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add leslie matrix dominant eigenvalue unit test

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Elizabeth Hunt 2023-11-27 10:14:50 -07:00
parent 4d2d4f5d7a
commit aa77d733b0
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GPG Key ID: 52B3774857EB24B1
7 changed files with 199 additions and 86 deletions
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doc/software_manual.org
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@ -1038,7 +1038,7 @@ double dominant_eigenvalue(Matrix_double *m, Array_double *v, double tolerance,
+ Input: two pointers to ~Array_double~'s representing the ratio of individuals in an age class + 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 $x$ getting to the next age class $x+1$ and the number of offspring that individuals in an age
class create in age class 0. class create in age class 0.
+ Output: the leslie matrix generated with the input vectors. + Output: the leslie matrix generated from the input vectors.
#+BEGIN_SRC c #+BEGIN_SRC c
Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio, Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,

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doc/software_manual.pdf
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doc/software_manual.tex
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@ -1,4 +1,4 @@
% Created 2023-11-10 Fri 20:54 % Created 2023-11-15 Wed 14:43
% Intended LaTeX compiler: pdflatex % Intended LaTeX compiler: pdflatex
\documentclass[11pt]{article} \documentclass[11pt]{article}
\usepackage[utf8]{inputenc} \usepackage[utf8]{inputenc}
@ -15,10 +15,10 @@
\notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry} \notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
\author{Elizabeth Hunt} \author{Elizabeth Hunt}
\date{\today} \date{\today}
\title{LIZFCM Software Manual (v0.3)} \title{LIZFCM Software Manual (v0.4)}
\hypersetup{ \hypersetup{
pdfauthor={Elizabeth Hunt}, pdfauthor={Elizabeth Hunt},
pdftitle={LIZFCM Software Manual (v0.3)}, pdftitle={LIZFCM Software Manual (v0.4)},
pdfkeywords={}, pdfkeywords={},
pdfsubject={}, pdfsubject={},
pdfcreator={Emacs 29.1 (Org mode 9.7-pre)}, pdfcreator={Emacs 29.1 (Org mode 9.7-pre)},
@ -30,7 +30,7 @@
\setlength\parindent{0pt} \setlength\parindent{0pt}
\section{Design} \section{Design}
\label{sec:orgdac8577} \label{sec:org78303cd}
The LIZFCM static library (at \url{https://github.com/Simponic/math-4610}) is a successor to my The LIZFCM static library (at \url{https://github.com/Simponic/math-4610}) is a successor to my
attempt at writing codes for the Fundamentals of Computational Mathematics course in Common attempt at writing codes for the Fundamentals of Computational Mathematics course in Common
Lisp, but the effort required to meet the requirement of creating a static library became Lisp, but the effort required to meet the requirement of creating a static library became
@ -47,7 +47,7 @@ the C programming language. I have a couple tenets for its design:
in files, and not individual files per function. in files, and not individual files per function.
\end{itemize} \end{itemize}
\section{Compilation} \section{Compilation}
\label{sec:org7755023} \label{sec:orgb417494}
A provided \texttt{Makefile} is added for convencience. It has been tested on an \texttt{arm}-based M1 machine running A provided \texttt{Makefile} is added for convencience. It has been tested on an \texttt{arm}-based M1 machine running
MacOS as well as \texttt{x86} Arch Linux. MacOS as well as \texttt{x86} Arch Linux.
@ -72,11 +72,11 @@ produce an object file:
Which is then bundled into a static library in \texttt{lib/lizfcm.a} and can be linked Which is then bundled into a static library in \texttt{lib/lizfcm.a} and can be linked
in the standard method. in the standard method.
