From e43de3cb79a9fad846babf0ddfdca21622b903dc Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Sun, 8 Apr 2018 18:01:07 -0500
Subject: 2018-04-08 18:01

---
 processing/chapter.tex | 79 ++++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 76 insertions(+), 3 deletions(-)

(limited to 'processing/chapter.tex')

diff --git a/processing/chapter.tex b/processing/chapter.tex
index e430e1d..1ec2c37 100644
--- a/processing/chapter.tex
+++ b/processing/chapter.tex
@@ -1004,12 +1004,83 @@ Guess...
 
 Can be used directly...
 
+[USERS CAN WRITE THEIR OWN FUNCTION OBJECTS]
+
+\begin{figure}
+  \includegraphics[width=0.5\textwidth]{"processing/fit_function"}
+  \includepython{"processing/fit_function.py"}
+  \caption[CAPTION TODO]{
+    CAPTION TODO
+  }
+\end{figure}
+
 \subsection{Fitter}  % ----------------------------------------------------------------------------
 
-Loops through...
-Returns model and outs...
+The Fitter class is specially made to work seamlessly with data objects.  %
+
+WrightTools is especially good at dimensionality reduction through fitting.  %
+This concept is best demonstrated through an example.  %
+
+Let’s load in some test data.  %
+\begin{codefragment}{python}
+#import
+import WrightTools as wt
+from WrightTools import datasets
+# create
+ps = datasets.COLORS.v2p1_MoS2_TrEE_movie
+data = wt.data.from_COLORS(ps)
+# cleanup
+data.level('ai0', 'd2', -3)
+data.scale()
+data.convert('eV')
+data.name = 'MoS2'
+\end{codefragment}
+This is a three-dimensional dataset:  %
+\begin{codefragment}{python}
+>>> data.axis_names
+['w2', 'w1', 'd2']
+>>> data.shape
+(41, 41, 23)
+\end{codefragment}
+We could create an animation to see every single pixel, but we can't see everything at once that
+way.  %
+Instead we could imagine fitting every decay ($\tau_{21}$ trace) to an exponential.  %
+Then we could plot the amplitude and time constant of that exponential decay.  %
+This helps us get at subtle questions about the data.  %
+Do the lineshapes narrow with time? Does the redder feature decay slower than the bluer feature?  %
+Faster?  %
+
+Using the \python{Fitter} class, it is easy to perform an exponential fit along each TAU21 trace at
+each OMEGA1, OMEGA2 coordinate.  %
+\begin{codefragment}{python}
+# isolate only relevant data
+data = data.split('w1', 1.75)[1].split('d2', 0)[0]
+# prepare a function
+function = wt.fit.Exponential()
+function.limits['amplitude'] = [0, 1]
+function.limits['offset'] = [0, 0]
+function.limits['tau'] = [0, 2000]
+# do the fit
+fitter = wt.fit.Fitter(function, data, 'd2')
+outs = fitter.run()
+\end{codefragment}
+When we call fitter.run(), every slice of the data object will be fit according to the given
+function object. Fitter automatically creates two new data objects when this happens. outs contains
+the fit parameters, in this case amplitude, tau, and offset. Accordingly, outs is lower-dimensional
+than the original data object. model contains the fit evaluated at each coordinate of the original
+dataset—it’s really useful for inspecting the quality of your fit procedure.
+
+[ALSO GOOD FOR WORKUP OF TUNING DATA: SEE SECTION ...]
+
+\begin{figure}
+  \includegraphics[width=0.4\textwidth]{"processing/fit_amplitude"}
+  \includegraphics[width=0.4\textwidth]{"processing/fit_tau"}
+  \caption[CAPTION TODO]{
+    CAPTION TODO
+  }
+  \label{pro:fig:fitted_movie}
+\end{figure}
 
-\clearpage
 \section{Construction, maintenance, and distribution}  % ==========================================
 
 While WrightTools has already been useful to the work done in the WrightGroup over the last 3
@@ -1098,6 +1169,8 @@ WrightTools uses semantic versioning.  %
 
 Git...
 
+As of 2018-04-08, WrightTools has ........ commits from ..... developers
+
 \subsection{Unit tests}  % ------------------------------------------------------------------------
 
 Unit testing...
-- 
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