1 .. Objectives

     2 .. ----------

     3 

     4 .. Plotting a least square fit line

     5 

     6 .. Prerequisites

     7 .. -------------

     8 

     9 ..   1. Basic Plotting

    10 ..   2. Arrays

    11 ..   3. Loading data from files 

    12      

    13 .. Author              : Nishanth Amuluru

    14    Internal Reviewer   : Punch

    15    External Reviewer   :

    16    Language Reviewer   : Bhanukiran

    17    Checklist OK?       : <put date stamp here, not OK> [2010-10-05]

    18 

    19 

    20 .. #[Puneeth: Add pre-requisites.]

    21 

    22 Script

    23 ------

    24 

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

    26 

    27 {{{ Show the slide containing title }}}

    28 

    29 {{{ Show the slide containing the outline slide }}}

    30 

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

    32 given set of points.

    33 

    34 First let us have a look at the problem.

    35 

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

    37 

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

    39 

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

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

    42 

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

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

    45 

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

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

    48 ..  should work?

    49 

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

    51 loadtxt function.  Type 

    52 ::

    53 

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

    55     l

    56     t

    57 

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

    59 correspondingly.

    60 

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

    62 ::

    63 

    64     tsq = t * t

    65     plot(l, tsq, 'bo')

    66 

    67 {{{ switch to the plot window }}}

    68 

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

    70 .. apt. 

    71 

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

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

    74 square fit line.

    75 

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

    77 

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

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

    80 values of m and c.

    81 

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

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

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

    85 ::

    86 

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

    88     inter_mat

    89 

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

    91 ::

    92 

    93     A = inter_mat.T

    94     A

    95 

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

    97 Type

    98 ::

    99 

   100     result = lstsq(A, tsq)

   101 

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

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

   104 ::

   105 

   106     m, c = result[0]

   107     m

   108     c

   109 

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

   111 ::

   112 

   113     tsq_fit = m * l + c

   114     plot(l, tsq, 'bo')

   115     plot(l, tsq_fit, 'r')

   116 

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

   118 

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

   120 

   121 %% 2 %% change the label on y-axis to "y" and save the lines of code

   122         accordingly

   123 

   124 {{{ continue from paused state }}}

   125 

   126 {{{ Show summary slide }}}

   127 

   128 This brings us to the end of the tutorial.

   129 we have learnt

   130 

   131  * how to generate a least square fit

   132 

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

   134 

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

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

   137 

   138 Hope you have enjoyed and found it useful.

   139 Thank you

   140 

   141 

   142 .. 

   143    Local Variables:

   144    mode: rst

   145    indent-tabs-mode: nil

   146    sentence-end-double-space: nil

   147    fill-column: 75

   148    End: