add leslie matrix dominant eigenvalue unit test
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@ -1038,7 +1038,7 @@ double dominant_eigenvalue(Matrix_double *m, Array_double *v, double tolerance,
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+ Input: two pointers to ~Array_double~'s representing the ratio of individuals in an age class
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$x$ getting to the next age class $x+1$ and the number of offspring that individuals in an age
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class create in age class 0.
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+ Output: the leslie matrix generated with the input vectors.
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+ Output: the leslie matrix generated from the input vectors.
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#+BEGIN_SRC c
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Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
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Binary file not shown.
@ -1,4 +1,4 @@
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% Created 2023-11-10 Fri 20:54
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% Created 2023-11-15 Wed 14:43
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% Intended LaTeX compiler: pdflatex
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\documentclass[11pt]{article}
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\usepackage[utf8]{inputenc}
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@ -15,10 +15,10 @@
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\notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
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\author{Elizabeth Hunt}
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\date{\today}
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\title{LIZFCM Software Manual (v0.3)}
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\title{LIZFCM Software Manual (v0.4)}
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\hypersetup{
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pdfauthor={Elizabeth Hunt},
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pdftitle={LIZFCM Software Manual (v0.3)},
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pdftitle={LIZFCM Software Manual (v0.4)},
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pdfkeywords={},
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pdfsubject={},
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pdfcreator={Emacs 29.1 (Org mode 9.7-pre)},
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@ -30,7 +30,7 @@
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\setlength\parindent{0pt}
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\section{Design}
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\label{sec:orgdac8577}
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\label{sec:org78303cd}
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The LIZFCM static library (at \url{https://github.com/Simponic/math-4610}) is a successor to my
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attempt at writing codes for the Fundamentals of Computational Mathematics course in Common
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Lisp, but the effort required to meet the requirement of creating a static library became
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@ -47,7 +47,7 @@ the C programming language. I have a couple tenets for its design:
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in files, and not individual files per function.
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\end{itemize}
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\section{Compilation}
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\label{sec:org7755023}
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\label{sec:orgb417494}
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A provided \texttt{Makefile} is added for convencience. It has been tested on an \texttt{arm}-based M1 machine running
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MacOS as well as \texttt{x86} Arch Linux.
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@ -72,11 +72,11 @@ produce an object file:
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Which is then bundled into a static library in \texttt{lib/lizfcm.a} and can be linked
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in the standard method.
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\section{The LIZFCM API}
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\label{sec:org940357c}
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\label{sec:org2144095}
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\subsection{Simple Routines}
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\label{sec:org28486b0}
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\label{sec:orgc9edf4b}
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\subsubsection{\texttt{smaceps}}
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\label{sec:org1de3a4e}
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\label{sec:org449b8ec}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{smaceps}
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@ -101,7 +101,7 @@ float smaceps() {
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}
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\end{verbatim}
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\subsubsection{\texttt{dmaceps}}
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\label{sec:org742e61e}
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\label{sec:org9a9ac05}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{dmaceps}
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@ -126,9 +126,9 @@ double dmaceps() {
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}
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\end{verbatim}
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\subsection{Derivative Routines}
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\label{sec:org21233d3}
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\label{sec:orgc31ab7b}
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\subsubsection{\texttt{central\_derivative\_at}}
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\label{sec:org6a00f6c}
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\label{sec:org83dc368}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{central\_derivative\_at}
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@ -151,14 +151,14 @@ double central_derivative_at(double (*f)(double), double a, double h) {
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double x2 = a + h;
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double x1 = a - h;
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double y2 = (*f)(x2);
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double y1 = (*f)(x1);
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double y2 = f(x2);
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double y1 = f(x1);
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return (y2 - y1) / (x2 - x1);
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}
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\end{verbatim}
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\subsubsection{\texttt{forward\_derivative\_at}}
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\label{sec:org78f40a9}
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\label{sec:orgf1ec748}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{forward\_derivative\_at}
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@ -181,14 +181,14 @@ double forward_derivative_at(double (*f)(double), double a, double h) {