\section{The LIZFCM API} \section{The LIZFCM API}
\label{sec:org940357c} \label{sec:org2144095}
\subsection{Simple Routines} \subsection{Simple Routines}
\label{sec:org28486b0} \label{sec:orgc9edf4b}
\subsubsection{\texttt{smaceps}} \subsubsection{\texttt{smaceps}}
\label{sec:org1de3a4e} \label{sec:org449b8ec}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{smaceps} \item Name: \texttt{smaceps}
@ -101,7 +101,7 @@ float smaceps() {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{dmaceps}} \subsubsection{\texttt{dmaceps}}
\label{sec:org742e61e} \label{sec:org9a9ac05}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{dmaceps} \item Name: \texttt{dmaceps}
@ -126,9 +126,9 @@ double dmaceps() {
} }
\end{verbatim} \end{verbatim}
\subsection{Derivative Routines} \subsection{Derivative Routines}
\label{sec:org21233d3} \label{sec:orgc31ab7b}
\subsubsection{\texttt{central\_derivative\_at}} \subsubsection{\texttt{central\_derivative\_at}}
\label{sec:org6a00f6c} \label{sec:org83dc368}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{central\_derivative\_at} \item Name: \texttt{central\_derivative\_at}
@ -151,14 +151,14 @@ double central_derivative_at(double (*f)(double), double a, double h) {
double x2 = a + h; double x2 = a + h;
double x1 = a - h; double x1 = a - h;
double y2 = (*f)(x2); double y2 = f(x2);
double y1 = (*f)(x1); double y1 = f(x1);
return (y2 - y1) / (x2 - x1); return (y2 - y1) / (x2 - x1);
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{forward\_derivative\_at}} \subsubsection{\texttt{forward\_derivative\_at}}
\label{sec:org78f40a9} \label{sec:orgf1ec748}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{forward\_derivative\_at} \item Name: \texttt{forward\_derivative\_at}
@ -181,14 +181,14 @@ double forward_derivative_at(double (*f)(double), double a, double h) {
double x2 = a + h; double x2 = a + h;
double x1 = a; double x1 = a;
double y2 = (*f)(x2); double y2 = f(x2);
double y1 = (*f)(x1); double y1 = f(x1);
return (y2 - y1) / (x2 - x1); return (y2 - y1) / (x2 - x1);
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{backward\_derivative\_at}} \subsubsection{\texttt{backward\_derivative\_at}}
\label{sec:org888d29e} \label{sec:orga2827be}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{backward\_derivative\_at} \item Name: \texttt{backward\_derivative\_at}
@ -211,16 +211,16 @@ double backward_derivative_at(double (*f)(double), double a, double h) {
double x2 = a; double x2 = a;
double x1 = a - h; double x1 = a - h;
double y2 = (*f)(x2); double y2 = f(x2);
double y1 = (*f)(x1); double y1 = f(x1);
return (y2 - y1) / (x2 - x1); return (y2 - y1) / (x2 - x1);
} }
\end{verbatim} \end{verbatim}
\subsection{Vector Routines} \subsection{Vector Routines}
\label{sec:org73b87ea} \label{sec:org4bc395e}
\subsubsection{Vector Arithmetic: \texttt{add\_v, minus\_v}} \subsubsection{Vector Arithmetic: \texttt{add\_v, minus\_v}}
\label{sec:orgf8b5da1} \label{sec:orgcc76baa}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name(s): \texttt{add\_v}, \texttt{minus\_v} \item Name(s): \texttt{add\_v}, \texttt{minus\_v}
@ -250,7 +250,7 @@ Array_double *minus_v(Array_double *v1, Array_double *v2) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{Norms: \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}} \subsubsection{Norms: \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}}
\label{sec:orgc5368a1} \label{sec:org015b19a}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name(s): \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm} \item Name(s): \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}
@ -283,7 +283,7 @@ double linf_norm(Array_double *v) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{vector\_distance}} \subsubsection{\texttt{vector\_distance}}
\label{sec:org0505e0b} \label{sec:org78137a7}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{vector\_distance} \item Name: \texttt{vector\_distance}
@ -303,7 +303,7 @@ double vector_distance(Array_double *v1, Array_double *v2,
} }
\end{verbatim} \end{verbatim}
