poly.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* interpolation/interp_poly.c
 * 
 * Copyright (C) 2001 DAN, HO-JIN
 * 
 * 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., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#include <config.h>
#include <math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_poly.h>
#include <gsl/gsl_interp.h>

typedef struct
{
  double *d;
  double *coeff;
  double *work;
}
polynomial_state_t;

static void *
polynomial_alloc (size_t size)
{
  polynomial_state_t *state =
    (polynomial_state_t *) malloc (sizeof (polynomial_state_t));

  if (state == 0)
    {
      GSL_ERROR_NULL ("failed to allocate space for polynomial state",
                      GSL_ENOMEM);
    }

  state->d = (double *) malloc (sizeof (double) * size);

  if (state->d == 0)
    {
      free (state);
      GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM);
    }

  state->coeff = (double *) malloc (sizeof (double) * size);

  if (state->coeff == 0)
    {
      free (state->d);
      free (state);
      GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM);
    }

  state->work = (double *) malloc (sizeof (double) * size);

  if (state->work == 0)
    {
      free (state->coeff);
      free (state->d);
      free (state);
      GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM);
    }

  return state;
}

static int
polynomial_init (void *vstate,
                 const double xa[], const double ya[], size_t size)
{
  polynomial_state_t *state = (polynomial_state_t *) vstate;

  int status = gsl_poly_dd_init (state->d, xa, ya, size);

  return status;
}

static int
polynomial_eval (const void *vstate,
                 const double xa[], const double ya[], size_t size, double x,
                 gsl_interp_accel * acc, double *y)
{
  polynomial_state_t *state = (polynomial_state_t *) vstate;

  *y = gsl_poly_dd_eval (state->d, xa, size, x);

  return GSL_SUCCESS;
}


static int
polynomial_deriv (const void *vstate,
                  const double xa[], const double ya[], size_t size, double x,
                  gsl_interp_accel * acc, double *y)
{
  polynomial_state_t *state = (polynomial_state_t *) vstate;

  gsl_poly_dd_taylor (state->coeff, x, state->d, xa, size, state->work);

  *y = state->coeff[1];

  return GSL_SUCCESS;
}

static int
polynomial_deriv2 (const void *vstate,
                   const double xa[], const double ya[], size_t size,
                   double x, gsl_interp_accel * acc, double *y)
{
  polynomial_state_t *state = (polynomial_state_t *) vstate;

  gsl_poly_dd_taylor (state->coeff, x, state->d, xa, size, state->work);

  *y = 2.0 * state->coeff[2];

  return GSL_SUCCESS;
}

static int
polynomial_integ (const void *vstate, const double xa[], const double ya[],
                  size_t size, gsl_interp_accel * acc, double a, double b,
                  double *result)
{
  polynomial_state_t *state = (polynomial_state_t *) vstate;
  size_t i;
  double sum;

  gsl_poly_dd_taylor (state->coeff, 0.0, state->d, xa, size, state->work);

  sum = state->coeff[0] * (b - a);

  for (i = 1; i < size; i++)
    {
      sum += state->coeff[i] * (pow (b, i + 1) - pow (a, i + 1)) / (i + 1.0);
    }

  *result = sum;

  return GSL_SUCCESS;
}

static void
polynomial_free (void *vstate)
{
  polynomial_state_t *state = (polynomial_state_t *) vstate;
  free (state->d);
  free (state->coeff);
  free (state->work);
  free (state);
}

static const gsl_interp_type polynomial_type = {
  "polynomial",
  3,
  &polynomial_alloc,
  &polynomial_init,
  &polynomial_eval,
  &polynomial_deriv,
  &polynomial_deriv2,
  &polynomial_integ,
  &polynomial_free,
};

const gsl_interp_type *gsl_interp_polynomial = &polynomial_type;