--- rpl/lapack/lapack/dlaed7.f 2011/07/22 07:38:06 1.8 +++ rpl/lapack/lapack/dlaed7.f 2011/11/21 20:42:54 1.9 @@ -1,12 +1,269 @@ +*> \brief \b DLAED7 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAED7 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, +* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, +* PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, +* INFO ) +* +* .. Scalar Arguments .. +* INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, +* $ QSIZ, TLVLS +* DOUBLE PRECISION RHO +* .. +* .. Array Arguments .. +* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), +* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) +* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), +* $ QSTORE( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAED7 computes the updated eigensystem of a diagonal +*> matrix after modification by a rank-one symmetric matrix. This +*> routine is used only for the eigenproblem which requires all +*> eigenvalues and optionally eigenvectors of a dense symmetric matrix +*> that has been reduced to tridiagonal form. DLAED1 handles +*> the case in which all eigenvalues and eigenvectors of a symmetric +*> tridiagonal matrix are desired. +*> +*> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) +*> +*> where Z = Q**Tu, u is a vector of length N with ones in the +*> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. +*> +*> The eigenvectors of the original matrix are stored in Q, and the +*> eigenvalues are in D. The algorithm consists of three stages: +*> +*> The first stage consists of deflating the size of the problem +*> when there are multiple eigenvalues or if there is a zero in +*> the Z vector. For each such occurence the dimension of the +*> secular equation problem is reduced by one. This stage is +*> performed by the routine DLAED8. +*> +*> The second stage consists of calculating the updated +*> eigenvalues. This is done by finding the roots of the secular +*> equation via the routine DLAED4 (as called by DLAED9). +*> This routine also calculates the eigenvectors of the current +*> problem. +*> +*> The final stage consists of computing the updated eigenvectors +*> directly using the updated eigenvalues. The eigenvectors for +*> the current problem are multiplied with the eigenvectors from +*> the overall problem. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ICOMPQ +*> \verbatim +*> ICOMPQ is INTEGER +*> = 0: Compute eigenvalues only. +*> = 1: Compute eigenvectors of original dense symmetric matrix +*> also. On entry, Q contains the orthogonal matrix used +*> to reduce the original matrix to tridiagonal form. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension of the symmetric tridiagonal matrix. N >= 0. +*> \endverbatim +*> +*> \param[in] QSIZ +*> \verbatim +*> QSIZ is INTEGER +*> The dimension of the orthogonal matrix used to reduce +*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. +*> \endverbatim +*> +*> \param[in] TLVLS +*> \verbatim +*> TLVLS is INTEGER +*> The total number of merging levels in the overall divide and +*> conquer tree. +*> \endverbatim +*> +*> \param[in] CURLVL +*> \verbatim +*> CURLVL is INTEGER +*> The current level in the overall merge routine, +*> 0 <= CURLVL <= TLVLS. +*> \endverbatim +*> +*> \param[in] CURPBM +*> \verbatim +*> CURPBM is INTEGER +*> The current problem in the current level in the overall +*> merge routine (counting from upper left to lower right). +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the eigenvalues of the rank-1-perturbed matrix. +*> On exit, the eigenvalues of the repaired matrix. +*> \endverbatim +*> +*> \param[in,out] Q +*> \verbatim +*> Q is DOUBLE PRECISION array, dimension (LDQ, N) +*> On entry, the eigenvectors of the rank-1-perturbed matrix. +*> On exit, the eigenvectors of the repaired tridiagonal matrix. +*> \endverbatim +*> +*> \param[in] LDQ +*> \verbatim +*> LDQ is INTEGER +*> The leading dimension of the array Q. LDQ >= max(1,N). +*> \endverbatim +*> +*> \param[out] INDXQ +*> \verbatim +*> INDXQ is INTEGER array, dimension (N) +*> The permutation which will reintegrate the subproblem just +*> solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) +*> will be in ascending order. +*> \endverbatim +*> +*> \param[in] RHO +*> \verbatim +*> RHO is DOUBLE PRECISION +*> The subdiagonal element used to create the rank-1 +*> modification. +*> \endverbatim +*> +*> \param[in] CUTPNT +*> \verbatim +*> CUTPNT is INTEGER +*> Contains the location of the last eigenvalue in the leading +*> sub-matrix. min(1,N) <= CUTPNT <= N. +*> \endverbatim +*> +*> \param[in,out] QSTORE +*> \verbatim +*> QSTORE is DOUBLE PRECISION array, dimension (N**2+1) +*> Stores eigenvectors of submatrices encountered during +*> divide and conquer, packed together. QPTR points to +*> beginning of the submatrices. +*> \endverbatim +*> +*> \param[in,out] QPTR +*> \verbatim +*> QPTR is INTEGER array, dimension (N+2) +*> List of indices pointing to beginning of submatrices stored +*> in QSTORE. The submatrices are numbered starting at the +*> bottom left of the divide and conquer tree, from left to +*> right and bottom to top. +*> \endverbatim +*> +*> \param[in] PRMPTR +*> \verbatim +*> PRMPTR is INTEGER array, dimension (N lg N) +*> Contains a list of pointers which indicate where in PERM a +*> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) +*> indicates the size of the permutation and also the size of +*> the full, non-deflated problem. +*> \endverbatim +*> +*> \param[in] PERM +*> \verbatim +*> PERM is INTEGER array, dimension (N lg N) +*> Contains the permutations (from deflation and sorting) to be +*> applied to each eigenblock. +*> \endverbatim +*> +*> \param[in] GIVPTR +*> \verbatim +*> GIVPTR is INTEGER array, dimension (N lg N) +*> Contains a list of pointers which indicate where in GIVCOL a +*> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) +*> indicates the number of Givens rotations. +*> \endverbatim +*> +*> \param[in] GIVCOL +*> \verbatim +*> GIVCOL is INTEGER array, dimension (2, N lg N) +*> Each pair of numbers indicates a pair of columns to take place +*> in a Givens rotation. +*> \endverbatim +*> +*> \param[in] GIVNUM +*> \verbatim +*> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) +*> Each number indicates the S value to be used in the +*> corresponding Givens rotation. