Python/C3/Least-square-fit/English-timed
From Script | Spoken-Tutorial
| Time | Narration |
| 00:01 | Hello friends and welcome to the tutorial on 'Least Square Fit'. |
| 00:05 | At the end of this tutorial, you will be able to,
Generate the least square fit line for a given set of points. |
| 00:11 | 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". |
| 00:22 | Let us start this tutorial with the help of an example. |
| 00:27 | Generate a least square fit line for l versus t square using the data in the file 'pendulum.txt'. |
| 00:36 | We have an input file generated from a simple pendulum experiment. |
| 00:40 | It contains two columns of data. |
| 00:43 | The first column is the length of the pendulum and the second is the corresponding time series of the pendulum. |
| 00:48 | As we know, the square of time period of a pendulum is directly proportional to its length, |
| 00:54 | we shall plot l versus t square and verify this. |
| 00:58 | To read the file input and parse the data, we are going to use the loadtxt function. |
| 01:04 | Switch to the terminal. |
| 01:08 | We can see that l and t are two sequences containing length and time values correspondingly. |
| 01:15 | Let us first plot l versus t square. |
| 01:18 | Type in the terminal ipython hypen pylab |
| 01:27 | Type l comma t = loadtxt within brackets in double quotes slash home slash fossee slash pendulum.txt comma unpack=True then bracket closed.
Then type l Secondly type t |
| 02:05 | We can see that there is a visible linear trend, but we do not get a straight line connecting them. |
| 02:11 | We shall, therefore, generate a least square fit line. |
| 02:15 | We will first generate the two matrices tsq and A. |
| 02:22 | Then we will use the lstsq function to find the values of m and c. |
| 02:32 | Type tsq = t star t hit enter. Type plot within brackets l comma tsq comma within single quotes bo hit enter |
| 02:57 | let us now generate the A matrix with l values. |
| 03:01 | We shall first generate a 2 into 90 matrix with the first row as l values and the second row as ones. |
| 03:13 | Then take the transpose of it. |
| 03:16 | Type in the terminal inter underscore mat = array within brackets l comma ones underscore like within brackets one then closing bracket |
| 03:44 | Now we can see an error. |
| 03:47 | The error is in the one underscore like function we typed one instead of l so you have to put l there. |
| 03:59 | We can see that we have intermediate matrix. |
| 04:02 | Now we need the transpose. |
| 04:04 | So type on the terminal A = inter underscore mat.T |
| 04:19 | Type A and hit enter |
| 04:22 | Now we have both the matrices A and tsq. |
| 04:27 | We only need to use the lstsq . |
| 04:33 | Type result = lstsq within brackets A comma tsq where lstsq stands for least square |
| 04:49 | The result is a sequence of values. |
| 04:51 | The first item in this sequence, is the matrix p i.e., the values of m and c. |
| 04:58 | Type m comma c = result within square brackets 0 .Then type m. Then type c so you can see the output. |
| 05:20 | Now that we have m and c,So we need to generate the fitted values of t square. |
| 05:28 | Type on terminal. tsq underscore fit = m star l plus c Type plot within brackets l comma tsq comma within single quote bo |
| 06:06 | Before typing that plot we have to type clear function. Type plot within brackets l comma tsq comma bo. |
| 06:24 | Now i can see the plot. Type plot within brackets l comma tsq underscore fit comma r |
| 06:41 | We get the least square fit of l versus t square. |
| 06:49 | This brings us to the end of this tutorial. |
| 06:52 | In this tutorial, we have learnt to, 1. Generate a least square fit using matrices. |
| 06:57 | 2. Use the function lstsq() to generate a least square fit line. |
| 07:03 | Here are some self assessment questions for you to solve |
| 07:07 | 1. What does ones underscore like 1 comma 2 comma 3 produce array 1 comma 1 comma 1. 1 comma 1 comma 1 in square brackets. square brackets 1 point 0 comma 1 point 0 comma 1 point 0 Error |
| 07:25 | 2. The plot of u versus v is a bunch of scattered points that show a linear trend. |
| 07:33 | How do you find the least square fit line of u versus v . |
| 07:38 | And will look at the answers, |
| 07:42 | 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. |
| 07:54 | 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 |
| 08:34 | Hope you have enjoyed this tutorial and found it useful. |
| 08:37 | Thank you! |
