From aa77d733b0cb100b63a824c60548f19526711bbc Mon Sep 17 00:00:00 2001 From: Elizabeth Hunt Date: Mon, 27 Nov 2023 10:14:50 -0700 Subject: [PATCH] add leslie matrix dominant eigenvalue unit test --- doc/software_manual.org | 2 +- doc/software_manual.pdf | Bin 269159 -> 270972 bytes doc/software_manual.tex | 234 +++++++++++++++++++++++++--------------- homeworks/hw-7.org | 5 + notes/Nov-27.org | 18 ++++ src/eigen.c | 2 +- test/eigen.t.c | 24 +++++ 7 files changed, 199 insertions(+), 86 deletions(-) create mode 100644 notes/Nov-27.org diff --git a/doc/software_manual.org b/doc/software_manual.org index a54006a..f438534 100644 --- a/doc/software_manual.org +++ b/doc/software_manual.org @@ -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 $x$ 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. ++ Output: the leslie matrix generated from the input vectors. #+BEGIN_SRC c Matrix_double *leslie_matrix(Array_double *age_class_surivor_ratio, diff --git a/doc/software_manual.pdf b/doc/software_manual.pdf index 4355e3f3bf6e7628c66788536b99bc14350778eb..d099736d16f89d4813f1b7ba04d24712d4235d1d 100644 GIT binary patch delta 101707 zcmZsCV~i$H(`DPXHO*<;wr$%srk}R`v~AnA?e1xt)3*10clXcc+oX~@sXsTB+}x@< zr|xMh%I7c&3WbuG1U)kYI~>LQ^2j*Vo zOe|cu{mKd}B1KD$iKeR_@E-7P!m^{?mSL7@W|0P%>xg5m@2}65L4Vu0;}&?C!WD+Z zRe{u2VP7$`MT1n2g7E*e(t?ak3SlSz{fQwhtWuehOpa+0W)?Y+bmYlSV+Sr_%@?IM zLTNo;nbbU>lsH<5Wd<;7SWJpR^%5>^ET;bp)>R;8J7^ItUQ`azv!Ir`uCGGDq?S-I z4p%AD(wJmp4uf}z7F>eYeufZ0K|sAnq!v{;3{w_`cS-RPf$9KDpaL7yqNAP^GK`AJ zm)h;X98?UJhZbaWOXH>Nnl7Z{nqX5MtVkQPw{$CpL9(2pFARW;!E=KoDq8QiEh<96 z!9;+N(u!jW-^Sypw>hLmNlQYkPK^LR8Yq8~A%QJ4DL;C|;po>>w+rY<9m(#;^C88P 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zlPz$UZlo7mMw;B}J;$mU=|EcDmNv!OkR!-Zq|f%-uAe}&Z-KuT6+J{hz zRDW^XE{Rc|G>8ni?W~DW#&i)Ga@%_&ru%7LCAY%^u`&KgqlL%F89Yg&>ayDhAL%Ph zv%G@v=Q;Brad@REw~v3;R~Tfu2ALjr9+`Ffp%?-|(q-n8@Xhv|(Bu$1LMDsxP)xpAM zCytY(0kDrK_6G>(M>=%-c3LNdd9nCs{bc`bP}bf4QIYe^z4W(M1^3}!v?{tUt!UNY ze)yqQjqaZowQ6$z<~yyL-G3U>s>QSZAG9iYwqMn%?AezUty(?%`gg6`yioW`t9y1Y z%xr1Z;e}WKKV&DOA+4#bx72y51CkfadBL0)%ymF=BG&5f*8M#= 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\_} and \texttt{Matrix\_} -\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} diff --git a/homeworks/hw-7.org b/homeworks/hw-7.org index bbd0f49..1a5ebb0 100644 --- a/homeworks/hw-7.org +++ b/homeworks/hw-7.org @@ -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 + diff --git a/notes/Nov-27.org b/notes/Nov-27.org new file mode 100644 index 0000000..c4d38b0 --- /dev/null +++ b/notes/Nov-27.org @@ -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 diff --git a/src/eigen.c b/src/eigen.c index 40b41b8..83b1127 100644 --- a/src/eigen.c +++ b/src/eigen.c @@ -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]; diff --git a/test/eigen.t.c b/test/eigen.t.c index 9b2f6f0..31c3500 100644 --- a/test/eigen.t.c +++ b/test/eigen.t.c @@ -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) {