\subsubsection{Distances: \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}} \subsubsection{Distances: \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}}
\label{sec:org1c45dae} \label{sec:orgd71d562}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name(s): \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance} \item Name(s): \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}
@ -328,7 +328,7 @@ double linf_distance(Array_double *v1, Array_double *v2) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{sum\_v}} \subsubsection{\texttt{sum\_v}}
\label{sec:org687d1bd} \label{sec:orgb188125}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{sum\_v} \item Name: \texttt{sum\_v}
@ -346,7 +346,7 @@ double sum_v(Array_double *v) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{scale\_v}} \subsubsection{\texttt{scale\_v}}
\label{sec:org5926df1} \label{sec:org0a828aa}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{scale\_v} \item Name: \texttt{scale\_v}
@ -364,7 +364,7 @@ Array_double *scale_v(Array_double *v, double m) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{free\_vector}} \subsubsection{\texttt{free\_vector}}
\label{sec:org3458f6a} \label{sec:orgfff2e8b}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{free\_vector} \item Name: \texttt{free\_vector}
@ -381,7 +381,7 @@ void free_vector(Array_double *v) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{add\_element}} \subsubsection{\texttt{add\_element}}
\label{sec:org54cba50} \label{sec:orgf002846}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{add\_element} \item Name: \texttt{add\_element}
@ -400,7 +400,7 @@ Array_double *add_element(Array_double *v, double x) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{slice\_element}} \subsubsection{\texttt{slice\_element}}
\label{sec:org02cd40a} \label{sec:org8ef8f62}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{slice\_element} \item Name: \texttt{slice\_element}
@ -418,7 +418,7 @@ Array_double *slice_element(Array_double *v, size_t x) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{copy\_vector}} \subsubsection{\texttt{copy\_vector}}
\label{sec:org4b0c599} \label{sec:org6794d79}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{copy\_vector} \item Name: \texttt{copy\_vector}
@ -437,7 +437,7 @@ Array_double *copy_vector(Array_double *v) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{format\_vector\_into}} \subsubsection{\texttt{format\_vector\_into}}
\label{sec:orgde12441} \label{sec:orgaaea3a7}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{format\_vector\_into} \item Name: \texttt{format\_vector\_into}
@ -466,9 +466,9 @@ void format_vector_into(Array_double *v, char *s) {
} }
\end{verbatim} \end{verbatim}
\subsection{Matrix Routines} \subsection{Matrix Routines}
\label{sec:orgd85d8ec} \label{sec:org7b74a8b}
\subsubsection{\texttt{lu\_decomp}} \subsubsection{\texttt{lu\_decomp}}
\label{sec:org6a14cbd} \label{sec:orgb5ebd91}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{lu\_decomp} \item Name: \texttt{lu\_decomp}
@ -528,7 +528,7 @@ Matrix_double **lu_decomp(Matrix_double *m) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{bsubst}} \subsubsection{\texttt{bsubst}}
\label{sec:org8b51171} \label{sec:org4b2bdc3}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{bsubst} \item Name: \texttt{bsubst}
@ -553,7 +553,7 @@ Array_double *bsubst(Matrix_double *u, Array_double *b) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{fsubst}} \subsubsection{\texttt{fsubst}}
\label{sec:orgf9180a0} \label{sec:orgf6f799e}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{fsubst} \item Name: \texttt{fsubst}
@ -580,7 +580,7 @@ Array_double *fsubst(Matrix_double *l, Array_double *b) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{solve\_matrix\_lu\_bsubst}} \subsubsection{\texttt{solve\_matrix\_lu\_bsubst}}
\label{sec:orgf3845f4} \label{sec:org789acbf}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -616,7 +616,7 @@ Array_double *solve_matrix_lu_bsubst(Matrix_double *m, Array_double *b) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{gaussian\_elimination}} \subsubsection{\texttt{gaussian\_elimination}}
