| /* fit/linear.c |
| * |
| * Copyright (C) 2000 Brian Gough |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU General Public License as published by |
| * the Free Software Foundation; either version 2 of the License, or (at |
| * your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, but |
| * WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
| */ |
| |
| #include <config.h> |
| #include <gsl/gsl_errno.h> |
| #include <gsl/gsl_fit.h> |
| |
| /* Fit the data (x_i, y_i) to the linear relationship |
| |
| Y = c0 + c1 x |
| |
| returning, |
| |
| c0, c1 -- coefficients |
| cov00, cov01, cov11 -- variance-covariance matrix of c0 and c1, |
| sumsq -- sum of squares of residuals |
| |
| This fit can be used in the case where the errors for the data are |
| uknown, but assumed equal for all points. The resulting |
| variance-covariance matrix estimates the error in the coefficients |
| from the observed variance of the points around the best fit line. |
| */ |
| |
| int |
| gsl_fit_linear (const double *x, const size_t xstride, |
| const double *y, const size_t ystride, |
| const size_t n, |
| double *c0, double *c1, |
| double *cov_00, double *cov_01, double *cov_11, double *sumsq) |
| { |
| double m_x = 0, m_y = 0, m_dx2 = 0, m_dxdy = 0; |
| |
| size_t i; |
| |
| for (i = 0; i < n; i++) |
| { |
| m_x += (x[i * xstride] - m_x) / (i + 1.0); |
| m_y += (y[i * ystride] - m_y) / (i + 1.0); |
| } |
| |
| for (i = 0; i < n; i++) |
| { |
| const double dx = x[i * xstride] - m_x; |
| const double dy = y[i * ystride] - m_y; |
| |
| m_dx2 += (dx * dx - m_dx2) / (i + 1.0); |
| m_dxdy += (dx * dy - m_dxdy) / (i + 1.0); |
| } |
| |
| /* In terms of y = a + b x */ |
| |
| { |
| double s2 = 0, d2 = 0; |
| double b = m_dxdy / m_dx2; |
| double a = m_y - m_x * b; |
| |
| *c0 = a; |
| *c1 = b; |
| |
| /* Compute chi^2 = \sum (y_i - (a + b * x_i))^2 */ |
| |
| for (i = 0; i < n; i++) |
| { |
| const double dx = x[i * xstride] - m_x; |
| const double dy = y[i * ystride] - m_y; |
| const double d = dy - b * dx; |
| d2 += d * d; |
| } |
| |
| s2 = d2 / (n - 2.0); /* chisq per degree of freedom */ |
| |
| *cov_00 = s2 * (1.0 / n) * (1 + m_x * m_x / m_dx2); |
| *cov_11 = s2 * 1.0 / (n * m_dx2); |
| |
| *cov_01 = s2 * (-m_x) / (n * m_dx2); |
| |
| *sumsq = d2; |
| } |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| /* Fit the weighted data (x_i, w_i, y_i) to the linear relationship |
| |
| Y = c0 + c1 x |
| |
| returning, |
| |
| c0, c1 -- coefficients |
| s0, s1 -- the standard deviations of c0 and c1, |
| r -- the correlation coefficient between c0 and c1, |
| chisq -- weighted sum of squares of residuals */ |
| |
| int |
| gsl_fit_wlinear (const double *x, const size_t xstride, |
| const double *w, const size_t wstride, |
| const double *y, const size_t ystride, |
| const size_t n, |
| double *c0, double *c1, |
| double *cov_00, double *cov_01, double *cov_11, |
| double *chisq) |
| { |
| |
| /* compute the weighted means and weighted deviations from the means */ |
| |
| /* wm denotes a "weighted mean", wm(f) = (sum_i w_i f_i) / (sum_i w_i) */ |
| |
| double W = 0, wm_x = 0, wm_y = 0, wm_dx2 = 0, wm_dxdy = 0; |
| |
| size_t i; |
| |
| for (i = 0; i < n; i++) |
| { |
| const double wi = w[i * wstride]; |
| |
| if (wi > 0) |
| { |
| W += wi; |
| wm_x += (x[i * xstride] - wm_x) * (wi / W); |
| wm_y += (y[i * ystride] - wm_y) * (wi / W); |
| } |
| } |
| |
| W = 0; /* reset the total weight */ |
| |
| for (i = 0; i < n; i++) |
| { |
| const double wi = w[i * wstride]; |
| |
| if (wi > 0) |
| { |
| const double dx = x[i * xstride] - wm_x; |
| const double dy = y[i * ystride] - wm_y; |
| |
| W += wi; |
| wm_dx2 += (dx * dx - wm_dx2) * (wi / W); |
| wm_dxdy += (dx * dy - wm_dxdy) * (wi / W); |
| } |
| } |
| |
| /* In terms of y = a + b x */ |
| |
| { |
| double d2 = 0; |
| double b = wm_dxdy / wm_dx2; |
| double a = wm_y - wm_x * b; |
| |
| *c0 = a; |
