diff options
Diffstat (limited to 'doc')
| -rw-r--r-- | doc/software_manual.org | 243 | ||||
| -rw-r--r-- | doc/software_manual.pdf | bin | 180558 -> 179781 bytes | |||
| -rw-r--r-- | doc/software_manual.tex | 96 |
3 files changed, 250 insertions, 89 deletions
diff --git a/doc/software_manual.org b/doc/software_manual.org index 981d863..eebcf17 100644 --- a/doc/software_manual.org +++ b/doc/software_manual.org @@ -5,7 +5,7 @@ #+STARTUP: entitiespretty fold inlineimages * Design -The LIZFCM static library (at [[https://github.com/Simponic/math-4610][[https://github.com/Simponic/math-4610]] is a successor to my +The LIZFCM static library (at [[https://github.com/Simponic/math-4610]]) is a successor to my 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 too difficult to integrate outside of the ~ASDF~ solution that Common Lisp already brings @@ -14,13 +14,14 @@ to the table. All of the work established in ~deprecated-cl~ has been painstakingly translated into the C programming language. I have a couple tenets for its design: -+ Implemntations of routines should all be done immutably in respect to arguments. ++ Implementations of routines should all be done immutably in respect to arguments. + Functional programming is good (it's... rough in C though). -+ Routines are separated into "module" c files, and not individual files per function. ++ Routines are separated into "modules" that follow a form of separation of concerns + in files, and not individual files per function. * Compilation -A provided ~Makefile~ is added for convencience. It has been tested on an M1 machine running MacOS as -well as Arch Linux. +A provided ~Makefile~ is added for convencience. It has been tested on an ~arm~-based M1 machine running +MacOS as well as ~x86~ Arch Linux. 1. ~cd~ into the root of the repo 2. ~make~ @@ -317,6 +318,39 @@ void free_vector(Array_double *v) { } #+END_SRC +*** ~add_element~ ++ Author: Elizabeth Hunt ++ Name: ~add_element~ ++ Location: ~src/vector.c~ ++ Input: a pointer to an ~Array_double~ ++ Output: a new ~Array_double~ with element ~x~ appended. + +#+BEGIN_SRC c +Array_double *add_element(Array_double *v, double x) { + Array_double *pushed = InitArrayWithSize(double, v->size + 1, 0.0); + for (size_t i = 0; i < v->size; ++i) + pushed->data[i] = v->data[i]; + pushed->data[v->size] = x; + return pushed; +} +#+END_SRC + +*** ~slice_element~ ++ Author: Elizabeth Hunt ++ Name: ~slice_element~ ++ Location: ~src/vector.c~ ++ Input: a pointer to an ~Array_double~ ++ Output: a new ~Array_double~ with element ~x~ sliced. + +#+BEGIN_SRC c +Array_double *slice_element(Array_double *v, size_t x) { + Array_double *sliced = InitArrayWithSize(double, v->size - 1, 0.0); + for (size_t i = 0; i < v->size - 1; ++i) + sliced->data[i] = i >= x ? v->data[i + 1] : v->data[i]; + return sliced; +} +#+END_SRC + *** ~copy_vector~ + Author: Elizabeth Hunt + Name: ~copy_vector~ @@ -370,55 +404,54 @@ void format_vector_into(Array_double *v, char *s) { matrix $L$, $U$, respectively such that $LU = m$. + Output: a pointer to the location in memory in which two ~Matrix_double~'s reside: the first representing $L$, the second, $U$. -+ Errors: Exits and throws a status code of ~-1~ when encountering a matrix that cannot be ++ Errors: Fails assertions when encountering a matrix that cannot be decomposed #+BEGIN_SRC c - Matrix_double **lu_decomp(Matrix_double *m) { - assert(m->cols == m->rows); +Matrix_double **lu_decomp(Matrix_double *m) { + assert(m->cols == m->rows); - Matrix_double *u = copy_matrix(m); - Matrix_double *l_empt = InitMatrixWithSize(double, m->rows, m->cols, 0.0); - Matrix_double *l = put_identity_diagonal(l_empt); - free(l_empt); + Matrix_double *u = copy_matrix(m); + Matrix_double *l_empt = InitMatrixWithSize(double, m->rows, m->cols, 0.0); + Matrix_double *l = put_identity_diagonal(l_empt); + free_matrix(l_empt); + Matrix_double **u_l = malloc(sizeof(Matrix_double *) * 2); - Matrix_double **u_l = malloc(sizeof(Matrix_double *) * 2); - - for (size_t y = 0; y < m->rows; y++) { - if (u->data[y]->data[y] == 0) { - printf("ERROR: a pivot is zero in given matrix\n"); - exit(-1); - } + for (size_t y = 0; y < m->rows; y++) { + if (u->data[y]->data[y] == 0) { + printf("ERROR: a pivot is zero in given matrix\n"); + assert(false); } + } - if (u && l) { - for (size_t x = 0; x < m->cols; x++) { - for (size_t y = x + 1; y < m->rows; y++) { - double denom = u->data[x]->data[x]; + if (u && l) { + for (size_t x = 0; x < m->cols; x++) { + for (size_t y = x + 1; y < m->rows; y++) { + double denom = u->data[x]->data[x]; - if (denom == 0) { - printf("ERROR: non-factorable matrix\n"); - exit(-1); - } + if (denom == 0) { + printf("ERROR: non-factorable matrix\n"); + assert(false); + } - double factor = -(u->data[y]->data[x] / denom); + double factor = -(u->data[y]->data[x] / denom); - Array_double *scaled = scale_v(u->data[x], factor); - Array_double *added = add_v(scaled, u->data[y]); - free_vector(scaled); - free_vector(u->data[y]); + Array_double *scaled = scale_v(u->data[x], factor); + Array_double *added = add_v(scaled, u->data[y]); + free_vector(scaled); + free_vector(u->data[y]); - u->data[y] = added; - l->data[y]->data[x] = -factor; - } + u->data[y] = added; + l->data[y]->data[x] = -factor; } } - - u_l[0] = u; - u_l[1] = l; - return u_l; } + + u_l[0] = u; + u_l[1] = l; + return u_l; +} #+END_SRC *** ~bsubst~ + Author: Elizabeth Hunt @@ -467,7 +500,7 @@ Array_double *fsubst(Matrix_double *l, Array_double *b) { } #+END_SRC -*** ~solve_matrix~ +*** ~solve_matrix_lu_bsubst~ + Author: Elizabeth Hunt + Location: ~src/matrix.c~ + Input: a pointer to a ~Matrix_double~ $m$ and a pointer to an ~Array_double~ $b$ @@ -480,7 +513,7 @@ Here we make use of forward substitution to first solve $Ly = b$ given $L$ as th Then, $LUx = b$, thus $x$ is a solution. #+BEGIN_SRC c -Array_double *solve_matrix(Matrix_double *m, Array_double *b) { +Array_double *solve_matrix_lu_bsubst(Matrix_double *m, Array_double *b) { assert(b->size == m->rows); assert(m->rows == m->cols); @@ -495,11 +528,97 @@ Array_double *solve_matrix(Matrix_double *m, Array_double *b) { free_matrix(u); free_matrix(l); + free(u_l); return x; } #+END_SRC +*** ~gaussian_elimination~ ++ Author: Elizabeth Hunt ++ Location: ~src/matrix.c~ ++ Input: a pointer to a ~Matrix_double~ $m$ ++ Output: a pointer to a copy of $m$ in reduced echelon form + +This works by finding the row with a maximum value in the column $k$. Then, it uses that as a pivot, and +applying reduction to all other rows. The general idea is available at [[https://en.wikipedia.org/wiki/Gaussian_elimination]]. + +#+BEGIN_SRC c +Matrix_double *gaussian_elimination(Matrix_double *m) { + uint64_t h = 0; + uint64_t k = 0; + + Matrix_double *m_cp = copy_matrix(m); + + while (h < m_cp->rows && k < m_cp->cols) { + uint64_t max_row = 0; + double total_max = 0.0; + + for (uint64_t row = h; row < m_cp->rows; row++) { + double