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+++ b/least_square_fit/script.rst	Wed Dec 01 16:51:35 2010 +0530
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+.. Objectives
+.. ----------
+
+.. Plotting a least square fit line
+
+.. Prerequisites
+.. -------------
+
+..   1. Basic Plotting
+..   2. Arrays
+..   3. Loading data from files 
+     
+.. Author              : Nishanth Amuluru
+   Internal Reviewer   : Punch
+   External Reviewer   :
+   Language Reviewer   : Bhanukiran
+   Checklist OK?       : <put date stamp here, not OK> [2010-10-05]
+
+
+.. #[Puneeth: Add pre-requisites.]
+
+Script
+------
+
+Hello friends and welcome to the tutorial on Least Square Fit
+
+{{{ Show the slide containing title }}}
+
+{{{ Show the slide containing the outline slide }}}
+
+In this tutorial, we shall look at generating the least square fit line for a
+given set of points.
+
+First let us have a look at the problem.
+
+{{{ Show the slide containing problem statement. }}}
+
+We have an input file generated from a simple pendulum experiment.
+
+It contains two columns of data. The first column is the length of the
+pendulum and the second is the corresponding time period of the pendulum.
+
+As we know, the square of time period of a pendulum is directly proportional to
+its length, we shall plot l vs t^2 and verify this. 
+
+.. #[Puneeth:] removed the explanation about loadtxt and unpack
+..  option. It's been done in another LO already. simple dependency 
+..  should work?
+
+To read the input file and parse the data, we are going to use the
+loadtxt function.  Type 
+::
+
+    l, t = loadtxt("/home/fossee/pendulum.txt", unpack=True)
+    l
+    t
+
+We can see that l and t are two sequences containing length and time values
+correspondingly.
+
+Let us first plot l vs t^2. Type
+::
+
+    tsq = t * t
+    plot(l, tsq, 'bo')
+
+{{{ switch to the plot window }}}
+
+.. #[Puneeth:] Moved explanation of least square fit here. seems more
+.. apt. 
+
+We can see that there is a visible linear trend, but we do not get a
+straight line connecting them. We shall, therefore, generate a least
+square fit line.
+
+{{{ show the slide containing explanation on least square fit }}}
+
+As shown in the slide, we are first going to generate the two matrices
+tsq and A. Then we are going to use the ``lstsq`` function to find the
+values of m and c.
+
+let us now generate the A matrix with l values.
+We shall first generate a 2 x 90 matrix with the first row as l values and the
+second row as ones. Then take the transpose of it. Type
+::
+
+    inter_mat = array((l, ones_like(l)))
+    inter_mat
+
+We see that we have intermediate matrix. Now we need the transpose. Type
+::
+
+    A = inter_mat.T
+    A
+
+Now we have both the matrices A and tsq. We only need to use the ``lstsq``
+Type
+::
+
+    result = lstsq(A, tsq)
+
+The result is a sequence of values. The first item in this sequence,
+is the matrix p i.e., the values of m and c. Hence, 
+::
+
+    m, c = result[0]
+    m
+    c
+
+Now that we have m and c, we need to generate the fitted values of t^2. Type
+::
+
+    tsq_fit = m * l + c
+    plot(l, tsq, 'bo')
+    plot(l, tsq_fit, 'r')
+
+We get the least square fit of l vs t^2
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 2 %% change the label on y-axis to "y" and save the lines of code
+        accordingly
+
+{{{ continue from paused state }}}
+
+{{{ Show summary slide }}}
+
+This brings us to the end of the tutorial.
+we have learnt
+
+ * how to generate a least square fit
+
+{{{ Show the "sponsored by FOSSEE" slide }}}
+
+.. #[Nishanth]: Will add this line after all of us fix on one.
+.. This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
+
+Hope you have enjoyed and found it useful.
+Thank you
+
+
+.. 
+   Local Variables:
+   mode: rst
+   indent-tabs-mode: nil
+   sentence-end-double-space: nil
+   fill-column: 75
+   End: