+/* The MIT License
+
+ Copyright (c) 2008, 2010 by Attractive Chaos <attractor@live.co.uk>
+
+ Permission is hereby granted, free of charge, to any person obtaining
+ a copy of this software and associated documentation files (the
+ "Software"), to deal in the Software without restriction, including
+ without limitation the rights to use, copy, modify, merge, publish,
+ distribute, sublicense, and/or sell copies of the Software, and to
+ permit persons to whom the Software is furnished to do so, subject to
+ the following conditions:
+
+ The above copyright notice and this permission notice shall be
+ included in all copies or substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ SOFTWARE.
+*/
+
+/* Hooke-Jeeves algorithm for nonlinear minimization
+
+ Based on the pseudocodes by Bell and Pike (CACM 9(9):684-685), and
+ the revision by Tomlin and Smith (CACM 12(11):637-638). Both of the
+ papers are comments on Kaupe's Algorithm 178 "Direct Search" (ACM
+ 6(6):313-314). The original algorithm was designed by Hooke and
+ Jeeves (ACM 8:212-229). This program is further revised according to
+ Johnson's implementation at Netlib (opt/hooke.c).
+
+ Hooke-Jeeves algorithm is very simple and it works quite well on a
+ few examples. However, it might fail to converge due to its heuristic
+ nature. A possible improvement, as is suggested by Johnson, may be to
+ choose a small r at the beginning to quickly approach to the minimum
+ and a large r at later step to hit the minimum.
+ */
+
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include "kmin.h"
+
+static double __kmin_hj_aux(kmin_f func, int n, double *x1, void *data, double fx1, double *dx, int *n_calls)
+{
+ int k, j = *n_calls;
+ double ftmp;
+ for (k = 0; k != n; ++k) {
+ x1[k] += dx[k];
+ ftmp = func(n, x1, data); ++j;
+ if (ftmp < fx1) fx1 = ftmp;
+ else { /* search the opposite direction */
+ dx[k] = 0.0 - dx[k];
+ x1[k] += dx[k] + dx[k];
+ ftmp = func(n, x1, data); ++j;
+ if (ftmp < fx1) fx1 = ftmp;
+ else x1[k] -= dx[k]; /* back to the original x[k] */
+ }
+ }
+ *n_calls = j;
+ return fx1; /* here: fx1=f(n,x1) */
+}
+
+double kmin_hj(kmin_f func, int n, double *x, void *data, double r, double eps, int max_calls)
+{
+ double fx, fx1, *x1, *dx, radius;
+ int k, n_calls = 0;
+ x1 = (double*)calloc(n, sizeof(double));
+ dx = (double*)calloc(n, sizeof(double));
+ for (k = 0; k != n; ++k) { /* initial directions, based on MGJ */
+ dx[k] = fabs(x[k]) * r;
+ if (dx[k] == 0) dx[k] = r;
+ }
+ radius = r;
+ fx1 = fx = func(n, x, data); ++n_calls;
+ for (;;) {
+ memcpy(x1, x, n * sizeof(double)); /* x1 = x */
+ fx1 = __kmin_hj_aux(func, n, x1, data, fx, dx, &n_calls);
+ while (fx1 < fx) {
+ for (k = 0; k != n; ++k) {
+ double t = x[k];
+ dx[k] = x1[k] > x[k]? fabs(dx[k]) : 0.0 - fabs(dx[k]);
+ x[k] = x1[k];
+ x1[k] = x1[k] + x1[k] - t;
+ }
+ fx = fx1;
+ if (n_calls >= max_calls) break;
+ fx1 = func(n, x1, data); ++n_calls;
+ fx1 = __kmin_hj_aux(func, n, x1, data, fx1, dx, &n_calls);
+ if (fx1 >= fx) break;
+ for (k = 0; k != n; ++k)
+ if (fabs(x1[k] - x[k]) > .5 * fabs(dx[k])) break;
+ if (k == n) break;
+ }
+ if (radius >= eps) {
+ if (n_calls >= max_calls) break;
+ radius *= r;
+ for (k = 0; k != n; ++k) dx[k] *= r;
+ } else break; /* converge */
+ }
+ free(x1); free(dx);
+ return fx1;
+}
+
+// I copied this function somewhere several years ago with some of my modifications, but I forgot the source.
