Difference between revisions of "Scilab/C4/Interpolation/Gujarati"

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| '''Numerical Interpolation''' નું સામન્ય જ્ઞાન હોવું જોઈએ. .
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| '''Numerical Interpolation''' નું સામન્ય જ્ઞાન હોવું જોઈએ.  
  
 
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| To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.
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| સાઈલેબ માટે સ્પોકન ટ્યુટોરિયલ વેબ સાઈટ પર ઉપલબ્ધ સંબંધિત ટ્યુટોરિયલ જુઓ.  
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| '''Numerical interpolation''' is a method of
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| '''Numerical interpolation''' મેળવેલ '''data points''' ના  '''discrete set''' ના રેંજના અંદર  ડેટા પોઈન્ટસ ને બનાવવાનું એક મેથડ છે.
  
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|constructing new '''data points'''
 
  
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| within the range of a  '''discrete set''' of known '''data points.'''
 
  
 
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|We can solve '''interpolation''' problems using '''numerical methods.'''  
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|આપણે '''numerical methods.''' નો ઉપયોગ કરીને  '''interpolation''' ના પ્રશ્નને હલ કરી શકીએ છીએ.
  
 
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|In '''Lagrange interpolation,'''  
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| '''Lagrange interpolation,''' માં
  
 
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|We pass a '''polynomial''' of '''degree N – 1''' through '''N''' points.
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|આપણે '''N''' પોઈન્ટસ થી  '''N – 1''' ના  '''polynomial''' ને પાસ કરીએ છીએ
  
 
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||Then, we find the unique '''N order polynomial y of x''' which '''interpolates''' the '''data''' samples.  
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|| પછી આપણે વિશિષ્ટ '''N order polynomial y of x''' ને મેળવીએ છીએ જે ડેટા સેમ્પલને ઇન્ટરપોલેટ કરે છે.
  
 
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|| We are given the '''natural logarithm'''  values for nine, nine point five and eleven.  
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|| આપણે '''nine, nine point five અને eleven'''  ની '''natural logarithm'''  વેલ્યુ આપેલ છે.  
  
 
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| We have to find the value of '''natural logarithm''' of nine point two.  
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| આપણે '''nine point two''' ની '''natural logarithm'''  વેલ્યુ મેળવવાની છે.
  
 
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|Let us solve this problem using '''Lagrange interpolation method.'''
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|ચાલો  '''Lagrange interpolation method.''' (લેગરેંગ ઇન્ટરપોલેશન મેથડ) નો ઉપયોગ કરીને આ સવાલને હલ કરીએ.
  
 
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|Let us look at the code for '''Lagrange interpolation.'''
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|ચાલો '''Lagrange interpolation.''' (લેગરેંગ ઇન્ટરપોલેશન મેથડ) ના માટે કોડ જોઈએ.
  
 
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||We define the function '''Lagrange''' with '''arguments x zero, x, f and n.'''  
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||આપણે '''arguments x zero, x, f અને  n.''' ના સાથે  '''Lagrange''' (લેગરેંગ)  ફંક્શનને વ્યાખ્યાયિત કરીએ છીએ.
  
 
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Revision as of 15:12, 30 December 2015

Time Narration
00:01 નમસ્તે મિત્રો,
00:02 Numerical Interpolation પરના આ સ્પોકન ટ્યુટોરિયલમાં તમારું સ્વાગત છે. .
00:06 આ ટ્યુટોરીયલના અંતમાં તમે શીખીશું કેવી રીતે:
00:10 વિવિધ Numerical Interpolation algorithms ના માટે સાઈલેબ કોડ કેવી રીતે બનાવાય છે.
00:16 આપેલ પોઈન્ટસ થી function ની નવી વેલ્યુની ગણતરી કરવી.
00:21 આ ટ્યુટોરિયલ રિકોર્ડ કરવા માટે હું ઉપયોગ કરી રહી છું,
00:24 Scilab 5.3.3 વર્જનના સાથે.


00:27 Ubuntu 12.04 ઓપરેટીંગ સીસ્ટમ
00:31 આ ટ્યુટોરિયલ ના અભ્યાસ પહેલા શીખનારને
00:34 Scilab અને
00:36 Numerical Interpolation નું સામન્ય જ્ઞાન હોવું જોઈએ.
00:40 સાઈલેબ માટે સ્પોકન ટ્યુટોરિયલ વેબ સાઈટ પર ઉપલબ્ધ સંબંધિત ટ્યુટોરિયલ જુઓ.
00:47 Numerical interpolation મેળવેલ data points ના discrete set ના રેંજના અંદર ડેટા પોઈન્ટસ ને બનાવવાનું એક મેથડ છે.


