459 lines
14 KiB
C++
459 lines
14 KiB
C++
/* fortran/zlaed0.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__9 = 9;
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static integer c__0 = 0;
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static integer c__2 = 2;
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static integer c__1 = 1;
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/* > \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced
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symmetric tridiagonal matrix using the divide and conquer method. */
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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 ZLAED0 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaed0.
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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/zlaed0.
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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/zlaed0.
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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 ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, */
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/* IWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER INFO, LDQ, LDQS, N, QSIZ */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER IWORK( * ) */
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/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */
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/* COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) */
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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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/* > Using the divide and conquer method, ZLAED0 computes all eigenvalues */
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/* > of a symmetric tridiagonal matrix which is one diagonal block of */
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/* > those from reducing a dense or band Hermitian matrix and */
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/* > corresponding eigenvectors of the dense or band matrix. */
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/* > \endverbatim */
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/* Arguments: */
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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 if ICOMPQ = 1. */
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/* > \endverbatim */
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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,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 diagonal elements of the tridiagonal matrix. */
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/* > On exit, the eigenvalues in ascending order. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] E */
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/* > \verbatim */
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/* > E is DOUBLE PRECISION array, dimension (N-1) */
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/* > On entry, the off-diagonal elements of the tridiagonal matrix. */
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/* > On exit, E has been destroyed. */
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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, Q must contain an QSIZ x N matrix whose columns */
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/* > unitarily orthonormal. It is a part of the unitary matrix */
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/* > that reduces the full dense Hermitian matrix to a */
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/* > (reducible) symmetric 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[out] IWORK */
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/* > \verbatim */
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/* > IWORK is INTEGER array, */
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/* > the dimension of IWORK must be at least */
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/* > 6 + 6*N + 5*N*lg N */
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/* > ( lg( N ) = smallest integer k */
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/* > such that 2^k >= 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 (1 + 3*N + 2*N*lg N + 3*N**2) */
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/* > ( lg( N ) = smallest integer k */
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/* > such that 2^k >= N ) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] QSTORE */
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/* > \verbatim */
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/* > QSTORE is COMPLEX*16 array, dimension (LDQS, N) */
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/* > Used to store parts of */
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/* > the eigenvector matrix when the updating matrix multiplies */
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/* > take place. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDQS */
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/* > \verbatim */
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/* > LDQS is INTEGER */
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/* > The leading dimension of the array QSTORE. */
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/* > LDQS >= max(1,N). */
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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: The algorithm failed to compute an eigenvalue while */
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/* > working on the submatrix lying in rows and columns */
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/* > INFO/(N+1) through mod(INFO,N+1). */
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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 zlaed0_(integer *qsiz, integer *n, doublereal *d__,
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doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore,
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integer *ldqs, 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, qstore_dim1, qstore_offset, i__1, i__2;
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doublereal d__1;
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/* Builtin functions */
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double log(doublereal);
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integer pow_ii(integer *, integer *);
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/* Local variables */
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integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2;
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doublereal temp;
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integer curr, iperm;
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *);
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integer indxq, iwrem, iqptr, tlvls;
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extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
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doublecomplex *, integer *), zlaed7_(integer *, integer *,
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integer *, integer *, integer *, integer *, doublereal *,
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doublecomplex *, integer *, doublereal *, integer *, doublereal *,
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integer *, integer *, integer *, integer *, integer *,
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doublereal *, doublecomplex *, doublereal *, integer *, integer *)
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;
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integer igivcl;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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extern /* Subroutine */ int zlacrm_(integer *, integer *, doublecomplex *,
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integer *, doublereal *, integer *, doublecomplex *, integer *,
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doublereal *);
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integer igivnm, submat, curprb, subpbs, igivpt;
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extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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ftnlen);
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integer curlvl, matsiz, iprmpt, smlsiz;
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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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/* Warning: N could be as big as QSIZ! */
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/* .. Parameters .. */
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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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/* .. External Functions .. */
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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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--e;
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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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qstore_dim1 = *ldqs;
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qstore_offset = 1 + qstore_dim1;
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qstore -= qstore_offset;
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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. 2 ) THEN */
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/* INFO = -1 */
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/* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) */
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/* $ THEN */
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if (*qsiz < max(0,*n)) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*ldq < max(1,*n)) {
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*info = -6;
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} else if (*ldqs < max(1,*n)) {
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*info = -8;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"ZLAED0", &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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smlsiz = ilaenv_(&c__9, (char *)"ZLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, (
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ftnlen)6, (ftnlen)1);
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/* Determine the size and placement of the submatrices, and save in */
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/* the leading elements of IWORK. */
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iwork[1] = *n;
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subpbs = 1;
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tlvls = 0;
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L10:
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if (iwork[subpbs] > smlsiz) {
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for (j = subpbs; j >= 1; --j) {