\label{sec:orge926b79} \label{sec:orge5cbe95}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -671,7 +671,7 @@ Matrix_double *gaussian_elimination(Matrix_double *m) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{solve\_matrix\_gaussian}} \subsubsection{\texttt{solve\_matrix\_gaussian}}
\label{sec:orgc4f0d99} \label{sec:org9c2b7c3}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -704,7 +704,7 @@ Array_double *solve_matrix_gaussian(Matrix_double *m, Array_double *b) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{m\_dot\_v}} \subsubsection{\texttt{m\_dot\_v}}
\label{sec:orgb7015af} \label{sec:org4c184b5}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -725,7 +725,7 @@ Array_double *m_dot_v(Matrix_double *m, Array_double *v) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{put\_identity\_diagonal}} \subsubsection{\texttt{put\_identity\_diagonal}}
\label{sec:orge955396} \label{sec:org45882fa}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -743,7 +743,7 @@ Matrix_double *put_identity_diagonal(Matrix_double *m) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{slice\_column}} \subsubsection{\texttt{slice\_column}}
\label{sec:org886997f} \label{sec:org520c709}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -766,7 +766,7 @@ Matrix_double *slice_column(Matrix_double *m, size_t x) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{add\_column}} \subsubsection{\texttt{add\_column}}
\label{sec:org405e1c5} \label{sec:org84191b6}
\begin{itemize} \begin{itemize}
\item Author: Elizabet Hunt \item Author: Elizabet Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -789,7 +789,7 @@ Matrix_double *add_column(Matrix_double *m, Array_double *v) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{copy\_matrix}} \subsubsection{\texttt{copy\_matrix}}
\label{sec:org01ea984} \label{sec:orgb84b548}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -808,7 +808,7 @@ Matrix_double *copy_matrix(Matrix_double *m) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{free\_matrix}} \subsubsection{\texttt{free\_matrix}}
\label{sec:orgab8c2cf} \label{sec:org0de0d86}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{src/matrix.c} \item Location: \texttt{src/matrix.c}
@ -826,7 +826,7 @@ void free_matrix(Matrix_double *m) {
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{format\_matrix\_into}} \subsubsection{\texttt{format\_matrix\_into}}
\label{sec:org9e01978} \label{sec:orgf8ba876}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{format\_matrix\_into} \item Name: \texttt{format\_matrix\_into}
@ -853,9 +853,9 @@ void format_matrix_into(Matrix_double *m, char *s) {
} }
\end{verbatim} \end{verbatim}
\subsection{Root Finding Methods} \subsection{Root Finding Methods}
\label{sec:org81f315b} \label{sec:org8f80c14}
\subsubsection{\texttt{find\_ivt\_range}} \subsubsection{\texttt{find\_ivt\_range}}
\label{sec:orgc1dde4d} \label{sec:orgf7fc734}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{find\_ivt\_range} \item Name: \texttt{find\_ivt\_range}
@ -887,14 +887,15 @@ Array_double *find_ivt_range(double (*f)(double), double start_x, double delta,
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{bisect\_find\_root}} \subsubsection{\texttt{bisect\_find\_root}}
\label{sec:orgb42a836} \label{sec:orgcf0f46b}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name(s): \texttt{bisect\_find\_root} \item Name(s): \texttt{bisect\_find\_root}
\item Input: a one-ary function taking a double and producing a double, a closed interval represented \item Input: a one-ary function taking a double and producing a double, a closed interval represented
by \texttt{a} and \texttt{b}: \texttt{[a, b]}, a \texttt{tolerance} at which we return the estimated root once \(b-a < \text{tolerance}\), and a by \texttt{a} and \texttt{b}: \texttt{[a, b]}, a \texttt{tolerance} at which we return the estimated root once \(b-a < \text{tolerance}\), and a
\texttt{max\_iterations} to break us out of a loop if we can never reach the \texttt{tolerance}. \texttt{max\_iterations} to break us out of a loop if we can never reach the \texttt{tolerance}.
