Difference between revisions of "Python/C3/Least-square-fit/English-timed"

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{| border=1
 
{| border=1
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!Visual Cue
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|'''Time'''
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!Narration
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|'''Narration'''
 +
 
 
|-
 
|-
−
| 0:01
+
| 00:01
 
| Hello friends and welcome to the tutorial on 'Least Square Fit'.
 
| Hello friends and welcome to the tutorial on 'Least Square Fit'.
  
 
|-
 
|-
−
| 0:05
+
| 00:05
 
| At the end of this tutorial, you will be able to,
 
| At the end of this tutorial, you will be able to,
−
 
+
Generate the least square fit line for a given set of points.
−
# Generate the least square fit line for a given set of points.
+
  
 
|-
 
|-
−
| 0:11
+
| 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".
 
| 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
+
| 00:22
 
| Let us start this tutorial with the help of an example.
 
| Let us start this tutorial with the help of an example.
  
 
|-
 
|-
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| 0:27
+
| 00:27
 
| Generate a least square fit line for l versus t square using the data in the file 'pendulum.txt'.
 
| Generate a least square fit line for l versus t square using the data in the file 'pendulum.txt'.
  
 
|-
 
|-
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|  0:36
+
|  00:36
 
| We have an input file generated from a simple pendulum experiment.
 
| We have an input file generated from a simple pendulum experiment.
  
 
|-
 
|-
−
| 0:40
+
| 00:40
 
| It contains two columns of data.
 
| It contains two columns of data.
  
 
|-
 
|-
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|0:43
+
|00:43
 
| The first column is the length of the pendulum and the second is the corresponding time series of the pendulum.
 
| The first column is the length of the pendulum and the second is the corresponding time series of the pendulum.
  
 
|-
 
|-
−
| 0:48
+
| 00:48
 
| As we know, the square of time period of a pendulum is directly proportional to its length,
 
| As we know, the square of time period of a pendulum is directly proportional to its length,
  
 
|-
 
|-
−
|0:54
+
|00:54
 
| we shall plot l versus t square and verify this.
 
| we shall plot l versus t square and verify this.
  
 
|-
 
|-
−
|0:58
+
|00:58
 
| To read the file input and parse the data, we are going to use the loadtxt function.
 
| To read the file input and parse the data, we are going to use the loadtxt function.
  
 
|-
 
|-
−
|1:04
+
|01:04
 
| Switch to the terminal.
 
| Switch to the terminal.
  
 
|-
 
|-
−
|1:08
+
|01:08
 
| We can see that l and t are two sequences containing length and time values correspondingly.
 
| We can see that l and t are two sequences containing length and time values correspondingly.
  
 
|-
 
|-
−
|1:15
+
|01:15
 
| Let us first plot l versus t square.
 
| Let us first plot l versus t square.
  
 
|-
 
|-
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|1:18
+
|01:18
 
|Type in the terminal ipython hypen pylab   
 
|Type in the terminal ipython hypen pylab   
  
 
|-
 
|-
−
|1:27
+
|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.
 
|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
+
Then type l Secondly type t
−
l
+
−
Secondly type
+
−
t
+
  
 
|-
 
|-
−
|2:05  
+
|02:05  
 
| We can see that there is a visible linear trend, but we do not get a straight line connecting them.
 
| We can see that there is a visible linear trend, but we do not get a straight line connecting them.
  
 
|-
 
|-
−
|2:11
+
|02:11
 
| We shall, therefore, generate a least square fit line.
 
| We shall, therefore, generate a least square fit line.
  
 
|-
 
|-
−
| 2:15
+
| 02:15
 
| We will first generate the two matrices tsq and A.
 
| We will first generate the two matrices tsq and A.
  
 
|-
 
|-
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| 2:22
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| 02:22
 
| Then we will use the  lstsq  function to find the values of m and c.
 
| Then we will use the  lstsq  function to find the values of m and c.
  
 
|-
 
|-
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|2:32
+
|02:32
−
|Type tsq = t star t hit enter
+
|Type tsq = t star t hit enter. Type plot within brackets l comma  tsq comma within single quotes bo hit enter
−
Type plot within brackets l comma  tsq comma within single quotes bo hit enter
+
  
 
|-
 
|-
−
| 2:57
+
| 02:57
 
| let us now generate the A matrix with l values.
 
| let us now generate the A matrix with l values.
  
 
|-
 
|-
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| 3:01
+
| 03:01
 
| We shall first generate a 2 into 90 matrix with the first row as l values and the second row as ones.
 
| We shall first generate a 2 into 90 matrix with the first row as l values and the second row as ones.
  
 
|-
 
|-
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|3:13
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|03:13
 
| Then take the transpose of it.
 
| Then take the transpose of it.
  
 
|-
 
|-
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|3:16
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|03:16
 
|Type in the terminal inter underscore mat = array  within brackets l comma  ones underscore like  within brackets one then closing  bracket
 
|Type in the terminal inter underscore mat = array  within brackets l comma  ones underscore like  within brackets one then closing  bracket
  
 
|-
 
|-
−
|3:44
+
|03:44
 
|Now we can see an error.
 
|Now we can see an error.
  
 
|-
 
|-
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|3:47
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|03:47
 
|The error is in the one underscore like function we typed one instead of l so you have to put l there.
 
|The error is in the one underscore like function we typed one instead of l so you have to put l there.
  
 
|-
 
|-
−
| 3:59
+
| 03:59
 
| We can see that we have intermediate matrix.
 
| We can see that we have intermediate matrix.
  
 
|-
 
|-
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| 4:02
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| 04:02
 
| Now we need the transpose.
 
| Now we need the transpose.
  
