1 .. Author              : Nishanth

     2    Internal Reviewer 1 : Puneeth

     3    Internal Reviewer 2 : 

     4    External Reviewer   :

     5 

     6 Hello friends and welcome to the tutorial on Least Square Fit

     7 

     8 {{{ Show the slide containing title }}}

     9 

    10 {{{ Show the slide containing the outline slide }}}

    11 

    12 In this tutorial, we shall look at generating the least square fit line for a

    13 given set of points.

    14 

    15 First let us have a look at the problem.

    16 

    17 {{{ Show the slide containing problem statement. }}}

    18 

    19 We have an input file generated from a simple pendulum experiment.

    20 

    21 It contains two columns of data. The first column is the length of the

    22 pendulum and the second is the corresponding time period of the pendulum.

    23 

    24 As we know, the square of time period of a pendulum is directly proportional to

    25 its length, we shall plot l vs t^2 and verify this. 

    26 

    27 #[Puneeth:] removed the explanation about loadtxt and unpack

    28  option. It's been done in another LO already. simple dependency 

    29  should work?

    30 

    31 To read the input file and parse the data, we are going to use the

    32 loadtxt function.  Type 

    33 ::

    34 

    35     l, t = loadtxt("/home/fossee/pendulum.txt", unpack=True)

    36     l

    37     t

    38 

    39 We can see that l and t are two sequences containing length and time values

    40 correspondingly.

    41 

    42 Let us first plot l vs t^2. Type

    43 ::

    44 

    45     tsq = t * t

    46     plot(l, tsq, 'bo')

    47 

    48 {{{ switch to the plot window }}}

    49 

    50 #[Puneeth:] Moved explanation of least square fit here. seems more

    51 apt. 

    52 

    53 We can see that there is a visible linear trend, but we do not get a

    54 straight line connecting them. We shall, therefore, generate a least

    55 square fit line.

    56 

    57 {{{ show the slide containing explanation on least square fit }}}

    58 

    59 As shown in the slide, we are first going to generate the two matrices

    60 tsq and A. Then we are going to use the ``lstsq`` function to find the

    61 values of m and c.

    62 

    63 let us now generate the A matrix with l values.

    64 We shall first generate a 2 x 90 matrix with the first row as l values and the

    65 second row as ones. Then take the transpose of it. Type

    66 ::

    67 

    68     inter_mat = array((l, ones_like(l)))

    69     inter_mat

    70 

    71 We see that we have intermediate matrix. Now we need the transpose. Type

    72 ::

    73 

    74     A = inter_mat.T

    75     A

    76 

    77 Now we have both the matrices A and tsq. We only need to use the ``lstsq``

    78 Type

    79 ::

    80 

    81     result = lstsq(A, tsq)

    82 

    83 The result is a sequence of values. The first item in this sequence,

    84 is the matrix p i.e., the values of m and c. Hence, 

    85 ::

    86 

    87     m, c = result[0]

    88     m

    89     c

    90 

    91 Now that we have m and c, we need to generate the fitted values of t^2. Type

    92 ::

    93 

    94     tsq_fit = m * l + c

    95     plot(l, tsq, 'bo')

    96     plot(l, tsq_fit, 'r')

    97 

    98 We get the least square fit of l vs t^2

    99 

   100 {{{ Pause here and try out the following exercises }}}

   101 

   102 %% 2 %% change the label on y-axis to "y" and save the lines of code

   103         accordingly

   104 

   105 {{{ continue from paused state }}}

   106 

   107 {{{ Show summary slide }}}

   108 

   109 This brings us to the end of the tutorial.

   110 we have learnt

   111 

   112  * how to generate a least square fit

   113 

   114 {{{ Show the "sponsored by FOSSEE" slide }}}

   115 

   116 #[Nishanth]: Will add this line after all of us fix on one.

   117 This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India

   118 

   119 Hope you have enjoyed and found it useful.

   120 Thank you

   121 

   122 Questions

   123 =========

   124 

   125  1. What does ones_like([1, 2, 3]) produce

   126 

   127    a. array([1, 1, 1])

   128    #. [1, 1, 1]

   129    #. [1.0, 1.0, 1.0]

   130    #. Error

   131    

   132  2. What does ones_like([1.2, 3, 4, 5]) produce

   133 

   134    a. [1.2, 3, 4, 5]

   135    #. array([1.0, 1.0, 1.0, 1.0])

   136    #. array([1, 1, 1, 1])

   137    #. array([1.2, 3, 4, 5])

   138 

   139  3. What is the shape of the