3 files changed, 141 insertions, 10 deletions
diff --git a/processing/chapter.tex b/processing/chapter.tex
index 28d1858..40055c4 100644
--- a/processing/chapter.tex
+++ b/processing/chapter.tex
@@ -1,6 +1,25 @@
-\chapter{Processing}
-
-% TODO: cool quote, if I can think of one
+\chapter{Processing} \label{cha:pro}
+
+\begin{dquote}
+  What we have is data glut.
+  What we really want is the ability to manipulate the information and to reach conclusions from
+  it.
+  I think we are at the point where that is slipping beyond unaided humans’ abilities.
+  So the real thing to be looking for is processing schemes.
+  One way is automatic processing: for instance, the sort of analysis that we saw with the IBM
+  Watson on Jeopardy.
+  Putting that in service to humankind in fields that are suffering from data glut at least gives
+  people who are in charge the ability to keep some sort of track of what is going on.
+
+  The other great thing that we have going for us is that we have billions of very intelligent
+  people out there in the world.
+  :With the networking that we have now, we’re beginning to see that those large populations,
+  coordinating amongst themselves, are an intellectual resource that trumps all institutional
+  intellectual resources and has a real possibility, if it’s supported by the proper automation, of
+  creating solutions to problems, including the problem of the data glut.
+
+  \dsignature{Vernor Vinge \cite{VingeVernor2012a}}
+\end{dquote}
 
 \clearpage
 
@@ -290,6 +309,64 @@ Users can configure which files are routed to which from-function.  %
 
 % TODO (also document on wright.tools)
 
+\subsection{Variables and channels}  % ------------------------------------------------------------
+
+Data objects are made up of many component channels and variables, each array having the same
+dimensionality of its parent data.  %
+This strategy allows for maximal flexibility in data representation, but it can be overly expensive
+if certain arrays do not actually change against all of the dimensions.  %
+This is often especially true with variables, which typically correspond to scannable hardware that
+may not have even moved across some (or any) dimensions.  %
+To avoid unnecessarily large arrays, WrightTools allows Channels and Variables to have different
+sizes than the parent data.  %
+As an example, consider the following object.
+\begin{codefragment}{bash}  % TODO: need to use bash here because of box charachters :-(
+>>> import WrightTools as wt; from WrightTools import datasets
+>>> data = wt.data.from_COLORS(datasets.COLORS.v2p1_MoS2_TrEE_movie)
+>>> data.print_tree()
+MoS2 (/tmp/qhg_1b3l.wt5)
+├── axes
+│   ├── 0: w2 (nm) (41, 1, 1)
+│   ├── 1: w1=wm (nm) (1, 41, 1)
+│   └── 2: d2 (fs) (1, 1, 23)
+├── variables
+│   ├── 0: w2 (nm) (41, 1, 1)
+│   ├── 1: w1 (nm) (1, 41, 1)
+│   ├── 2: wm (nm) (1, 41, 1)
+│   ├── 3: d2 (fs) (1, 1, 23)
+│   ├── 4: w3 (nm) (1, 1, 1)
+│   ├── 5: d0 (fs) (1, 1, 1)
+│   └── 6: d1 (fs) (1, 1, 1)
+└── channels
+    ├── 0: ai0 (41, 41, 23)
+    ├── 1: ai1 (41, 41, 23)
+    ├── 2: ai2 (41, 41, 23)
+    ├── 3: ai3 (41, 41, 23)
+    ├── 4: ai4 (41, 41, 23)
+    └── 5: mc (41, 41, 23)
+\end{codefragment}
+Note that this is the primary dataset discussed in \autoref{cha:mx2}.  %
+The shape of this data object is \python{(41, 41, 23)}, but none of the variables have that full
+shape.  %
+From a quick inspection, one can see that \python{w1} and \python{wm} were scanned together, while
+\python{w2} and \python{d2} were the other two dimensions.  %
+\python{w3}, \python{d0}, and \python{d1} were not moved at all, yet their coordinates are still
+propagated.  %
+The axes have the joint shape of their component variables.  %
+Although not shown in this example, channels also may have axes with length 1.
+
+Axes, variables, and channels are array-likes, so they support slicing operations.  %
+In addition, all three classes have \python{points} and \python{full} attributes that return the
+squeezed and broadcasted array, respectively.  %
+
+\begin{figure}
+  \includegraphics[width=\textwidth]{"processing/fringes_transform"}
+  \includepython{"processing/fringes_transform.py"}
+  \caption[CAPTION TODO]{
+    CAPTION TODO}
+\end{figure}
+
+
 \subsection{Math}  % ------------------------------------------------------------------------------
 
