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

::

    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 }}}

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

::

    A = inter_mat.T

    A

Type

::

    result = lstsq(A, tsq)

::

    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.