add hw 7 and documentation for q1 and part of q2 in lizfcm api reference

This commit is contained in:
Elizabeth Hunt 2023-11-15 14:43:22 -07:00
parent c02573cb66
commit 4d2d4f5d7a
Signed by: simponic
GPG Key ID: 52B3774857EB24B1
3 changed files with 78 additions and 6 deletions

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@ -1,4 +1,4 @@
#+TITLE: LIZFCM Software Manual (v0.3) #+TITLE: LIZFCM Software Manual (v0.4)
#+AUTHOR: Elizabeth Hunt #+AUTHOR: Elizabeth Hunt
#+LATEX_HEADER: \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry} #+LATEX_HEADER: \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
#+LATEX: \setlength\parindent{0pt} #+LATEX: \setlength\parindent{0pt}
@ -286,7 +286,6 @@ double sum_v(Array_double *v) {
} }
#+END_SRC #+END_SRC
*** ~scale_v~ *** ~scale_v~
+ Author: Elizabeth Hunt + Author: Elizabeth Hunt
+ Name: ~scale_v~ + Name: ~scale_v~
@ -993,6 +992,71 @@ Line *least_squares_lin_reg(Array_double *x, Array_double *y) {
return line; return line;
} }
#+END_SRC #+END_SRC
** Eigen-Adjacent
*** ~dominant_eigenvalue~
+ Author: Elizabeth Hunt
+ Name: ~dominant_eigenvalue~
+ Location: ~src/eigen.c~
+ Input: a pointer to an invertible matrix ~m~, an initial eigenvector guess ~v~ (that is non
zero or orthogonal to an eigenvector with the dominant eigenvalue), a ~tolerance~ and
~max_iterations~ that act as stop conditions
+ Output: the dominant eigenvalue with the highest magnitude, approximated with the Power
Iteration Method
#+BEGIN_SRC c
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 *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;
}
#+END_SRC
*** ~leslie_matrix~
+ Author: Elizabeth Hunt
+ Name: ~leslie_matrix~
+ Location: ~src/eigen.c~
+ Input: two pointers to ~Array_double~'s representing the ratio of individuals in an age class
$x$ getting to the next age class $x+1$ and the number of offspring that individuals in an age
class create in age class 0.
+ Output: the leslie matrix generated with the input vectors.
#+BEGIN_SRC c
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] = 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;
}
#+END_SRC
** Appendix / Miscellaneous ** Appendix / Miscellaneous
*** Data Types *** Data Types
**** ~Line~ **** ~Line~

10
homeworks/hw-7.org Normal file
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@ -0,0 +1,10 @@
#+TITLE: Homework 6
#+AUTHOR: Elizabeth Hunt
#+LATEX_HEADER: \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
#+LATEX: \setlength\parindent{0pt}
#+OPTIONS: toc:nil
* Question One
See ~UTEST(eigen, dominant_eigenvalue)~ in ~test/eigen.t.c~ and the entry
~Eigen-Adjacent -> dominant_eigenvalue~ in the LIZFCM API documentation.
* Question Two

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@ -14,10 +14,8 @@ Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
free_vector(leslie->data[0]); free_vector(leslie->data[0]);
leslie->data[0] = age_class_offspring; leslie->data[0] = age_class_offspring;
for (size_t i = 0; i < age_class_surivor_ratio->size; i++) { for (size_t i = 0; i < age_class_surivor_ratio->size; i++)
leslie->data[i + 1]->data[i] = age_class_surivor_ratio->data[i]; leslie->data[i + 1]->data[i] = age_class_surivor_ratio->data[i];
}
return leslie; return leslie;
} }
@ -37,9 +35,9 @@ double dominant_eigenvalue(Matrix_double *m, Array_double *v, double tolerance,
Array_double *mx = m_dot_v(m, eigenvector_2); Array_double *mx = m_dot_v(m, eigenvector_2);
double new_lambda = double new_lambda =
v_dot_v(mx, eigenvector_2) / v_dot_v(eigenvector_2, eigenvector_2); v_dot_v(mx, eigenvector_2) / v_dot_v(eigenvector_2, eigenvector_2);
error = fabs(new_lambda - lambda); error = fabs(new_lambda - lambda);
lambda = new_lambda; lambda = new_lambda;
free_vector(eigenvector_1); free_vector(eigenvector_1);
eigenvector_1 = eigenvector_2; eigenvector_1 = eigenvector_2;
} }