\chapter{Operators}
\label{chap:operators}

\section{Precedence}

Table~\ref{tab:ops} lists the operators available in \app{gretl} in
order of decreasing precedence: the operators on the first row have
the highest precedence, those on the second row have the second
highest, and so on. Operators on any given row have equal
precedence. Where successive operators have the same precedence the
order of evaluation is in general left to right. The exceptions are
exponentiation and matrix transpose-multiply. The expression
\verb|a^b^c| is equivalent to \verb|a^(b^c)|, not \verb|(a^b)^c|, 
and similarly \verb|A'B'C'| is equivalent to \verb|A'(B'(C'))|.

\begin{table}[htbp]
\caption{Operator precedence}
\label{tab:ops}
\begin{center}
\begin{tabular}{lllllllll}
\verb|()| & \verb|[]| & \verb|{}| \\
\texttt{!} & \texttt{++} & \verb|--| & \verb|^| & \verb|'| \\
\texttt{*} & \texttt{/} & \texttt{\%} & \verb+\+ & \texttt{**} \\
\texttt{+} & \texttt{-} & \verb|~| & \verb+|+ & \\
\verb|>| & \verb|<| & \verb|>=| & \verb|<=| & \texttt{..} \\
\texttt{==} & \texttt{!=} \\
\verb|&&| \\
\verb+||+ \\
\texttt{?:} \\
\end{tabular}
\end{center}
\end{table}

In addition to the basic forms shown in the Table, several operators
also have a ``dot form'' (as in ``\texttt{.+}'' which is read as ``dot
plus''). These are element-wise versions of the basic operators, for
use with matrices exclusively; they have the same precedence as their
basic counterparts. The available dot operators are as follows.

\begin{center}
\begin{tabular}{cccccccccc}
\verb|.^| & \texttt{.*} & \texttt{./} & \texttt{.+} &
 \texttt{.-} & \verb|.>| & \verb|.<| & \verb|.>=| &
 \verb|.<=| & \texttt{.=} \\
\end{tabular}
\end{center}

Each basic operator is shown once again in the following list along
with a brief account of its meaning. Apart from the first three sets
of grouping symbols, all operators are binary except where otherwise
noted.

\begin{longtable}{ll}
\verb|()| & Function call \\
\verb|[]|  & Subscripting \\
\verb|{}|  & Matrix definition \\
\texttt{!} & Unary logical NOT \\
\texttt{++} & Increment (unary) \\
\verb|--| & Decrement (unary) \\
\verb|^|  & Exponentiation \\
\verb|'|  & Matrix transpose (unary) or transpose-multiply (binary) \\
\texttt{*} & Multiplication \\
\texttt{/} & Division, matrix ``right division'' \\
\texttt{\%} & Modulus \\
\verb+\+    & Matrix ``left division'' \\
\texttt{**} & Kronecker product \\
\texttt{+} & Addition \\
\texttt{-} & Subtraction \\
\verb|~| & Matrix horizontal concatenation \\
\verb+|+ & Matrix vertical concatenation \\
\verb|>| & Boolean greater than \\
\verb|<| & Boolean less than \\
\verb|>=| & Greater than or equal \\
\verb|<=| & Less than or equal \\
\texttt{..} & Range from--to (in constructing lists) \\
\texttt{==} & Boolean equality test \\
\texttt{!=} & Boolean inequality test \\
\verb|&&| & Logical AND \\
\verb+||+ & Logical OR \\
\texttt{?:} & Conditional expression \\
\end{longtable}

Details on the use of the matrix-related operators (including the dot
operators) can be found in the chapter on matrices in the
\textit{Gretl User's Guide}.

\section{Assignment}

The operators mentioned above are all intended for use on the
right-hand side of an expression which assigns a value to a variable
(or which just computes and displays a value --- see the \texttt{eval}
command). In addition we have the assignment operator itself,
``\texttt{=}''. In effect this has the lowest precedence of all: the
entire right-hand side is evaluated before assignment takes place.

Besides plain ``\texttt{=}'' several ``inflected'' versions of
assignment are available. These may be used only when the left-hand
side variable is already defined. The inflected assignment yields a
value that is a function of the prior value on the left and the
computed value on the right. Such operators are formed by prepending a
regular operator symbol to the equals sign. For example,
%
\begin{code}
y += x
\end{code}
%
The new value assigned to \texttt{y} by the statement above is the
prior value of \texttt{y} plus \texttt{x}. The other available
inflected operators, which work in an exactly analogous fashion, are
as follows.

\begin{center}
\begin{tabular}{ccccccc}
\texttt{-=} & \texttt{*=} & \texttt{/=} & \verb|%=| & 
  \verb|^=| & \verb|~=| & \verb+|=+ \\
\end{tabular}
\end{center}

In addition, a special form of inflected assignment is provided for
matrices. Say matrix \texttt{M} is $2 \times 2$. If you execute
\texttt{M = 5} this has the effect of replacing \texttt{M} with a $1
\times 1$ matrix with single element 5. But if you do \texttt{M .= 5}
this assigns the value 5 to all elements of \texttt{M} without
changing its dimensions.

\section{Increment and decrement}

The unary operators \texttt{++} and \verb|--| follow their
operand,\footnote{The C programming language also supports prefix
  versions of \texttt{++} and \verb|--|, which increment or decrement
  their operand before yielding its value. Only the postfix form is
  supported by \app{gretl}.}  which must be a variable of scalar
type. Their simplest use is in stand-alone expressions, such as
%
\begin{code}
j++  # shorthand for j = j + 1
k--  # shorthand for k = k - 1
\end{code}
%
However, they can also be embedded in more complex expressions, in
which case they first yield the original value of the variable in
question, then have the side-effect of incrementing or decrementing
the variable's value. For example:
%
\begin{code}
scalar i = 3
k = i++
matrix M = zeros(10, 1)
M[i++] = 1
\end{code}
%
After the second line, \texttt{k} has the value 3 and \texttt{i} has
value 4. The last line assigns the value 1 to element 4 of
matrix \texttt{M} and sets \texttt{i} = 5.