 Now that we know the basics of how the WrightTools \python{Data} class stores data, it's time to do
@@ -300,7 +377,7 @@ Let's start with some elementary algebra.  %
 
 In Python, operators are symbols that carry out some computation.  %
 Consider the following:
-\begin{codefragment}{python, label=abcdefg}
+\begin{codefragment}{python, label=pro:lst:array_addition}
 >>> import numpy as np
 >>> a = np.array([4, 5, 6])
 >>> b = np.array([-1, -2, -3])
@@ -312,7 +389,7 @@ Here, \python{a} and \python{b} are operands and \python{+} is an operator.  %
 When used in this simple way, operators typically create and return a \emph{new} object in the
 computers memory.  %
 We can verify this by using Python's built-in \python{id} function on the objects created in
-\ref{abcdefg}.  %
+\ref{pro:lst:array_addition}.  %
 \begin{codefragment}{python}
 >>> id(a), id(b), id(c)
 (139712529580400, 139712333712320, 139712333713040)
@@ -321,12 +398,39 @@ This is usually fine, but sometimes the operands are unwieldy large objects that
 memory to store.  %
 In other cases operators are used millions of times such that, used as above, millions of new
 arrays will be created.  %
-One way to avoid these problems is to use \emph{in-place} operators
-
-Because the \python{Data} object is mostly stored outside of memory, it is better to do
-in-place... % TODO
 
-Broadcasting... % TODO
+One way to avoid these problems is to use \emph{in-place} operators.  %
+Using a slightly different syntax, one can tell Python to overwrite one of the operands with the
+new value. %
+Continuing from \ref{pro:lst:array_addition}:
+\begin{codefragment}{python, label=pro:lst:in_place_addition}
+>>> a += b
+>>> a
+array([3, 3, 3])
+\end{codefragment}
+No output \python{c} array was created, so no additional memory footprint is needed in
+\ref{pro:lst:in_place_addition}.  %
+Since WrightTools channels and variables are typically large arrays, and since these arrays are
+stored on disk inside of a larger file, WrightTools requires the use of in-place operators for all
+normal math.  %
+Currently WrightTools supports addition (\python{+=}), multiplication(\python{*=}),
+power (\python{**=}), subtraction (\python{-=}), and division (\python{/=}).  %
+As an example, consider dividing a channel by a specific factor:
+\begin{codefragment}{python}
+>>> import WrightTools as wt; from WrightTools import datasets
+>>> data = wt.data.from_JASCO(datasets.JASCO.PbSe_batch_1)
+data.created at /tmp/tdyvfxu8.wt5::/
+  range: 2500.0 to 700.0 (nm)
+  size: 1801
+>>> data.signal
+<WrightTools.Channel 'signal' at /tmp/tdyvfxu8.wt5::/signal>
+>>> data.signal.min(), data.signal.max()
+(0.10755, 1.58144)
+>>> data.signal /= 2
+>>> data.signal.max(), data.signal.min()
+(0.053775, 0.79072)
+\end{codefragment}
+Variables also support in-place operators.  %
 
 \subsubsection{Clip}
 
diff --git a/processing/fringes_transform.png b/processing/fringes_transform.png
new file mode 100644
index 0000000..4d400d2
--- /dev/null
+++ b/processing/fringes_transform.png
diff --git a/processing/fringes_transform.py b/processing/fringes_transform.py
new file mode 100644
index 0000000..1f80a86
--- /dev/null
+++ b/processing/fringes_transform.py
@@ -0,0 +1,27 @@
+import os
+import matplotlib.pyplot as plt
+import WrightTools as wt; from WrightTools import datasets
+
+here = os.path.abspath(os.path.dirname(__file__))
+
+data = wt.data.from_PyCMDS(datasets.PyCMDS.w2_w1_000)
+data.signal_mean.symmetric_root(0.5)  # to amplitude level
+data.convert('wn')
+
+fig, gs = wt.artists.create_figure(width='double', cols=[1, 1, 'cbar'])
+# as taken
+ax = plt.subplot(gs[0, 0])
+ax.pcolor(data)
+wt.artists.set_ax_labels(xlabel=data.w2.label, ylabel=data.w1.label)
+ax.grid(); ax.set_title('as taken', fontsize=20)
+# transformed
+ax = plt.subplot(gs[0, 1])
+data.transform('wm', 'w1')
+data.convert('wn')
+ax.pcolor(data)
+wt.artists.set_ax_labels(xlabel=data.wm.label, yticks=False)
+ax.grid(); ax.set_title('transformed', fontsize=20)
+# colorbar
+wt.artists.plot_colorbar(plt.subplot(gs[0, -1]), label='amplitude')
+# save
+wt.artists.savefig(os.path.join(here, 'fringes_transform.png'))