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iwork[j * 2] = (iwork[j] + 1) / 2;
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iwork[(j << 1) - 1] = iwork[j] / 2;
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/* L20: */
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}
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++tlvls;
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subpbs <<= 1;
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goto L10;
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}
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i__1 = subpbs;
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for (j = 2; j <= i__1; ++j) {
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iwork[j] += iwork[j - 1];
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/* L30: */
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}
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/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */
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/* using rank-1 modifications (cuts). */
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spm1 = subpbs - 1;
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i__1 = spm1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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submat = iwork[i__] + 1;
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smm1 = submat - 1;
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d__[smm1] -= (d__1 = e[smm1], abs(d__1));
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d__[submat] -= (d__1 = e[smm1], abs(d__1));
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/* L40: */
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}
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indxq = (*n << 2) + 3;
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/* Set up workspaces for eigenvalues only/accumulate new vectors */
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/* routine */
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temp = log((doublereal) (*n)) / log(2.);
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lgn = (integer) temp;
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if (pow_ii(&c__2, &lgn) < *n) {
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++lgn;
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}
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if (pow_ii(&c__2, &lgn) < *n) {
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++lgn;
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}
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iprmpt = indxq + *n + 1;
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iperm = iprmpt + *n * lgn;
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iqptr = iperm + *n * lgn;
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igivpt = iqptr + *n + 2;
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igivcl = igivpt + *n * lgn;
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igivnm = 1;
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iq = igivnm + (*n << 1) * lgn;
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/* Computing 2nd power */
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i__1 = *n;
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iwrem = iq + i__1 * i__1 + 1;
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/* Initialize pointers */
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i__1 = subpbs;
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for (i__ = 0; i__ <= i__1; ++i__) {
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iwork[iprmpt + i__] = 1;
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iwork[igivpt + i__] = 1;
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/* L50: */
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}
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iwork[iqptr] = 1;
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/* Solve each submatrix eigenproblem at the bottom of the divide and */
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/* conquer tree. */
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curr = 0;
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i__1 = spm1;
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for (i__ = 0; i__ <= i__1; ++i__) {
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if (i__ == 0) {
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submat = 1;
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matsiz = iwork[1];
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} else {
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submat = iwork[i__] + 1;
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matsiz = iwork[i__ + 1] - iwork[i__];
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}
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ll = iq - 1 + iwork[iqptr + curr];
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dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, &
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rwork[1], info, (ftnlen)1);
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zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], &
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matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem]
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);
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/* Computing 2nd power */
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i__2 = matsiz;
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iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
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++curr;
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if (*info > 0) {
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*info = submat * (*n + 1) + submat + matsiz - 1;
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return 0;
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}
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k = 1;
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i__2 = iwork[i__ + 1];
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for (j = submat; j <= i__2; ++j) {
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iwork[indxq + j] = k;
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++k;
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/* L60: */
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}
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/* L70: */
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}
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/* Successively merge eigensystems of adjacent submatrices */
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/* into eigensystem for the corresponding larger matrix. */
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/* while ( SUBPBS > 1 ) */
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curlvl = 1;
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L80:
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if (subpbs > 1) {
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spm2 = subpbs - 2;
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i__1 = spm2;
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for (i__ = 0; i__ <= i__1; i__ += 2) {
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if (i__ == 0) {
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submat = 1;
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matsiz = iwork[2];
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msd2 = iwork[1];
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curprb = 0;
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} else {
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submat = iwork[i__] + 1;
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matsiz = iwork[i__ + 2] - iwork[i__];
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msd2 = matsiz / 2;
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++curprb;
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}
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/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */
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/* into an eigensystem of size MATSIZ. ZLAED7 handles the case */
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/* when the eigenvectors of a full or band Hermitian matrix (which */
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/* was reduced to tridiagonal form) are desired. */
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/* I am free to use Q as a valuable working space until Loop 150. */
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zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[
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submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[
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submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], &
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iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[
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igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat *
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q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info);
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if (*info > 0) {
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*info = submat * (*n + 1) + submat + matsiz - 1;
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return 0;
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}
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iwork[i__ / 2 + 1] = iwork[i__ + 2];
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/* L90: */
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}
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subpbs /= 2;
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++curlvl;
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goto L80;
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}
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/* end while */
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/* Re-merge the eigenvalues/vectors which were deflated at the final */
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/* merge step. */
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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j = iwork[indxq + i__];
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rwork[i__] = d__[j];
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zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1]
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, &c__1);
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/* L100: */
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}
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dcopy_(n, &rwork[1], &c__1, &d__[1], &c__1);
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return 0;
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/* End of ZLAED0 */
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} /* zlaed0_ */
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#ifdef __cplusplus
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}
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#endif
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