\item Output: a vector of size of 3 \texttt{double}'s representing first the . \item Output: a vector of size of 3, \texttt{double}'s representing first the range \texttt{[a,b]} and then the midpoint,
\texttt{c} of the range.
\item Description: recursively uses binary search to split the interval until we reach \texttt{tolerance}. We \item Description: recursively uses binary search to split the interval until we reach \texttt{tolerance}. We
also assume the function \texttt{f} is continuous on \texttt{[a, b]}. also assume the function \texttt{f} is continuous on \texttt{[a, b]}.
\end{itemize} \end{itemize}
@ -909,7 +910,7 @@ Array_double *bisect_find_root(double (*f)(double), double a, double b,
double c = (1.0 / 2) * (a + b); double c = (1.0 / 2) * (a + b);
if (b - a < tolerance || max_iterations == 0) if (b - a < tolerance || max_iterations == 0)
return InitArray(double, a, b, c); return InitArray(double, {a, b, c});
if (f(a) * f(c) < 0) if (f(a) * f(c) < 0)
return bisect_find_root(f, a, c, tolerance, max_iterations - 1); return bisect_find_root(f, a, c, tolerance, max_iterations - 1);
@ -917,7 +918,7 @@ Array_double *bisect_find_root(double (*f)(double), double a, double b,
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{bisect\_find\_root\_with\_error\_assumption}} \subsubsection{\texttt{bisect\_find\_root\_with\_error\_assumption}}
\label{sec:org762134e} \label{sec:org64e4346}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{bisect\_find\_root\_with\_error\_assumption} \item Name: \texttt{bisect\_find\_root\_with\_error\_assumption}
@ -945,7 +946,7 @@ double bisect_find_root_with_error_assumption(double (*f)(double), double a,
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{fixed\_point\_iteration\_method}} \subsubsection{\texttt{fixed\_point\_iteration\_method}}
\label{sec:org9f210ad} \label{sec:orge6f6ba8}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{fixed\_point\_iteration\_method} \item Name: \texttt{fixed\_point\_iteration\_method}
@ -976,7 +977,7 @@ double fixed_point_iteration_method(double (*f)(double), double (*g)(double),
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{fixed\_point\_newton\_method}} \subsubsection{\texttt{fixed\_point\_newton\_method}}
\label{sec:orgedecc45} \label{sec:org9c22d8f}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{fixed\_point\_newton\_method} \item Name: \texttt{fixed\_point\_newton\_method}
@ -1004,44 +1005,40 @@ double fixed_point_newton_method(double (*f)(double), double (*fprime)(double),
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{fixed\_point\_secant\_method}} \subsubsection{\texttt{fixed\_point\_secant\_method}}
\label{sec:org63bcbe2} \label{sec:org446d473}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{fixed\_point\_secant\_method} \item Name: \texttt{fixed\_point\_secant\_method}
\item Location: \texttt{src/roots.c} \item Location: \texttt{src/roots.c}
\item Input: a pointer to a oneary function \(f\) taking a double and producing a double of which we are \item Input: a pointer to a oneary function \(f\) taking a double and producing a double of which we are
trying to find a root, a guess \(x_0\), and a \(\delta\) of our first guess at which we draw the first trying to find a root, a guess \(x_0\) and \(x_1\) in which a root lies between \([x_0, x_1]\); applying the
secant line according to the sequence \(x_n = x_{n-1} - f(x_{n-1}) \frac{x_{n-1} - x_{n-2}}{f(x_{n-1}) - f(x_{n-2})}\) which sequence \(x_n = x_{n-1} - f(x_{n-1}) \frac{x_{n-1} - x_{n-2}}{f(x_{n-1}) - f(x_{n-2})}\).
thus simplifies to \(x_1 = (x_0 + \delta) - f(x_0 + \delta) \frac{(x_0 + \delta) - x_0}{f(x_0 + \delta) - f(x_0)} = (x_0 + \delta) - f(x_0 + \delta) \frac{\delta}{f(x_0 + \delta) - f(x_0)}\).
