% refcard.tex
%
% This file is TeX source for a reference card describing Octave.
%
% Copyright (C) 1996-2022 The Octave Project Developers
%
% See the file COPYRIGHT.md in the top-level directory of this
% distribution or <https://octave.org/copyright/>.
%
% This file is part of Octave.
%
% Octave is free software: you can redistribute it and/or modify it
% under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Octave is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Octave; see the file COPYING.  If not, see
% <https://www.gnu.org/licenses/>.
%
%
% Heavily modified by jwe from the source for the gdb reference card,
% which was originally written by Roland Pesch <pesch@cygnus.com>.
%
%   Copyright (C) 1991, 1992 Free Software Foundation, Inc.
%   Permission is granted to make and distribute verbatim copies of
%   this reference provided the copyright notices and permission notices
%   are preserved on all copies.
%
%
% TeX markup is a programming language; accordingly this file is source
% for a program to generate a reference.
%
% You only have to set the total width and height of the paper, the
% horizontal and vertical margin space measured from *paper edge*
% and the interline and interspec spacing.
% In order to support a new papersize, you have to fiddle with the
% latter four dimensions. Just try out a few values.
% All other values will be computed at process time so it should be
% quite easy to support different paper sizes - only four values to
% guess :-)
%
% To find the configuration places, just search for the string
% "User configuration".
%
%   -- Andreas Vogel (av@ssw.de)
%
% NOTE ON INTENTIONAL OMISSIONS: This reference card includes many
% Octave commands, but due to space constraints there are some things
% I chose to omit.  In general, not all synonyms for commands are
% covered, nor all variations of a command.

\def\octaveversion{8.0.0}
\def\refcardedition{3.1.1}

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% Declarations (these must come first)

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\newdimen\barwidth
\newdimen\barheight
\newdimen\intersecwidth

\newcount\columnsperpage

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% CONFIGURATION                                                       %
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\def\refcardlettersize{letter} % 3 columns, US letter paper (8.5 x 11in)

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  \totalwidth=297mm     % total width of paper
  \totalheight=210mm    % total height of paper
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  \vmargin=7mm          % vertical margin width
  \secskip=3mm          % space between refcard secs
  \lskip=0.4mm          % extra skip between \sec entries
\else
  \ifx\refcardsize\refcardlegalsize
    \columnsperpage=4   % total number of columns to typeset
    \totalwidth=14in    % total width of paper
    \totalheight=8.5in  % total height of paper
    \hmargin=0.20in     % horizontal margin width
    \vmargin=0.25in     % vertical margin width
    \secskip=0.75pc     % space between refcard secs
    \lskip=2pt          % extra skip between \sec entries
  \else
    \columnsperpage=3   % total number of columns to typeset
    \totalwidth=11in    % total width of paper
    \totalheight=8.5in  % total height of paper
    \hmargin=0.25in     % horizontal margin width
    \vmargin=0.25in     % vertical margin width
    \secskip=0.75pc     % space between refcard secs
    \lskip=2pt          % extra skip between \sec entries
  \fi
\fi

\ifx\pdfoutput\undefined
\else
  \pdfpageheight=\totalheight
  \pdfpagewidth=\totalwidth
\fi

% Change according to personal taste, not papersize dependent.

\barwidth=.1pt       % width of the cropmark bar
\barheight=2pt       % height of the cropmark bar
\intersecwidth=0.5em % width between \itmwid and \dfnwid

% Uncomment only one of the following definitions for folding guides.

% No printed folding guide:

%\def\vdecor{\hskip\hmargin plus1fil
%  \hskip\barwidth plus1fil
%  \hskip\hmargin plus1fil}

% Solid line folding guide:

%\def\vdecor{\hskip\hmargin plus1fil%
%  \vrule width \barwidth%
%  \hskip\hmargin plus1fil}

% For small marks near top and bottom as folding guide:

\def\vdecor{\hskip\hmargin plus1fil%
  \vbox to \vsize{\hbox to \barwidth{\vrule height\barheight width\barwidth}%
  \vfill
  \hbox to \barwidth{\vrule height\barheight width\barwidth}}%
  \hskip\hmargin plus1fil}

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% END CONFIGURATION                                                    %
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% values to be computed based on above definitions.
% nothing to configure

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% an alternate section format, used in some cases to make text fit better.

