--- /dev/null
+#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)
+{
+ /* Initialized data */
+
+ static integer ttype = 0;
+ static real dmin1 = 0.f;
+ static real dmin2 = 0.f;
+ static real dn = 0.f;
+ static real dn1 = 0.f;
+ static real dn2 = 0.f;
+ static real tau = 0.f;
+
+ /* 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 *), 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 *);
+ real safmin;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. 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) INTEGER */
+/* PP=0 for ping, PP=1 for pong. */
+
+/* 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. */
+
+/* TTYPE (output) INTEGER */
+/* Shift type. */
+
+/* IEEE (input) LOGICAL */
+/* Flag for IEEE or non IEEE arithmetic (passed to SLASQ5). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Function .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statement .. */
+ /* Parameter adjustments */
+ --z__;
+
+ /* Function Body */
+/* .. */
+/* .. Executable Statements .. */
+
+ n0in = *n0;
+ eps = slamch_("Precision");
+ safmin = slamch_("Safe minimum");
+ 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:
+
+/* 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;
+ }
+ }
+
+/* Computing MIN */
+ r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*n0 << 2) + *pp - 9], r__1 =
+ min(r__1,r__2), r__2 = dmin2 + z__[(*n0 << 2) - *pp];
+ if (*dmin__ < 0.f || safmin * *qmax < dmin(r__1,r__2)) {
+
+/* Choose a shift. */
+
+ slasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, &dmin1, &dmin2, &dn, &dn1,
+ &dn2, &tau, &ttype);
+
+/* Call dqds until DMIN > 0. */
+
+L80:
+
+ 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 L100;
+
+ } 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 L100;
+ } 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 L80;
+ } else if (*dmin__ != *dmin__) {
+
+/* NaN. */
+
+ tau = 0.f;
+ goto L80;
+ } else {
+
+/* Possible underflow. Play it safe. */
+
+ goto L90;
+ }
+ }
+
+/* Risk of underflow. */
+
+L90:
+ slasq6_(i0, n0, &z__[1], pp, dmin__, &dmin1, &dmin2, &dn, &dn1, &dn2);
+ *ndiv += *n0 - *i0 + 2;
+ ++(*iter);
+ tau = 0.f;
+
+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 SLASQ3 */
+
+} /* slasq3_ */
projects / opencv / blobdiff