poly.c File Reference

Detailed Description

Functions for evaluating polynomials and their derivatives, as well as solving quadratic equations.

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 poly.c.

#include "mdb.h"

Go to the source code of this file.

Functions
double	poly (double *a, long n, double x)
	Evaluate a polynomial at a given point.
double	dpoly (double *a, long n, double x)
	Evaluate the derivative of a polynomial at a given point.
double	polyp (double *a, long *power, long n, double x)
	Evaluate a polynomial with arbitrary powers at a given point.
double	dpolyp (double *a, long *power, long n, double x)
	Evaluate the derivative of a polynomial with arbitrary powers at a given point.
int	solveQuadratic (double a, double b, double c, double *solution)
	Solve a quadratic equation for real solutions.

Function Documentation

dpoly()

double dpoly	(	double *	a,
		long	n,
		double	x )

Evaluate the derivative of a polynomial at a given point.

Given an array of coefficients a and the number of terms n, this function returns the value of the derivative of the polynomial at x. The polynomial is assumed to be: a[0] + a[1]*x + a[2]*x^2 + ... Its derivative is: a[1] + 2*a[2]*x + 3*a[3]*x^2 + ...

Parameters

[in]	a	Pointer to the array of polynomial coefficients.
[in]	n	Number of coefficients (degree+1 of the polynomial).
[in]	x	The point at which to evaluate the derivative.

Returns

The value of the derivative at x.

Definition at line 58 of file poly.c.

                                          {
  register long i;
  register double sum, xp;
 
  sum = 0;
  xp = 1;
  for (i = 1; i < n; i++) {
    sum += i * xp * a[i];
    xp *= x;
  }
  return (sum);
}

dpolyp()

double dpolyp	(	double *	a,
		long *	power,
		long	n,
		double	x )

Evaluate the derivative of a polynomial with arbitrary powers at a given point.

Given arrays a and power that define a polynomial a[0]*x^(power[0]) + a[1]*x^(power[1]) + ... + a[n-1]*x^(power[n-1]), this function returns the derivative of that polynomial at x: power[0]*a[0]*x^(power[0]-1) + power[1]*a[1]*x^(power[1]-1) + ...

Parameters

[in]	a	Pointer to the array of polynomial coefficients.
[in]	power	Pointer to the array of powers for each term.
[in]	n	Number of terms.
[in]	x	The point at which to evaluate the derivative.

Returns

The value of the derivative at x.

Definition at line 111 of file poly.c.

                                                        {
  register long i;
  register double sum, xp;
 
  xp = ipow(x, power[0] - 1);
  sum = power[0] * xp * a[0];
  for (i = 1; i < n; i++) {
    xp *= ipow(x, power[i] - power[i - 1]);
    sum += power[i] * xp * a[i];
  }
  return (sum);
}

poly()

double poly	(	double *	a,
		long	n,
		double	x )

Evaluate a polynomial at a given point.

Given an array of coefficients a and the number of terms n, this function returns the value of the polynomial at x. The polynomial is assumed to be of the form: a[0] + a[1]*x + a[2]*x^2 + ... + a[n-1]*x^(n-1).

Parameters

[in]	a	Pointer to the array of polynomial coefficients.
[in]	n	Number of coefficients (degree+1 of the polynomial).
[in]	x	The point at which to evaluate the polynomial.

Returns

The value of the polynomial at x.

Definition at line 30 of file poly.c.

{
  register long i;
  register double sum, xp;
 
  sum = 0;
  xp = 1;
  for (i = 0; i < n; i++) {
    sum += xp * a[i];
    xp *= x;
  }
  return (sum);
}

polyp()

double polyp	(	double *	a,
		long *	power,
		long	n,
		double	x )

Evaluate a polynomial with arbitrary powers at a given point.

This function computes the value of a polynomial at x, where each term may have an arbitrary power. Given arrays a and power, the polynomial is: a[0]*x^(power[0]) + a[1]*x^(power[1]) + ... + a[n-1]*x^(power[n-1]).

Parameters

[in]	a	Pointer to the array of polynomial coefficients.
[in]	power	Pointer to the array of powers for each term.
[in]	n	Number of terms.
[in]	x	The point at which to evaluate the polynomial.

Returns

The value of the polynomial at x.

Definition at line 84 of file poly.c.

                                                       {
  register long i;
  register double sum, xp;
 
  xp = ipow(x, power[0]);
  sum = xp * a[0];
  for (i = 1; i < n; i++) {
    xp *= ipow(x, power[i] - power[i - 1]);
    sum += xp * a[i];
  }
  return (sum);
}

solveQuadratic()

int solveQuadratic	(	double	a,
		double	b,
		double	c,
		double *	solution )

Solve a quadratic equation for real solutions.

Given a quadratic equation of the form a*x^2 + b*x + c = 0, this function finds its real solutions, if any. The solutions are returned in the array solution. The function returns the number of real solutions found:

• 0 if no real solutions,
• 1 if one real solution (repeated root),
• 2 if two real solutions.

Parameters

[in]	a	Quadratic coefficient (for x^2).
[in]	b	Linear coefficient (for x).
[in]	c	Constant term.
[out]	solution	Array of size 2 for storing the found solutions.

Returns

The number of real solutions (0, 1, or 2).

Definition at line 139 of file poly.c.

                                                                   {
  double det;
  if (a == 0) {
    if (b == 0)
      return 0;
    solution[0] = -c / b;
    return 1;
  }
  if ((det = b * b - 4 * a * c) < 0)
    return 0;
  if (det == 0) {
    solution[0] = -b / a;
    return 1;
  }
  solution[0] = (-b - sqrt(det)) / (2 * a);
  solution[1] = (-b + sqrt(det)) / (2 * a);
  return 2;
}