# HG changeset patch
# User nishanth
# Date 1284543541 -19800
# Node ID b8f7ee434b9171f9b640e471edd1f6fbb187ed31
# Parent  ca42b98210198779a46b53822c654238f088b5a0
initial commit of lstsq

diff -r ca42b9821019 -r b8f7ee434b91 lstsq.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lstsq.rst	Wed Sep 15 15:09:01 2010 +0530
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+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 if the proportionality is linear.
+
+If it is not linear, we shall 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.
+
+To read the input file and parse the data, we are going to loadtxt function.
+Type::
+
+    data = loadtxt("/home/fossee/pendulum.txt")
+    data
+
+As you can see, data is a sequence containing 90 records. Each record contains
+two values. The first is length and second is time period. But what we need is 
+two sequences. One sequence containing all the length values and one containing
+all the time values.
+
+Hence we have to use the unpack option with loadtxt. It unpacks the data into
+ sequences depending on the structure of data.
+
+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 }}}
+
+We can see that there is a visible linear trend.
+
+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 is the matrix p or in simple
+words, 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 use loadtxt to read files
+ * 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.
+Thankyou
+ 
+.. Author              : Nishanth
+   Internal Reviewer 1 : 
+   Internal Reviewer 2 : 
+   External Reviewer   :