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

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     3 {{{ Show the slide containing title }}}

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     5 {{{ Show the slide containing the outline slide }}}

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

     8 given set of points.

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    10 First let us have a look at the problem.

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

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

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

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

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

    20 its length, we shall plot l vs t^2 and verify if the proportionality is linear.

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    22 If it is not linear, we shall generate a least square fit line.

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

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    26 As shown in the slide, we are first going to generate the two matrices tsq and

    27 A. Then we are going to use the =lstsq= function to find the values of m and c.

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    29 To read the input file and parse the data, we are going to loadtxt function.

    30 Type

    31 ::

    32 

    33     data = loadtxt("/home/fossee/pendulum.txt")

    34     data

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    36 As you can see, data is a sequence containing 90 records. Each record contains

    37 two values. The first is length and second is time period. But what we need is 

    38 two sequences. One sequence containing all the length values and one containing

    39 all the time values.

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    41 Hence we have to use the unpack option with loadtxt. It unpacks the data into

    42  sequences depending on the structure of data.

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    44 Type

    45 ::

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

    48     l

    49     t

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

    52 correspondingly.

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

    55 ::

    56 

    57     tsq = t * t

    58     plot(l, tsq, 'bo')

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    60 

    61 {{{ switch to the plot window }}}

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    63 We can see that there is a visible linear trend.

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

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

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

    68 ::

    69 

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

    71     inter_mat

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

    74 ::

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    76     A = inter_mat.T

    77     A

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

    80 Type

    81 ::

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    83     result = lstsq(A, tsq)

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    85 The result is a sequence of values. The first item is the matrix p or in simple

    86 words, the values of m and c. Hence, 

    87 ::

    88 

    89     m, c = result[0]

    90     m

    91     c

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

    94 ::

    95 

    96     tsq_fit = m * l + c

    97     plot(l, tsq, 'bo')

    98     plot(l, tsq_fit, 'r')

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

   101 

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

   103 

   104 %% 2 %% change the label on y-axis to "y" and save the lines of code

   105         accordingly

   106 

   107 {{{ continue from paused state }}}

   108 

   109 {{{ Show summary slide }}}

   110 

   111 This brings us to the end of the tutorial.

   112 we have learnt

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   114  * how to use loadtxt to read files

   115  * how to generate a least square fit

   116 

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

   118 

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

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

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   122 Hope you have enjoyed and found it useful.

   123 Thankyou

   124  

   125 .. Author              : Nishanth

   126    Internal Reviewer 1 : 

   127    Internal Reviewer 2 : 

   128    External Reviewer   :