Additionally, a \texttt{max\_iterations} and \texttt{tolerance} as defined in the above method are required Additionally, a \texttt{max\_iterations} and \texttt{tolerance} as defined in the above method are required
inputs. inputs.
\item Output: a double representing the found approximate root \(\approx x^*\) recursively applied to the sequence. \item Output: a double representing the found approximate root \(\approx x^*\) recursively applied to the sequence.
\end{itemize} \end{itemize}
\begin{verbatim} \begin{verbatim}
double fixed_point_secant_method(double (*f)(double), double x_0, double delta, double fixed_point_secant_method(double (*f)(double), double x_0, double x_1,
double tolerance, size_t max_iterations) { double tolerance, size_t max_iterations) {
if (max_iterations <= 0) if (max_iterations == 0)
return x_0; return x_1;
double x_1 = x_0 + delta; double root = x_1 - f(x_1) * ((x_1 - x_0) / (f(x_1) - f(x_0)));
double root = x_1 - f(x_1) * (delta / (f(x_1) - f(x_0)));
if (tolerance >= fabs(f(root))) if (tolerance >= fabs(f(root)))
return root; return root;
double new_delta = root - x_1; return fixed_point_secant_method(f, x_1, root, tolerance, max_iterations - 1);
return fixed_point_secant_method(f, x_1, new_delta, tolerance,
max_iterations);
} }
\end{verbatim} \end{verbatim}
\subsubsection{\texttt{fixed\_point\_secant\_bisection\_method}} \subsubsection{\texttt{fixed\_point\_secant\_bisection\_method}}
\label{sec:org72d3074} \label{sec:orgade170f}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{fixed\_point\_secant\_method} \item Name: \texttt{fixed\_point\_secant\_method}
\item Location: \texttt{src/roots.c} \item Location: \texttt{src/roots.c}
\item Input: a pointer to a oneary function \(f\) taking a double and producing a double of which we are \item Input: a pointer to a oneary function \(f\) taking a double and producing a double of which we are
trying to find a root, a guess \(x_0\), and a \(\delta\) of which we define our first interval \([x_0, x_0 + \delta]\). trying to find a root, a guess \(x_0\), and a \(x_1\) of which we define our first interval \([x_0, x_1]\).
Then, we perform a single iteration of the \texttt{fixed\_point\_secant\_method} on this interval; if it Then, we perform a single iteration of the \texttt{fixed\_point\_secant\_method} on this interval; if it
produces a root outside, we refresh the interval and root respectively with the given produces a root outside, we refresh the interval and root respectively with the given
\texttt{bisect\_find\_root} method. Additionally, a \texttt{max\_iterations} and \texttt{tolerance} as defined in the above method are required \texttt{bisect\_find\_root} method. Additionally, a \texttt{max\_iterations} and \texttt{tolerance} as defined in the above method are required
@ -1052,17 +1049,16 @@ constraints defined.