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double x2 = a + h;
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double x1 = a;
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double y2 = (*f)(x2);
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double y1 = (*f)(x1);
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double y2 = f(x2);
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double y1 = f(x1);
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return (y2 - y1) / (x2 - x1);
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}
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\end{verbatim}
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\subsubsection{\texttt{backward\_derivative\_at}}
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\label{sec:org888d29e}
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\label{sec:orga2827be}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{backward\_derivative\_at}
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@ -211,16 +211,16 @@ double backward_derivative_at(double (*f)(double), double a, double h) {
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double x2 = a;
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double x1 = a - h;
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double y2 = (*f)(x2);
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double y1 = (*f)(x1);
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double y2 = f(x2);
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double y1 = f(x1);
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return (y2 - y1) / (x2 - x1);
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}
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\end{verbatim}
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\subsection{Vector Routines}
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\label{sec:org73b87ea}
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\label{sec:org4bc395e}
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\subsubsection{Vector Arithmetic: \texttt{add\_v, minus\_v}}
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\label{sec:orgf8b5da1}
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\label{sec:orgcc76baa}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{add\_v}, \texttt{minus\_v}
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@ -250,7 +250,7 @@ Array_double *minus_v(Array_double *v1, Array_double *v2) {
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}
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\end{verbatim}
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\subsubsection{Norms: \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}}
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\label{sec:orgc5368a1}
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\label{sec:org015b19a}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}
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@ -283,7 +283,7 @@ double linf_norm(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{vector\_distance}}
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\label{sec:org0505e0b}
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\label{sec:org78137a7}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{vector\_distance}
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@ -303,7 +303,7 @@ double vector_distance(Array_double *v1, Array_double *v2,
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}
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\end{verbatim}
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\subsubsection{Distances: \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}}
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\label{sec:org1c45dae}
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\label{sec:orgd71d562}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}
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@ -328,7 +328,7 @@ double linf_distance(Array_double *v1, Array_double *v2) {
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}
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\end{verbatim}
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\subsubsection{\texttt{sum\_v}}
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\label{sec:org687d1bd}
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\label{sec:orgb188125}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{sum\_v}
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@ -346,7 +346,7 @@ double sum_v(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{scale\_v}}
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\label{sec:org5926df1}
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\label{sec:org0a828aa}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{scale\_v}
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@ -364,7 +364,7 @@ Array_double *scale_v(Array_double *v, double m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{free\_vector}}
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\label{sec:org3458f6a}
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\label{sec:orgfff2e8b}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{free\_vector}
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@ -381,7 +381,7 @@ void free_vector(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{add\_element}}
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\label{sec:org54cba50}
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\label{sec:orgf002846}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{add\_element}
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@ -400,7 +400,7 @@ Array_double *add_element(Array_double *v, double x) {
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}
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\end{verbatim}
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\subsubsection{\texttt{slice\_element}}
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\label{sec:org02cd40a}
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\label{sec:org8ef8f62}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{slice\_element}
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@ -418,7 +418,7 @@ Array_double *slice_element(Array_double *v, size_t x) {
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}
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\end{verbatim}
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\subsubsection{\texttt{copy\_vector}}
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\label{sec:org4b0c599}
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\label{sec:org6794d79}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{copy\_vector}
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@ -437,7 +437,7 @@ Array_double *copy_vector(Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{format\_vector\_into}}
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\label{sec:orgde12441}
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\label{sec:orgaaea3a7}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{format\_vector\_into}
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@ -466,9 +466,9 @@ void format_vector_into(Array_double *v, char *s) {
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}
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\end{verbatim}
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\subsection{Matrix Routines}
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\label{sec:orgd85d8ec}
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\label{sec:org7b74a8b}
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\subsubsection{\texttt{lu\_decomp}}
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\label{sec:org6a14cbd}
