PoojaMoolya: Created page with "{| border=1 | '''Time''' | '''Narration''' |- | 00:01 | Welcome to the spoken tutorial on '''Least Square Fit'''. |- |00:06 | In this tuto..."

2019-06-03T07:21:23Z

Created page with "{| border=1 | <center>'''Time'''</center> | <center>'''Narration'''</center> |- | 00:01 | Welcome to the spoken tutorial on '''Least Square Fit'''. |- |00:06 | In this tuto..."

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{| border=1
| <center>'''Time'''</center>
| <center>'''Narration'''</center>

|-
| 00:01
| Welcome to the spoken tutorial on '''Least Square Fit'''.

|-
|00:06
| In this tutorial, you will learn to,

Generate the '''least square fit '''line for a given set of '''points.'''

|-
| 00:16
| To record this tutorial, I am using '''Ubuntu Linux 16.04''' operating system

|-
| 00:24
| '''Python 3.4.3 '''and '''IPython 5.1.0'''

|-
| 00:31
| To practise this tutorial, you should know about

using '''plot''' interactively

|-
| 00:38
|Loading data from files

|-
| 00:41
| Using '''arrays''' and '''matrices '''and theoretical knowledge of''' least square method'''

|-
| 00:48
| If not, see the relevant '''Python '''tutorials on this website.

|-
| 00:53
| Before beginning this tutorial, please download the file''' pendulum.txt '''from the '''Code files''' link of this tutorial.

|-
| 01:03
| Save it in the current '''working directory'''.

|-
| 01:07
| Let us start the tutorial with the help of an example.

|-
| 01:12
| Generate a '''least square fit''' line for''' L '''versus '''t square''' using the data in the file ''''pendulum.txt''''.

|-
| 01:22
| Let us open the file '''pendulum.txt.'''

|-
| 01:26
| This is an '''input file''' generated from a simple '''pendulum experiment'''.

|-
| 01:32
| The first column is the '''length''' of the '''pendulum.'''

|-
| 01:36
| The second is the corresponding '''time period''' of the '''pendulum'''.

|-
| 01:41
| The '''square''' of '''time period''' is directly proportional to its '''length.'''

|-
| 01:47
| We shall plot '''L''' versus '''t square''' and verify this.

|-
|01:52
| Let us start '''ipython.''' Open the '''terminal'''.

|-
|01:57
| Type '''ipython3 '''and press '''Enter'''.

|-
| 02:03
| From here onwards remember to press the '''Enter''' key after typing every command on the '''terminal'''.

|-
| 02:10
| To read the input file and '''parse''' the data, we are going to use the '''loadtxt function'''.

|-
| 02:17
| Type, '''from numpy import loadtxt'''

|-
| 02:23
| Now type, Capital '''L '''''comma''''' t '''''is equal to''''' loadtxt''''' inside brackets inside double quotes '''''pendulum.txt '''''comma''''' unpack '''''is equal to''''' True'''

|-
| 02:37
| '''loadtxt''' is a '''method''' available in the '''numpy library'''.

|-
| 02:42
| Since '''True''' is passed to '''unpack argument''', the returned '''array''' is transposed.

|-
| 02:49
| This means that we will get one '''array''' per column in the file.

|-
| 02:54
| Type capital '''L'''

|-
| 02:59
| Then type '''t'''

|-
| 03:03
| We can see that''' L '''and '''t''' are '''length''' and '''time''' values.

|-
| 03:08
| To know more about '''loadtxt, '''type '''loadtxt '''''question mark''

|-
| 03:16
| Press '''q '''to exit.

|-
|03:19
| Let us first '''plot L '''versus '''t square. '''

Type as shown.

|-
| 03:27
| Here '''bo''' represents the blue circle marker.

|-
| 03:32
| Then type, '''plt.show '''''open and close brackets''

|-
| 03:38
| We can see that there is a '''visible linear trend''', but we do not get a straight line connecting them.

|-
| 03:45
| Looking at the '''trend''', we can now propose a '''model''' for the data.

|-
| 03:50
| Let me close this image.

|-
| 03:53
| We need to fit a line through points for the the equation.