\begin{verbatim} \begin{verbatim}
double fixed_point_secant_bisection_method(double (*f)(double), double x_0, double fixed_point_secant_bisection_method(double (*f)(double), double x_0,
double delta, double tolerance, double x_1, double tolerance,
size_t max_iterations) { size_t max_iterations) {
double begin = x_0; double begin = x_0;
double end = x_0 + delta; double end = x_1;
double root = x_0; double root = x_0;
while (tolerance < fabs(f(root)) && max_iterations > 0) { while (tolerance < fabs(f(root)) && max_iterations > 0) {
max_iterations--; max_iterations--;
double secant_root = double secant_root = fixed_point_secant_method(f, begin, end, tolerance, 1);
fixed_point_secant_method(f, begin, end - begin, tolerance, 1);
if (secant_root < begin || secant_root > end) { if (secant_root < begin || secant_root > end) {
Array_double *range_root = bisect_find_root(f, begin, end, tolerance, 1); Array_double *range_root = bisect_find_root(f, begin, end, tolerance, 1);
@ -1076,9 +1072,9 @@ double fixed_point_secant_bisection_method(double (*f)(double), double x_0,
} }
root = secant_root; root = secant_root;
// the root exists in [begin, secant_root]
if (f(root) * f(begin) < 0) if (f(root) * f(begin) < 0)
end = secant_root; end = secant_root; // the root exists in [begin, secant_root]
else else
begin = secant_root; begin = secant_root;
} }
@ -1087,9 +1083,9 @@ double fixed_point_secant_bisection_method(double (*f)(double), double x_0,
} }
\end{verbatim} \end{verbatim}
\subsection{Linear Routines} \subsection{Linear Routines}
\label{sec:org04f3e56} \label{sec:orgc389980}
\subsubsection{\texttt{least\_squares\_lin\_reg}} \subsubsection{\texttt{least\_squares\_lin\_reg}}
\label{sec:orgbd48d8e} \label{sec:org850d9f6}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Name: \texttt{least\_squares\_lin\_reg} \item Name: \texttt{least\_squares\_lin\_reg}
@ -1118,13 +1114,83 @@ Line *least_squares_lin_reg(Array_double *x, Array_double *y) {
return line; return line;
} }
\end{verbatim} \end{verbatim}
\subsection{Eigen-Adjacent}
\label{sec:org6bea1aa}
\subsubsection{\texttt{dominant\_eigenvalue}}
\label{sec:org0e70920}
\begin{itemize}
\item Author: Elizabeth Hunt
\item Name: \texttt{dominant\_eigenvalue}
\item Location: \texttt{src/eigen.c}
\item Input: a pointer to an invertible matrix \texttt{m}, an initial eigenvector guess \texttt{v} (that is non
zero or orthogonal to an eigenvector with the dominant eigenvalue), a \texttt{tolerance} and
\texttt{max\_iterations} that act as stop conditions
\item Output: the dominant eigenvalue with the highest magnitude, approximated with the Power
Iteration Method
\end{itemize}
\begin{verbatim}
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{verbatim}
\subsubsection{\texttt{leslie\_matrix}}
\label{sec:org88d4547}
\begin{itemize}
\item Author: Elizabeth Hunt
\item Name: \texttt{leslie\_matrix}
\item Location: \texttt{src/eigen.c}
\item Input: two pointers to \texttt{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.
\item Output: the leslie matrix generated with the input vectors.
