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'''
 +
 
 
|-
 
|-
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| 0:01
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| 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,
  
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|-
 
|-
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| 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".
  
 
|-
 
|-
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| 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
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| 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
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|  00:36
 
| We have an input file generated from a simple pendulum experiment.
 
| We have an input file generated from a simple pendulum experiment.
  
 
|-
 
|-
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| 0:40
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| 00:40
 
| It contains two columns of data.
 
| It contains two columns of data.
  
 
|-
 
|-
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|0:43
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|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.
  
 
|-
 
|-
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| 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,
  
 
|-
 
|-
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|0:54
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|00:54
 
| we shall plot l versus t square and verify this.
 
| we shall plot l versus t square and verify this.
  
 
|-
 
|-
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|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.
  
 
|-
 
|-
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|1:04
+
|01:04
 
| Switch to the terminal.
 
| Switch to the terminal.
  
 
|-
 
|-
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|1:08
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|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.
  
 
|-
 
|-
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|1:15
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|01:15
 
| Let us first plot l versus t square.
 
| Let us first plot l versus t square.
  
 
|-
 
|-
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|1:18
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|01:18
 
|Type in the terminal ipython hypen pylab   
 
|Type in the terminal ipython hypen pylab   
  
 
|-
 
|-
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|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
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|-
 
|-
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|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.
  
 
|-
 
|-
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|2:11
+
|02:11
 
| We shall, therefore, generate a least square fit line.
 
| We shall, therefore, generate a least square fit line.
  
 
|-
 
|-
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| 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
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|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
  
 
|-
 
|-
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| 2:57
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| 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
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| 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
  
 
|-
 
|-
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|3:44
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|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.
  
 
|-
 
|-
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| 3:59
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| 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
 
|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
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| 04:27
 
| We only need to use the lstsq  .
 
| We only need to use the lstsq  .
  
 
|-
 
|-
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|4:33
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|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
  
 
|-
 
|-
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| 4:49
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| 04:49
 
| The result is a sequence of values.
 
| The result is a sequence of values.
  
 
|-
 
|-
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| 4:51
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| 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
+
|04:58
 
|Type m comma  c = result within square brackets 0 .Then type  
 
|Type m comma  c = result within square brackets 0 .Then type  
 
  m
 
  m
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|-
 
|-
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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.
  
 
|-
 
|-
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|5:28
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|05:28
 
|Type on terminal.
 
|Type on terminal.
 
  tsq underscore fit = m star l plus c
 
  tsq underscore fit = m star l plus c
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|-
 
|-
−
|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  
 
   array 1 comma  1 comma  1  
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|-
 
|-
−
| 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  
  
Line 236: Line 237:
  
 
|-
 
|-
−
| 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!
  
 
|}
 
|}

Revision as of 14:52, 10 July 2014

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,
  1. 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.
   then 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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