502 lines
14 KiB
C++
502 lines
14 KiB
C++
/* fortran/dlasq4.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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/* > \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous
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transform. Used by sbdsqr. */
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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 DLASQ4 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq4.
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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/dlasq4.
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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/dlasq4.
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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 DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, */
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/* DN1, DN2, TAU, TTYPE, G ) */
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/* .. Scalar Arguments .. */
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/* INTEGER I0, N0, N0IN, PP, TTYPE */
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/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION Z( * ) */
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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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/* > DLASQ4 computes an approximation TAU to the smallest eigenvalue */
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/* > using values of d from the previous transform. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] I0 */
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/* > \verbatim */
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/* > I0 is INTEGER */
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/* > First index. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N0 */
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/* > \verbatim */
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/* > N0 is INTEGER */
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/* > Last index. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] Z */
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/* > \verbatim */
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/* > Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */
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/* > Z holds the qd array. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] PP */
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/* > \verbatim */
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/* > PP is INTEGER */
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/* > PP=0 for ping, PP=1 for pong. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N0IN */
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/* > \verbatim */
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/* > N0IN is INTEGER */
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/* > The value of N0 at start of EIGTEST. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DMIN */
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/* > \verbatim */
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/* > DMIN is DOUBLE PRECISION */
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/* > Minimum value of d. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DMIN1 */
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/* > \verbatim */
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/* > DMIN1 is DOUBLE PRECISION */
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/* > Minimum value of d, excluding D( N0 ). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DMIN2 */
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/* > \verbatim */
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/* > DMIN2 is DOUBLE PRECISION */
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/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DN */
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/* > \verbatim */
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/* > DN is DOUBLE PRECISION */
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/* > d(N) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DN1 */
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/* > \verbatim */
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/* > DN1 is DOUBLE PRECISION */
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/* > d(N-1) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DN2 */
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/* > \verbatim */
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/* > DN2 is DOUBLE PRECISION */
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/* > d(N-2) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION */
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/* > This is the shift. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TTYPE */
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/* > \verbatim */
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/* > TTYPE is INTEGER */
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/* > Shift type. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] G */
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/* > \verbatim */
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/* > G is DOUBLE PRECISION */
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/* > G is passed as an argument in order to save its value between */
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/* > calls to DLASQ4. */
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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 auxOTHERcomputational */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > CNST1 = 9/16 */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__,
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integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1,
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doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2,
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doublereal *tau, integer *ttype, doublereal *g)
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{
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/* System generated locals */
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integer i__1;
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doublereal d__1, d__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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doublereal s, a2, b1, b2;
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integer i4, nn, np;
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doublereal gam, gap1, gap2;
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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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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* A negative DMIN forces the shift to take that absolute value */
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/* TTYPE records the type of shift. */
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/* Parameter adjustments */
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--z__;
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/* Function Body */
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if (*dmin__ <= 0.) {
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*tau = -(*dmin__);
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*ttype = -1;
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return 0;
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}
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nn = (*n0 << 2) + *pp;
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if (*n0in == *n0) {
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/* No eigenvalues deflated. */
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if (*dmin__ == *dn || *dmin__ == *dn1) {
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b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);
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b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);
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a2 = z__[nn - 7] + z__[nn - 5];
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/* Cases 2 and 3. */
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if (*dmin__ == *dn && *dmin1 == *dn1) {
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gap2 = *dmin2 - a2 - *dmin2 * .25;
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if (gap2 > 0. && gap2 > b2) {
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gap1 = a2 - *dn - b2 / gap2 * b2;
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} else {
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gap1 = a2 - *dn - (b1 + b2);
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}
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if (gap1 > 0. && gap1 > b1) {
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/* Computing MAX */
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d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5;
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s = max(d__1,d__2);
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*ttype = -2;
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} else {
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s = 0.;
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if (*dn > b1) {
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s = *dn - b1;
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}
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if (a2 > b1 + b2) {
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/* Computing MIN */
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d__1 = s, d__2 = a2 - (b1 + b2);
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s = min(d__1,d__2);
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}
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/* Computing MAX */
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d__1 = s, d__2 = *dmin__ * .333;
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s = max(d__1,d__2);
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*ttype = -3;
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}
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} else {
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/* Case 4. */
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*ttype = -4;
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s = *dmin__ * .25;
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if (*dmin__ == *dn) {
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gam = *dn;
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a2 = 0.;
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if (z__[nn - 5] > z__[nn - 7]) {
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return 0;
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}
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b2 = z__[nn - 5] / z__[nn - 7];
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np = nn - 9;
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} else {
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np = nn - (*pp << 1);
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gam = *dn1;
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if (z__[np - 4] > z__[np - 2]) {
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return 0;
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}
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a2 = z__[np - 4] / z__[np - 2];
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if (z__[nn - 9] > z__[nn - 11]) {
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return 0;
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}
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b2 = z__[nn - 9] / z__[nn - 11];
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np = nn - 13;
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}
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/* Approximate contribution to norm squared from I < NN-1. */
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a2 += b2;
