1 files changed, 116 insertions, 0 deletions
diff --git a/Homework/math4610/src/eigen.c b/Homework/math4610/src/eigen.c
new file mode 100644
index 0000000..49cc0e4
--- /dev/null
+++ b/Homework/math4610/src/eigen.c
@@ -0,0 +1,116 @@
+#include "lizfcm.h"
+#include <assert.h>
+#include <math.h>
+#include <stdio.h>
+#include <string.h>
+
+double least_dominant_eigenvalue(Matrix_double *m, Array_double *v,
+                                 double tolerance, size_t max_iterations) {
+  return shift_inverse_power_eigenvalue(m, v, 0.0, tolerance, max_iterations);
+}
+
+double dominant_eigenvalue(Matrix_double *m, Array_double *v, double tolerance,
+                           size_t max_iterations) {
+  assert(m->rows == m->cols);
+  assert(m->rows == v->size);
+
+  double error = tolerance;
+  size_t iter = max_iterations;
+  double lambda = 0.0;
+  Array_double *eigenvector_1 = copy_vector(v);
+
+  while (error >= tolerance && (--iter) > 0) {
+    Array_double *eigenvector_2 = m_dot_v(m, eigenvector_1);
+    Array_double *normalized_eigenvector_2 =
+        scale_v(eigenvector_2, 1.0 / linf_norm(eigenvector_2));
+    free_vector(eigenvector_2);
+    eigenvector_2 = normalized_eigenvector_2;
+
+    Array_double *mx = m_dot_v(m, eigenvector_2);
+    double new_lambda =
+        v_dot_v(mx, eigenvector_2) / v_dot_v(eigenvector_2, eigenvector_2);
+
+    error = fabs(new_lambda - lambda);
+    lambda = new_lambda;
+    free_vector(eigenvector_1);
+    eigenvector_1 = eigenvector_2;
+  }
+
+  return lambda;
+}
+
+double shift_inverse_power_eigenvalue(Matrix_double *m, Array_double *v,
+                                      double shift, double tolerance,
+                                      size_t max_iterations) {
+  assert(m->rows == m->cols);
+  assert(m->rows == v->size);
+
+  Matrix_double *m_c = copy_matrix(m);
+  for (size_t y = 0; y < m_c->rows; ++y)
+    m_c->data[y]->data[y] = m_c->data[y]->data[y] - shift;
+
+  double error = tolerance;
+  size_t iter = max_iterations;
+  double lambda = shift;
+  Array_double *eigenvector_1 = copy_vector(v);
+
+  while (error >= tolerance && (--iter) > 0) {
+    Array_double *eigenvector_2 = solve_matrix_lu_bsubst(m_c, eigenvector_1);
+    Array_double *normalized_eigenvector_2 =
+        scale_v(eigenvector_2, 1.0 / linf_norm(eigenvector_2));
+    free_vector(eigenvector_2);
+
+    Array_double *mx = m_dot_v(m, normalized_eigenvector_2);
+    double new_lambda =
+        v_dot_v(mx, normalized_eigenvector_2) /
+        v_dot_v(normalized_eigenvector_2, normalized_eigenvector_2);
+
+    error = fabs(new_lambda - lambda);
+    lambda = new_lambda;
+    free_vector(eigenvector_1);
+    eigenvector_1 = normalized_eigenvector_2;
+  }
+
+  return lambda;
+}
+
+Array_double *partition_find_eigenvalues(Matrix_double *m,
+                                         Matrix_double *guesses,
+                                         double tolerance,
+                                         size_t max_iterations) {
+  assert(guesses->rows >=
+         2); // we need at least, the most and least dominant eigenvalues
+
+  double end = dominant_eigenvalue(m, guesses->data[guesses->rows - 1],
+                                   tolerance, max_iterations);
+  double begin =
+      least_dominant_eigenvalue(m, guesses->data[0], tolerance, max_iterations);
+
+  double delta = (end - begin) / guesses->rows;
+  Array_double *eigenvalues = InitArrayWithSize(double, guesses->rows, 0.0);
+  for (size_t i = 0; i < guesses->rows; i++) {
+    double box_midpoint = ((delta * i) + (delta * (i + 1))) / 2;
+
+    double nearest_eigenvalue = shift_inverse_power_eigenvalue(
+        m, guesses->data[i], box_midpoint, tolerance, max_iterations);
+
+    eigenvalues->data[i] = nearest_eigenvalue;
+  }
+
+  return eigenvalues;
+}
+
+Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
+                             Array_double *age_class_offspring) {
+  assert(age_class_surivor_ratio->size + 1 == age_class_offspring->size);
+
+  Matrix_double *leslie = InitMatrixWithSize(double, age_class_offspring->size,
+                                             age_class_offspring->size, 0.0);
+
+  free_vector(leslie->data[0]);
+  leslie->data[0] = copy_vector(age_class_offspring);
+
+  for (size_t i = 0; i < age_class_surivor_ratio->size; i++)
+    leslie->data[i + 1]->data[i] = age_class_surivor_ratio->data[i];
+  return leslie;
+}