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1 files changed, 114 insertions, 0 deletions

diff --git a/Homework/math4610/test/roots.t.c b/Homework/math4610/test/roots.t.c
new file mode 100644
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+++ b/Homework/math4610/test/roots.t.c
@@ -0,0 +1,114 @@
+#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);
+}