diff options
Diffstat (limited to 'lorenz.c')
-rw-r--r-- | lorenz.c | 396 |
1 files changed, 302 insertions, 94 deletions
@@ -1,8 +1,6 @@ -/////////////////////////////////////////////////////////////////////////////////// -/* Lorenz's Attractor PD External */ -/* Copyright Ben Bogart 2002 */ -/* This program is distributed under the terms of the GNU General Public License */ -/////////////////////////////////////////////////////////////////////////////////// +/* lorenz Attractor PD External */ +/* Copyright Ben Bogart, 2002 */ +/* This program is distributed under the params of the GNU Public License */ /////////////////////////////////////////////////////////////////////////////////// /* This file is part of Chaos PD Externals. */ @@ -22,106 +20,316 @@ /* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ /////////////////////////////////////////////////////////////////////////////////// -#include "m_pd.h" +#include <stdio.h> +#include <stdlib.h> #include <math.h> +#include <time.h> +#include "lyapunov.h" + +#define M_h_lo -1000 +#define M_h_hi 1000 +#define M_a_lo -1000 +#define M_a_hi 1000 +#define M_b_lo -1000 +#define M_b_hi 1000 +#define M_c_lo -1000 +#define M_c_hi 1000 + +#define M_h 0 +#define M_a 1 +#define M_b 2 +#define M_c 3 + +#define M_x 0 +#define M_y 1 +#define M_z 2 + +#define M_param_count 4 +#define M_var_count 3 +#define M_search_count 3 +#define M_failure_limit 1000 + +static char *version = "lorenz v0.0, by Ben Bogart, 2002"; t_class *lorenz_class; -typedef struct lorenz_struct -{ - t_object lorenz_obj; - double h, a, b, c, lx0, ly0, lz0; - t_outlet *y_outlet; - t_outlet *z_outlet; -} lorenz_struct; - -static void calculate(lorenz_struct *x) -{ - double lx0, ly0, lz0, lx1, ly1, lz1; - double h, a, b, c; - - h = x->h; - a = x->a; - b = x->b; - c = x->c; - lx0 = x->lx0; - ly0 = x->ly0; - lz0 = x->lz0; - - lx1 = lx0 + h * a * (ly0 - lx0); - ly1 = ly0 + h * (lx0 * (b - lz0) - ly0); - lz1 = lz0 + h * (lx0 * ly0 - c * lz0); - x->lx0 = lx1; - x->ly0 = ly1; - x->lz0 = lz1; - - outlet_float(x->lorenz_obj.ob_outlet, (t_float)lx1); - outlet_float(x->y_outlet, (t_float)ly1); - outlet_float(x->z_outlet, (t_float)lz1); +typedef struct lorenz_struct { + t_object x_obj; + + double vars[M_var_count]; + double vars_init[M_var_count]; + t_atom vars_out[M_var_count]; + t_outlet *vars_outlet; + + t_atom search_out[M_search_count]; + t_outlet *search_outlet; + + double h, h_lo, h_hi, a, a_lo, a_hi, b, b_lo, b_hi, c, c_lo, c_hi; + t_atom params_out[M_param_count]; + t_outlet *params_outlet; + double lyap_exp, lyap_lo, lyap_hi, lyap_limit, failure_ratio; + + t_outlet *outlets[M_var_count - 1]; +} lorenz_struct; + +static void calc(lorenz_struct *lorenz, double *vars) { + double x_0, y_0, z_0; + x_0 =vars[M_x]+lorenz -> h*lorenz -> a*(vars[M_y]-vars[M_x]); + y_0 =vars[M_y]+lorenz -> h*(vars[M_x]*(lorenz -> b-vars[M_z])-vars[M_y]); + z_0 =vars[M_z]+lorenz -> h*(vars[M_x]*vars[M_y]-lorenz -> c*vars[M_z]); + vars[M_x] = x_0; + vars[M_y] = y_0; + vars[M_z] = z_0; +} // end