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a guest May 5th, 2010 663 Never
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1. #include <iostream>
2. #include <iterator>
3. #include <vector>
4. #include <cmath>
5. #include <gsl_multifit.h>
6. #include "NumericUtils.h"
7.
8. double tricube(double u, double t)
9. {
10.     // In our case, u represents a distance and hence should be strictly positive.
11.     if (u < 0) {
12.         std::cout << "In tricube(u, t), u < 0" << std::endl;
13.         std::abort();
14.     }
15.
16.     // 0 <= u < t
17.     if ( (closeAtTolerance(u, 0.0) || 0.0 < u) && (u < t) ) {
18.         // (1 - (u/t)^3)^3
19.         return pow( ( 1.0 - pow(u/t, 3.0)), 3.0 );
20.     }
21.     // u >= t
22.     else {
23.         return 0.0;
24.     }
25. }
26.
27. double getDistance(double x, double xi)
28. {
29.     return fabs(x - xi);
30. }
31.
32. int main (int argc, char* argv[])
33. {
34.     // Loess algorithm parameters.
35.     double alpha = 0.33;
36.
37.     // Create test dataset.
38.     const unsigned n = 21;
39.
40.     double xValues[n] = { 0.5578196, 2.0217271, 2.5773252, 3.4140288, 4.3014084, 4.7448394, 5.1073781,
41.                          6.5411662, 6.7216176, 7.2600583, 8.1335874, 9.1224379, 11.9296663, 12.3797674,
42.                          13.2728619, 14.2767453, 15.3731026, 15.6476637, 18.5605355, 18.5866354, 18.7572812 };
43.
44.     double yValues[n] = { 18.63654, 103.49646, 150.35391, 190.51031, 208.70115, 213.71135, 228.49353,
45.                          233.55387, 234.55054, 223.89225, 227.68339, 223.91982, 168.01999, 164.95750,
46.                          152.61107, 160.78742, 168.55567, 152.42658, 221.70702, 222.69040, 243.18828 };
47.
48.     // Loess neighborhood parameter.
49.     // XXX: Careful, alpha is assume to be <= 1 here.
50.     const unsigned q = floor(n * alpha);
51.
52.     // Working arrays. Yes we need both distances and sortedDistances.
53.     double distances[n];
54.     double sortedDistances[n];
55.     double ySmooth[n];
56.
57.     gsl_matrix *X = gsl_matrix_alloc(n, 3);
58.     gsl_matrix *cov = gsl_matrix_alloc(3, 3);
59.     gsl_vector *weights = gsl_vector_alloc(n);
60.     gsl_vector *c = gsl_vector_alloc(3);
61.     gsl_vector *x = gsl_vector_alloc(3);
62.
63.     double y, yErr, chisq;
64.
65.     // Setup the model matrix X for a quadratic fit.
66.     for (unsigned i = 0; i < n; ++i) {
67.         gsl_matrix_set(X, i, 0, 1.0);
68.         gsl_matrix_set(X, i, 1, xValues[i]);
69.         gsl_matrix_set(X, i, 2, xValues[i] * xValues[i]);
70.     }
71.
72.     for (unsigned i = 0; i < n; ++i) {
73.
74.         // Compute distances.
75.         for (unsigned j = 0; j < n; ++j) {
76.             distances[j] = getDistance(xValues[i], xValues[j]);
77.             sortedDistances[j] = distances[j];
78.         }
79.
80.         // Sort distances in order from smallest to largest.
81.         std::sort(sortedDistances, sortedDistances + n);
82.
83.         // Compute weights.
84.         for (unsigned j = 0; j < n; ++j) {
85.             gsl_vector_set(weights, j, tricube(distances[j], sortedDistances[q]));
86.         }
87.
88.         gsl_multifit_linear_workspace *work = gsl_multifit_linear_alloc(n, 3);
89.         gsl_multifit_wlinear(X, weights, &gsl_vector_view_array(yValues, n).vector, c, cov, &chisq, work);
90.         gsl_multifit_linear_free(work);
91.
92.         gsl_vector_set(x, 0, 1.0);
93.         gsl_vector_set(x, 1, xValues[i]);
94.         gsl_vector_set(x, 2, xValues[i] * xValues[i]);
95.         gsl_multifit_linear_est (x, c, cov, &y, &yErr);
96.
97.         ySmooth[i] = y;
98.     }
99.
100.     std::cout.setf(std::ios::fixed, std::ios::floatfield);
101.     for (unsigned i = 0; i < n; ++i) {
102.         std::cout << xValues[i] << " "
103.                   << yValues[i] << " "
104.                   << ySmooth[i]
105.                   << std::endl;
106.     }
107.
108.     gsl_matrix_free(X);
109.     gsl_vector_free(weights);
110.     gsl_vector_free(c);
111.     gsl_matrix_free(cov);
112.
113.     return 0;
114. }
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