 
|-
 
|-
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|4:04
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|04:04
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|So type on the terminal
+
|So type on the terminal A = inter underscore mat.T  
−
A = inter underscore mat.T  
+
  
 
|-
 
|-
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|4:19
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|04:19
 
|Type A and hit enter
 
|Type A and hit enter
  
 
|-
 
|-
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| 4:22
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| 04:22
 
| Now we have both the matrices A and tsq.
 
| Now we have both the matrices A and tsq.
  
 
|-
 
|-
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| 4:27
+
| 04:27
 
| We only need to use the lstsq  .
 
| We only need to use the lstsq  .
  
 
|-
 
|-
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|4:33
+
|04:33
 
|Type result = lstsq within brackets A comma  tsq where lstsq stands for least square
 
|Type result = lstsq within brackets A comma  tsq where lstsq stands for least square
  
 
|-
 
|-
−
| 4:49
+
| 04:49
 
| The result is a sequence of values.
 
| The result is a sequence of values.
  
 
|-
 
|-
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| 4:51
+
| 04:51
 
| The first item in this sequence, is the matrix p i.e., the values of m and c.
 
| The first item in this sequence, is the matrix p i.e., the values of m and c.
  
 
|-
 
|-
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|4:58
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|04:58
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|Type m comma  c = result within square brackets 0 .Then type  
+
|Type m comma  c = result within square brackets 0 .Then type  m. Then type  c so you can see the output.
−
  m
+
−
Then type  
+
−
  c so you can see the output.
+
  
 
|-
 
|-
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| 5:20
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| 05:20
 
| Now that we have m and c,So we need to generate the fitted values of t square.
 
| Now that we have m and c,So we need to generate the fitted values of t square.
  
 
|-
 
|-
−
|5:28
+
|05:28
−
|Type on terminal.
+
|Type on terminal. tsq underscore fit = m star l plus c  Type plot within brackets l comma tsq comma  within single quote bo
−
tsq underscore fit = m star l plus c
+
−
  Type plot within brackets l comma tsq comma  within single quote bo
+
  
 
|-
 
|-
−
|6:06
+
|06:06
−
|Before typing that plot we have to type clear function.
+
|Before typing that plot we have to type clear function. Type plot within brackets l comma  tsq comma bo.
−
Type plot within brackets l comma  tsq comma bo.
+
  
 
|-
 
|-
−
|6:24
+
|06:24
−
|Now i can see the plot
+
|Now i can see the plot. Type plot within brackets l comma  tsq underscore fit comma r
−
Type plot within brackets l comma  tsq underscore fit comma r
+
  
 
|-
 
|-
−
| 6:41
+
| 06:41
 
| We get the least square fit of l versus t square.
 
| We get the least square fit of l versus t square.
  
 
|-
 
|-
−
| 6:49
+
| 06:49
 
| This brings us to the end of this tutorial.
 
| This brings us to the end of this tutorial.
  
 
|-
 
|-
−
| 6:52
+
| 06:52
 
| In this tutorial, we have learnt to, 1. Generate a least square fit using matrices.
 
| In this tutorial, we have learnt to, 1. Generate a least square fit using matrices.
  
 
|-
 
|-
−
| 6:57
+
| 06:57
 
| 2. Use the function lstsq() to generate a least square fit line.
 
| 2. Use the function lstsq() to generate a least square fit line.
  
 
|-
 
|-
−
| 7:03
+
| 07:03
 
| Here are some self assessment questions for you to solve
 
| Here are some self assessment questions for you to solve
  
 
|-
 
|-
−
| 7:07
+
| 07:07
−
| 1. What does ones underscore like 1 comma  2 comma  3 produce
+
| 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
−
  array 1 comma  1 comma  1  
+
−
  1 comma  1 comma  1  in square brackets.
+
−
    then square brackets 1 point 0 comma  1 point 0 comma  1 point 0  
+
−
  Error
+
  
 
|-
 
|-
−
| 7:25
+
| 07:25
 
| 2. The plot of  u  versus  v  is a bunch of scattered points that show a linear trend.
 
| 2. The plot of  u  versus  v  is a bunch of scattered points that show a linear trend.
  
 
|-
 
|-
−
| 7:33
+
| 07:33
 
| How do you find the least square fit line of  u  versus v .
 
| How do you find the least square fit line of  u  versus v .
  
 
|-
 
|-
−
| 7:38
+
| 07:38
 
| And will look at the answers,
 
| And will look at the answers,
  
 
|-
 
|-
−
| 7:42
+
| 07:42
 
| 1. The function  ones underscore like in 1 comma  2 comma  3  will generate array 1 comma  1 comma  1.  
 
| 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.
 
So that is the first questions answer.
  
 
|-
 
|-
−
| 7:54
+
| 07:54
 
| 2. The following set of commands will produce the least square fit line of u  versus  v  
 
| 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
−
A = array within brackets u comma  ones underscore like within brackets u.T
+
result = lstsq  within brackets A comma  v
−
result = lstsq  within brackets A comma  v
+
m comma  c = result within square brackets 0  
−
  m comma  c = result within square brackets 0  
+
lst underscore line = m star u plus c
−
lst underscore line = m star u plus c
+
  
 
|-
 
|-
−
| 8:34
+
| 08:34
 
| Hope you have enjoyed this tutorial and found it useful.  
 
| Hope you have enjoyed this tutorial and found it useful.  
  
 
|-
 
|-
−
|8:37
+
|08:37
 
|Thank you!
 
|Thank you!
  
 
|}
 
|}

Latest revision as of 17:04, 20 February 2017

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!

Contributors and Content Editors

Gaurav, Minal, PoojaMoolya, Sneha

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