\newdimen\altitmwid        % width of item column in altsec
\newdimen\altdfnwid        % width of definition column in altsec

% Subtract hmargin for left and right sides of paper from full width.
%
%   fullhsize = totalwidth - (2 * hmargin)

\fullhsize=\totalwidth
\temp=\hmargin
\multiply \temp by 2
\advance \fullhsize by -\temp

% intercolumn space is composed of hmargin barwidth hmargin so that we
% get the same amount of space on either side of the (optional) rule
% between columns.  For N columns, we need to subtract this amount of
% space N-1 times.  Divide by the number of columns to get the final
% value of \hsize that we use to typeset columns.

% hsize = (fullhsize - (ncols-1)*barwidth - 2*(ncols-1)*hmargin) / ncols

\newcount\tmpcnt
\tmpcnt\columnsperpage
\advance \tmpcnt by -1

\hsize=\fullhsize

\temp=\barwidth
\multiply \temp by \tmpcnt
\advance \hsize by -\temp

\multiply \tmpcnt by 2

\temp=\hmargin
\multiply \temp by \tmpcnt
\advance \hsize by -\temp

\divide \hsize by \columnsperpage

% Vertical size is easy -- same amount of space above and below.
%
%   vsize = totalheight - (2 * vmargin)

\vsize=\totalheight
\temp=\vmargin
\multiply \temp by 2
\advance \vsize by -\temp

% adjust the offsets so the margins are measured *from paper edge*

\hoffset=-1in \advance \hoffset by \hmargin
\voffset=-1in \advance \voffset by \vmargin

% Width of items in a section.

% itmwid = (hsize - intersecwidth) * 1/3
% dfnwid = (hsize - intersecwidth) * 2/3

% width of the item

\temp=\hsize
\advance \temp by -\intersecwidth
\divide \temp by 3
\itmwid=\temp

% width of the corresponding definition

\dfnwid=\hsize
\advance \dfnwid by -\itmwid

% indentation for sub items, etc.

\temp=\hsize \advance\temp by -1em
\idnwid=\temp

% Width of items in an alt section.

\altitmwid=\itmwid \advance \altitmwid by 0.35in
\altdfnwid=\dfnwid \advance \altdfnwid by -0.35in

% Output macros.
%
% Strategy:
%
%   * set each column in a box
%   * append new columns in a global `holding' box, inserting
%     intercolumn decorations as necessary.
%   * when we fill a page, dump the saved box and the latest column,
%     separated by the intercolumn decoration.

\newbox\holdbox
\newcount\colno
\colno=0

\output={\relax
  \global\advance\colno by 1
  \ifnum\colno=1
    \global\setbox\holdbox=\columnbox
  \else
    \ifnum\colno=\columnsperpage
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      \advancepageno
      \global\colno=0
    \else
      \global\setbox\holdbox=\vbox{\hbox{\box\holdbox\vdecor\columnbox}}
    \fi
  \fi}

\def\columnbox{\leftline{\pagebody}}

\def\bye{\par\vfill
  \supereject
  \if R\lcr \null\vfill\eject \fi
  \end}

% -----
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% We can afford to allow some slop

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\normalbaselineskip=9pt
\baselineskip=9pt

\parindent=0pt
\parskip=0pt
\footline={\vbox to0pt{\hss}}

\def\ctl#1{{\tt C-#1}}
\def\opt#1{{\brm[{\rm #1}]}}
\def\xtra#1{\noalign{\smallskip{\tt#1}}}

% A normal section

\long\def\sec#1;#2\endsec{\vskip \secskip
  \halign{%
%
% column 1 (of halign):
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    \vtop{\hsize=\itmwid\tt ##\par\vskip \lskip }\hfil
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      \hangafter=1
      \hangindent=\intersecwidth
      \rm ##\par\vskip \lskip}\cr
%
% Tail of \long\def fills in halign body with \sec args:
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    \noalign{{\bbf #1}%
      \vskip \lskip}
    #2}}

\long\def\widesec#1;#2\endsec{\vskip \secskip
  \halign{%
%
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      ##\par\vskip \lskip }\cr
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      \noalign{{\bbf #1}\vskip 3\lskip}
    #2}}

% an alternate section format, used in some cases to make text fit better.

