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

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, 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 terminal 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