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//
// gradsearch_datafit_example.c
//
// Fit 3-parameter curve to sampled data set in the minimum
// mean-squared error sense.
//
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "liquid.h"
#define OUTPUT_FILENAME "gradsearch_datafit_example.m"
// gradient search data set
struct gsdataset {
float * x;
float * y;
unsigned int n;
};
// gradient search curve-fit error
float gserror(void * _dataset,
float * _v,
unsigned int _n);
// parameterized function
float gsfunc(float _x, float * _v)
{
float c0 = _v[0];
float c1 = _v[1];
float c2 = _v[2];
return c0 + sincf(c1*(_x-c2));
}
int main() {
// options
unsigned int num_samples = 400; // number of samples
float sig = 0.1f; // noise variance
unsigned int num_iterations = 1000; // number of iterations to run
float v[3] = {1, 1, 1};
unsigned int i;
// range
float xmin = 0.0f;
float xmax = 6.0f;
float dx = (xmax - xmin) / (num_samples-1);
// generate data set
float x[num_samples];
float y[num_samples];
for (i=0; i<num_samples; i++) {
x[i] = xmin + i*dx;
y[i] = sincf(x[i]) + randnf()*sig;
}
struct gsdataset q = {x, y, num_samples};
// create gradsearch object
gradsearch gs = gradsearch_create((void*)&q, v, 3, gserror, LIQUID_OPTIM_MINIMIZE);
float rmse;
// execute search
//rmse = gradsearch_run(gs, num_iterations, -1e-6f);
// open output file
FILE*fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
// execute search one iteration at a time
fprintf(fid,"u = zeros(1,%u);\n", num_iterations);
for (i=0; i<num_iterations; i++) {
rmse = gserror((void*)&q,v,3);
fprintf(fid,"u(%3u) = %12.4e;\n", i+1, rmse);
gradsearch_step(gs);
if (((i+1)%100)==0)
gradsearch_print(gs);
}
// print results
printf("\n");
gradsearch_print(gs);
printf(" c0 = %12.8f, opt = 1\n", v[0]);
printf(" c1 = %12.8f, opt = 0\n", v[1]);
printf(" c2 = %12.8f, opt = 1\n", v[2]);
printf(" rmse = %12.4e\n", rmse);
fprintf(fid,"figure;\n");
fprintf(fid,"semilogy(u);\n");
fprintf(fid,"xlabel('iteration');\n");
fprintf(fid,"ylabel('error');\n");
fprintf(fid,"title('gradient search results');\n");
fprintf(fid,"grid on;\n");
// save sampled data set
for (i=0; i<num_samples; i++) {
fprintf(fid," x(%4u) = %12.8f;\n", i+1, x[i]);
fprintf(fid," y(%4u) = %12.8f;\n", i+1, y[i]);
fprintf(fid," y_hat(%4u) = %12.8f;\n", i+1, gsfunc(x[i],v));
}
fprintf(fid,"figure;\n");
fprintf(fid,"plot(x,y,'x', x,y_hat,'-');\n");
fprintf(fid,"xlabel('x');\n");
fprintf(fid,"ylabel('f(x)');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('data','fit',1);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
gradsearch_destroy(gs);
return 0;
}
// gradient search fit
float gserror(void * _dataset,
float * _v,
unsigned int _n)
{
struct gsdataset * p = (struct gsdataset *) _dataset;
float rmse = 0.0f; // mean-squared error
unsigned int i;
for (i=0; i<p->n; i++) {
// compute function estimate
float y_hat = gsfunc(p->x[i], _v);
// compute error
float e = p->y[i] - y_hat;
// accumulate RMS error
rmse += e*e;
}
// normalize error and return
rmse = sqrtf(rmse / (float)(p->n));
return rmse;
}
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