\long\def\altsec#1;#2\endsec{\vskip \secskip
  \halign{%
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      ##\par\vskip \lskip}\hfil
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    &\vtop{%
      \hsize=\altdfnwid
      \hangafter=1
      \hangindent=\intersecwidth
      \rm ##\par\vskip \lskip}\cr
%
% Tail of \long\def fills in halign body with \sec args:
%
    \noalign{{\bbf #1}\vskip \lskip}
    #2}}

% -------------------------------------
% The actual text of the reference card
% -------------------------------------

{\vbbf Octave Quick Reference}\hfil{\smrm Octave Version \octaveversion}\qquad
\centerline{\smrm Copyright 1996-2022 The Octave Project Developers
\qquad Permissions on back}

\sec Starting And Stopping;
octave&start interactive Octave session\cr
octave {\it file}&run Octave on commands in {\it file}\cr
octave --eval {\it code}&Evaluate {\it code} using Octave\cr
octave --help&describe command line options\cr
quit {\rm or} exit&exit Octave\cr
Ctrl-C&terminate current command and return to top-level prompt\cr
\endsec

\sec Getting Help;
help {\it command}&briefly describe {\it command}\cr
doc&use Info to browse Octave manual\cr
doc {\it command}&search for {\it command} in Octave manual\cr
lookfor {\it str}&search for {\it command} based on {\it str}\cr
\endsec

\sec Command Completion and History;
TAB&complete a command or variable name\cr
Alt-?&list possible completions\cr
Ctrl-r, Ctrl-s&search command history\cr
\endsec

\sec Directory and Path Commands;
cd {\it dir}&change working directory to {\it dir}\cr
pwd&print working directory\cr
ls \opt{{\it options}}&print directory listing\cr
getenv ({\it string})&return value of named environment variable\cr
what&list .m and .mat files in the current directory\cr
path&display the current Octave function path\cr
pathdef&display the default path\cr
addpath ({\it dir})&add a directory to the path\cr
EXEC\_PATH&manipulate the Octave executable path\cr
\endsec

\sec Package Management;
pkg install -forge&download and install package\cr
pkg install &install an already downloaded package\cr
pkg list&display installed packages\cr
pkg load / pkg unload &Load and unload an installed package\cr
\endsec

\sec Matrices;
\omit\vbox{\rm\vskip0.25ex
  Square brackets delimit literal matrices.  Commas separate elements
  on the same row.  Semicolons separate rows.  Commas may be replaced
  by spaces, and semicolons may be replaced by one or more newlines.
  Elements of a matrix may be arbitrary expressions, assuming
  all the dimensions agree.\vskip0.75ex}\span\cr
[ {\it x}, {\it y}, ... ]&enter a row vector\cr
[ {\it x}; {\it y}; ... ]&enter a column vector\cr
[ {\it w}, {\it x}; {\it y}, {\it z} ]&enter a 2$\times$2 matrix\cr
rows&number of rows of matrix\cr
columns&number of columns of matrix\cr
zeros&create matrix of zeros\cr
ones&create matrix of ones\cr
eye&create identity matrix\cr
diag&create diagonal matrix\cr
rand randi randn&create matrix of random values\cr
all&true if all elements nonzero\cr
any&true if at least one element nonzero\cr
nnz &count nonzero elements\cr
sparse&create a sparse matrix\cr
\endsec

\sec Multi-dimensional Arrays;
cat&concatenate along a given dimension\cr
reshape&change the shape of an array\cr
squeeze&remove singleton dimensions\cr
ndims&number of dimensions\cr
permute, ipermute, shiftdim&like N-dimensional transpose\cr
circshift&cyclically shift array elements\cr
meshgrid&matrices useful for vectorization\cr
\endsec

\sec Ranges;
{\it base} : {\it limit}\cr
{\it base} : {\it incr} : {\it limit}\cr
\omit\hfill\vbox{\hsize=\idnwid\rm\vskip0.75ex
  {\it incr} == 1 if not specified. Negative ranges allowed.}\span\cr
\endsec