+double kmin_brent(kmin1_f func, double a, double b, void *data, double tol, double *xmin)
+{
+ double bound, u, r, q, fu, tmp, fa, fb, fc, c;
+ const double gold1 = 1.6180339887;
+ const double gold2 = 0.3819660113;
+ const double tiny = 1e-20;
+ const int max_iter = 100;
+
+ double e, d, w, v, mid, tol1, tol2, p, eold, fv, fw;
+ int iter;
+
+ fa = func(a, data); fb = func(b, data);
+ if (fb > fa) { // swap, such that f(a) > f(b)
+ tmp = a; a = b; b = tmp;
+ tmp = fa; fa = fb; fb = tmp;
+ }
+ c = b + gold1 * (b - a), fc = func(c, data); // golden section extrapolation
+ while (fb > fc) {
+ bound = b + 100.0 * (c - b); // the farthest point where we want to go
+ r = (b - a) * (fb - fc);
+ q = (b - c) * (fb - fa);
+ if (fabs(q - r) < tiny) { // avoid 0 denominator
+ tmp = q > r? tiny : 0.0 - tiny;
+ } else tmp = q - r;
+ u = b - ((b - c) * q - (b - a) * r) / (2.0 * tmp); // u is the parabolic extrapolation point
+ if ((b > u && u > c) || (b < u && u < c)) { // u lies between b and c
+ fu = func(u, data);
+ if (fu < fc) { // (b,u,c) bracket the minimum
+ a = b; b = u; fa = fb; fb = fu;
+ break;
+ } else if (fu > fb) { // (a,b,u) bracket the minimum
+ c = u; fc = fu;
+ break;
+ }
+ u = c + gold1 * (c - b); fu = func(u, data); // golden section extrapolation
+ } else if ((c > u && u > bound) || (c < u && u < bound)) { // u lies between c and bound
+ fu = func(u, data);
+ if (fu < fc) { // fb > fc > fu
+ b = c; c = u; u = c + gold1 * (c - b);
+ fb = fc; fc = fu; fu = func(u, data);
+ } else { // (b,c,u) bracket the minimum
+ a = b; b = c; c = u;
+ fa = fb; fb = fc; fc = fu;
+ break;
+ }
+ } else if ((u > bound && bound > c) || (u < bound && bound < c)) { // u goes beyond the bound
+ u = bound; fu = func(u, data);
+ } else { // u goes the other way around, use golden section extrapolation
+ u = c + gold1 * (c - b); fu = func(u, data);
+ }
+ a = b; b = c; c = u;
+ fa = fb; fb = fc; fc = fu;
+ }
+ if (a > c) u = a, a = c, c = u; // swap
+
+ // now, a<b<c, fa>fb and fb<fc, move on to Brent's algorithm
+ e = d = 0.0;
+ w = v = b; fv = fw = fb;
+ for (iter = 0; iter != max_iter; ++iter) {
+ mid = 0.5 * (a + c);
+ tol2 = 2.0 * (tol1 = tol * fabs(b) + tiny);
+ if (fabs(b - mid) <= (tol2 - 0.5 * (c - a))) {
+ *xmin = b; return fb; // found
+ }
+ if (fabs(e) > tol1) {
+ // related to parabolic interpolation
+ r = (b - w) * (fb - fv);
+ q = (b - v) * (fb - fw);
+ p = (b - v) * q - (b - w) * r;
+ q = 2.0 * (q - r);
+ if (q > 0.0) p = 0.0 - p;
+ else q = 0.0 - q;
+ eold = e; e = d;
+ if (fabs(p) >= fabs(0.5 * q * eold) || p <= q * (a - b) || p >= q * (c - b)) {
+ d = gold2 * (e = (b >= mid ? a - b : c - b));
+ } else {
+ d = p / q; u = b + d; // actual parabolic interpolation happens here
+ if (u - a < tol2 || c - u < tol2)
+ d = (mid > b)? tol1 : 0.0 - tol1;
+ }
+ } else d = gold2 * (e = (b >= mid ? a - b : c - b)); // golden section interpolation
+ u = fabs(d) >= tol1 ? b + d : b + (d > 0.0? tol1 : -tol1);
+ fu = func(u, data);
+ if (fu <= fb) { // u is the minimum point so far
+ if (u >= b) a = b;
+ else c = b;
+ v = w; w = b; b = u; fv = fw; fw = fb; fb = fu;
+ } else { // adjust (a,c) and (u,v,w)
+ if (u < b) a = u;
+ else c = u;
+ if (fu <= fw || w == b) {
+ v = w; w = u;
+ fv = fw; fw = fu;
+ } else if (fu <= fv || v == b || v == w) {
+ v = u; fv = fu;
+ }
+ }
+ }
+ *xmin = b;
+ return fb;
+}
projects / samtools.git / blobdiff