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338 lines
8.5 KiB
338 lines
8.5 KiB
#include "clapack.h" |
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/* Subroutine */ int dlazq3_(integer *i0, integer *n0, doublereal *z__, |
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integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, |
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doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, |
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logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, |
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doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *tau) |
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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 g, s, t; |
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integer j4, nn; |
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doublereal eps, tol; |
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integer n0in, ipn4; |
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doublereal tol2, temp; |
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extern /* Subroutine */ int dlasq5_(integer *, integer *, doublereal *, |
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integer *, doublereal *, doublereal *, doublereal *, doublereal *, |
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doublereal *, doublereal *, doublereal *, logical *), dlasq6_( |
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integer *, integer *, doublereal *, integer *, doublereal *, |
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doublereal *, doublereal *, doublereal *, doublereal *, |
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doublereal *), dlazq4_(integer *, integer *, doublereal *, |
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integer *, integer *, doublereal *, doublereal *, doublereal *, |
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doublereal *, doublereal *, doublereal *, doublereal *, integer *, |
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doublereal *); |
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extern doublereal dlamch_(char *); |
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doublereal safmin; |
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/* -- LAPACK auxiliary routine (version 3.1) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* DLAZQ3 checks for deflation, computes a shift (TAU) and calls dqds. */ |
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/* In case of failure it changes shifts, and tries again until output */ |
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/* is positive. */ |
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/* Arguments */ |
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/* ========= */ |
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/* I0 (input) INTEGER */ |
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/* First index. */ |
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/* N0 (input) INTEGER */ |
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/* Last index. */ |
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/* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) */ |
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/* Z holds the qd array. */ |
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/* PP (input) INTEGER */ |
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/* PP=0 for ping, PP=1 for pong. */ |
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/* DMIN (output) DOUBLE PRECISION */ |
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/* Minimum value of d. */ |
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/* SIGMA (output) DOUBLE PRECISION */ |
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/* Sum of shifts used in current segment. */ |
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/* DESIG (input/output) DOUBLE PRECISION */ |
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/* Lower order part of SIGMA */ |
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/* QMAX (input) DOUBLE PRECISION */ |
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/* Maximum value of q. */ |
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/* NFAIL (output) INTEGER */ |
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/* Number of times shift was too big. */ |
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/* ITER (output) INTEGER */ |
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/* Number of iterations. */ |
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/* NDIV (output) INTEGER */ |
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/* Number of divisions. */ |
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/* IEEE (input) LOGICAL */ |
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/* Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */ |
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/* TTYPE (input/output) INTEGER */ |
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/* Shift type. TTYPE is passed as an argument in order to save */ |
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/* its value between calls to DLAZQ3 */ |
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/* DMIN1 (input/output) REAL */ |
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/* DMIN2 (input/output) REAL */ |
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/* DN (input/output) REAL */ |
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/* DN1 (input/output) REAL */ |
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/* DN2 (input/output) REAL */ |
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/* TAU (input/output) REAL */ |
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/* These are passed as arguments in order to save their values */ |
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/* between calls to DLAZQ3 */ |
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/* This is a thread safe version of DLASQ3, which passes TTYPE, DMIN1, */ |
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/* DMIN2, DN, DN1. DN2 and TAU through the argument list in place of */ |
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/* declaring them in a SAVE statment. */ |
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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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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. External Function .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Parameter adjustments */ |
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--z__; |
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/* Function Body */ |
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n0in = *n0; |
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eps = dlamch_("Precision"); |
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safmin = dlamch_("Safe minimum"); |
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tol = eps * 100.; |
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/* Computing 2nd power */ |
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d__1 = tol; |
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tol2 = d__1 * d__1; |
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g = 0.; |
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/* Check for deflation. */ |
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L10: |
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if (*n0 < *i0) { |
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return 0; |
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} |
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if (*n0 == *i0) { |
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goto L20; |
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} |
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nn = (*n0 << 2) + *pp; |
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if (*n0 == *i0 + 1) { |
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goto L40; |
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} |
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/* Check whether E(N0-1) is negligible, 1 eigenvalue. */ |
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if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - |
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4] > tol2 * z__[nn - 7]) { |
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goto L30; |
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} |
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L20: |
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z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma; |
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--(*n0); |
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goto L10; |
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/* Check whether E(N0-2) is negligible, 2 eigenvalues. */ |
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L30: |
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if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[ |
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nn - 11]) { |
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goto L50; |
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} |
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L40: |
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if (z__[nn - 3] > z__[nn - 7]) { |
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s = z__[nn - 3]; |
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z__[nn - 3] = z__[nn - 7]; |
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z__[nn - 7] = s; |
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} |
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if (z__[nn - 5] > z__[nn - 3] * tol2) { |
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t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5; |
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s = z__[nn - 3] * (z__[nn - 5] / t); |