calc + +static void calculate(lorenz_struct *lorenz) { + calc(lorenz, lorenz -> vars); + outlet_float(lorenz -> x_obj.ob_outlet, lorenz -> vars[M_x]); + outlet_float(lorenz -> outlets[M_y - 1], lorenz -> vars[M_y]); + outlet_float(lorenz -> outlets[M_z - 1], lorenz -> vars[M_z]); +} // end calculate + +static void reset(lorenz_struct *lorenz, t_symbol *s, int argc, t_atom *argv) { + if (argc == M_var_count) { + lorenz -> vars[M_x] = (double) atom_getfloatarg(M_x, argc, argv); + lorenz -> vars[M_y] = (double) atom_getfloatarg(M_y, argc, argv); + lorenz -> vars[M_z] = (double) atom_getfloatarg(M_z, argc, argv); + } else { + lorenz -> vars[M_x] = lorenz -> vars_init[M_x]; + lorenz -> vars[M_y] = lorenz -> vars_init[M_y]; + lorenz -> vars[M_z] = lorenz -> vars_init[M_z]; + } // end if +} // end reset + +static char *classify(lorenz_struct *lorenz) { + static char buff[5]; + char *c = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; + buff[0] = c[(int) (((lorenz -> h - M_h_lo) * (1.0 / (M_h_hi - M_h_lo))) * 26)]; + buff[1] = c[(int) (((lorenz -> a - M_a_lo) * (1.0 / (M_a_hi - M_a_lo))) * 26)]; + buff[2] = c[(int) (((lorenz -> b - M_b_lo) * (1.0 / (M_b_hi - M_b_lo))) * 26)]; + buff[3] = c[(int) (((lorenz -> c - M_c_lo) * (1.0 / (M_c_hi - M_c_lo))) * 26)]; + buff[4] = '\0'; + return buff; } -static void reset(lorenz_struct *x, t_floatarg lx0, t_floatarg ly0, t_floatarg lz0) -{ - x->lx0 = lx0; - x->ly0 = ly0; - x->lz0 = lz0; -} - -static void param(lorenz_struct *x, t_floatarg h, t_floatarg a, t_floatarg b, t_floatarg c) -{ - x->h = (double)h; - x->a = (double)a; - x->b = (double)b; - x->c = (double)c; +static void make_results(lorenz_struct *lorenz) { + SETFLOAT(&lorenz -> search_out[0], lorenz -> lyap_exp); + SETSYMBOL(&lorenz -> search_out[1], gensym(classify(lorenz))); + SETFLOAT(&lorenz -> search_out[2], lorenz -> failure_ratio); + SETFLOAT(&lorenz -> vars_out[M_x], lorenz -> vars[M_x]); + SETFLOAT(&lorenz -> vars_out[M_y], lorenz -> vars[M_y]); + SETFLOAT(&lorenz -> vars_out[M_z], lorenz -> vars[M_z]); + SETFLOAT(&lorenz -> params_out[M_h], lorenz -> h); + SETFLOAT(&lorenz -> params_out[M_a], lorenz -> a); + SETFLOAT(&lorenz -> params_out[M_b], lorenz -> b); + SETFLOAT(&lorenz -> params_out[M_c], lorenz -> c); + outlet_list(lorenz -> params_outlet, gensym("list"), M_param_count, lorenz -> params_out); + outlet_list(lorenz -> vars_outlet, gensym("list"), M_var_count, lorenz -> vars_out); } -void *lorenz_new(void) -{ - lorenz_struct *x = (lorenz_struct *)pd_new(lorenz_class); - x->h = 0.01; - x->a = 10.0; - x->b = 28.0; - x->c = 8.0/3.0; - x->lx0 = 0.1; - x->ly0 = 0; - x->lz0 = 0; - - outlet_new(&x->lorenz_obj, &s_float); /* Default float outlet */ - x->y_outlet = outlet_new(&x->lorenz_obj, &s_float); /* Two New Outlets */ - x->z_outlet = outlet_new(&x->lorenz_obj, &s_float); - - return (void *)x; +static void show(lorenz_struct *lorenz) { + make_results(lorenz); + outlet_anything(lorenz -> search_outlet, gensym("show"), M_search_count, lorenz -> search_out); } +static void param(lorenz_struct *lorenz, t_symbol *s, int argc, t_atom *argv) { + if (argc != 4) { + post("Incorrect number of arguments for lorenz fractal. Expecting 4 arguments."); + return; + } + lorenz -> h = (double) atom_getfloatarg(0, argc, argv); + lorenz -> a = (double) atom_getfloatarg(1, argc, argv); + lorenz -> b = (double) atom_getfloatarg(2, argc, argv); + lorenz -> c = (double) atom_getfloatarg(3, argc, argv); +} -void lorenz_setup(void) -{ - - post("lorenz"); +static void seed(lorenz_struct *lorenz, t_symbol *s, int argc, t_atom *argv) { + if (argc > 0) { + srand48(((unsigned int)time(0))|1); + } else { + srand48((unsigned int) atom_getfloatarg(0, argc, argv)); + } +} - lorenz_class = class_new(gensym("lorenz"), /* symname is the symbolic name */ - (t_newmethod)lorenz_new, /* Constructor Function */ - 0, /* Destructor Function */ - sizeof(lorenz_struct), /* Size of the structure */ - CLASS_DEFAULT, /* Graphical Representation */ - 0); /* 0 Terminates Argument List */ +static void lyap(lorenz_struct *lorenz, t_floatarg l, t_floatarg h, t_floatarg lim) { + lorenz -> lyap_lo = l; + lorenz -> lyap_hi = h; + lorenz -> lyap_limit = (double) ((int) lim); +} - class_addbang(lorenz_class, (t_method)calculate); - - class_addmethod(lorenz_class, - (t_method)reset, - gensym("reset"), - A_DEFFLOAT, - A_DEFFLOAT, - A_DEFFLOAT, - 0); - - class_addmethod(lorenz_class, - (t_method)param, - gensym("param"), - A_DEFFLOAT, - A_DEFFLOAT, - A_DEFFLOAT, - A_DEFFLOAT, - 0); +static void elyap(lorenz_struct *lorenz) { + double results[M_var_count]; + int i; + if (lyapunov_full((void *) lorenz, (t_gotfn) calc, M_var_count, lorenz -> vars, results) != NULL) { + post("elyapunov:"); + for(i = 0; i < M_var_count; i++) { post("%d: %3.80f", i, results[i]); } + } +} + +static void limiter(lorenz_struct *lorenz) { + if (lorenz -> h_lo < M_h_lo) { lorenz -> h_lo = M_h_lo; } + if (lorenz -> h_lo > M_h_hi) { lorenz -> h_lo = M_h_hi; } + if (lorenz -> h_hi < M_h_lo) { lorenz -> h_hi = M_h_lo; } + if (lorenz -> h_hi > M_h_hi) { lorenz -> h_hi = M_h_hi; } + if (lorenz -> a_lo < M_a_lo) { lorenz -> a_lo = M_a_lo; } + if (lorenz -> a_lo > M_a_hi) { lorenz -> a_lo = M_a_hi; } + if (lorenz -> a_hi < M_a_lo) { lorenz -> a_hi = M_a_lo; } + if (lorenz -> a_hi > M_a_hi) { lorenz -> a_hi = M_a_hi; } + if (lorenz -> b_lo < M_b_lo) { lorenz -> b_lo = M_b_lo; } + if (lorenz -> b_lo > M_b_hi) { lorenz -> b_lo = M_b_hi; } + if (lorenz -> b_hi < M_b_lo) { lorenz -> b_hi = M_b_lo; } + if (lorenz -> b_hi > M_b_hi) { lorenz -> b_hi = M_b_hi; } + if (lorenz -> c_lo < M_c_lo) { lorenz -> c_lo = M_c_lo; } + if (lorenz -> c_lo > M_c_hi) { lorenz -> c_lo = M_c_hi; } + if (lorenz -> c_hi < M_c_lo) { lorenz -> c_hi = M_c_lo; } + if (lorenz -> c_hi > M_c_hi) { lorenz -> c_hi = M_c_hi; } +} + +static void constrain(lorenz_struct *lorenz, t_symbol *s, int argc, t_atom *argv) { + int i; + t_atom *arg = argv; + if (argc == 0) { + // reset to full limits of search ranges + lorenz -> h_lo = M_h_lo; + lorenz -> h_hi = M_h_hi; + lorenz -> a_lo = M_a_lo; + lorenz -> a_hi = M_a_hi; + lorenz -> b_lo = M_b_lo; + lorenz -> b_hi = M_b_hi; + lorenz -> c_lo = M_c_lo; + lorenz -> c_hi = M_c_hi; + return; + } + if (argc == 1) { + // set the ranges based on percentage of full range + double percent = atom_getfloat(arg); + double h_spread = ((M_h_hi - M_h_lo) * percent) / 2; + double a_spread = ((M_a_hi - M_a_lo) * percent) / 2; + double b_spread = ((M_b_hi - M_b_lo) * percent) / 2; + double c_spread = ((M_c_hi - M_c_lo) * percent) / 2; + lorenz -> h_lo = lorenz -> h - h_spread; + lorenz -> h_hi = lorenz -> h + h_spread; + lorenz -> a_lo = lorenz -> a - a_spread; + lorenz -> a_hi = lorenz -> a + a_spread; + lorenz -> b_lo = lorenz -> b - b_spread; + lorenz -> b_hi = lorenz -> b + b_spread; + lorenz -> c_lo = lorenz -> c - c_spread; + lorenz -> c_hi = lorenz -> c + c_spread; + limiter(lorenz); + return; + } + if (argc != M_param_count * 2) { + post("Invalid number of arguments for lorenz constraints, requires 8 values, got %d", argc); + return; + } + lorenz -> h_lo = atom_getfloat(arg++); + lorenz -> h_hi = atom_getfloat(arg++); + lorenz -> a_lo = atom_getfloat(arg++); + lorenz -> a_hi = atom_getfloat(arg++); + lorenz -> b_lo = atom_getfloat(arg++); + lorenz -> b_hi = atom_getfloat(arg++); + lorenz -> c_lo = atom_getfloat(arg++); + lorenz -> c_hi = atom_getfloat(arg++); + limiter(lorenz); } + +static void search(lorenz_struct *lorenz, t_symbol *s, int argc, t_atom *argv) { + int not_found, not_expired = lorenz -> lyap_limit; + int jump, i, iterations; + t_atom vars[M_var_count]; + double temp_h = lorenz -> h; + double temp_a = lorenz -> a; + double temp_b = lorenz -> b; + double temp_c = lorenz -> c; + if (argc > 0) { + for (i = 0; i < M_var_count; i++) { + SETFLOAT(&vars[i], atom_getfloatarg(i, argc, argv)); + } + } else { + for (i = 0; i < M_var_count; i++) { + SETFLOAT(&vars[i], lorenz -> vars_init[i]); + } + } + do { + jump = 500; + not_found = 0; + iterations = 10000; + bad_params: + lorenz -> h = (drand48() * (lorenz -> h_hi - lorenz -> h_lo)) + lorenz -> h_lo; + lorenz -> a = (drand48() * (lorenz -> a_hi - lorenz -> a_lo)) + lorenz -> a_lo; + lorenz -> b = (drand48() * (lorenz -> b_hi - lorenz -> b_lo)) + lorenz -> b_lo; + lorenz -> c = (drand48() * (lorenz -> c_hi - lorenz -> c_lo)) + lorenz -> c_lo; + // put any preliminary checks specific to this fractal to eliminate bad_params + + reset(lorenz, NULL, argc, vars); + do { calc(lorenz, lorenz -> vars); } while(jump--); + lorenz -> lyap_exp = lyapunov((void *) lorenz, (t_gotfn) calc, M_var_count, (double *) lorenz -> vars); + if (isnan(lorenz -> lyap_exp)) { not_found = 1; } + if (lorenz -> lyap_exp < lorenz -> lyap_lo || lorenz -> lyap_exp > lorenz -> lyap_hi) { not_found = 1; } + not_expired--; + } while(not_found && not_expired); + reset(lorenz, NULL, argc, vars); + if (!not_expired) { + post("Could