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opencv/3rdparty/lapack/dlasq3.c

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#include "clapack.h"
/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
logical *ieee)
{
/* Initialized data */
static integer ttype = 0;
static doublereal dmin1 = 0.;
static doublereal dmin2 = 0.;
static doublereal dn = 0.;
static doublereal dn1 = 0.;
static doublereal dn2 = 0.;
static doublereal tau = 0.;
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal s, t;
integer j4, nn;
doublereal eps, tol;
integer n0in, ipn4;
doublereal tol2, temp;
extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *)
, dlasq5_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, logical *), dlasq6_(
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
extern doublereal dlamch_(char *);
doublereal safmin;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */
/* In case of failure it changes shifts, and tries again until output */
/* is positive. */
/* Arguments */
/* ========= */
/* I0 (input) INTEGER */
/* First index. */
/* N0 (input) INTEGER */
/* Last index. */
/* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) */
/* Z holds the qd array. */
/* PP (input) INTEGER */
/* PP=0 for ping, PP=1 for pong. */
/* DMIN (output) DOUBLE PRECISION */
/* Minimum value of d. */
/* SIGMA (output) DOUBLE PRECISION */
/* Sum of shifts used in current segment. */
/* DESIG (input/output) DOUBLE PRECISION */
/* Lower order part of SIGMA */
/* QMAX (input) DOUBLE PRECISION */
/* Maximum value of q. */
/* NFAIL (output) INTEGER */
/* Number of times shift was too big. */
/* ITER (output) INTEGER */
/* Number of iterations. */
/* NDIV (output) INTEGER */
/* Number of divisions. */
/* TTYPE (output) INTEGER */
/* Shift type. */
/* IEEE (input) LOGICAL */
/* Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Function .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Save statement .. */
/* .. */
/* .. Data statement .. */
/* Parameter adjustments */
--z__;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
n0in = *n0;
eps = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
tol = eps * 100.;
/* Computing 2nd power */
d__1 = tol;
tol2 = d__1 * d__1;
/* Check for deflation. */
L10:
if (*n0 < *i0) {
return 0;
}
if (*n0 == *i0) {
goto L20;
}
nn = (*n0 << 2) + *pp;
if (*n0 == *i0 + 1) {
goto L40;
}
/* Check whether E(N0-1) is negligible, 1 eigenvalue. */
if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
4] > tol2 * z__[nn - 7]) {
goto L30;
}
L20:
z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
--(*n0);
goto L10;
/* Check whether E(N0-2) is negligible, 2 eigenvalues. */
L30:
if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
nn - 11]) {
goto L50;
}
L40:
if (z__[nn - 3] > z__[nn - 7]) {
s = z__[nn - 3];
z__[nn - 3] = z__[nn - 7];
z__[nn - 7] = s;
}
if (z__[nn - 5] > z__[nn - 3] * tol2) {
t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
s = z__[nn - 3] * (z__[nn - 5] / t);
if (s <= t) {
s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
} else {
s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
}
t = z__[nn - 7] + (s + z__[nn - 5]);
z__[nn - 3] *= z__[nn - 7] / t;
z__[nn - 7] = t;
}
z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
*n0 += -2;
goto L10;
L50:
/* Reverse the qd-array, if warranted. */
if (*dmin__ <= 0. || *n0 < n0in) {
if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
ipn4 = *i0 + *n0 << 2;
i__1 = *i0 + *n0 - 1 << 1;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
temp = z__[j4 - 3];
z__[j4 - 3] = z__[ipn4 - j4 - 3];
z__[ipn4 - j4 - 3] = temp;
temp = z__[j4 - 2];
z__[j4 - 2] = z__[ipn4 - j4 - 2];
z__[ipn4 - j4 - 2] = temp;
temp = z__[j4 - 1];
z__[j4 - 1] = z__[ipn4 - j4 - 5];
z__[ipn4 - j4 - 5] = temp;
temp = z__[j4];
z__[j4] = z__[ipn4 - j4 - 4];
z__[ipn4 - j4 - 4] = temp;
/* L60: */
}
if (*n0 - *i0 <= 4) {
z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
}
/* Computing MIN */
d__1 = dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
dmin2 = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
/* Computing MIN */
d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
z__[(*n0 << 2) - *pp] = min(d__1,d__2);
/* Computing MAX */
d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
*qmax = max(d__1,d__2);
*dmin__ = -0.;
}
}
/* Computing MIN */
d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*n0 << 2) + *pp - 9], d__1 =
min(d__1,d__2), d__2 = dmin2 + z__[(*n0 << 2) - *pp];
if (*dmin__ < 0. || safmin * *qmax < min(d__1,d__2)) {
/* Choose a shift. */
dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, &dmin1, &dmin2, &dn, &dn1,
&dn2, &tau, &ttype);
/* Call dqds until DMIN > 0. */
L80:
dlasq5_(i0, n0, &z__[1], pp, &tau, dmin__, &dmin1, &dmin2, &dn, &dn1,
&dn2, ieee);
*ndiv += *n0 - *i0 + 2;
++(*iter);
/* Check status. */
if (*dmin__ >= 0. && dmin1 > 0.) {
/* Success. */
goto L100;
} else if (*dmin__ < 0. && dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] <
tol * (*sigma + dn1) && abs(dn) < tol * *sigma) {
/* Convergence hidden by negative DN. */
z__[(*n0 - 1 << 2) - *pp + 2] = 0.;
*dmin__ = 0.;
goto L100;
} else if (*dmin__ < 0.) {
/* TAU too big. Select new TAU and try again. */
++(*nfail);
if (ttype < -22) {
/* Failed twice. Play it safe. */
tau = 0.;
} else if (dmin1 > 0.) {
/* Late failure. Gives excellent shift. */
tau = (tau + *dmin__) * (1. - eps * 2.);
ttype += -11;
} else {
/* Early failure. Divide by 4. */
tau *= .25;
ttype += -12;
}
goto L80;
} else if (*dmin__ != *dmin__) {
/* NaN. */
tau = 0.;
goto L80;
} else {
/* Possible underflow. Play it safe. */
goto L90;
}
}
/* Risk of underflow. */
L90:
dlasq6_(i0, n0, &z__[1], pp, dmin__, &dmin1, &dmin2, &dn, &dn1, &dn2);
*ndiv += *n0 - *i0 + 2;
++(*iter);
tau = 0.;
L100:
if (tau < *sigma) {
*desig += tau;
t = *sigma + *desig;
*desig -= t - *sigma;
} else {
t = *sigma + tau;
*desig = *sigma - (t - tau) + *desig;
}
*sigma = t;
return 0;
/* End of DLASQ3 */
} /* dlasq3_ */
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