\sec Numeric Types And Values;
\omit\vbox{\rm\vskip0.5ex
  Integers saturate in Octave. They do not wrap around.
  \vskip0.75ex}\span\cr
int8 int16 int32 int64&Signed integers\cr
uint8 uint16 uint32 uint64&Unsigned integers\cr
single double&32-bit / 64-bit IEEE floating point\cr
intmin intmax, flintmax&Integer limits of given type\cr
realmax realmin&Floating point limits of given type\cr
inf nan NA&IEEE infinity, NaN, missing value\cr
eps&machine precision\cr
pi e&3.14159..., 2.71828...\cr
i j&$\sqrt{-1}$\cr
\endsec

\sec Strings;
\omit\vbox{\rm\vskip0.5ex
  A {\it string constant\/} consists of a sequence of characters
  enclosed in either double-quote or single-quote marks. Strings
  in double-quotes allow the use of the escape sequences below.
  \vskip0.75ex}\span\cr
\char'134\char'134&a literal backslash\cr
\char'134 "&a literal double-quote character\cr
\char'134 '&a literal single-quote character\cr
\char'134 n&newline, ASCII code 10\cr
\char'134 t&horizontal tab, ASCII code 9\cr
sprintf sscanf&formatted IO to/from string\cr
strcmp&compare strings\cr
strcat&concatenate strings\cr
strfind regexp&find matching patterns\cr
strrep regexprep&find and replace patterns\cr
\endsec

\sec Index Expressions;
{\it var}({\it idx})&select elements of a vector\cr
{\it var}({\it idx1}, {\it idx2})&select elements of a matrix\cr
{\it var}({\it [1 3]}, {\it :})&rows 1 and 3\cr
{\it var}({\it :}, {\it [2 end]})&the second and last columns\cr
{\it var}({\it 1:2:end}, {\it 2:2:end})&get odd rows and even columns\cr
{\it var1}({\it var2} == 0)&elements of {\it var1} corresponding to zero
elements of {\it var2}\cr
{\it var}({:})&all elements as a column vector\cr
\endsec

\sec Cells, Structures, and Classdefs;
{\it{var}}.{\it{field}} = ...&set a field of a structure\cr
{\it{var}}$\{${\it{idx}}$\}$ = ...&set an element of a cell array\cr
cellfun ({\it f}, {\it c})&apply a function to elements of cell array\cr
fieldnames ({\it s})&returns the fields of a structure\cr
classdef&define new classes for OOP\cr
\endsec

\sec Assignment Expressions;
{\it var} = {\it expr}&assign value to variable\cr
{\it var}({\it idx}) = {\it expr}&only the indexed elements are changed\cr
{\it var}({\it idx}) = []&delete the indexed elements\cr
\endsec

\sec Arithmetic Operators;
%
% FIXME These operators look ugly, but putting them in math mode causes
% some of them to break even more.
%
\omit \vbox{\rm\vskip0.75ex
  If two operands are of different sizes, scalars and singleton dimensions are
  automatically expanded. Non-singleton dimensions need to match.
  \vskip0.75ex}\span\cr
{\it x} + {\it y}, {\it x} - {\it y}&addition, subtraction\cr
{\it x} * {\it y}&matrix multiplication\cr
{\it x} .* {\it y}&element by element multiplication\cr
{\it x} / {\it y}&right division, conceptually equivalent to
  {\tt (inverse~(y')~*~x')'}\cr
{\it x} ./ {\it y}&element by element right division\cr
{\it x} \char'134{} {\it y}&left division, conceptually equivalent to
  {\tt inverse~(x)~*~y}\cr
{\it x} .\char'134{} {\it y}&element by element left division\cr
{\it x} \char'136{} {\it y}&power operator\cr
{\it x} .\char'136{} {\it y}&element by element power operator\cr
+= -= *= .*= /= ./= \char'134{}= .\char'134{}= \char'136{}= .\char'136{}=&
in-place equivalents of the above operators\cr
-{\it x}&negation\cr
+{\it x}&unary plus (a no-op)\cr
{\it x}$'$&complex conjugate transpose\cr
{\it x}.$'$&transpose\cr
++{\it x} --{\it x}&increment / decrement, return {\it new\/} value\cr
{\it x}++ {\it x}--&increment / decrement, return {\it old\/} value\cr
\endsec

