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#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);
}
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