This commit is contained in:
Elizabeth Hunt 2023-11-27 14:45:48 -07:00
parent 793c01c9bd
commit 0981ffa00c
Signed by: simponic
GPG Key ID: 52B3774857EB24B1
6 changed files with 124 additions and 3 deletions

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@ -1096,7 +1096,44 @@ double least_dominant_eigenvalue(Matrix_double *m, Array_double *v,
return shift_inverse_power_eigenvalue(m, v, 0.0, tolerance, max_iterations);
}
#+END_SRC
*** ~partition_find_eigenvalues~
+ Author: Elizabeth Hunt
+ Name: ~partition_find_eigenvalues~
+ Location: ~src/eigen.c~
+ Input: a pointer to an invertible matrix ~m~, a matrix whose rows correspond to initial
eigenvector guesses at each "partition" which is computed from a uniform distribution
between the number of rows this "guess matrix" has and the distance between the least
dominant eigenvalue and the most dominant. Additionally, a ~max_iterations~ and a ~tolerance~
that act as stop conditions.
+ Output: a vector of ~doubles~ corresponding to the "nearest" eigenvalue at the midpoint of
each partition, via the given guess of that partition.
#+BEGIN_SRC c
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;
}
#+END_SRC
*** ~leslie_matrix~
+ Author: Elizabeth Hunt
+ Name: ~leslie_matrix~

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@ -41,3 +41,21 @@ With the initial guess: $[0.5, 1.0, 0.75]$.
See also the entry ~Eigen-Adjacent -> shift_inverse_power_eigenvalue~ in the LIZFCM API
documentation.
* Question Five
See ~UTEST(eigen, partition_find_eigenvalues)~ in ~test/eigen.t.c~ which
finds the eigenvalues in a partition of 10 on the matrix:
\begin{bmatrix}
2 & 2 & 4 \\
1 & 4 & 7 \\
0 & 2 & 6
\end{bmatrix}
which has eigenvalues: $5 + \sqrt{17}, 2, 5 - \sqrt{17}$, and should produce all three from
the partitions when given the guesses $[0.5, 1.0, 0.75]$ from the questions above.
See also the entry ~Eigen-Adjacent -> partition_find_eigenvalues~ in the LIZFCM API
documentation.
* Question Six

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@ -82,6 +82,10 @@ extern double shift_inverse_power_eigenvalue(Matrix_double *m, Array_double *v,
extern double least_dominant_eigenvalue(Matrix_double *m, Array_double *v,
double tolerance,
size_t max_iterations);
extern Array_double *partition_find_eigenvalues(Matrix_double *m,
Matrix_double *guesses,
double tolerance,
size_t max_iterations);
extern Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
Array_double *age_class_offspring);
#endif // LIZFCM_H

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@ -84,6 +84,32 @@ double shift_inverse_power_eigenvalue(Matrix_double *m, Array_double *v,
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;
}
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);

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@ -1,4 +1,5 @@
#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}]
@ -69,6 +70,40 @@ UTEST(eigen, shifted_eigenvalue) {
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});

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@ -1,7 +1,8 @@
#include "lizfcm.h"
#include "utest.h"
#ifndef LIZFCM_TEST_H
#define LIZFCM_TEST_H
#include "lizfcm.h"
#include "utest.h"
#endif // LIZFCM_TEST_H