lsfBasisFns.c File Reference

Basis functions for Least Squares Fits (LSFs) using ordinary and Chebyshev polynomials. More...

#include "mdb.h"

Go to the source code of this file.

Functions
void	set_argument_offset (double offset)
	Set the offset applied to the input argument of basis functions.
void	set_argument_scale (double scale)
	Set the scale factor applied to the input argument of basis functions.
double	get_argument_offset ()
	Get the current argument offset applied before function evaluations.
double	get_argument_scale ()
	Get the current argument scale factor used before function evaluations.
double	tcheby (double x, long n)
	Evaluate the Chebyshev polynomial of the first kind T_n(x).
double	dtcheby (double x, long n)
	Evaluate the derivative of the Chebyshev polynomial T_n(x).
double	ipower (double x, long n)
	Evaluate a power function x^n.
double	dipower (double x, long n)
	Evaluate the derivative of x^n.
double	eval_sum (double(*fn)(double x, long ord), double *coef, int32_t *order, long n_coefs, double x0)
	Evaluate a sum of basis functions.

Variables
static double	x_offset = 0
static double	x_scale = 1

Detailed Description

Basis functions for Least Squares Fits (LSFs) using ordinary and Chebyshev polynomials.

This file provides a set of functions for evaluating basis functions and their derivatives for least squares fitting. It includes functions to set and retrieve scaling offsets, as well as polynomial and Chebyshev polynomial basis functions and their derivatives.

Copyright

• (c) 2002 The University of Chicago, as Operator of Argonne National Laboratory.
• (c) 2002 The Regents of the University of California, as Operator of Los Alamos National Laboratory.

License

This file is distributed under the terms of the Software License Agreement found in the file LICENSE included with this distribution.

Author

M. Borland, C. Saunders, R. Soliday

Definition in file lsfBasisFns.c.

Function Documentation

dipower()

double dipower	(	double	x,
		long	n )

Evaluate the derivative of x^n.

This function returns d/dx [ (x - x_offset)/x_scale ]^n = n * ((x - x_offset)/x_scale)^(n-1) / x_scale.

Parameters

x	The point at which to evaluate the derivative.
n	The exponent.

Returns

The derivative of the power function at the given x.

Definition at line 127 of file lsfBasisFns.c.

                                 {
  x = (x - x_offset) / x_scale;
  return (n * ipow(x, n - 1));
}

dtcheby()

double dtcheby	(	double	x,
		long	n )

Evaluate the derivative of the Chebyshev polynomial T_n(x).

This function returns d/dx [T_n((x - x_offset)/x_scale)]. If x is out of the domain [-1,1], it is clipped to ±1 before evaluation.

Parameters

x	The point at which to evaluate the derivative of T_n.
n	The order of the Chebyshev polynomial.

Returns

The derivative dT_n/dx at the given x.

Definition at line 92 of file lsfBasisFns.c.

                                 {
  x = (x - x_offset) / x_scale;
  if (x > 1 || x < -1) {
    /* fprintf(stderr, "warning: argument %e is out of range for tcheby()\n",
     * x); */
    x = SIGN(x);
  }
  if (x != 1 && x != -1)
    return (n * sin(n * acos(x)) / sqrt(1 - sqr(x)));
  return (1.0 * n * n);
}

eval_sum()

double eval_sum	(	double(*	fn )(double x, long ord),
		double *	coef,
		int32_t *	order,
		long	n_coefs,
		double	x0 )

Evaluate a sum of basis functions.

Given a pointer to a function that evaluates a basis function fn(x,order), this function computes the weighted sum of these functions at x0 using the provided coefficients.

Parameters

fn	A pointer to the basis function to evaluate (fn(x, order)).
coef	An array of coefficients for each basis function.
order	An array of orders corresponding to each coefficient.
n_coefs	The number of coefficients (and basis functions).
x0	The point at which to evaluate the sum.

Returns

The computed sum of the basis functions.

Definition at line 145 of file lsfBasisFns.c.

                                         {
  double sum = 0;
  long i;
 
  for (i = sum = 0; i < n_coefs; i++)
    sum += (fn)(x0, order[i]) * coef[i];
  return (sum);
}

get_argument_offset()

double get_argument_offset

(

)

Get the current argument offset applied before function evaluations.

Returns

The current argument offset.

Definition at line 53 of file lsfBasisFns.c.

{ return x_offset; }

get_argument_scale()

double get_argument_scale

(

)

Get the current argument scale factor used before function evaluations.

Returns

The current argument scale factor.

Definition at line 60 of file lsfBasisFns.c.

{ return x_scale; }

ipower()

double ipower	(	double	x,
		long	n )

Evaluate a power function x^n.

This function returns ( (x - x_offset)/x_scale )^n.

Parameters

x	The point at which to evaluate the power.
n	The exponent.

Returns

The value of ((x - x_offset)/x_scale)^n.

Definition at line 113 of file lsfBasisFns.c.

                                {
  x = (x - x_offset) / x_scale;
  return (ipow(x, n));
}

set_argument_offset()

void set_argument_offset

(

double

offset

)

Set the offset applied to the input argument of basis functions.

This function updates the global variable used to shift the input argument before evaluating polynomial or Chebyshev functions.

Parameters

offset

The new offset to apply to the argument.

Definition at line 33 of file lsfBasisFns.c.

{ x_offset = offset; }

set_argument_scale()

void set_argument_scale

(

double

scale

)

Set the scale factor applied to the input argument of basis functions.

This function updates the global variable used to scale the input argument before evaluating polynomial or Chebyshev functions. It ensures the scale factor is not zero.

Parameters

scale

The new scale factor for the argument.

Definition at line 43 of file lsfBasisFns.c.

                                      {
  if (!(x_scale = scale))
    bomb("argument scale factor is zero", NULL);
}

tcheby()

double tcheby	(	double	x,
		long	n )

Evaluate the Chebyshev polynomial of the first kind T_n(x).

Given x and an order n, this function returns T_n((x - x_offset) / x_scale). If x is out of the domain [-1,1], it is clipped to ±1 before evaluation.

Parameters

x	The point at which to evaluate the Chebyshev polynomial.
n	The order of the Chebyshev polynomial.

Returns

The value of T_n(x).

Definition at line 72 of file lsfBasisFns.c.

                                {
  x = (x - x_offset) / x_scale;
  if (x > 1 || x < -1) {
    /*  fprintf(stderr, "warning: argument %e is out of range for tcheby()\n",
     * x); */
    x = SIGN(x);
  }
  return (cos(n * acos(x)));
}

Variable Documentation

x_offset

double x_offset = 0

static

Definition at line 22 of file lsfBasisFns.c.

x_scale

double x_scale = 1

static

Definition at line 23 of file lsfBasisFns.c.