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opencv/3rdparty/lapack/slasq3.c

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/* slasq3.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "clapack.h"
/* Subroutine */ int slasq3_(integer *i0, integer *n0, real *z__, integer *pp,
real *dmin__, real *sigma, real *desig, real *qmax, integer *nfail,
integer *iter, integer *ndiv, logical *ieee, integer *ttype, real *
dmin1, real *dmin2, real *dn, real *dn1, real *dn2, real *g, real *
tau)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real s, t;
integer j4, nn;
real eps, tol;
integer n0in, ipn4;
real tol2, temp;
extern /* Subroutine */ int slasq4_(integer *, integer *, real *, integer
*, integer *, real *, real *, real *, real *, real *, real *,
real *, integer *, real *), slasq5_(integer *, integer *, real *,
integer *, real *, real *, real *, real *, real *, real *, real *,
logical *), slasq6_(integer *, integer *, real *, integer *,
real *, real *, real *, real *, real *, real *);
extern doublereal slamch_(char *);
extern logical sisnan_(real *);
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */
/* -- Laboratory and Beresford Parlett of the Univ. of California at -- */
/* -- Berkeley -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLASQ3 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) REAL array, dimension ( 4*N ) */
/* Z holds the qd array. */
/* PP (input/output) INTEGER */
/* PP=0 for ping, PP=1 for pong. */
/* PP=2 indicates that flipping was applied to the Z array */
/* and that the initial tests for deflation should not be */
/* performed. */
/* DMIN (output) REAL */
/* Minimum value of d. */
/* SIGMA (output) REAL */
/* Sum of shifts used in current segment. */
/* DESIG (input/output) REAL */
/* Lower order part of SIGMA */
/* QMAX (input) REAL */
/* 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. */
/* IEEE (input) LOGICAL */
/* Flag for IEEE or non IEEE arithmetic (passed to SLASQ5). */
/* TTYPE (input/output) INTEGER */
/* Shift type. */
/* DMIN1, DMIN2, DN, DN1, DN2, G, TAU (input/output) REAL */
/* These are passed as arguments in order to save their values */
/* between calls to SLASQ3. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Function .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--z__;
/* Function Body */
n0in = *n0;
eps = slamch_("Precision");
tol = eps * 100.f;
/* Computing 2nd power */
r__1 = tol;
tol2 = r__1 * r__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]) * .5f;
s = z__[nn - 3] * (z__[nn - 5] / t);
if (s <= t) {
s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.f) + 1.f)));
} 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:
if (*pp == 2) {
*pp = 0;
}
/* Reverse the qd-array, if warranted. */
if (*dmin__ <= 0.f || *n0 < n0in) {
if (z__[(*i0 << 2) + *pp - 3] * 1.5f < 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 */
r__1 = *dmin2, r__2 = z__[(*n0 << 2) + *pp - 1];
*dmin2 = dmin(r__1,r__2);
/* Computing MIN */
r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*i0 << 2) + *pp - 1]
, r__1 = min(r__1,r__2), r__2 = z__[(*i0 << 2) + *pp + 3];
z__[(*n0 << 2) + *pp - 1] = dmin(r__1,r__2);
/* Computing MIN */
r__1 = z__[(*n0 << 2) - *pp], r__2 = z__[(*i0 << 2) - *pp], r__1 =
min(r__1,r__2), r__2 = z__[(*i0 << 2) - *pp + 4];
z__[(*n0 << 2) - *pp] = dmin(r__1,r__2);
/* Computing MAX */
r__1 = *qmax, r__2 = z__[(*i0 << 2) + *pp - 3], r__1 = max(r__1,
r__2), r__2 = z__[(*i0 << 2) + *pp + 1];
*qmax = dmax(r__1,r__2);
*dmin__ = -0.f;
}
}
/* Choose a shift. */
slasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2,
tau, ttype, g);
/* Call dqds until DMIN > 0. */
L70:
slasq5_(i0, n0, &z__[1], pp, tau, dmin__, dmin1, dmin2, dn, dn1, dn2,
ieee);
*ndiv += *n0 - *i0 + 2;
++(*iter);
/* Check status. */
if (*dmin__ >= 0.f && *dmin1 > 0.f) {
/* Success. */
goto L90;
} else if (*dmin__ < 0.f && *dmin1 > 0.f && z__[(*n0 - 1 << 2) - *pp] <
tol * (*sigma + *dn1) && dabs(*dn) < tol * *sigma) {
/* Convergence hidden by negative DN. */
z__[(*n0 - 1 << 2) - *pp + 2] = 0.f;
*dmin__ = 0.f;
goto L90;
} else if (*dmin__ < 0.f) {
/* TAU too big. Select new TAU and try again. */
++(*nfail);
if (*ttype < -22) {
/* Failed twice. Play it safe. */
*tau = 0.f;
} else if (*dmin1 > 0.f) {
/* Late failure. Gives excellent shift. */
*tau = (*tau + *dmin__) * (1.f - eps * 2.f);
*ttype += -11;
} else {
/* Early failure. Divide by 4. */
*tau *= .25f;
*ttype += -12;
}
goto L70;
} else if (sisnan_(dmin__)) {
/* NaN. */
if (*tau == 0.f) {
goto L80;
} else {
*tau = 0.f;
goto L70;
}
} else {
/* Possible underflow. Play it safe. */
goto L80;
}
/* Risk of underflow. */
L80:
slasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);
*ndiv += *n0 - *i0 + 2;
++(*iter);
*tau = 0.f;
L90:
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 SLASQ3 */
} /* slasq3_ */
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