notation_index.tex

\lab{Index of Pseudocode Notation}{Index of Notation}
\label{notation_index}

\section*{Objects}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l l}
$A$ 					& A capitol letter typically denotes a matrix, or 2-D NumPy array\\
$[[a, b], [c, d]]$ 			& The explicit array $\left(\begin{array}{cc}
a & b\\
c & d\\\end{array}\right)$\\
$A \gets \allocate{m}{n}$, 
$\v \gets \allocate{k}$ 	& Allocate memory for an $m \times n$ NumPy array $A$
						or for a vector $\v$ of length $k$\\
$\Id{n}$	 			& The $n\times n$ array with 1's on the diagonal and 0's elsewhere \\
$a$ 					& A lowercase letter typically denotes a scalar\\

$A[:, j], \v[i]$ 			& Slice the 2-D array $A$ or 1-D array $\v$ as in Python\\
$\v$ 					& A boldface letter typically denotes a vector, or 1-D NumPy array\\
$\zeros{m}{n}$,
$\zeros{k}$	 		& The $m\times n$ array or length-$k$ vector of zeros 
\end{tabular}

\section*{Operations}
\begin{tabular}{l l}
$\makecopy{A}$		& Make a copy of the array $A$\\
$A/a$, $\v/a$, $b/a$ 		& Divide by the scalar $a$\\
$AB$, $aB$			& Multiply scalars or matrices\\
$\norm{\v}, \norm{\v}_2$ 		& Find the (Euclidean) norm of $\v$\\
$\shape{A}$			& Return the dimensions of the array $A$\\
$\sign(a)$				& Return the sign of the scalar $a$\\
$\size{A}$				& Return the number of elements in the array $A$\\
$A\trp$				& Transpose the array $A$
\end{tabular}

\section*{Programming constructs}
\begin{tabular}{p{5.5cm} p{8cm}}
$\vartriangleright$		& Comment\\
${\bf for}\; i=1 \ldots n\; {\bf do}$ & ``For'' loop. Iterate from 1 to $n$.\\
$\gets$				& Assignment operator. If $a \gets b$ then $a$ is assigned the value of $b$.\\
$\bf{if} \;\ldots\; \bf{else}$		& ``If'' construction with optional ``else''\\
$\bf{Procedure}<${\sc Name}$>$(Parameters)		& Defines the start of the algorithm called $<${\sc Name}$>$ which accepts the specified parameters as inputs\\
$\bf{while}$			& ``While'' construction\\
$\bf{return}$			& End of algorithm. Return any values specified.
\end{tabular}