457 lines
15 KiB
C++
457 lines
15 KiB
C++
/* fortran/zlaed7.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__2 = 2;
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static integer c__1 = 1;
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static integer c_n1 = -1;
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/* > \brief \b ZLAED7 used by ZSTEDC. Computes the updated eigensystem of a diagonal matrix after modification
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by a rank-one symmetric matrix. Used when the original matrix is dense. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download ZLAED7 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaed7.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaed7.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaed7.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */
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/* LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, */
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/* GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, */
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/* INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, */
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/* $ TLVLS */
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/* DOUBLE PRECISION RHO */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */
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/* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */
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/* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) */
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/* COMPLEX*16 Q( LDQ, * ), WORK( * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > ZLAED7 computes the updated eigensystem of a diagonal */
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/* > matrix after modification by a rank-one symmetric matrix. This */
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/* > routine is used only for the eigenproblem which requires all */
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/* > eigenvalues and optionally eigenvectors of a dense or banded */
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/* > Hermitian matrix that has been reduced to tridiagonal form. */
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/* > */
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/* > T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) */
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/* > */
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/* > where Z = Q**Hu, u is a vector of length N with ones in the */
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/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
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/* > */
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/* > The eigenvectors of the original matrix are stored in Q, and the */
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/* > eigenvalues are in D. The algorithm consists of three stages: */
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/* > */
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/* > The first stage consists of deflating the size of the problem */
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/* > when there are multiple eigenvalues or if there is a zero in */
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/* > the Z vector. For each such occurrence the dimension of the */
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/* > secular equation problem is reduced by one. This stage is */
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/* > performed by the routine DLAED2. */
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/* > */
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/* > The second stage consists of calculating the updated */
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/* > eigenvalues. This is done by finding the roots of the secular */
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/* > equation via the routine DLAED4 (as called by SLAED3). */
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/* > This routine also calculates the eigenvectors of the current */
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/* > problem. */
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/* > */
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/* > The final stage consists of computing the updated eigenvectors */
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/* > directly using the updated eigenvalues. The eigenvectors for */
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/* > the current problem are multiplied with the eigenvectors from */
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/* > the overall problem. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] CUTPNT */
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/* > \verbatim */
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/* > CUTPNT is INTEGER */
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/* > Contains the location of the last eigenvalue in the leading */
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/* > sub-matrix. min(1,N) <= CUTPNT <= N. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] QSIZ */
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/* > \verbatim */
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/* > QSIZ is INTEGER */
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/* > The dimension of the unitary matrix used to reduce */
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/* > the full matrix to tridiagonal form. QSIZ >= N. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TLVLS */
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/* > \verbatim */
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/* > TLVLS is INTEGER */
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/* > The total number of merging levels in the overall divide and */
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/* > conquer tree. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] CURLVL */
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/* > \verbatim */
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/* > CURLVL is INTEGER */
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/* > The current level in the overall merge routine, */
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/* > 0 <= curlvl <= tlvls. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] CURPBM */
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/* > \verbatim */
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/* > CURPBM is INTEGER */
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/* > The current problem in the current level in the overall */
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/* > merge routine (counting from upper left to lower right). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] D */
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/* > \verbatim */
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/* > D is DOUBLE PRECISION array, dimension (N) */
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/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */
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/* > On exit, the eigenvalues of the repaired matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] Q */
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/* > \verbatim */
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/* > Q is COMPLEX*16 array, dimension (LDQ,N) */
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/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */
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/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDQ */
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/* > \verbatim */
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/* > LDQ is INTEGER */
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/* > The leading dimension of the array Q. LDQ >= max(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] RHO */
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/* > \verbatim */
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/* > RHO is DOUBLE PRECISION */
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/* > Contains the subdiagonal element used to create the rank-1 */
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/* > modification. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INDXQ */
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/* > \verbatim */
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/* > INDXQ is INTEGER array, dimension (N) */
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/* > This contains the permutation which will reintegrate the */
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/* > subproblem just solved back into sorted order, */
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/* > ie. D( INDXQ( I = 1, N ) ) will be in ascending order. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] IWORK */
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/* > \verbatim */
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/* > IWORK is INTEGER array, dimension (4*N) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] RWORK */
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/* > \verbatim */
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/* > RWORK is DOUBLE PRECISION array, */
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/* > dimension (3*N+2*QSIZ*N) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is COMPLEX*16 array, dimension (QSIZ*N) */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] QSTORE */
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/* > \verbatim */
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/* > QSTORE is DOUBLE PRECISION array, dimension (N**2+1) */
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/* > Stores eigenvectors of submatrices encountered during */
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/* > divide and conquer, packed together. QPTR points to */
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/* > beginning of the submatrices. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] QPTR */
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/* > \verbatim */
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/* > QPTR is INTEGER array, dimension (N+2) */
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/* > List of indices pointing to beginning of submatrices stored */
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/* > in QSTORE. The submatrices are numbered starting at the */
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/* > bottom left of the divide and conquer tree, from left to */
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/* > right and bottom to top. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] PRMPTR */
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/* > \verbatim */
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/* > PRMPTR is INTEGER array, dimension (N lg N) */
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/* > Contains a list of pointers which indicate where in PERM a */
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/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */
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/* > indicates the size of the permutation and also the size of */
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/* > the full, non-deflated problem. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] PERM */
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/* > \verbatim */
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/* > PERM is INTEGER array, dimension (N lg N) */
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/* > Contains the permutations (from deflation and sorting) to be */
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/* > applied to each eigenblock. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVPTR */
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/* > \verbatim */
