Python/C3/Least-square-fit/English-timed

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Visual Cue Narration
0:01 Hello friends and welcome to the tutorial on 'Least Square Fit'.
0:05 At the end of this tutorial, you will be able to,
  1. Generate the least square fit line for a given set of points.
0:11 Before beginning this tutorial,we would suggest you to complete the tutorial on "Using plot interactively", "Loading data from files" and "Getting started with arrays".
0:22 Let us start this tutorial with the help of an example.
0:27 Generate a least square fit line for l versus t square using the data in the file 'pendulum.txt'.
0:36 We have an input file generated from a simple pendulum experiment.
0:40 It contains two columns of data.
0:43 The first column is the length of the pendulum and the second is the corresponding time period of the pendulum.
0:48 As we know, the square of time period of a pendulum is directly proportional to its length,
0:54 we shall plot l versus t square and verify this.
0:58 To read the file input and parse the data, we are going to use the loadtxt function.
1:04 Switch to the terminal.
1:08 We can see that l and t are two sequences containing length and time values correspondingly.
1:15 Let us first plot l versus t square.
1:18 Type in the terminal ipython hypen pylab
1:27 Type l comma t = loadtxt within brackets in double quotes slash home slash fossee slash pendulum.txt comma unpack=True and bracket closed.

Then type l Secondly type t

2:05 We can see that there is a visible linear trend, but we do not get a straight line connecting them.
2:11 We shall, therefore, generate a least square fit line.
2:15 We will first generate the two matrices tsq and A.
2:22 Then we will use the lstsq function to find the values of m and c.
2:32 Type tsq = t star t hit enter

Type plot within brackets l comma tsq comma within single quotes bo hit enter

2:57 let us now generate the A matrix with l values.
3:01 We shall first generate a 2 into 90 matrix with the first row as l values and the second row as ones.
3:13 Then take the transpose of it.
3:16 Type in the termianl inter underscore mat = array within brackets l comma ones underscore like within brackets one then close the bracket
3:44 Now we can see an error.
3:47 The error is in the one underscore like function we typed one instead of l so you have to put l there.
3:59 We can see that we have intermediate matrix.
4:02 Now we need the transpose.
4:04 So type on the terminal
A = inter underscore mat.T 
4:19 Type A and hit enter
4:22 Now we have both the matrices A and tsq.
4:27 We only need to use the lstsq .
4:33 Type result = lstsq within brackets A comma tsq where lstsq stands for least square
4:49 The result is a sequence of values.
4:51 The first item in this sequence, is the matrix p i.e., the values of m and c.
4:58 Type m comma c = result within square brackets 0 .Then type
m

Then type

c so you can see the output.
5:20 Now that we have m and c,So we need to generate the fitted values of t square.
5:28 Type on terminal.
tsq underscore fit = m star l plus c
Type plot within brackets l comma tsq comma  within single quote bo
6:06 Before typing that plot we have to type clear function.
Type plot within brackets l comma  tsq comma bo.
6:24 Now you can see the plot
Type plot within brackets l comma  tsq underscore fit comma r
6:41 We get the least square fit of l versus t square.
6:49 This brings us to the end of this tutorial.
6:52 In this tutorial, we have learnt to, 1. Generate a least square fit using matrices.
6:57 2. Use the function lstsq() to generate a least square fit line.
7:03 Here are some self assessment questions for you to solve
7:07 1. What does ones underscore like 1 comma 2 comma 3 produce
  array 1 comma  1 comma  1
   1 comma  1 comma  1 within square brackets.
   within square brackets 1 point 0 comma  1 point 0 comma  1 point 0
 Error
7:25 2. The plot of u versus v is a bunch of scattered points that show a linear trend.
7:33 How do you find the least square fit line of u versus v.
7:38 And will look at the answers,
7:42 1. The function ones underscore like in 1 comma 2 comma 3 will generate array 1 comma 1 comma 1.

So that is the first questions answer.

7:54 2. The following set of commands will produce the least square fit line of u versus v
A = array within brackets u comma  ones underscore like within brackets u.T
result = lstsq  within brackets A comma  v
m comma  c = result within square brackets 0
lst underscore line = m star u plus c
8:34 Hope you have enjoyed this tutorial and found it useful.
8:37 Thank you!

Contributors and Content Editors

Gaurav, Minal, PoojaMoolya, Sneha