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\label{sec:orgb5ebd91}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{lu\_decomp}
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@ -528,7 +528,7 @@ Matrix_double **lu_decomp(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{bsubst}}
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\label{sec:org8b51171}
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\label{sec:org4b2bdc3}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{bsubst}
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@ -553,7 +553,7 @@ Array_double *bsubst(Matrix_double *u, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{fsubst}}
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\label{sec:orgf9180a0}
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\label{sec:orgf6f799e}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{fsubst}
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@ -580,7 +580,7 @@ Array_double *fsubst(Matrix_double *l, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{solve\_matrix\_lu\_bsubst}}
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\label{sec:orgf3845f4}
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\label{sec:org789acbf}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -616,7 +616,7 @@ Array_double *solve_matrix_lu_bsubst(Matrix_double *m, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{gaussian\_elimination}}
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\label{sec:orge926b79}
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\label{sec:orge5cbe95}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -671,7 +671,7 @@ Matrix_double *gaussian_elimination(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{solve\_matrix\_gaussian}}
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\label{sec:orgc4f0d99}
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\label{sec:org9c2b7c3}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -704,7 +704,7 @@ Array_double *solve_matrix_gaussian(Matrix_double *m, Array_double *b) {
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}
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\end{verbatim}
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\subsubsection{\texttt{m\_dot\_v}}
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\label{sec:orgb7015af}
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\label{sec:org4c184b5}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -725,7 +725,7 @@ Array_double *m_dot_v(Matrix_double *m, Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{put\_identity\_diagonal}}
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\label{sec:orge955396}
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\label{sec:org45882fa}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -743,7 +743,7 @@ Matrix_double *put_identity_diagonal(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{slice\_column}}
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\label{sec:org886997f}
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\label{sec:org520c709}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -766,7 +766,7 @@ Matrix_double *slice_column(Matrix_double *m, size_t x) {
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}
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\end{verbatim}
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\subsubsection{\texttt{add\_column}}
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\label{sec:org405e1c5}
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\label{sec:org84191b6}
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\begin{itemize}
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\item Author: Elizabet Hunt
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\item Location: \texttt{src/matrix.c}
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@ -789,7 +789,7 @@ Matrix_double *add_column(Matrix_double *m, Array_double *v) {
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}
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\end{verbatim}
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\subsubsection{\texttt{copy\_matrix}}
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\label{sec:org01ea984}
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\label{sec:orgb84b548}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -808,7 +808,7 @@ Matrix_double *copy_matrix(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{free\_matrix}}
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\label{sec:orgab8c2cf}
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\label{sec:org0de0d86}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Location: \texttt{src/matrix.c}
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@ -826,7 +826,7 @@ void free_matrix(Matrix_double *m) {
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}
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\end{verbatim}
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\subsubsection{\texttt{format\_matrix\_into}}
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\label{sec:org9e01978}
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\label{sec:orgf8ba876}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{format\_matrix\_into}
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@ -853,9 +853,9 @@ void format_matrix_into(Matrix_double *m, char *s) {
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}
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\end{verbatim}
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\subsection{Root Finding Methods}
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\label{sec:org81f315b}
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\label{sec:org8f80c14}
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\subsubsection{\texttt{find\_ivt\_range}}
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\label{sec:orgc1dde4d}
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\label{sec:orgf7fc734}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{find\_ivt\_range}
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@ -887,14 +887,15 @@ Array_double *find_ivt_range(double (*f)(double), double start_x, double delta,
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}
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\end{verbatim}
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\subsubsection{\texttt{bisect\_find\_root}}
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\label{sec:orgb42a836}
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\label{sec:orgcf0f46b}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name(s): \texttt{bisect\_find\_root}
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\item Input: a one-ary function taking a double and producing a double, a closed interval represented
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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
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\texttt{max\_iterations} to break us out of a loop if we can never reach the \texttt{tolerance}.
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\item Output: a vector of size of 3 \texttt{double}'s representing first the .
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\item Output: a vector of size of 3, \texttt{double}'s representing first the range \texttt{[a,b]} and then the midpoint,
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\texttt{c} of the range.
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\item Description: recursively uses binary search to split the interval until we reach \texttt{tolerance}. We
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also assume the function \texttt{f} is continuous on \texttt{[a, b]}.
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\end{itemize}
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@ -909,7 +910,7 @@ Array_double *bisect_find_root(double (*f)(double), double a, double b,
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double c = (1.0 / 2) * (a + b);
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if (b - a < tolerance || max_iterations == 0)
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return InitArray(double, a, b, c);
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return InitArray(double, {a, b, c});
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if (f(a) * f(c) < 0)
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return bisect_find_root(f, a, c, tolerance, max_iterations - 1);
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@ -917,7 +918,7 @@ Array_double *bisect_find_root(double (*f)(double), double a, double b,
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}
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\end{verbatim}
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\subsubsection{\texttt{bisect\_find\_root\_with\_error\_assumption}}
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\label{sec:org762134e}
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\label{sec:org64e4346}
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\begin{itemize}
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\item Author: Elizabeth Hunt
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\item Name: \texttt{bisect\_find\_root\_with\_error\_assumption}
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@ -945,7 +946,7 @@ double bisect_find_root_with_error_assumption(double (*f)(double), double a,
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}
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\end{verbatim}
|
||||
\subsubsection{\texttt{fixed\_point\_iteration\_method}}
|
||||
\label{sec:org9f210ad}
|
||||
\label{sec:orge6f6ba8}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{fixed\_point\_iteration\_method}
|
||||
@ -976,7 +977,7 @@ double fixed_point_iteration_method(double (*f)(double), double (*g)(double),
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsubsection{\texttt{fixed\_point\_newton\_method}}
|
||||
\label{sec:orgedecc45}
|
||||
\label{sec:org9c22d8f}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{fixed\_point\_newton\_method}
|
||||
@ -1004,44 +1005,40 @@ double fixed_point_newton_method(double (*f)(double), double (*fprime)(double),
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsubsection{\texttt{fixed\_point\_secant\_method}}
|
||||
\label{sec:org63bcbe2}
|
||||
\label{sec:org446d473}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{fixed\_point\_secant\_method}
|
||||
\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
|
||||
trying to find a root, a guess \(x_0\), and a \(\delta\) of our first guess at which we draw the first
|
||||
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
|
||||
thus simplifies to \(x_1 = (x_0 + \delta) - f(x_0 + \delta) \frac{(x_0 + \delta) - x_0}{f(x_0 + \delta) - f(x_0)} = (x_0 + \delta) - f(x_0 + \delta) \frac{\delta}{f(x_0 + \delta) - f(x_0)}\).
|
||||
trying to find a root, a guess \(x_0\) and \(x_1\) in which a root lies between \([x_0, x_1]\); applying the
|
||||
sequence \(x_n = x_{n-1} - f(x_{n-1}) \frac{x_{n-1} - x_{n-2}}{f(x_{n-1}) - f(x_{n-2})}\).
|
||||
Additionally, a \texttt{max\_iterations} and \texttt{tolerance} as defined in the above method are required
|
||||
inputs.
|
||||
\item Output: a double representing the found approximate root \(\approx x^*\) recursively applied to the sequence.
|
||||
\end{itemize}
|
||||
\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) {
|
||||
if (max_iterations <= 0)
|
||||
return x_0;
|
||||
if (max_iterations == 0)
|
||||
return x_1;
|
||||
|
||||
double x_1 = x_0 + delta;
|
||||
double root = x_1 - f(x_1) * (delta / (f(x_1) - f(x_0)));
|
||||
double root = x_1 - f(x_1) * ((x_1 - x_0) / (f(x_1) - f(x_0)));
|
||||
|
||||
if (tolerance >= fabs(f(root)))
|
||||
return root;
|
||||
|
||||
double new_delta = root - x_1;
|
||||
return fixed_point_secant_method(f, x_1, new_delta, tolerance,
|
||||
max_iterations);
|
||||
return fixed_point_secant_method(f, x_1, root, tolerance, max_iterations - 1);
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsubsection{\texttt{fixed\_point\_secant\_bisection\_method}}
|
||||
\label{sec:org72d3074}
|
||||
\label{sec:orgade170f}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{fixed\_point\_secant\_method}
|
||||
\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
|
||||
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
|
||||
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
|
||||
@ -1052,17 +1049,16 @@ constraints defined.
|
||||
|
||||
\begin{verbatim}
|
||||
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) {
|
||||
double begin = x_0;
|
||||
double end = x_0 + delta;
|
||||
double end = x_1;
|
||||
double root = x_0;
|
||||
|
||||
while (tolerance < fabs(f(root)) && max_iterations > 0) {
|
||||
max_iterations--;
|
||||
|
||||
double secant_root =
|
||||
fixed_point_secant_method(f, begin, end - begin, tolerance, 1);
|
||||
double secant_root = fixed_point_secant_method(f, begin, end, tolerance, 1);
|
||||
|
||||
if (secant_root < begin || secant_root > end) {
|
||||
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;
|
||||
// the root exists in [begin, secant_root]
|
||||
|
||||
if (f(root) * f(begin) < 0)
|
||||
end = secant_root;
|
||||
end = secant_root; // the root exists in [begin, secant_root]
|
||||
else
|
||||
begin = secant_root;
|
||||
}
|
||||
@ -1087,9 +1083,9 @@ double fixed_point_secant_bisection_method(double (*f)(double), double x_0,
|
||||
}
|
||||
\end{verbatim}
|
||||
\subsection{Linear Routines}
|
||||
\label{sec:org04f3e56}
|
||||
\label{sec:orgc389980}
|
||||
\subsubsection{\texttt{least\_squares\_lin\_reg}}
|
||||
\label{sec:orgbd48d8e}
|
||||
\label{sec:org850d9f6}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Name: \texttt{least\_squares\_lin\_reg}
|
||||
@ -1118,13 +1114,83 @@ Line *least_squares_lin_reg(Array_double *x, Array_double *y) {
|
||||
return line;
|
||||
}
|
||||
\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}
|
||||
\label{sec:orgf6b30a5}
|
||||
\label{sec:org925aa32}
|
||||
\subsubsection{Data Types}
|
||||
\label{sec:orgd382789}
|
||||
\label{sec:org37335a1}
|
||||
\begin{enumerate}
|
||||
\item \texttt{Line}
|
||||
\label{sec:orgab590b9}
|
||||
\label{sec:orgaf72b30}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/types.h}
|
||||
@ -1137,7 +1203,7 @@ typedef struct Line {
|
||||
} Line;
|
||||
\end{verbatim}
|
||||
\item The \texttt{Array\_<type>} and \texttt{Matrix\_<type>}
|
||||
\label{sec:org5be3024}
|
||||
\label{sec:org82faf8e}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/types.h}
|
||||
@ -1168,10 +1234,10 @@ typedef struct {
|
||||
\end{verbatim}
|
||||
\end{enumerate}
|
||||
\subsubsection{Macros}
|
||||
\label{sec:org20a391c}
|
||||
\label{sec:org1f988ea}
|
||||
\begin{enumerate}
|
||||
\item \texttt{c\_max} and \texttt{c\_min}
|
||||
\label{sec:orgfc6117a}
|
||||
\label{sec:org8b37b18}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
@ -1184,7 +1250,7 @@ typedef struct {
|
||||
#define c_min(x, y) (((x) <= (y)) ? (x) : (y))
|
||||
\end{verbatim}
|
||||
\item \texttt{InitArray}
|
||||
\label{sec:org472f039}
|
||||
\label{sec:org04ec2d7}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
@ -1204,7 +1270,7 @@ typedef struct {
|
||||
})
|
||||
\end{verbatim}
|
||||
\item \texttt{InitArrayWithSize}
|
||||
\label{sec:orgbe950b8}
|
||||
\label{sec:org4aff8f6}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
@ -1224,7 +1290,7 @@ typedef struct {
|
||||
})
|
||||
\end{verbatim}
|
||||
\item \texttt{InitMatrixWithSize}
|
||||
\label{sec:org5965f3b}
|
||||
\label{sec:org3457577}
|
||||
\begin{itemize}
|
||||
\item Author: Elizabeth Hunt
|
||||
\item Location: \texttt{inc/macros.h}
|
||||
|
||||
@ -8,3 +8,8 @@
|
||||
See ~UTEST(eigen, dominant_eigenvalue)~ in ~test/eigen.t.c~ and the entry
|
||||
~Eigen-Adjacent -> dominant_eigenvalue~ in the LIZFCM API documentation.
|
||||
* 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
18
notes/Nov-27.org
Normal 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
|
||||
@ -12,7 +12,7 @@ Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio,
|
||||
age_class_offspring->size, 0.0);
|
||||
|
||||
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++)
|
||||
leslie->data[i + 1]->data[i] = age_class_surivor_ratio->data[i];
|
||||
|
||||
@ -17,6 +17,30 @@ UTEST(eigen, leslie_matrix) {
|
||||
|
||||
free_matrix(leslie);
|
||||
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) {
|
||||
|
||||
Loading…
Reference in New Issue
Block a user