input) INTEGER array, dimension (4) -* A count of the total number of the various types of columns -* in Q, as described in INDX. The fourth column type is any -* column which has been deflated. -* -* W (input/output) DOUBLE PRECISION array, dimension (K) -* The first K elements of this array contain the components -* of the deflation-adjusted updating vector. Destroyed on -* output. -* -* S (workspace) DOUBLE PRECISION array, dimension (N1 + 1)*K -* Will contain the eigenvectors of the repaired matrix which -* will be 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 -* Modified by Francoise Tisseur, University of Tennessee. -* * ===================================================================== * * .. Parameters ..