this_max = c_max(fabs(m_cp->data[row]->data[k]), total_max); + if (c_max(this_max, total_max) == this_max) { + max_row = row; + } + } + + if (max_row == 0) { + k++; + continue; + } + + Array_double *swp = m_cp->data[max_row]; + m_cp->data[max_row] = m_cp->data[h]; + m_cp->data[h] = swp; + + for (uint64_t row = h + 1; row < m_cp->rows; row++) { + double factor = m_cp->data[row]->data[k] / m_cp->data[h]->data[k]; + m_cp->data[row]->data[k] = 0.0; + + for (uint64_t col = k + 1; col < m_cp->cols; col++) { + m_cp->data[row]->data[col] -= m_cp->data[h]->data[col] * factor; + } + } + + h++; + k++; + } + + return m_cp; +} +#+END_SRC + +*** ~solve_matrix_gaussian~ ++ Author: Elizabeth Hunt ++ Location: ~src/matrix.c~ ++ Input: a pointer to a ~Matrix_double~ $m$ and a target ~Array_double~ $b$ ++ Output: a pointer to a vector $x$ being the solution to the equation $mx = b$ + +We first perform ~gaussian_elimination~ after augmenting $m$ and $b$. Then, as $m$ is in reduced echelon form, it's an upper +triangular matrix, so we can perform back substitution to compute $x$. + +#+BEGIN_SRC c +Array_double *solve_matrix_gaussian(Matrix_double *m, Array_double *b) { + assert(b->size == m->rows); + assert(m->rows == m->cols); + + Matrix_double *m_augment_b = add_column(m, b); + Matrix_double *eliminated = gaussian_elimination(m_augment_b); + + Array_double *b_gauss = col_v(eliminated, m->cols); + Matrix_double *u = slice_column(eliminated, m->rows); + + Array_double *solution = bsubst(u, b_gauss); + + free_matrix(m_augment_b); + free_matrix(eliminated); + free_matrix(u); + free_vector(b_gauss); + + return solution; +} +#+END_SRC + + *** ~m_dot_v~ + Author: Elizabeth Hunt + Location: ~src/matrix.c~ @@ -535,6 +654,48 @@ Matrix_double *put_identity_diagonal(Matrix_double *m) { } #+END_SRC +*** ~slice_column~ ++ Author: Elizabeth Hunt ++ Location: ~src/matrix.c~ ++ Input: a pointer to a ~Matrix_double~ ++ Output: a pointer to a copy of the given ~Matrix_double~ with column at ~x~ sliced + +#+BEGIN_SRC c +Matrix_double *slice_column(Matrix_double *m, size_t x) { + Matrix_double *sliced = copy_matrix(m); + + for (size_t row = 0; row < m->rows; row++) { + Array_double *old_row = sliced->data[row]; + sliced->data[row] = slice_element(old_row, x); + free_vector(old_row); + } + sliced->cols--; + + return sliced; +} +#+END_SRC + +*** ~add_column~ ++ Author: Elizabet Hunt ++ Location: ~src/matrix.c~ ++ Input: a pointer to a ~Matrix_double~ and a new vector representing the appended column ~x~ ++ Output: a pointer to a copy of the given ~Matrix_double~ with a new column ~x~ + +#+BEGIN_SRC c +Matrix_double *add_column(Matrix_double *m, Array_double *v) { + Matrix_double *pushed = copy_matrix(m); + + for (size_t row = 0; row < m->rows; row++) { + Array_double *old_row = pushed->data[row]; + pushed->data[row] = add_element(old_row, v->data[row]); + free_vector(old_row); + } + + pushed->cols++; + return pushed; +} +#+END_SRC + *** ~copy_matrix~ + Author: Elizabeth Hunt + Location: ~src/matrix.c~ diff --git a/doc/software_manual.pdf b/doc/software_manual.pdf Binary files differindex ba0b14b..8cd70f4 100644 --- a/doc/software_manual.pdf +++ b/doc/software_manual.pdf diff --git a/doc/software_manual.tex b/doc/software_manual.tex index 292f868..c6eb910 100644 --- a/doc/software_manual.tex +++ b/doc/software_manual.tex @@ -1,4 +1,4 @@ -% Created 2023-10-18 Wed 13:06 +% Created 2023-10-30 Mon 09:44 % Intended LaTeX compiler: pdflatex \documentclass[11pt]{article} \usepackage[utf8]{inputenc} @@ -31,8 +31,8 @@ \setlength\parindent{0pt} \section{Design} -\label{sec:org7204e7c} -The LIZFCM static library (at \href{https://github.com/Simponic/math-4610}{[https://github.com/Simponic/math-4610} is a successor to my +\label{sec:org7f9c526} +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 Lisp, but the effort required to meet the requirement of creating a static library became too difficult to integrate outside of the \texttt{ASDF} solution that Common Lisp already brings @@ -42,13 +42,13 @@ All of the work established in \texttt{deprecated-cl} has been painstakingly tra the C programming language. I have a couple tenets for its design: \begin{itemize} -\item Implemntations of routines should all be done immutably in respect to arguments. +\item Implementations of routines should all be done immutably in respect to arguments. \item Functional programming is good (it's\ldots{} rough in C though). \item Routines are separated into "module" c files, and not individual files per function. \end{itemize} \section{Compilation} -\label{sec:org16cc307} +\label{sec:org911a41e} A provided \texttt{Makefile} is added for convencience. It has been tested on an M1 machine running MacOS as well as Arch Linux. @@ -74,11 +74,11 @@ Which is then bundled into a static library in \texttt{lib/lizfcm.a} which can b in the standard method. \section{The LIZFCM API} -\label{sec:org832532a} +\label{sec:orgd74cd2d} \subsection{Simple Routines} -\label{sec:org540b602} +\label{sec:org66bba13} \subsubsection{\texttt{smaceps}} -\label{sec:org4d03b6e} +\label{sec:orgeae9531} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{smaceps} @@ -104,7 +104,7 @@ float smaceps() { \end{verbatim} \subsubsection{\texttt{dmaceps}} -\label{sec:org2603bfc} +\label{sec:org237c904} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{dmaceps} @@ -130,9 +130,9 @@ double dmaceps() { \end{verbatim} \subsection{Derivative Routines} -\label{sec:org95c28e9} +\label{sec:org9cf9027} \subsubsection{\texttt{central\_derivative\_at}} -\label{sec:org950de62} +\label{sec:org1fcd333} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{central\_derivative\_at} @@ -163,7 +163,7 @@ double central_derivative_at(double (*f)(double), double a, double h) { \end{verbatim} \subsubsection{\texttt{forward\_derivative\_at}} -\label{sec:org832eda6} +\label{sec:org6a768fc} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{forward\_derivative\_at} @@ -194,7 +194,7 @@ double forward_derivative_at(double (*f)(double), double a, double h) { \end{verbatim} \subsubsection{\texttt{backward\_derivative\_at}} -\label{sec:org591836d} +\label{sec:org610ce76} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{backward\_derivative\_at} @@ -225,9 +225,9 @@ double backward_derivative_at(double (*f)(double), double a, double h) { \end{verbatim} \subsection{Vector Routines} -\label{sec:org5254fe4} +\label{sec:orgfd176e6} \subsubsection{Vector Arithmetic: \texttt{add\_v, minus\_v}} -\label{sec:orgf802d61} +\label{sec:org2dbc55f} \begin{itemize} \item Author: Elizabeth Hunt \item Name(s): \texttt{add\_v}, \texttt{minus\_v} @@ -258,7 +258,7 @@ Array_double *minus_v(Array_double *v1, Array_double *v2) { \end{verbatim} \subsubsection{Norms: \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm}} -\label{sec:orgc56e22d} +\label{sec:org53a2ffc} \begin{itemize} \item Author: Elizabeth Hunt \item