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<h1>Getting started with Julia</h1><p>Julia is a freely available open-source programming language aimed at technical computing.</p><p>As it is open source, indeed with a liberal MIT license, it can be installed for free on many types of computers (though not phones or tablets). There are some web sites that provide access to <code>Julia</code>:</p><p><a href="http://www.juliabox.org">JuliaBox</a> provides a web-based interface to <code>Julia</code> built around <code>IJulia</code>. An account is needed and can be requested.</p><p><a href="http://cloud.sagemath.org">Sagemath</a> provides another web-based solution and an <code>Jupyter</code> front end, as well. This is free for most use.</p><h3>Installing Julia locally</h3><p>Binaries of <code>Julia</code> are provided at <a href="http://julialang.org/downloads/">julialang.org</a>. Julia has an official released version and a developmental version. Unless there is a compelling reason, the latest released version should be downloaded and installed for use.</p><p>The base <code>Julia</code> provides a <em>command-line interface</em>, or REPL (read-evaluate-parse).</p><h3>Basic interactive usage</h3><p>Once installed, <code>Julia</code> can be started by clicking on an icon or typing <code>julia</code> at the command line. Either will open a <em>command line interface</em> for a user to interact with a <code>Julia</code> process. The basic workflow is easy: commands are typed then sent to a <code>Julia</code> process when the "return" key is pressed for a complete expression. Then the output is displayed.</p><p>A command is typed following the <em>prompt</em>. An example might be <code>2 + 2</code>. To send the command to the <code>Julia</code> interpreter the "return" key is pressed. A complete expression or expressions will then be parsed and evaluated (executed). If the expression is not complete, <code>julia</code>'s prompt will still accept input to complete the expression. Type <code>2 +</code> to see. (The expression <code>2 +</code> is not complete, as the infix operator <code>+</code> expects two arguments, one on its left and one on its right.)</p><pre class="sourceCode julia"> _
_ _ _(_)_ | A fresh approach to technical computing
(_) | (_) (_) | Documentation: http://docs.julialang.org
_ _ _| |_ __ _ | Type "?help" for help.
| | | | | | |/ _` | |
| | |_| | | | (_| | | Version 0.4.1 (2015-11-08 10:33 UTC)
_/ |\__'_|_|_|\__'_| | Official http://julialang.org/ release
|__/ | x86_64-apple-darwin13.4.0
julia> 2 + 2
4</pre>
<p>Above, <code>julia></code> is the prompt. These notes will not include the prompt, so that copying-and-pasting can be more easily used. Input and output cells display similarly, though with differences in coloring. For example:</p><pre class="sourceCode julia">2 + 2</pre>
<pre class="output">
4</pre>
<h3>IJulia, a better learning enviroment for <code>Julia</code></h3><p>A more forgiving interface for learning is provided through the <code>IJulia</code> interface. This is the interface for <code>JuliaBox</code>. The <code>IJulia</code> interface can be installed relatively easily by following these steps:</p><ul>
<li>Run these commands to install two packages:</li>
</ul><pre class="sourceCode julia">Pkg.update()
Pkg.add("PyCall")
Pkg.add("IJulia")</pre>
<ul>
<li>Once this is done, you can start the notebook with these commands:</li>
</ul><pre class="sourceCode julia">using IJulia
notebook()</pre>
<h2>Add-on packages</h2><p><code>Julia</code> has 100s of external, add-on packages that enhance the offerings of base <code>Julia</code>. The above showed how to add two packages to a system. In these notes, we will rely on a few packages. These will need to be installed. The following commands will download and install the needed packages:</p><pre class="sourceCode julia">Pkg.update()
Pkg.add("Plots")
Pkg.add("Gadfly")
Pkg.add("PyCall")
Pkg.add("SymPy")
Pkg.add("Roots")
Pkg.add("ImplicitEquations")
Pkg.add("PyPlot")
""")</pre>
<p>The <code>SymPy</code> package and the <code>PyPlot</code> package require some add-ons for the <code>Python</code> environment. These should be installed as well, a <code>Python</code> environment, if not already existing, should be installed withe <code>PyCall</code> package.</p><h2>The basics of working with IJulia</h2><p>The <strong>very</strong> basics of IJulia are covered here.</p><p>An <code>IJulia</code> notebook is made up of cells. Within a cell a collection of commands may be typed (one or more).</p><p>When a cell is executed (by the triangle icon or under the Cell menu) the contents of the cell are evaluated by the <code>Julia</code> kernel and any output is displayed below the cell. Typically this is just the output of the last command.</p><pre class="sourceCode julia">2 + 2
3 + 3</pre>
<pre class="output">
6</pre>
<p>If the last commands are separated by commas, then a "tuple" will be formed and each output will be displayed, separated by commas.</p><pre class="sourceCode julia">2 + 2, 3 + 3</pre>
<pre class="output">
(4,6)</pre>
<p>Comments can be made in a cell. Anything after a <code>#</code> will be ignored.</p><pre class="sourceCode julia">2 + 2 # this is a comment, you can ignore me...</pre>
<pre class="output">
4</pre>
<p>Graphics are provided by external packages. There is no built-in graphing. We primarily use the <code>Gadfly</code> package for graphics, but through the <code>Plots</code> package.</p><p>The plots package is loaded and the <code>Gadfly</code> backend is chosen via</p><pre class="sourceCode julia">using Plots
gadfly()</pre>
<pre class="output">
Plots.GadflyPackage()</pre>
<p>The choice of <code>Gadfly</code> as a backend is optional, the <code>Plots</code> package does its best to be backend agnostic.</p><p>With that in hand, to make a graph of a function over a range, we follow this pattern:</p><pre class="sourceCode julia">plot(sin, 0, 2pi)</pre>
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Element.prototype.init_gadfly = function() {
this.mouseenter(Gadfly.plot_mouseover)
.mouseleave(Gadfly.plot_mouseout)
.dblclick(Gadfly.plot_dblclick)
.mousewheel(Gadfly.guide_background_scroll)
.drag(Gadfly.guide_background_drag_onmove,
Gadfly.guide_background_drag_onstart,
Gadfly.guide_background_drag_onend);
this.mouseenter(function (event) {
init_pan_zoom(this.plotroot());
});
return this;
};
});
// When the plot is moused over, emphasize the grid lines.
Gadfly.plot_mouseover = function(event) {
var root = this.plotroot();
var keyboard_zoom = function(event) {
if (event.which == 187) { // plus
increase_zoom_by_position(root, 0.1, true);
} else if (event.which == 189) { // minus
increase_zoom_by_position(root, -0.1, true);
}
};
root.data("keyboard_zoom", keyboard_zoom);
window.addEventListener("keyup", keyboard_zoom);
var xgridlines = root.select(".xgridlines"),
ygridlines = root.select(".ygridlines");
xgridlines.data("unfocused_strokedash",
xgridlines.attribute("stroke-dasharray").replace(/(\d)(,|$)/g, "$1mm$2"));
ygridlines.data("unfocused_strokedash",