not find a fractal after %d attempts.", (int) lorenz -> lyap_limit); + post("Try using wider constraints."); + lorenz -> h = temp_h; + lorenz -> a = temp_a; + lorenz -> b = temp_b; + lorenz -> c = temp_c; + outlet_anything(lorenz -> search_outlet, gensym("invalid"), 0, NULL); + } else { + lorenz -> failure_ratio = (lorenz -> lyap_limit - not_expired) / lorenz -> lyap_limit; + make_results(lorenz); + outlet_anything(lorenz -> search_outlet, gensym("search"), M_search_count, lorenz -> search_out); + } +} + +void *lorenz_new(t_symbol *s, int argc, t_atom *argv) { + lorenz_struct *lorenz = (lorenz_struct *) pd_new(lorenz_class); + if (lorenz != NULL) { + outlet_new(&lorenz -> x_obj, &s_float); + lorenz -> outlets[0] = outlet_new(&lorenz -> x_obj, &s_float); + lorenz -> outlets[1] = outlet_new(&lorenz -> x_obj, &s_float); + lorenz -> search_outlet = outlet_new(&lorenz -> x_obj, &s_list); + lorenz -> vars_outlet = outlet_new(&lorenz -> x_obj, &s_list); + lorenz -> params_outlet = outlet_new(&lorenz -> x_obj, &s_list); + if (argc == M_param_count + M_var_count) { + lorenz -> vars_init[M_x] = lorenz -> vars[M_x] = (double) atom_getfloatarg(0, argc, argv); + lorenz -> vars_init[M_y] = lorenz -> vars[M_y] = (double) atom_getfloatarg(1, argc, argv); + lorenz -> vars_init[M_z] = lorenz -> vars[M_z] = (double) atom_getfloatarg(2, argc, argv); + lorenz -> h = (double) atom_getfloatarg(3, argc, argv); + lorenz -> a = (double) atom_getfloatarg(4, argc, argv); + lorenz -> b = (double) atom_getfloatarg(5, argc, argv); + lorenz -> c = (double) atom_getfloatarg(6, argc, argv); + } else { + if (argc != 0 && argc != M_param_count + M_var_count) { + post("Incorrect number of arguments for lorenz fractal. Expecting 7 arguments."); + } + lorenz -> vars_init[M_x] = 0.1; + lorenz -> vars_init[M_y] = 0; + lorenz -> vars_init[M_z] = 0; + lorenz -> h = 0.01; + lorenz -> a = 10; + lorenz -> b = 28; + lorenz -> c = 2.66667; + } + constrain(lorenz, NULL, 0, NULL); + lyap(lorenz, -1000000.0, 1000000.0, M_failure_limit); + } + return (void *)lorenz; +} + +void lorenz_setup(void) { + lorenz_class = class_new(gensym("lorenz"), (t_newmethod) lorenz_new, 0, sizeof(lorenz_struct), 0, A_GIMME, 0); + class_addbang(lorenz_class, (t_method) calculate); + class_addmethod(lorenz_class, (t_method) reset, gensym("reset"), A_GIMME, 0); + class_addmethod(lorenz_class, (t_method) show, gensym("show"), 0); + class_addmethod(lorenz_class, (t_method) param, gensym("param"), A_GIMME, 0); + class_addmethod(lorenz_class, (t_method) seed, gensym("seed"), A_GIMME, 0); + class_addmethod(lorenz_class, (t_method) lyap, gensym("lyapunov"), A_DEFFLOAT, A_DEFFLOAT, A_DEFFLOAT, 0); + class_addmethod(lorenz_class, (t_method) elyap, gensym("elyapunov"), 0); + class_addmethod(lorenz_class, (t_method) search, gensym("search"), A_GIMME, 0); + class_addmethod(lorenz_class, (t_method) constrain, gensym("constrain"), A_GIMME, 0); + class_sethelpsymbol(lorenz_class, gensym("help-lorenz.pd")); +} + |