Name(s): \texttt{l1\_norm}, \texttt{l2\_norm}, \texttt{linf\_norm} @@ -292,7 +292,7 @@ double linf_norm(Array_double *v) { \end{verbatim} \subsubsection{\texttt{vector\_distance}} -\label{sec:orgb54922f} +\label{sec:org1fb3f8c} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{vector\_distance} @@ -313,7 +313,7 @@ double vector_distance(Array_double *v1, Array_double *v2, \end{verbatim} \subsubsection{Distances: \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance}} -\label{sec:orgf22f8e0} +\label{sec:org4a25a94} \begin{itemize} \item Author: Elizabeth Hunt \item Name(s): \texttt{l1\_distance}, \texttt{l2\_distance}, \texttt{linf\_distance} @@ -339,7 +339,7 @@ double linf_distance(Array_double *v1, Array_double *v2) { \end{verbatim} \subsubsection{\texttt{sum\_v}} -\label{sec:org4593341} +\label{sec:org035a547} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{sum\_v} @@ -359,7 +359,7 @@ double sum_v(Array_double *v) { \subsubsection{\texttt{scale\_v}} -\label{sec:org3123f61} +\label{sec:org12b0853} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{scale\_v} @@ -378,7 +378,7 @@ Array_double *scale_v(Array_double *v, double m) { \end{verbatim} \subsubsection{\texttt{free\_vector}} -\label{sec:org983efcf} +\label{sec:org70ba90c} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{free\_vector} @@ -396,7 +396,7 @@ void free_vector(Array_double *v) { \end{verbatim} \subsubsection{\texttt{copy\_vector}} -\label{sec:orgde05d32} +\label{sec:org57afc74} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{copy\_vector} @@ -416,7 +416,7 @@ Array_double *copy_vector(Array_double *v) { \end{verbatim} \subsubsection{\texttt{format\_vector\_into}} -\label{sec:org2e779f3} +\label{sec:orgc346c3c} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{format\_vector\_into} @@ -446,9 +446,9 @@ void format_vector_into(Array_double *v, char *s) { \end{verbatim} \subsection{Matrix Routines} -\label{sec:org2354147} +\label{sec:org3b053ab} \subsubsection{\texttt{lu\_decomp}} -\label{sec:org3690faa} +\label{sec:org5553968} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{lu\_decomp} @@ -509,7 +509,7 @@ Matrix_double **lu_decomp(Matrix_double *m) { } \end{verbatim} \subsubsection{\texttt{bsubst}} -\label{sec:orgdeba296} +\label{sec:org253efdc} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{bsubst} @@ -534,7 +534,7 @@ Array_double *bsubst(Matrix_double *u, Array_double *b) { } \end{verbatim} \subsubsection{\texttt{fsubst}} -\label{sec:org60d3435} +\label{sec:orge0c7bc6} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{fsubst} @@ -562,7 +562,7 @@ Array_double *fsubst(Matrix_double *l, Array_double *b) { \end{verbatim} \subsubsection{\texttt{solve\_matrix}} -\label{sec:org914121f} +\label{sec:orgbcd445a} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{src/matrix.c} @@ -598,7 +598,7 @@ Array_double *solve_matrix(Matrix_double *m, Array_double *b) { \end{verbatim} \subsubsection{\texttt{m\_dot\_v}} -\label{sec:orgae0f4c9} +\label{sec:orga9b1f68} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{src/matrix.c} @@ -620,7 +620,7 @@ Array_double *m_dot_v(Matrix_double *m, Array_double *v) { \end{verbatim} \subsubsection{\texttt{put\_identity\_diagonal}} -\label{sec:org6d84f6a} +\label{sec:org33ead5e} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{src/matrix.c} @@ -639,7 +639,7 @@ Matrix_double *put_identity_diagonal(Matrix_double *m) { \end{verbatim} \subsubsection{\texttt{copy\_matrix}} -\label{sec:orge750c56} +\label{sec:org34b3f5b} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{src/matrix.c} @@ -659,7 +659,7 @@ Matrix_double *copy_matrix(Matrix_double *m) { \end{verbatim} \subsubsection{\texttt{free\_matrix}} -\label{sec:org4ebcf85} +\label{sec:org9c91101} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{src/matrix.c} @@ -678,7 +678,7 @@ void free_matrix(Matrix_double *m) { \end{verbatim} \subsubsection{\texttt{format\_matrix\_into}} -\label{sec:org308ee0d} +\label{sec:org51f3e27} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{format\_matrix\_into} @@ -705,9 +705,9 @@ void format_matrix_into(Matrix_double *m, char *s) { } \end{verbatim} \subsection{Root Finding Methods} -\label{sec:org8981156} +\label{sec:org0e83d47} \subsubsection{\texttt{find\_ivt\_range}} -\label{sec:orga5835b0} +\label{sec:org3e4e34e} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{find\_ivt\_range} @@ -737,7 +737,7 @@ double *find_ivt_range(double (*f)(double), double start_x, double delta, } \end{verbatim} \subsubsection{\texttt{bisect\_find\_root}} -\label{sec:orgb118fc7} +\label{sec:org48f0967} \begin{itemize} \item Author: Elizabeth Hunt \item Name(s): \texttt{bisect\_find\_root} @@ -765,7 +765,7 @@ double bisect_find_root(double (*f)(double), double a, double b, } \end{verbatim} \subsubsection{\texttt{bisect\_find\_root\_with\_error\_assumption}} -\label{sec:orgf5124e7} +\label{sec:org15e3c2d} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{bisect\_find\_root\_with\_error\_assumption} @@ -789,9 +789,9 @@ double bisect_find_root_with_error_assumption(double (*f)(double), double a, \end{verbatim} \subsection{Linear Routines} -\label{sec:org6f4fce5} +\label{sec:org98cb54b} \subsubsection{\texttt{least\_squares\_lin\_reg}} -\label{sec:orge810f5f} +\label{sec:org0c0c5d7} \begin{itemize} \item Author: Elizabeth Hunt \item Name: \texttt{least\_squares\_lin\_reg} @@ -821,12 +821,12 @@ Line *least_squares_lin_reg(Array_double *x, Array_double *y) { } \end{verbatim} \subsection{Appendix / Miscellaneous} -\label{sec:org85d2eae} +\label{sec:orge34af18} \subsubsection{Data Types} -\label{sec:org198ca2d} +\label{sec:org0f2f877} \begin{enumerate} \item \texttt{Line} -\label{sec:org1866885} +\label{sec:org3f27166} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{inc/types.h} @@ -839,7 +839,7 @@ typedef struct Line { } Line; \end{verbatim} \item The \texttt{Array\_<type>} and \texttt{Matrix\_<type>} -\label{sec:org4a1c956} +\label{sec:org83fc1f3} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{inc/types.h} @@ -871,10 +871,10 @@ typedef struct { \end{enumerate} \subsubsection{Macros} -\label{sec:org1976330} +\label{sec:org2bf9bf0} \begin{enumerate} \item \texttt{c\_max} and \texttt{c\_min} -\label{sec:org208b148} +\label{sec:orgcaa569e} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{inc/macros.h} @@ -888,7 +888,7 @@ typedef struct { \end{verbatim} \item \texttt{InitArray} -\label{sec:orgccc4528} +\label{sec:org5805999} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{inc/macros.h} @@ -909,7 +909,7 @@ typedef struct { \end{verbatim} \item \texttt{InitArrayWithSize} -\label{sec:org7e87550} +\label{sec:org264d6b7} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{inc/macros.h} @@ -930,7 +930,7 @@ typedef struct { \end{verbatim} \item \texttt{InitMatrixWithSize} -\label{sec:orge6ec2b1} +\label{sec:org310d41a} \begin{itemize} \item Author: Elizabeth Hunt \item Location: \texttt{inc/macros.h} |