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

PoojaMoolya at 11:34, 20 February 2017

2017-02-20T11:34:53Z

Gaurav at 09:22, 10 July 2014

2014-07-10T09:22:38Z

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Sneha at 07:04, 20 March 2013

2013-03-20T07:04:40Z

Sneha at 11:30, 18 March 2013

2013-03-18T11:30:34Z

Minal: Created page with '{| border=1 !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, # …'

2013-01-02T11:06:59Z

Created page with '{| border=1 !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, # …'

New page

{| border=1
!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 <tt>lstsq</tt> 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 <tt>lstsq</tt> .

|-
|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 <tt>lstsq()</tt> to generate a least square fit line.

|-
| 7:03
| Here are some self assessment questions for you to solve

|-
| 7:07
| 1. <nowiki>What does ones underscore like 1 comma 2 comma 3 produce</nowiki>
<nowiki>array 1 comma 1 comma 1</nowiki>
<nowiki> 1 comma 1 comma 1</nowiki> within square brackets.
<nowiki> within square brackets 1 point 0 comma 1 point 0 comma 1 point 0</nowiki>
Error

|-
| 7:25
| 2. The plot of <tt>u</tt> versus <tt>v</tt> is a bunch of scattered points that show a linear trend.

|-
| 7:33
| How do you find the least square fit line of <tt>u</tt> versus <tt>v</tt>.

|-
| 7:38
| And will look at the answers,

|-
| 7:42
| 1. The function <tt><nowiki>ones underscore like in 1 comma 2 comma 3</nowiki></tt><nowiki> will generate array 1 comma 1 comma 1.</nowiki>
So that is the first questions answer.

|-
| 7:54
| 2. The following set of commands will produce the least square fit line of <tt>u</tt> versus <tt>v</tt>

A = array within brackets u comma ones underscore like within brackets u.T
result = lstsq within brackets A comma v
<nowiki>m comma c = result within square brackets 0</nowiki>
lst underscore line = m star u plus c

|-
| 8:34
| Hope you have enjoyed this tutorial and found it useful.

|-
|8:37
|Thank you!

|}

@@ Line 34: / Line 34: @@
 |-
 |0:43
-| The first column is the length of the pendulum and the second is the corresponding time period of the pendulum.
+| The first column is the length of the pendulum and the second is the corresponding time series of the pendulum.
 |-
@@ Line 66: / Line 66: @@
 |-
 |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.
+|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
@@ Line 107: / Line 107: @@
 |-
 |3:16
-|Type in the terminal inter underscore mat = array  within brackets l comma  ones underscore like  within brackets one then close the bracket
+|Type in the terminal inter underscore mat = array  within brackets l comma  ones underscore like  within brackets one then closing  bracket
 |-
@@ Line 178: / Line 178: @@
 |-
 |6:24
-|Now you can see the plot
+|Now i can see the plot
   Type plot within brackets l comma  tsq underscore fit comma r
@@ Line 205: / Line 205: @@
 | 1. What does ones underscore like 1 comma  2 comma  3 produce
     array 1 comma  1 comma  1
-comma  1 comma  1 within square brackets.
+comma  1 comma  1  in square brackets.
-     within square brackets 1 point 0 comma  1 point 0 comma  1 point 0
+    then square brackets 1 point 0 comma  1 point 0 comma  1 point 0
    Error

@@ Line 10: / Line 10: @@
 | 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.
-# Generate the least square fit line for a given set of points.
 |-
@@ Line 68: / Line 67: @@
 |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
+Then type l Secondly type t
-−
 Secondly type
-−
 |-
@@ Line 91: / Line 87: @@
 |-
 |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
 |-
@@ Line 128: / Line 123: @@
 |-
 |04:04
-|So type on the terminal
+|So type on the terminal A = inter underscore mat.T
- A = inter underscore mat.T
 |-
@@ Line 157: / Line 151: @@
 |-
 |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. Then type  c so you can see the output.
-−
 Then type
   c so you can see the output.
 |-
@@ Line 168: / Line 159: @@
 |-
 |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
 |-
 |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.
 |-
 |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
 |-
@@ Line 204: / Line 191: @@
 |-
 | 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
-comma  1 comma  1  in square brackets.
-    then square brackets 1 point 0 comma  1 point 0 comma  1 point 0
-  Error
 |-
@@ Line 230: / Line 213: @@
 | 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
- 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
 |-

@@ Line 86: / Line 86: @@
 |-
 | 2:22
-| Then we will use the <tt>lstsq</tt> function to find the values of m and c.
+| Then we will use the  lstsq  function to find the values of m and c.
 |-
@@ Line 107: / Line 107: @@
 |-
 |3:16
-|Type in the termianl inter underscore mat = array  within brackets l comma  ones underscore like  within brackets one then close the bracket
+|Type in the terminal inter underscore mat = array  within brackets l comma  ones underscore like  within brackets one then close the bracket
 |-
@@ Line 140: / Line 140: @@
 |-
 | 4:27
-| We only need to use the <tt>lstsq</tt> .
+| We only need to use the lstsq  .
 |-
@@ Line 195: / Line 195: @@
 |-
 | 6:57
-| 2. Use the function <tt>lstsq()</tt> to generate a least square fit line.
+| 2. Use the function lstsq() to generate a least square fit line.
 |-
@@ Line 203: / Line 203: @@
 |-
 | 7:07
-| 1. <nowiki>What does ones underscore like 1 comma  2 comma  3 produce</nowiki>
+| 1. What does ones underscore like 1 comma  2 comma  3 produce
-    <nowiki>array 1 comma  1 comma  1</nowiki>
+    array 1 comma  1 comma  1
-    <nowiki> 1 comma  1 comma  1</nowiki> within square brackets.
+comma  1 comma  1 within square brackets.
-   <nowiki> within square brackets 1 point 0 comma  1 point 0 comma  1 point 0</nowiki>
+     within square brackets 1 point 0 comma  1 point 0 comma  1 point 0
    Error
 |-
 | 7:25
-| 2. The plot of <tt>u</tt> versus <tt>v</tt> 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
-| How do you find the least square fit line of <tt>u</tt> versus <tt>v</tt>.
+| How do you find the least square fit line of  u  versus v .
 |-
@@ Line 223: / Line 223: @@
 |-
 | 7:42
-| 1. The function <tt><nowiki>ones underscore like in 1 comma  2 comma  3</nowiki></tt><nowiki> will generate array 1 comma  1 comma  1.</nowiki>
+| 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 <tt>u</tt> versus <tt>v</tt>
+| 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
- <nowiki>m comma  c = result within square brackets 0</nowiki>
+  m comma  c = result within square brackets 0
   lst underscore line = m star u plus c