\sec Comparison and Boolean Operators;
\omit \vbox{\rm\vskip0.75ex
  These operators work on an element-by-element basis.  Both arguments
  are always evaluated.\vskip0.75ex}\span\cr
< <= == >= >&relational operators\cr
!= \char'176 =&not equal to\cr
\& &logical AND\cr
|  &logical OR\cr
! \char'176 &logical NOT\cr
\endsec

\sec Short-circuit Boolean Operators;
\omit \vbox{\rm\vskip0.75ex
  Operators evaluate left-to-right. Operands are only evaluated if
  necessary, stopping once overall truth value can be determined.
  Non-scalar operands are converted to scalars with
  {\tt all}.\vskip0.75ex}\span\cr
{\it x} \&\& {\it y}&logical AND\cr
{\it x} || {\it y}&logical OR\cr
\endsec

\vfill\eject

\sec Operator Precedence;
\omit \vbox{\rm\vskip0.5ex
  Table of Octave operators, in order of {\tt increasing}
  precedence.\vskip0.75ex}\span\cr
;\ \ ,&statement separators\cr
=&assignment, groups left to right\cr
+= -= *= /=  etc &in-place operators\cr
||\ \ \&\&&logical ``or'' and ``and''\cr
|\ \ \&&element-wise ``or'' and ``and''\cr
< <= == >= > !=&relational operators\cr
:&colon\cr
+\ \ -&addition and subtraction\cr
* / \char'134\ \ .*\ \ ./\ \ .\char'134&multiplication and division\cr
'\ \ .'&transpose\cr
+\ \ -\ \ ++\ \ --\ \ !&unary minus, increment, logical ``not''\cr
\char'136\ \ .\char'136&exponentiation\cr
\endsec

\sec General programming;
\omit \vbox{\rm\vskip0.5ex
  endfor, endwhile, endif etc can all be replaced by end.
  \vskip0.75ex}\span\cr
for x = 1:10

endfor & for loop\cr

while (x <= 10)

endwhile & while loop\cr

do

until (x > 10) & do-until loop\cr

if (x < 5)

elseif (x < 6)

else

endif & if-then-else\cr

switch (tf)

case "true"

case "false"

otherwise

endswitch & switch-case\cr

break & exit innermost loop\cr

continue & go to start of innermost loop\cr

return & jump back to calling location\cr

try

catch & cleanup only on exception\cr

unwind\char'137 protect

unwind\char'137 protect\char'137 cleanup & cleanup always \cr
\endsec

\widesec Functions;
function \opt{{\it ret-list}} {\it function-name}
  \opt{\hskip0.2em({\it arg-list})\hskip0.2em}\cr
\quad{\it function-body}\cr
endfunction\cr\cr
{\rm {\it ret-list\/} may be a single identifier or a comma-separated
  list of identifiers delimited by square-brackets.\vskip0.75ex}\cr
{\rm {\it arg-list\/} is a comma-separated list of identifiers and may
  be empty.}\cr
\endsec

\sec Function Handles;
@{\it{func}}& define a function handle to {\it func}\cr
@({\it var1}, ...) {\it expr}&define an anonymous function\cr
str2func func2str&convert function to/from string\cr
functions ({\it handle})&Return information about a function handle\cr
{\it handle} ({\it arg1}, ...)&Evaluate a function handle\cr
feval &Evaluate a function handle or string\cr
\omit\vbox{\rm\vskip0.25ex
  Anonymous function handles take a copy of the variables in the
  current workspace.\vskip0.75ex}\span\cr
\endsec

\sec Global and Persistent Variables;
global {\it var1} = ...&global variables\cr
persistent {\it var1} = ...&persistent / static variables\cr
\omit\hfill\vbox{\rm\vskip0.25ex
  Global variables may be accessed inside the body of a function
  without having to be passed in the function parameter list provided
  they are declared global when used.}\span\cr
\endsec