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = np; i4 >= i__1; i4 += -4) {
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if (b2 == 0.) {
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goto L20;
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}
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b1 = b2;
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b2 *= z__[i4] / z__[i4 - 2];
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a2 += b2;
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if (max(b2,b1) * 100. < a2 || .563 < a2) {
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goto L20;
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}
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/* L10: */
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}
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L20:
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a2 *= 1.05;
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/* Rayleigh quotient residual bound. */
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if (a2 < .563) {
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s = gam * (1. - sqrt(a2)) / (a2 + 1.);
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}
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}
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} else if (*dmin__ == *dn2) {
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/* Case 5. */
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*ttype = -5;
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s = *dmin__ * .25;
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/* Compute contribution to norm squared from I > NN-2. */
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np = nn - (*pp << 1);
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b1 = z__[np - 2];
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b2 = z__[np - 6];
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gam = *dn2;
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if (z__[np - 8] > b2 || z__[np - 4] > b1) {
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return 0;
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}
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a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.);
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/* Approximate contribution to norm squared from I < NN-2. */
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if (*n0 - *i0 > 2) {
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b2 = z__[nn - 13] / z__[nn - 15];
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a2 += b2;
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = nn - 17; i4 >= i__1; i4 += -4) {
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if (b2 == 0.) {
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goto L40;
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}
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b1 = b2;
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b2 *= z__[i4] / z__[i4 - 2];
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a2 += b2;
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if (max(b2,b1) * 100. < a2 || .563 < a2) {
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goto L40;
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}
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/* L30: */
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}
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L40:
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a2 *= 1.05;
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}
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if (a2 < .563) {
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s = gam * (1. - sqrt(a2)) / (a2 + 1.);
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}
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} else {
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/* Case 6, no information to guide us. */
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if (*ttype == -6) {
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*g += (1. - *g) * .333;
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} else if (*ttype == -18) {
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*g = .083250000000000005;
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} else {
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*g = .25;
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}
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s = *g * *dmin__;
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*ttype = -6;
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}
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} else if (*n0in == *n0 + 1) {
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/* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */
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if (*dmin1 == *dn1 && *dmin2 == *dn2) {
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/* Cases 7 and 8. */
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*ttype = -7;
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s = *dmin1 * .333;
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if (z__[nn - 5] > z__[nn - 7]) {
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return 0;
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}
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b1 = z__[nn - 5] / z__[nn - 7];
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b2 = b1;
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if (b2 == 0.) {
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goto L60;
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}
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
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a2 = b1;
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b1 *= z__[i4] / z__[i4 - 2];
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b2 += b1;
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if (max(b1,a2) * 100. < b2) {
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goto L60;
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}
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/* L50: */
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}
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L60:
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b2 = sqrt(b2 * 1.05);
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/* Computing 2nd power */
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d__1 = b2;
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a2 = *dmin1 / (d__1 * d__1 + 1.);
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gap2 = *dmin2 * .5 - a2;
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if (gap2 > 0. && gap2 > b2 * a2) {
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/* Computing MAX */
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d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2);
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s = max(d__1,d__2);
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} else {
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/* Computing MAX */
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d__1 = s, d__2 = a2 * (1. - b2 * 1.01);
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s = max(d__1,d__2);
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*ttype = -8;
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}
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} else {
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/* Case 9. */
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s = *dmin1 * .25;
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if (*dmin1 == *dn1) {
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s = *dmin1 * .5;
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}
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*ttype = -9;
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}
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} else if (*n0in == *n0 + 2) {
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/* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */
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/* Cases 10 and 11. */
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if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) {
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*ttype = -10;
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s = *dmin2 * .333;
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if (z__[nn - 5] > z__[nn - 7]) {
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return 0;
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}
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b1 = z__[nn - 5] / z__[nn - 7];
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b2 = b1;
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if (b2 == 0.) {
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goto L80;
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}
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i__1 = (*i0 << 2) - 1 + *pp;
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for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
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if (z__[i4] > z__[i4 - 2]) {
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return 0;
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}
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b1 *= z__[i4] / z__[i4 - 2];
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b2 += b1;
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if (b1 * 100. < b2) {
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goto L80;
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}
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/* L70: */
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}
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L80:
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b2 = sqrt(b2 * 1.05);
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/* Computing 2nd power */
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d__1 = b2;
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a2 = *dmin2 / (d__1 * d__1 + 1.);
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gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
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nn - 9]) - a2;
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if (gap2 > 0. && gap2 > b2 * a2) {
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/* Computing MAX */
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d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2);
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s = max(d__1,d__2);
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} else {
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/* Computing MAX */
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d__1 = s, d__2 = a2 * (1. - b2 * 1.01);
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s = max(d__1,d__2);
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}
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} else {
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s = *dmin2 * .25;
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*ttype = -11;
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}
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} else if (*n0in > *n0 + 2) {
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/* Case 12, more than two eigenvalues deflated. No information. */
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s = 0.;
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*ttype = -12;
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}
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*tau = s;
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return 0;
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/* End of DLASQ4 */
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} /* dlasq4_ */
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#ifdef __cplusplus
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}
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#endif
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