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#include "lizfcm.test.h"
#include <math.h>
#include <stdio.h>
double f1(double x) { return x * x - 9; }
double f2(double x) { return x * x - 5 * x + 6; }
double f2prime(double x) { return 2 * x - 5; }
double g1(double x) { return x + f2(x); }
double g2(double x) { return x - f2(x); }
UTEST(ivt, find_interval) {
Array_double *range = find_ivt_range(&f1, -10.0, 0.10, 200);
EXPECT_LT(f1(range->data[0]) * f1(range->data[1]), 0);
free_vector(range);
}
UTEST(root, bisection_with_error_assumption) {
Array_double *range = find_ivt_range(&f2, 2.5, 0.10, 200);
double tolerance = 0.01;
double root1 = bisect_find_root_with_error_assumption(
&f2, range->data[0], range->data[1], tolerance);
free_vector(range);
range = find_ivt_range(&f2, 0, 0.01, 500);
double root2 = bisect_find_root_with_error_assumption(
&f2, range->data[0], range->data[1], tolerance);
free_vector(range);
EXPECT_NEAR(3.0, root1, tolerance);
EXPECT_NEAR(2.0, root2, tolerance);
}
UTEST(root, fixed_point_iteration_method) {
// x^2 - 5x + 6 = (x - 3)(x - 2)
double expect_x2 = 3.0;
double expect_x1 = 2.0;
double tolerance = 0.001;
uint64_t max_iterations = 10;
double x_0 = 1.55; // 1.5 < 1.55 < 2.5
// g1(x) = x + f(x)
double root1 =
fixed_point_iteration_method(&f2, &g1, x_0, tolerance, max_iterations);
EXPECT_NEAR(root1, expect_x1, tolerance);
// g2(x) = x - f(x)
x_0 = 3.4; // 2.5 < 3.4 < 3.5
double root2 =
fixed_point_iteration_method(&f2, &g2, x_0, tolerance, max_iterations);
EXPECT_NEAR(root2, expect_x2, tolerance);
}
UTEST(root, fixed_point_newton_method) {
// x^2 - 5x + 6 = (x - 3)(x - 2)
double expect_x2 = 3.0;
double expect_x1 = 2.0;
double tolerance = 0.01;
uint64_t max_iterations = 10;
double x_0 = 1.55; // 1.5 < 1.55 < 2.5
double root1 =
fixed_point_newton_method(&f2, &f2prime, x_0, tolerance, max_iterations);
EXPECT_NEAR(root1, expect_x1, tolerance);
x_0 = 3.4; // 2.5 < 3.4 < 3.5
double root2 =
fixed_point_newton_method(&f2, &f2prime, x_0, tolerance, max_iterations);
EXPECT_NEAR(root2, expect_x2, tolerance);
}
UTEST(root, fixed_point_secant_method) {
// x^2 - 5x + 6 = (x - 3)(x - 2)
double expect_x2 = 3.0;
double expect_x1 = 2.0;
double delta = 0.01;
double tolerance = 0.01;
uint64_t max_iterations = 10;
double x_0 = 1.55; // 1.5 < 1.55 < 2.5
double root1 = fixed_point_secant_method(&f2, x_0, x_0 + delta, tolerance,
max_iterations);
EXPECT_NEAR(root1, expect_x1, tolerance);
x_0 = 3.4; // 2.5 < 3.4 < 3.5
double root2 = fixed_point_secant_method(&f2, x_0, x_0 + delta, tolerance,
max_iterations);
EXPECT_NEAR(root2, expect_x2, tolerance);
}
UTEST(root, fixed_point_hybrid_method) {
// x^2 - 5x + 6 = (x - 3)(x - 2)
double expect_x2 = 3.0;
double expect_x1 = 2.0;
double delta = 1.0;
double tolerance = 0.01;
uint64_t max_iterations = 10;
double x_0 = 1.55;
double root1 = fixed_point_secant_bisection_method(&f2, x_0, x_0 + delta,
tolerance, max_iterations);
EXPECT_NEAR(root1, expect_x1, tolerance);
x_0 = 2.5;
double root2 = fixed_point_secant_bisection_method(&f2, x_0, x_0 + delta,
tolerance, max_iterations);
EXPECT_NEAR(root2, expect_x2, tolerance);
}
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