\sec Common Functions;
disp&display value of variable\cr
printf&formatted output to {\tt stdout}\cr
input, scanf&input from {\tt stdin}\cr
who, whos&list current variables\cr
clear {\it pattern}&clear variables matching pattern\cr
exist&check existence of variable or function\cr
find&return indices of nonzero elements\cr
sort&return a sorted array\cr
unique&discard duplicate elements\cr
sortrows&sort whole rows in numerical or lexicographic order\cr
sum prod&sum or product\cr
mod rem&remainder functions\cr
min max range mean median std&basic statistics\cr
\endsec

\sec Error Handling;
eval ({\it str})&evaluate {\it str} as a command\cr
system ({\it cmd})&execute arbitrary shell command string\cr
error ({\it message})&print message and return to top level\cr
warning ({\it message})&print a warning message\cr
\endsec

\sec File I/O, Loading, Saving;
save load &save or load variables to or from file\cr
save -binary &save variables in binary format (faster)\cr
dlmread dlmwrite&read and write delimited data\cr
csvread csvwrite&read and write CSV files\cr
xlsread xlswrite&read and write XLS spreadsheets\cr

fopen fclose & open and close file\cr
fprintf fscanf textscan&formatted file I/O\cr
fflush&flush pending output\cr
\endsec

\sec Math Functions;
\omit \vbox{\rm\vskip0.5ex
  Run {\tt doc <function>} to find related functions.
  \vskip0.75ex}\span\cr
cov corrcoef&covariance, correlation coefficient\cr
tan tanh atan2&trig and hyperbolic functions\cr
cross curl del2&vector algebra functions\cr
&\cr
det inv& determinant matrix inverse\cr
eig &eigenvalues and eigenvectors\cr
norm &vector norm, matrix norm\cr
rank &matrix rank\cr
qr &QR factorization\cr
chol &Cholesky factorization\cr
svd &singular value decomposition\cr
&\cr
fsolve&solve nonlinear algebraic equations\cr
lsode&integrate nonlinear ODEs\cr
dassl&integrate nonlinear DAEs\cr
quad&integrate nonlinear functions\cr
&\cr
union&set union\cr
intersection&set intersection\cr
setdiff&set difference\cr
&\cr
roots &polynomial roots\cr
poly &matrix characteristic polynomial\cr
polyder polyint&polynomial derivative or integral\cr
polyfit polyval&polynomial fitting and evaluation\cr
residue &partial fraction expansion\cr
legendre bessel airy&special function\cr
&\cr
conv conv2& convolution, polynomial multiplication\cr
deconv& deconvolution, polynomial division\cr
&\cr
fft fft2 ifft({\it a})&FFT and inverse FFT\cr
freqz &FIR filter frequency response\cr
filter &filter by transfer function\cr
\endsec

\sec Plotting And Graphics;
plot plot3 &2D / 3D plot with linear axes\cr
line &2D or 3D line\cr
patch fill&2D patch, optionally colored\cr
semilogx semilogy loglog&2D plot with one or both axes on a log scale\cr
bar hist&bar chart, histogram\cr
stairs stem&stairsteps and stem graphs\cr
contour &contour plot\cr
mesh trimesh surf &plot 3D surfaces\cr
&\cr
figure&new figure\cr
hold on&add to existing figure\cr
title &set plot title\cr
axis &set axis range and aspect\cr
xlabel ylabel zlabel &set axis labels\cr
text &add text to a plot\cr
grid legend &draw grid or legend\cr
&\cr
image imagesc spy&display matrix as image\cr
imwrite saveas print&save figure or image\cr
imread&load an image\cr
colormap &get or set colormap\cr
\endsec

\vskip 0pt plus 2fill
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{\smrm\parskip=6pt
Edition \refcardedition\ for Octave Version \octaveversion.
Copyright 1996-2022 The Octave Project Developers.  The authors assume
no responsibility for any errors on this card.

This card may be freely distributed under the terms of the GNU
General Public License.

\TeX{} Macros for this card by Roland Pesch (pesch@cygnus.com),
originally for the GDB reference card

Octave itself is free software; you are welcome to distribute copies of
it under the terms of the GNU General Public License.  There is
absolutely no warranty for Octave.
}

\end

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