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if (s <= t) { |
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s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.))); |
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} else { |
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s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s))); |
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} |
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t = z__[nn - 7] + (s + z__[nn - 5]); |
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z__[nn - 3] *= z__[nn - 7] / t; |
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z__[nn - 7] = t; |
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} |
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z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma; |
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z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma; |
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*n0 += -2; |
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goto L10; |
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L50: |
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/* Reverse the qd-array, if warranted. */ |
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if (*dmin__ <= 0. || *n0 < n0in) { |
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if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) { |
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ipn4 = *i0 + *n0 << 2; |
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i__1 = *i0 + *n0 - 1 << 1; |
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for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { |
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temp = z__[j4 - 3]; |
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z__[j4 - 3] = z__[ipn4 - j4 - 3]; |
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z__[ipn4 - j4 - 3] = temp; |
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temp = z__[j4 - 2]; |
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z__[j4 - 2] = z__[ipn4 - j4 - 2]; |
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z__[ipn4 - j4 - 2] = temp; |
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temp = z__[j4 - 1]; |
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z__[j4 - 1] = z__[ipn4 - j4 - 5]; |
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z__[ipn4 - j4 - 5] = temp; |
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temp = z__[j4]; |
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z__[j4] = z__[ipn4 - j4 - 4]; |
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z__[ipn4 - j4 - 4] = temp; |
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/* L60: */ |
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} |
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if (*n0 - *i0 <= 4) { |
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z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; |
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z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; |
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} |
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/* Computing MIN */ |
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d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1]; |
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*dmin2 = min(d__1,d__2); |
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/* Computing MIN */ |
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d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1] |
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, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; |
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z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2); |
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/* Computing MIN */ |
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d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = |
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min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4]; |
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z__[(*n0 << 2) - *pp] = min(d__1,d__2); |
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/* Computing MAX */ |
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d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, |
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d__2), d__2 = z__[(*i0 << 2) + *pp + 1]; |
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*qmax = max(d__1,d__2); |
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*dmin__ = -0.; |
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} |
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} |
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/* Computing MIN */ |
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d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*n0 << 2) + *pp - 9], d__1 = |
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min(d__1,d__2), d__2 = *dmin2 + z__[(*n0 << 2) - *pp]; |
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if (*dmin__ < 0. || safmin * *qmax < min(d__1,d__2)) { |
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/* Choose a shift. */ |
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dlazq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, |
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dn2, tau, ttype, &g); |
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/* Call dqds until DMIN > 0. */ |
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L80: |
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dlasq5_(i0, n0, &z__[1], pp, tau, dmin__, dmin1, dmin2, dn, dn1, dn2, |
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ieee); |
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*ndiv += *n0 - *i0 + 2; |
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++(*iter); |
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/* Check status. */ |
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if (*dmin__ >= 0. && *dmin1 > 0.) { |
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/* Success. */ |
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goto L100; |
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} else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < |
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tol * (*sigma + *dn1) && abs(*dn) < tol * *sigma) { |
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/* Convergence hidden by negative DN. */ |
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z__[(*n0 - 1 << 2) - *pp + 2] = 0.; |
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*dmin__ = 0.; |
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goto L100; |
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} else if (*dmin__ < 0.) { |
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/* TAU too big. Select new TAU and try again. */ |
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++(*nfail); |
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if (*ttype < -22) { |
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/* Failed twice. Play it safe. */ |
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*tau = 0.; |
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} else if (*dmin1 > 0.) { |
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/* Late failure. Gives excellent shift. */ |
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*tau = (*tau + *dmin__) * (1. - eps * 2.); |
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*ttype += -11; |
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} else { |
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/* Early failure. Divide by 4. */ |
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*tau *= .25; |
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*ttype += -12; |
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} |
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goto L80; |
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} else if (*dmin__ != *dmin__) { |
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/* NaN. */ |
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*tau = 0.; |
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goto L80; |
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} else { |
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/* Possible underflow. Play it safe. */ |
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goto L90; |
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} |
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} |
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/* Risk of underflow. */ |
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L90: |
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dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2); |
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*ndiv += *n0 - *i0 + 2; |
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++(*iter); |
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*tau = 0.; |
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L100: |
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if (*tau < *sigma) { |
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*desig += *tau; |
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t = *sigma + *desig; |
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*desig -= t - *sigma; |
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} else { |
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t = *sigma + *tau; |
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*desig = *sigma - (t - *tau) + *desig; |
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} |
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*sigma = t; |
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return 0; |
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/* End of DLAZQ3 */ |
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} /* dlazq3_ */
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