| *c1 = b; |
| |
| *cov_00 = (1 / W) * (1 + wm_x * wm_x / wm_dx2); |
| *cov_11 = 1 / (W * wm_dx2); |
| |
| *cov_01 = -wm_x / (W * wm_dx2); |
| |
| /* Compute chi^2 = \sum w_i (y_i - (a + b * x_i))^2 */ |
| |
| for (i = 0; i < n; i++) |
| { |
| const double wi = w[i * wstride]; |
| |
| if (wi > 0) |
| { |
| const double dx = x[i * xstride] - wm_x; |
| const double dy = y[i * ystride] - wm_y; |
| const double d = dy - b * dx; |
| d2 += wi * d * d; |
| } |
| } |
| |
| *chisq = d2; |
| } |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| |
| int |
| gsl_fit_linear_est (const double x, |
| const double c0, const double c1, |
| const double c00, const double c01, const double c11, |
| double *y, double *y_err) |
| { |
| *y = c0 + c1 * x; |
| *y_err = sqrt (c00 + x * (2 * c01 + c11 * x)); |
| return GSL_SUCCESS; |
| } |
| |
| |
| int |
| gsl_fit_mul (const double *x, const size_t xstride, |
| const double *y, const size_t ystride, |
| const size_t n, |
| double *c1, double *cov_11, double *sumsq) |
| { |
| double m_x = 0, m_y = 0, m_dx2 = 0, m_dxdy = 0; |
| |
| size_t i; |
| |
| for (i = 0; i < n; i++) |
| { |
| m_x += (x[i * xstride] - m_x) / (i + 1.0); |
| m_y += (y[i * ystride] - m_y) / (i + 1.0); |
| } |
| |
| for (i = 0; i < n; i++) |
| { |
| const double dx = x[i * xstride] - m_x; |
| const double dy = y[i * ystride] - m_y; |
| |
| m_dx2 += (dx * dx - m_dx2) / (i + 1.0); |
| m_dxdy += (dx * dy - m_dxdy) / (i + 1.0); |
| } |
| |
| /* In terms of y = b x */ |
| |
| { |
| double s2 = 0, d2 = 0; |
| double b = (m_x * m_y + m_dxdy) / (m_x * m_x + m_dx2); |
| |
| *c1 = b; |
| |
| /* Compute chi^2 = \sum (y_i - b * x_i)^2 */ |
| |
| for (i = 0; i < n; i++) |
| { |
| const double dx = x[i * xstride] - m_x; |
| const double dy = y[i * ystride] - m_y; |
| const double d = (m_y - b * m_x) + dy - b * dx; |
| d2 += d * d; |
| } |
| |
| s2 = d2 / (n - 1.0); /* chisq per degree of freedom */ |
| |
| *cov_11 = s2 * 1.0 / (n * (m_x * m_x + m_dx2)); |
| |
| *sumsq = d2; |
| } |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| int |
| gsl_fit_wmul (const double *x, const size_t xstride, |
| const double *w, const size_t wstride, |
| const double *y, const size_t ystride, |
| const size_t n, |
| double *c1, double *cov_11, double *chisq) |
| { |
| |
| /* compute the weighted means and weighted deviations from the means */ |
| |
| /* wm denotes a "weighted mean", wm(f) = (sum_i w_i f_i) / (sum_i w_i) */ |
| |
| double W = 0, wm_x = 0, wm_y = 0, wm_dx2 = 0, wm_dxdy = 0; |
| |
| size_t i; |
| |
| for (i = 0; i < n; i++) |
| { |
| const double wi = w[i * wstride]; |
| |
| if (wi > 0) |
| { |
| W += wi; |
| wm_x += (x[i * xstride] - wm_x) * (wi / W); |
| wm_y += (y[i * ystride] - wm_y) * (wi / W); |
| } |
| } |
| |
| W = 0; /* reset the total weight */ |
| |
| for (i = 0; i < n; i++) |
| { |
| const double wi = w[i * wstride]; |
| |
| if (wi > 0) |
| { |
| const double dx = x[i * xstride] - wm_x; |
| const double dy = y[i * ystride] - wm_y; |
| |
| W += wi; |
| wm_dx2 += (dx * dx - wm_dx2) * (wi / W); |
| wm_dxdy += (dx * dy - wm_dxdy) * (wi / W); |
| } |
| } |
| |
| /* In terms of y = b x */ |
| |
| { |
| double d2 = 0; |
| double b = (wm_x * wm_y + wm_dxdy) / (wm_x * wm_x + wm_dx2); |
| |
| *c1 = b; |
| |
| *cov_11 = 1 / (W * (wm_x * wm_x + wm_dx2)); |
| |
| /* Compute chi^2 = \sum w_i (y_i - b * x_i)^2 */ |
| |
| for (i = 0; i < n; i++) |
| { |
| const double wi = w[i * wstride]; |
| |
| if (wi > 0) |
| { |
| const double dx = x[i * xstride] - wm_x; |
| const double dy = y[i * ystride] - wm_y; |
| const double d = (wm_y - b * wm_x) + (dy - b * dx); |
| d2 += wi * d * d; |
| } |
| } |
| |
| *chisq = d2; |
| } |
| |
| return GSL_SUCCESS; |
| } |
| |
| int |
| gsl_fit_mul_est (const double x, |
| const double c1, const double c11, |
| double *y, double *y_err) |
| { |
| *y = c1 * x; |
| *y_err = sqrt (c11) * fabs (x); |
| return GSL_SUCCESS; |
| } |