\end{itemize}
\begin{verbatim}
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{verbatim}
\subsection{Appendix / Miscellaneous} \subsection{Appendix / Miscellaneous}
\label{sec:orgf6b30a5} \label{sec:org925aa32}
\subsubsection{Data Types} \subsubsection{Data Types}
\label{sec:orgd382789} \label{sec:org37335a1}
\begin{enumerate} \begin{enumerate}
\item \texttt{Line} \item \texttt{Line}
\label{sec:orgab590b9} \label{sec:orgaf72b30}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{inc/types.h} \item Location: \texttt{inc/types.h}
@ -1137,7 +1203,7 @@ typedef struct Line {
} Line; } Line;
\end{verbatim} \end{verbatim}
\item The \texttt{Array\_<type>} and \texttt{Matrix\_<type>} \item The \texttt{Array\_<type>} and \texttt{Matrix\_<type>}
\label{sec:org5be3024} \label{sec:org82faf8e}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{inc/types.h} \item Location: \texttt{inc/types.h}
@ -1168,10 +1234,10 @@ typedef struct {
\end{verbatim} \end{verbatim}
\end{enumerate} \end{enumerate}
\subsubsection{Macros} \subsubsection{Macros}
\label{sec:org20a391c} \label{sec:org1f988ea}
\begin{enumerate} \begin{enumerate}
\item \texttt{c\_max} and \texttt{c\_min} \item \texttt{c\_max} and \texttt{c\_min}
\label{sec:orgfc6117a} \label{sec:org8b37b18}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{inc/macros.h} \item Location: \texttt{inc/macros.h}
@ -1184,7 +1250,7 @@ typedef struct {
#define c_min(x, y) (((x) <= (y)) ? (x) : (y)) #define c_min(x, y) (((x) <= (y)) ? (x) : (y))
\end{verbatim} \end{verbatim}
\item \texttt{InitArray} \item \texttt{InitArray}
\label{sec:org472f039} \label{sec:org04ec2d7}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{inc/macros.h} \item Location: \texttt{inc/macros.h}
@ -1204,7 +1270,7 @@ typedef struct {
}) })
\end{verbatim} \end{verbatim}
\item \texttt{InitArrayWithSize} \item \texttt{InitArrayWithSize}
\label{sec:orgbe950b8} \label{sec:org4aff8f6}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{inc/macros.h} \item Location: \texttt{inc/macros.h}
@ -1224,7 +1290,7 @@ typedef struct {
}) })
\end{verbatim} \end{verbatim}
\item \texttt{InitMatrixWithSize} \item \texttt{InitMatrixWithSize}
\label{sec:org5965f3b} \label{sec:org3457577}
\begin{itemize} \begin{itemize}
\item Author: Elizabeth Hunt \item Author: Elizabeth Hunt
\item Location: \texttt{inc/macros.h} \item Location: \texttt{inc/macros.h}

5
homeworks/hw-7.org
View File

@ -8,3 +8,8 @@
See ~UTEST(eigen, dominant_eigenvalue)~ in ~test/eigen.t.c~ and the entry See ~UTEST(eigen, dominant_eigenvalue)~ in ~test/eigen.t.c~ and the entry
~Eigen-Adjacent -> dominant_eigenvalue~ in the LIZFCM API documentation. ~Eigen-Adjacent -> dominant_eigenvalue~ in the LIZFCM API documentation.
* Question Two * Question Two
See ~UTEST(eigen, leslie_matrix_dominant_eigenvalue)~ in ~test/eigen.t.c~
and the entry ~Eigen-Adjacent -> leslie_matrix~ in the LIZFCM API
documentation.
* Question Three

18
notes/Nov-27.org Normal file
View File

@ -0,0 +1,18 @@
x^{k+1} = D^{-1}(b - (L + U) x^k)
x^{k + 1} \rightarrow Ax^k
#+BEGIN_SRC c
loop while (err > tol && iter < maxiter) {
for (int i = 0; i < n; i++) {
sum = b[i];
for (int j = 0; j < i; j++) {
sum = sum - a[i][x] * x_0[i];
}
for (int j = i; j < n; j++) {
sum = sum + a[i][j] * x_0[j];
}
x_1[i] = sum / a[i][i];
}
}
#+END_SRC

2
src/eigen.c
View File

@ -12,7 +12,7 @@ Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
age_class_offspring->size, 0.0); age_class_offspring->size, 0.0);
free_vector(leslie->data[0]); free_vector(leslie->data[0]);
leslie->data[0] = age_class_offspring; leslie->data[0] = copy_vector(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];

24
test/eigen.t.c
View File

@ -17,6 +17,30 @@ UTEST(eigen, leslie_matrix) {
free_matrix(leslie); free_matrix(leslie);
free_matrix(m); free_matrix(m);
free_vector(felicity);
free_vector(survivor_ratios);
}
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, 1.0);
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, dominant_eigenvalue) { UTEST(eigen, dominant_eigenvalue) {