/* fit/linear.c

 * 

 * Copyright (C) 2000, 2007 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 3 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 cov00, const double cov01, const double cov11,

                    double *y, double *y_err)

{

  *y = c0 + c1 * x;

  *y_err = sqrt (cov00 + x * (2 * cov01 + cov11 * 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 cov11, 

                 double *y, double *y_err)

{

  *y = c1 * x;

  *y_err = sqrt (cov11) * fabs (x);

  return GSL_SUCCESS;

}