00:59 આપણે numerical methods. નો ઉપયોગ કરીને interpolation ના પ્રશ્નને હલ કરી શકીએ છીએ.
01:05 Lagrange interpolation, માં
01:07 આપણે N પોઈન્ટસ થી N – 1 ના polynomial ને પાસ કરીએ છીએ
01:12 પછી આપણે વિશિષ્ટ N order polynomial y of x ને મેળવીએ છીએ જે ડેટા સેમ્પલને ઇન્ટરપોલેટ કરે છે.
01:22 આપણે nine, nine point five અને eleven ની natural logarithm વેલ્યુ આપેલ છે.
01:29 આપણે nine point two ની natural logarithm વેલ્યુ મેળવવાની છે.
01:35 ચાલો Lagrange interpolation method. (લેગરેંગ ઇન્ટરપોલેશન મેથડ) નો ઉપયોગ કરીને આ સવાલને હલ કરીએ.
01:41 ચાલો Lagrange interpolation. (લેગરેંગ ઇન્ટરપોલેશન મેથડ) ના માટે કોડ જોઈએ.
01:46 આપણે arguments x zero, x, f અને n. ના સાથે Lagrange (લેગરેંગ) ફંક્શનને વ્યાખ્યાયિત કરીએ છીએ.
01:53 X zero is the unknown interpolation point.
01:57 x is the vector containing the data points.
02:01 f is the vector containing the values of the function at corresponding data points.
02:08 And n is the order of the interpolating polynomial.
02:14 We use n to initialize m and vector N.
02:19 The order of the interpolating polynomial determines the number of nodes created.
02:25 Then, we apply Lagrange interpolation formula
02:29 to find the value of the numerator and denominator.
02:35 Then we divide the numerator and denominator to get the value of L.
02:41 We use L to find the value of the function y at the given data point.
02:48 Finally we display the value of L and f of x f(x).
02:53 Let us Save and execute the file.
02:57 Switch to Scilab console to solve the example problem.
03:02 Let us define the data points vector.
03:05 On the console, type:
03:07 x equal to open square bracket nine point zero comma nine point five comma eleven point zero close square bracket.
03:18 Press Enter.
03:21 Then type: f equal to open square bracket two point one nine seven two comma two point two five one three comma two point three nine seven nine close square bracket
03:39 Press Enter .
03:41 Then type x zero equal to nine point two
03:46 Press Enter.
03:48 Let us use a quadratic polynomial interpolating polynomial.
03:53 Type n equal to two.
03:58 Press Enter.
04:00 To call the function, type:
04:02 y equal to Lagrange open parenthesis x zero comma x comma f comma n close parenthesis
04:14 Press Enter.
04:16 The value of the function y at x equal to nine point two is displayed.
04:22 Let us look at Newton's Divided Difference Method.
04:26 In this method, Divided Differences recursive method is used.
04:32 It uses lesser number of computation than Lagrange method.
04:38 In spite of this, the same interpolating polynomial, as in Lagrange method, is generated.
04:47 Let us solve this example using Divided Difference method.
04:52 We are given the data points and
04:54 the corresponding values of the function at those data points.
05:00 We have to find the value of the function at x equal to three.
05:05 Let us look at the code for Newton Divided Difference method.
05:11 Open the file Newton underscore Divided dot sci on Scilab Editor.
05:18 We define the function Newton underscore Divided with arguments x, f and x zero.
05:29 x is a vector containing the data points,
05:33 f is the corresponding function value and
05:36 x zero is the unknown interpolation point.
05:41 We find the length of vector and then equate it to n.
05:46 The first value of vector is equated to a of one a(1).
05:51 Then we apply divided difference algorithm and compute the divided difference table.
05:57 Then we find the coefficient list of the Newton polynomial.
06:03 We sum the coefficient list to find the value of the function at given data point.
06:10 Save and execute the file Newton underscore Divided dot sci.
06:16 Switch to Scilab console.
06:19 Clear the screen by typing c l c.
06:22 Press Enter.
06:24 Let us enter the data points vector.
06:27 Type: x equal to open square bracket two comma two point five comma three point two five comma four close square bracket
06:39 Press Enter.
06:41 Then type values of the function
06:44 f equal to open square bracket zero point five comma zero point four comma zero point three zero seven seven comma zero point two five close square bracket
07:01 Press Enter.
07:03 Type x zero equal to three
07:06 Press Enter.
07:08 Then call the function by typing
07:11 I P equal to Newton underscore Divided open parenthesis x comma f comma x zero close parenthesis
07:23 Press Enter.
07:25 The value of y at x equal to three is shown.
07:30 Let us summarize this tutorial.
07:33 In this tutorial,
07:34 we have learnt to develop Scilab code for interpolation methods.
07:40 We have also learnt to find the value of a function at new data point.
07:46 Solve this problem on your own using Lagrange method and Newton's Divided Difference method.
07:54 Watch the video available at the link shown below.
07:57 It summarizes the Spoken Tutorial project.
08:00 If you do not have good bandwidth, you can download and watch it.
08:05 The spoken tutorial project Team:
08:07 Conducts workshops using spoken tutorials
08:10 Gives certificates to those who pass an online test.
08:14 For more details, please write to contact@spoken-tutorial.org
08:22 Spoken Tutorial Project is a part of the Talk to a Teacher project.
08:26 It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
08:33 More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro.
08:38 This is Ashwini Patil, signing off.
08:41 Thank you for joining.

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