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (4*N) +*> \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 DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, $ INFO ) * -* -- LAPACK routine (version 3.3.1) -- +* -- 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..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, @@ -20,144 +277,6 @@ $ QSTORE( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLAED7 computes the updated eigensystem of a diagonal -* matrix after modification by a rank-one symmetric matrix. This -* routine is used only for the eigenproblem which requires all -* eigenvalues and optionally eigenvectors of a dense symmetric matrix -* that has been reduced to tridiagonal form. DLAED1 handles -* the case in which all eigenvalues and eigenvectors of a symmetric -* tridiagonal matrix are desired. -* -* T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) -* -* where Z = Q**Tu, u is a vector of length N with ones in the -* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. -* -* The eigenvectors of the original matrix are stored in Q, and the -* eigenvalues are in D. The algorithm consists of three stages: -* -* The first stage consists of deflating the size of the problem -* when there are multiple eigenvalues or if there is a zero in -* the Z vector. For each such occurence the dimension of the -* secular equation problem is reduced by one. This stage is -* performed by the routine DLAED8. -* -* The second stage consists of calculating the updated -* eigenvalues. This is done by finding the roots of the secular -* equation via the routine DLAED4 (as called by DLAED9). -* This routine also calculates the eigenvectors of the current -* problem. -* -* The final stage consists of computing the updated eigenvectors -* directly using the updated eigenvalues. The eigenvectors for -* the current problem are multiplied with the eigenvectors from -* the overall problem. -* -* Arguments -* ========= -* -* ICOMPQ (input) INTEGER -* = 0: Compute eigenvalues only. -* = 1: Compute eigenvectors of original dense symmetric matrix -* also. On entry, Q contains the orthogonal matrix used -* to reduce the original matrix to tridiagonal form. -* -* N (input) INTEGER -* The dimension of the symmetric tridiagonal matrix. N >= 0. -* -* QSIZ (input) INTEGER -* The dimension of the orthogonal matrix used to reduce -* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. -* -* TLVLS (input) INTEGER -* The total number of merging levels in the overall divide and -* conquer tree. -* -* CURLVL (input) INTEGER -* The current level in the overall merge routine, -* 0 <= CURLVL <= TLVLS. -* -* CURPBM (input) INTEGER -* The current problem in the current level in the overall -* merge routine (counting from upper left to lower right). -* -* D (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, the eigenvalues of the rank-1-perturbed matrix. -* On exit, the eigenvalues of the repaired matrix. -* -* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) -* On entry, the eigenvectors of the rank-1-perturbed matrix. -* On exit, the eigenvectors of the repaired tridiagonal matrix. -* -* LDQ (input) INTEGER -* The leading dimension of the array Q. LDQ >= max(1,N). -* -* INDXQ (output) INTEGER array, dimension (N) -* The permutation which will reintegrate the subproblem just -* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) -* will be in ascending order. -* -* RHO (input) DOUBLE PRECISION -* The subdiagonal element used to create the rank-1 -* modification. -* -* CUTPNT (input) INTEGER -* Contains the location of the last eigenvalue in the leading -* sub-matrix. min(1,N) <= CUTPNT <= N. -* -* QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1) -* Stores eigenvectors of submatrices encountered during -* divide and conquer, packed together. QPTR points to -* beginning of the submatrices. -* -* QPTR (input/output) INTEGER array, dimension (N+2) -* List of indices pointing to beginning of submatrices stored -* in QSTORE. The submatrices are numbered starting at the -* bottom left of the divide and conquer tree, from left to -* right and bottom to top. -* -* PRMPTR (input) INTEGER array, dimension (N lg N) -* Contains a list of pointers which indicate where in PERM a -* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) -* indicates the size of the permutation and also the size of -* the full, non-deflated problem. -* -* PERM (input) INTEGER array, dimension (N lg N) -* Contains the permutations (from deflation and sorting) to be -* applied to each eigenblock. -* -* GIVPTR (input) INTEGER array, dimension (N lg N) -* Contains a list of pointers which indicate where in GIVCOL a -* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) -* indicates the number of Givens rotations. -* -* GIVCOL (input) INTEGER array, dimension (2, N lg N) -* Each pair of numbers indicates a pair of columns to take place -* in a Givens rotation. -* -* GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) -* Each number indicates the S value to be used in the -* corresponding Givens rotation. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N) -* -* IWORK (workspace) INTEGER array, dimension (4*N) -* -* 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 -* * ===================================================================== * * .. Parameters ..