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/*************************************************************************
* Copyright (C) 2009-2011 Tavian Barnes <tavianator@tavianator.com> *
* *
* This file is part of The Dimension Library. *
* *
* The Dimension Library is free software; you can redistribute it and/ *
* or modify it under the terms of the GNU Lesser General Public License *
* as published by the Free Software Foundation; either version 3 of the *
* License, or (at your option) any later version. *
* *
* The Dimension Library 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 *
* Lesser General Public License for more details. *
* *
* You should have received a copy of the GNU Lesser General Public *
* License along with this program. If not, see *
* <http://www.gnu.org/licenses/>. *
*************************************************************************/
/**
* @file
* Utility functions for working with and numerically solving polynomials.
* Polynomials are represented as simple arrays where the ith element is the
* coefficient on x^i. In general, we are only interested in positive roots.
*/
#include "internal.h"
#include <stddef.h>
#include <stdio.h>
/**
* Evaluate a polynomial at \p x.
* @param[in] poly The coefficients of the polynomial to evaluate, in order
* from lowest degree to highest degree. The array should
* have dimension <tt>degree + 1</tt>.
* @param[in] degree The degree of the polynomial.
* @param[in] x The value of the variable at which to evaluate.
*/
DMNSN_INTERNAL DMNSN_INLINE double
dmnsn_polynomial_evaluate(const double poly[], size_t degree, double x)
{
double ret = poly[degree];
size_t i;
for (i = degree; i-- > 0;) {
ret = ret*x + poly[i];
}
return ret;
}
/**
* Evaluate the derivative of a polynomial at \p x.
* @param[in] poly The coefficients of the polynomial to evaluate.
* @param[in] degree The degree of the polynomial.
* @param[in] x The value of the variable at which to evaluate.
*/
DMNSN_INTERNAL DMNSN_INLINE double
dmnsn_polynomial_evaluate_derivative(const double poly[], size_t degree, double x)
{
double ret = poly[degree]*degree;
size_t i;
for (i = degree - 1; i >= 1; --i) {
ret = ret*x + poly[i]*i;
}
return ret;
}
/**
* Find the positive roots of a polynomial.
* @param[in] poly The coefficients of the polynomial to solve.
* @param[in] degree The degree of the polynomial.
* @param[out] x An array in which to store the roots. It should have
* dimension \p degree.
* @return The number of positive roots stored in \c x[].
*/
DMNSN_INTERNAL size_t dmnsn_polynomial_solve(const double poly[], size_t degree, double x[]);
/**
* Output a polynomial. The polynomial is printed as a function of x suitable
* for input into a CAS, and without a trailing newline.
* @param[in,out] file The file to write to.
* @param[in] poly The coefficients of the polynomial to print.
* @param[in] degree The degree of the polynomial.
*/
DMNSN_INTERNAL void dmnsn_polynomial_print(FILE *file, const double poly[], size_t degree);
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