lizfcm/test/eigen.t.c

#include "lizfcm.test.h"
#include <math.h>

Matrix_double *eigen_test_matrix() {
  // produces a matrix that has eigenvalues [5 + sqrt{17}, 2, 5 - sqrt{17}]
  Matrix_double *m = InitMatrixWithSize(double, 3, 3, 0.0);
  m->data[0]->data[0] = 2.0;
  m->data[0]->data[1] = 2.0;
  m->data[0]->data[2] = 4.0;
  m->data[1]->data[0] = 1.0;
  m->data[1]->data[1] = 4.0;
  m->data[1]->data[2] = 7.0;
  m->data[2]->data[1] = 2.0;
  m->data[2]->data[2] = 6.0;
  return m;
}

UTEST(eigen, least_dominant_eigenvalue) {
  Matrix_double *m = eigen_test_matrix();

  double expected_least_dominant_eigenvalue = 0.87689; // 5 - sqrt(17)
  double tolerance = 0.0001;
  uint64_t max_iterations = 64;

  Array_double *v_guess = InitArrayWithSize(double, 3, 1.0);
  double approx_least_dominant_eigenvalue =
      least_dominant_eigenvalue(m, v_guess, tolerance, max_iterations);

  EXPECT_NEAR(expected_least_dominant_eigenvalue,
              approx_least_dominant_eigenvalue, tolerance);
}

UTEST(eigen, dominant_eigenvalue) {
  Matrix_double *m = InitMatrixWithSize(double, 2, 2, 0.0);
  m->data[0]->data[0] = 2.0;
  m->data[0]->data[1] = -12.0;
  m->data[1]->data[0] = 1.0;
  m->data[1]->data[1] = -5.0;

  Array_double *v_guess = InitArrayWithSize(double, 2, 1.0);
  double tolerance = 0.0001;
  uint64_t max_iterations = 64;

  double expect_dominant_eigenvalue = -2.0;

  double approx_dominant_eigenvalue =
      dominant_eigenvalue(m, v_guess, tolerance, max_iterations);

  EXPECT_NEAR(expect_dominant_eigenvalue, approx_dominant_eigenvalue,
              tolerance);
  free_matrix(m);
  free_vector(v_guess);
}

UTEST(eigen, shifted_eigenvalue) {
  Matrix_double *m = eigen_test_matrix();

  double least_dominant_eigenvalue = 0.87689; // 5 - sqrt{17}
  double dominant_eigenvalue = 9.12311;       // 5 + sqrt{17}
  double expected_middle_eigenvalue = 2.0;
  double shift = (dominant_eigenvalue + least_dominant_eigenvalue) / 2.0;

  double tolerance = 0.0001;
  uint64_t max_iterations = 64;
  Array_double *v_guess = InitArray(double, {0.5, 1.0, 0.75});

  double approx_middle_eigenvalue = shift_inverse_power_eigenvalue(
      m, v_guess, shift, tolerance, max_iterations);

  EXPECT_NEAR(approx_middle_eigenvalue, expected_middle_eigenvalue, tolerance);
}

UTEST(eigen, partition_find_eigenvalues) {
  Matrix_double *m = eigen_test_matrix();

  double least_dominant_eigenvalue = 0.87689; // 5 - sqrt{17}
  double dominant_eigenvalue = 9.12311;       // 5 + sqrt{17}
  double expected_middle_eigenvalue = 2.0;
  double expected_eigenvalues[3] = {least_dominant_eigenvalue,
                                    expected_middle_eigenvalue,
                                    dominant_eigenvalue};

  size_t partitions = 10;
  Matrix_double *guesses = InitMatrixWithSize(double, partitions, 3, 0.0);
  for (size_t y = 0; y < guesses->rows; y++) {
    free_vector(guesses->data[y]);
    guesses->data[y] = InitArray(double, {0.5, 1.0, 0.75});
  }

  double tolerance = 0.0001;
  uint64_t max_iterations = 64;

  int eigenvalues_found[3] = {false, false, false};
  Array_double *partition_eigenvalues =
      partition_find_eigenvalues(m, guesses, tolerance, max_iterations);

  for (size_t i = 0; i < partition_eigenvalues->size; i++)
    for (size_t eigenvalue_i = 0; eigenvalue_i < 3; eigenvalue_i++)
      if (fabs(partition_eigenvalues->data[i] - expected_eigenvalues[i]) <=
          tolerance)
        eigenvalues_found[eigenvalue_i] = true;

  for (size_t eigenvalue_i = 0; eigenvalue_i < 3; eigenvalue_i++)
    EXPECT_TRUE(eigenvalues_found[eigenvalue_i]);
}

UTEST(eigen, leslie_matrix_dominant_eigenvalue) {
  Array_double *felicity = InitArray(double, {0.0, 1.5, 0.8});
  Array_double *survivor_ratios = InitArray(double, {0.8, 0.55});
  Matrix_double *leslie = leslie_matrix(survivor_ratios, felicity);
  Array_double *v_guess = InitArrayWithSize(double, 3, 2.0);
  double tolerance = 0.0001;
  uint64_t max_iterations = 64;

  double expect_dominant_eigenvalue = 1.22005;

  double approx_dominant_eigenvalue =
      dominant_eigenvalue(leslie, v_guess, tolerance, max_iterations);

  EXPECT_NEAR(expect_dominant_eigenvalue, approx_dominant_eigenvalue,
              tolerance);

  free_vector(v_guess);
  free_vector(survivor_ratios);
  free_vector(felicity);
  free_matrix(leslie);
}
UTEST(eigen, leslie_matrix) {
  Array_double *felicity = InitArray(double, {0.0, 1.5, 0.8});
  Array_double *survivor_ratios = InitArray(double, {0.8, 0.55});

  Matrix_double *m = InitMatrixWithSize(double, 3, 3, 0.0);
  m->data[0]->data[0] = 0.0;
  m->data[0]->data[1] = 1.5;
  m->data[0]->data[2] = 0.8;
  m->data[1]->data[0] = 0.8;
  m->data[2]->data[1] = 0.55;

  Matrix_double *leslie = leslie_matrix(survivor_ratios, felicity);

  EXPECT_TRUE(matrix_equal(leslie, m));

  free_matrix(leslie);
  free_matrix(m);
  free_vector(felicity);
  free_vector(survivor_ratios);
}