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/* > GIVPTR is INTEGER array, dimension (N lg N) */
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/* > Contains a list of pointers which indicate where in GIVCOL a */
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/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */
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/* > indicates the number of Givens rotations. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVCOL */
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/* > \verbatim */
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/* > GIVCOL is INTEGER array, dimension (2, N lg N) */
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/* > Each pair of numbers indicates a pair of columns to take place */
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/* > in a Givens rotation. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVNUM */
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/* > \verbatim */
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/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */
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/* > Each number indicates the S value to be used in the */
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/* > corresponding Givens rotation. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit. */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > > 0: if INFO = 1, an eigenvalue did not converge */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup complex16OTHERcomputational */
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/* ===================================================================== */
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/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz,
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integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__,
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doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq,
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doublereal *qstore, integer *qptr, integer *prmptr, integer *perm,
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integer *givptr, integer *givcol, doublereal *givnum, doublecomplex *
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work, doublereal *rwork, integer *iwork, integer *info)
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{
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/* System generated locals */
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integer q_dim1, q_offset, i__1, i__2;
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/* Builtin functions */
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integer pow_lmp_ii(integer *, integer *);
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/* Local variables */
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integer i__, k, n1, n2, iq, iw, iz, ptr, indx, curr, indxc, indxp;
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extern /* Subroutine */ int dlaed9_(integer *, integer *, integer *,
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integer *, doublereal *, doublereal *, integer *, doublereal *,
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doublereal *, doublereal *, doublereal *, integer *, integer *),
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zlaed8_(integer *, integer *, integer *, doublecomplex *, integer
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*, doublereal *, doublereal *, integer *, doublereal *,
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doublereal *, doublecomplex *, integer *, doublereal *, integer *,
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integer *, integer *, integer *, integer *, integer *,
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doublereal *, integer *), dlaeda_(integer *, integer *, integer *,
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integer *, integer *, integer *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, doublereal *,
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integer *);
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integer idlmda;
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extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
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integer *, integer *, integer *), xerbla_(char *, integer *,
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ftnlen), zlacrm_(integer *, integer *, doublecomplex *, integer *,
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doublereal *, integer *, doublecomplex *, integer *, doublereal *
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);
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integer coltyp;
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1;
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q -= q_offset;
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--indxq;
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--qstore;
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--qptr;
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--prmptr;
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--perm;
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--givptr;
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givcol -= 3;
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givnum -= 3;
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--work;
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--rwork;
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--iwork;
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/* Function Body */
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*info = 0;
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/* IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN */
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/* INFO = -1 */
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/* ELSE IF( N.LT.0 ) THEN */
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if (*n < 0) {
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*info = -1;
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} else if (min(1,*n) > *cutpnt || *n < *cutpnt) {
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*info = -2;
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} else if (*qsiz < *n) {
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*info = -3;
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} else if (*ldq < max(1,*n)) {
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*info = -9;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"ZLAED7", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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/* The following values are for bookkeeping purposes only. They are */
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/* integer pointers which indicate the portion of the workspace */
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/* used by a particular array in DLAED2 and SLAED3. */
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iz = 1;
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idlmda = iz + *n;
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iw = idlmda + *n;
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iq = iw + *n;
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indx = 1;
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indxc = indx + *n;
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coltyp = indxc + *n;
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indxp = coltyp + *n;
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/* Form the z-vector which consists of the last row of Q_1 and the */
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/* first row of Q_2. */
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ptr = pow_lmp_ii(&c__2, tlvls) + 1;
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i__1 = *curlvl - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = *tlvls - i__;
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ptr += pow_lmp_ii(&c__2, &i__2);
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/* L10: */
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}
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curr = ptr + *curpbm;
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dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &
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givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[
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iz + *n], info);
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/* When solving the final problem, we no longer need the stored data, */
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/* so we will overwrite the data from this level onto the previously */
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/* used storage space. */
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if (*curlvl == *tlvls) {
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qptr[curr] = 1;
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prmptr[curr] = 1;
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givptr[curr] = 1;
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}
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/* Sort and Deflate eigenvalues. */
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zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz],
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&rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[
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indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[
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(givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], info);
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prmptr[curr + 1] = prmptr[curr] + *n;
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givptr[curr + 1] += givptr[curr];
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/* Solve Secular Equation. */
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if (k != 0) {
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dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda]
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, &rwork[iw], &qstore[qptr[curr]], &k, info);
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zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[
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q_offset], ldq, &rwork[iq]);
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/* Computing 2nd power */
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i__1 = k;
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qptr[curr + 1] = qptr[curr] + i__1 * i__1;
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if (*info != 0) {
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return 0;
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}
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/* Prepare the INDXQ sorting premutation. */
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n1 = k;
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n2 = *n - k;
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dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
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} else {
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qptr[curr + 1] = qptr[curr];
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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indxq[i__] = i__;
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/* L20: */
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}
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}
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return 0;
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/* End of ZLAED7 */
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} /* zlaed7_ */
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#ifdef __cplusplus
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}
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#endif
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