--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int dlazq3_(integer *i0, integer *n0, doublereal *z__,
+ integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
+ doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
+ logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2,
+ doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *tau)
+{
+ /* System generated locals */
+ integer i__1;
+ doublereal d__1, d__2;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ doublereal g, s, t;
+ integer j4, nn;
+ doublereal eps, tol;
+ integer n0in, ipn4;
+ doublereal tol2, temp;
+ extern /* Subroutine */ int dlasq5_(integer *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, logical *), dlasq6_(
+ integer *, integer *, doublereal *, integer *, doublereal *,
+ doublereal *, doublereal *, doublereal *, doublereal *,
+ doublereal *), dlazq4_(integer *, integer *, doublereal *,
+ integer *, integer *, doublereal *, doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, doublereal *, integer *,
+ 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 */
+/* ======= */
+
+/* DLAZQ3 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. */
+
+/* IEEE (input) LOGICAL */
+/* Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */
+
+/* TTYPE (input/output) INTEGER */
+/* Shift type. TTYPE is passed as an argument in order to save */
+/* its value between calls to DLAZQ3 */
+
+/* DMIN1 (input/output) REAL */
+/* DMIN2 (input/output) REAL */
+/* DN (input/output) REAL */
+/* DN1 (input/output) REAL */
+/* DN2 (input/output) REAL */
+/* TAU (input/output) REAL */
+/* These are passed as arguments in order to save their values */
+/* between calls to DLAZQ3 */
+
+/* This is a thread safe version of DLASQ3, which passes TTYPE, DMIN1, */
+/* DMIN2, DN, DN1. DN2 and TAU through the argument list in place of */
+/* declaring them in a SAVE statment. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Function .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --z__;
+
+ /* Function Body */
+ n0in = *n0;
+ eps = dlamch_("Precision");
+ safmin = dlamch_("Safe minimum");
+ tol = eps * 100.;
+/* Computing 2nd power */
+ d__1 = tol;
+ tol2 = d__1 * d__1;
+ g = 0.;
+
+/* 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. */
+
+ dlazq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1,
+ dn2, tau, ttype, &g);
+
+/* 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 DLAZQ3 */
+
+} /* dlazq3_ */
projects / opencv / blobdiff