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/*************************************************************************
* Copyright (C) 2010-2014 Tavian Barnes <tavianator@tavianator.com> *
* *
* This file is part of The Dimension Test Suite. *
* *
* The Dimension Test Suite 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. *
* *
* The Dimension Test Suite 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, see <http://www.gnu.org/licenses/>. *
*************************************************************************/
/**
* @file
* Basic tests of the polynomial root-finder.
*/
#include "tests.h"
#include "../polynomial.c"
#include <stdarg.h>
#define DMNSN_CLOSE_ENOUGH 1.0e-6
static void
dmnsn_assert_roots(const double poly[], size_t degree, size_t nroots_ex, ...)
{
double roots[degree];
size_t nroots = dmnsn_polynomial_solve(poly, degree, roots);
ck_assert_int_eq(nroots, nroots_ex);
va_list ap;
va_start(ap, nroots_ex);
for (size_t i = 0; i < nroots; ++i) {
double root_ex = va_arg(ap, double);
bool found = false;
for (size_t j = 0; j < nroots; ++j) {
double root = roots[j];
if (fabs(root_ex - root) >= dmnsn_epsilon) {
continue;
}
double evroot = dmnsn_polynomial_evaluate(poly, degree, root);
ck_assert(fabs(evroot) < DMNSN_CLOSE_ENOUGH);
double evmin = dmnsn_polynomial_evaluate(poly, degree, root - dmnsn_epsilon);
double evmax = dmnsn_polynomial_evaluate(poly, degree, root + dmnsn_epsilon);
ck_assert(fabs(evroot) <= fabs(evmin) && fabs(evroot) <= fabs(evmax));
found = true;
break;
}
if (!found) {
for (size_t j = 0; j < nroots; ++j) {
fprintf(stderr, "roots[%zu] == %.17g\n", j, roots[j]);
}
fprintf(stderr, "----\n");
ck_abort_msg("Expected root %.17g not found", root_ex);
}
}
va_end(ap);
}
DMNSN_TEST(linear, no_positive_roots)
{
// poly[] = x + 1
static const double poly[] = {
[1] = 1.0,
[0] = 1.0,
};
dmnsn_assert_roots(poly, 1, 0);
}
DMNSN_TEST(linear, one_root)
{
// poly[] = x - 1
static const double poly[] = {
[1] = 1.0,
[0] = -1.0,
};
dmnsn_assert_roots(poly, 1, 1, 1.0);
}
DMNSN_TEST(quadratic, no_roots)
{
// poly[] = x^2 + 1
static const double poly[] = {
[2] = 1.0,
[1] = 0.0,
[0] = 1.0,
};
dmnsn_assert_roots(poly, 2, 0);
}
DMNSN_TEST(quadratic, no_positive_roots)
{
// poly[] = (x + 1)^2
static const double poly[] = {
[2] = 1.0,
[1] = 2.0,
[0] = 1.0,
};
dmnsn_assert_roots(poly, 2, 0);
}
DMNSN_TEST(quadratic, one_positive_root)
{
// poly[] = (x + 1)*(x - 1)
static const double poly[] = {
[2] = 1.0,
[1] = 0.0,
[0] = -1.0,
};
dmnsn_assert_roots(poly, 2, 1, 1.0);
}
DMNSN_TEST(quadratic, two_roots)
{
// poly[] = (x - 1.2345)*(x - 2.3456)
static const double poly[] = {
[2] = 1.0,
[1] = -3.5801,
[0] = 2.8956432,
};
dmnsn_assert_roots(poly, 2, 2, 1.2345, 2.3456);
}
DMNSN_TEST(cubic, no_positive_roots)
{
// poly[] = x^3 + 1
static const double poly[] = {
[3] = 1.0,
[2] = 0.0,
[1] = 0.0,
[0] = 1.0,
};
dmnsn_assert_roots(poly, 3, 0);
}
DMNSN_TEST(cubic, one_root)
{
// poly[] = x^3 - 1
static const double poly[] = {
[3] = 1.0,
[2] = 0.0,
[1] = 0.0,
[0] = -1.0,
};
dmnsn_assert_roots(poly, 3, 1, 1.0);
}
DMNSN_TEST(cubic, two_roots)
{
// poly[] = (x - 1)*(x - 4)^2
static const double poly[] = {
[3] = 1.0,
[2] = -9.0,
[1] = 24.0,
[0] = -16.0,
};
dmnsn_assert_roots(poly, 3, 2, 1.0, 4.0);
}
DMNSN_TEST(cubic, three_roots)
{
// poly[] = (x - 1.2345)*(x - 2.3456)*(x - 100)
static const double poly[] = {
[3] = 1.0,
[2] = -103.5801,
[1] = 360.9056432,
[0] = -289.56432,
};
dmnsn_assert_roots(poly, 3, 3, 1.2345, 2.3456, 100.0);
}
DMNSN_TEST(quintic, four_roots)
{
// poly[] = 2*(x + 1)*(x - 1.2345)*(x - 2.3456)*(x - 5)*(x - 100)
static const double poly[] = {
[5] = 2.0,
[4] = -215.1602,
[3] = 1540.4520864,
[2] = -2430.5727856,
[1] = -1292.541872,
[0] = 2895.6432,
};
dmnsn_assert_roots(poly, 5, 4, 1.2345, 2.3456, 5.0, 100.0);
}
// repeated_root[] = (x - 1)^6
static const double repeated_root[7] = {
[6] = 1.0,
[5] = -6.0,
[4] = 15.0,
[3] = -20.0,
[2] = 15.0,
[1] = -6.0,
[0] = 1.0,
};
DMNSN_TEST(stability, equal_bounds)
{
double root = dmnsn_bisect_root(repeated_root, 6, 1.0, 1.0);
ck_assert_msg(root == 1.0, "root == %.17g", root);
}
DMNSN_TEST(stability, equal_values_at_bounds)
{
double root = dmnsn_bisect_root(repeated_root, 6, 0.9, 1.1);
ck_assert_msg(fabs(root - 1.0) < dmnsn_epsilon, "root == %.17g", root);
}
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