Capital '''T '''''square is''''' '''''equal to''''' m '''''asterisk''''' '''Capital '''L '''''plus''''' c'''

|-
| 04:03
| Where '''m''' represents the '''slope''' of the line and '''c''' represents the intercept of the line.

|-
| 04:10
| We will obtain '''m''' and '''c''' using '''linear regression'''.

|-
| 04:15
| Let us see the steps to generate a '''least''' '''square fit line.'''

|-
| 04:20
| First generate the two '''matrices tsq''' and '''A'''. Use the '''lstsq function''' to find the values of the slope '''m''' and the intercept '''c'''.

|-
| 04:33
| In '''matrix''' form, the equation can be represented as

'''tsq''' ''is equal to'' '''A '''''asterisk '''''p'''

|-
| 04:41
| '''tsq''' is a one-dimensional array of size '''n'''.

|-
| 04:46
| Each '''element''' of this '''array''' will contain the '''square''' of the '''time period'''.

|-
| 04:52
| '''A''' is a '''matrix''' of size '''n '''by '''2'''.

|-
| 04:56
| The first column will contain the '''length''' of the '''pendulum'''.

|-
| 05:00
| The second column will contain the number 1.

|-
| 05:04
| '''p''' is a one-dimensional '''array''' of size 2.

|-
| 05:08
| The first row contains the '''slope''' of the line.

|-
| 05:12
| The second row contains the '''intercept''' of the line.

We need to find '''p''' to '''plot''' the line.

|-
| 05:20
| Let us now generate the '''A matrix''' with '''L''' values.

|-
| 05:25
| We shall generate a '''matrix''' with the first '''row''' as '''L''' values and the second '''row''' as ones.

Then take the transpose of it.

|-
| 05:34
| Type as shown.

|-
| 05:38
| We see that we have intermediate '''matrix'''.

|-
| 05:42
| Now we need the transpose.

|-
| 05:45
| Type, Capital '''A '''is equal to''' inter''''' underscore '''''mat '''dot''' '''Capital '''T '''

|-
| 05:53
| Now type capital '''A'''

|-
| 05:56
| Now we have both the '''matrices''' '''A''' and '''tsq'''.

|-
| 06:01
| We only need to use '''lstsq.'''

Type as shown.

|-
| 06:08
| Now to see the result, type '''result'''

The '''result''' is a sequence of '''values'''.

|-
|06:16
| Now we will store result of '''index 0''' in '''m''' and '''c''' respectively.

|-
| 06:23
| Type, '''p '''''is equal to''''' result '''''inside square brackets''''' 0'''

Then type, '''m '''''comma '''''c '''''is equal to''''' p'''

|-
| 06:34
| Now type, '''m''' '''c'''

|-
| 06:39
| We can see the values for '''m''' and '''c'''.

|-
|06:43
| Now we have '''m''' and '''c.'''

We need to generate the fitted values of '''t square'''.

|-
| 06:51
| Type as shown.

|-
| 06:55
| Then type, '''plt.show''''' open and close brackets''

|-
| 07:01
| We get the least square fit of '''L''' versus '''t square'''.

|-
| 07:06
| Let me close this window.

|-
| 07:09
| This brings us to the end of this tutorial. Let us summarize.

|-
| 07:15
| In this tutorial, we have learnt to, Generate a '''least square fit''' using '''matrices'''

|-
| 07:23
| Use the '''function lstsq()''' to generate a '''least square fit''' line

|-
| 07:29
| Here is a self assessment question for you to solve

|-
| 07:33
| What does the following '''function''' produce?

|-
| 07:35
| And the answer,

The '''function ones''''' underscore '''''like '''''inside brackets inside square brackets ''1 ''comma'' 2 ''comma'' 3 will generate '''array''' ''inside brackets inside square brackets '''''1''' ''comma'' '''1''' ''comma'' '''1'''.

|-
| 07:51
| Please post your timed queries in this forum.

|-
| 07:55
| Please post your general queries on Python in this forum.

|-
| 08:00
| FOSSEE team coordinates the TBC project.

|-
| 08:04
| Spoken Tutorial Project is funded by NMEICT, MHRD, Govt. of India.

For more details, visit this website.

|-
| 08:14
| This is Priya from IIT Bombay signing off. Thanks for watching.

|}

Python-3.4.3/C3/Least-square-fit/English-timed - Revision history

PoojaMoolya: Created page with "{| border=1 | '''Time''' | '''Narration''' |- | 00:01 | Welcome to the spoken tutorial on '''Least Square Fit'''. |- |00:06 | In this tuto..."