Inverse error function using interpolation


In the previous post, https://autarkaw.wordpress.com/2010/09/01/using-int-and-solve-to-find-inverse-error-function-in-matlab/, we found the inverse error function by using the integral and solve MATLAB functions.  In this blog, we find the inverse error function by using interpolation.

The value of erf(x) is given at discrete data points of x, and we use spline interpolation to find the value of x at a given value of erf(x).  The given data points of (x,erf(x)) are (0,0), (0.1,0.1125), (0.25,0.2763), (0.75,0.7112), (1.0,0.8427), (1.5,0.9661), (2.0,0.9953), (5.0,1.000). 

It is better to download (right click and save target) the program as single quotes in the pasted version do not translate properly when pasted into a mfile editor of MATLAB or you can read the html version for clarity and sample output.

%% FINDING INVERSE ERROR FUNCTION
% In a previous blog at autarkaw.wordpress.com (Sep 1, 2010), we set up a
% nonlinear equation to find the inverse error function.
% In this blog, we will solve this equation
% by using interpolation.
% The problem is given at
% http://numericalmethods.eng.usf.edu/blog/inverseerror.pdf
% and we are solving Exercise 2 of the pdf file.

%% TOPIC
% Finding inverse error function

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/inverse_erf_interp_matlab.m;
% Last Revised : October 4 2010
% Abstract: This program shows you how to find the inverse error function
% using interpolation
clc
clear all

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to’)
disp(‘   find the inverse error function’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘ http://numericalmethods.eng.usf.edu/blog/inverse_erf_interp_matlab.m’)
disp(‘  ‘)
disp(‘PROBLEM STATEMENT’)
disp(‘ http://numericalmethods.eng.usf.edu/blog/inverseerror.pdf  Exercise 2′)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   October 4, 2010’)
disp(‘ ‘)

%% INPUTS
% Value of error function
erfx=0.1125;
% Table of erf(x) vs x
xx=[0  0.1  0.25  0.75  1.0  1.5  2.0  5.0];
erfxx=[0  0.1125  0.2763  0.7112  0.8427  0.9661  0.9953  1.0000];

%% DISPLAYING INPUTS

disp(‘INPUTS’)
fprintf(‘ Inverse error function is to be found for= %g’,erfx)
disp(‘  ‘)
disp(‘ Given erf(x) vs x values’)
disp(‘_______________________’)
disp(‘    x          erfx  ‘)
disp(‘________________________’)
dataval=[xx;erfxx]’;
disp(dataval)

%% CODE
if erfx>1.0 | erfx<0
    disp(‘Invalid value. erf(x) only takes values in [0,1] range’)
else
inverse_erf=interp1(erfxx,xx,erfx,’cubic’);
%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)
fprintf(‘ Value of inverse error func from this mfile is= %g’,inverse_erf)
fprintf(‘ \n Value of inverse error func from MATLAB is    = %g’,erfinv(erfx))
disp(‘  ‘)
end

__________________________________________________

This post is brought to you by

Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu,
the textbook on Numerical Methods with Applications available from the lulu storefront,
the textbook on Introduction to Programming Concepts Using MATLAB, and
the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos

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Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.

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