Error Function Matlab Erfc
Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation Toggle navigation Trial Software Product Updates Documentation Home MATLAB Examples Functions Release Notes PDF Documentation Mathematics Elementary Math Special Functions MATLAB Functions erf On this page Syntax Description Examples Find Error Function Find Cumulative Distribution Function of Normal Distribution Calculate Solution of Heat Equation with Initial Condition Input Arguments x More About Error Function Tall Array Support Tips See Also This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison of the page. Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Italian Japanese Korean Latvian Lithuanian Malay Maltese Norwegian Polish Portuguese Romanian Russian Slovak Slovenian Spanish Swedish Thai Turkish Ukrainian Vietnamese Welsh MathWorks Machine Translation The automated translation of this page is provided by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. Translate erfError functioncollapse all in page Syntaxerf(x) exampleDescriptionexampleerf(x
) returns the Error Function evaluated for each element of x.Examplescollapse allFind Error FunctionOpen ScriptFind the error function of a value.erf(0.76) ans = 0.7175 Find the error function of the elements of a vector.V = [-0.5 0 1 0.72]; erf(V) ans = -0.5205 0 0.8427 0.6914 Find the error function of the elements of a matrix.M = [0.29 -0.11; 3.1 -2.9]; erf(M) ans = 0.3183 -0.1236 1.0000 -1.0000 Find Cumulative Distribution Function of Normal DistributionOpen ScriptThe cumulative distribution function (CDF) of the normal, or Gaussian, distribution with standard deviation and mean is Note that for increased computational accuracy, you can rewrite the formula in terms of erfc . For details, see Tips.Plot the CDF of the normal distribution with and .x = -3:0.1:3; y = (1/2)*(1+erf(x/sqrt(2))); plot(x,y) grid on title('CDF of normal distribution with \mu = 0 and \sigma = 1') xlabel('x') ylabel('CDF') Calculate Solution of Heat Equation with Initial ConditionOpen ScriptWhere represents the temperature at position and time , the heat eq
Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation Toggle navigation Trial Software Product Updates Documentation Home Symbolic Math Toolbox Examples Functions and Other Reference Release Notes PDF Documentation Mathematics Mathematical Functions Symbolic Math Toolbox Functions erfc On this page Syntax Description Examples Complementary Error Function for Floating-Point and Symbolic Numbers Error Function for Variables and Expressions Complementary Error Function for Vectors and Matrices Special Values of Complementary Error Function Handling Expressions That Contain Complementary Error Function Plot https://www.mathworks.com/help/matlab/ref/erf.html Complementary Error Function Input Arguments X K More About Complementary Error Function Iterated Integral of Complementary Error Function Tips Algorithms References See Also This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison of the page. Back to English × Translate This Page Select Language Bulgarian https://www.mathworks.com/help/symbolic/erfc.html Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Italian Japanese Korean Latvian Lithuanian Malay Maltese Norwegian Polish Portuguese Romanian Russian Slovak Slovenian Spanish Swedish Thai Turkish Ukrainian Vietnamese Welsh MathWorks Machine Translation The automated translation of this page is provided by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. Translate erfcComplementary error functioncollapse all in page Syntaxerfc(X) exampleerfc(K,X) exampleDescriptionexampleerfc(X
) represents the complementary error function of X, that is,erfc(X) = 1 - erf(X).exampleerfc(K
,X) represents the iterated integral of the complementary error function of X, that is, erfc(K, X) = int(erfc(K - 1, y), y, X, inf).ExamplesComplementary Error Function for Floating-Point and Symbolic Numbers Depending on its arguments, erfc can return floating-point or exact symbolic results. Compute the complementary error function for these numbers. Because these numbers are not symbolic objects, you get the floating-point results:A = [erfc(1/2),
X = erfinv(Y) Inverse of the error function Definition The error function erf(X) is twice the integral of http://cens.ioc.ee/local/man/matlab/techdoc/ref/erf.html the Gaussian distribution with 0 mean and variance of:
The complementary error function erfc(X) is defined as: The scaled complementary error function erfcx(X) is defined http://stackoverflow.com/questions/34440230/customizing-erfc-function-matlab as: For large X, erfcx(X) is approximately . Description Y = erf(X) returns the value of the error function for each element of real array error function X. Y = erfc(X) computes the value of the complementary error function. Y = erfcx(X) computes the value of the scaled complementary error function. X = erfinv(Y) returns the value of the inverse error function for each element of Y. The elements of Y must fall within the domain Examples erfinv(1) error function matlab is Inf erfinv(-1) is -Inf. For abs(Y) > 1, erfinv(Y) is NaN. Remarks The relationship between the error function and the standard normal probability distribution is: x = -5:0.1:5; standard_normal_cdf = (1 + (erf(x/sqrt(2))))./2; Algorithms For the error functions, the MATLAB code is a translation of a Fortran program by W. J. Cody, Argonne National Laboratory, NETLIB/SPECFUN, March 19, 1990. The main computation evaluates near-minimax rational approximations from [1]. For the inverse of the error function, rational approximations accurate to approximately six significant digits are used to generate an initial approximation, which is then improved to full accuracy by two steps of Newton's method. The M-file is easily modified to eliminate the Newton improvement. The resulting code is about three times faster in execution, but is considerably less accurate. References [1] Cody, W. J., "Rational Chebyshev Approximations for the Error Function," Math. Comp., pgs. 631-638, 1969 [ Previous | Help Desk | Next ]here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Stack Overflow Questions Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 4.7 million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up Customizing ERFC function MATLAB up vote 0 down vote favorite erfc Matlab function is the Complementary Error Function and it's defined by : erfc(x) = 2/sqrt(pi) * integral from x to inf of exp(-t^2) dt I want to change this function to: erfc_change(a+b*R) = 1/2*sqrt(pi) * integral from (a+b*vec_x) to inf of exp(-t^2/2) dt %note here exp(-t^2/2) and vec_x is a vector of values that represent the values of x in the erfc function for using it in least square error curve fitting (constants 'a' and 'b' should be approximated). So i made a variables change and i had this result : erfc_change(a+b*vec_x) = (sqrt(2*pi)/2)*erfc(a+b*vec_x/sqrt(2)) I'm not sure of the reliability of my change of variables. After this, i perform my Least Square Fitting like this ==> This i runnable code: vec_x= [0;0.4636;0.6616;0.8225;0.1095;0.1706;0.2302;0.1603; 0.2392;0.3245;0.3741;0.5376;0.6675;0.1308;0.1881; 0.2296;0.03740;0.002600;0.04530;0.02660;0.02990;0.0297]; vec_y=[3.3010;5.5840;7.2970;8.8660;4.1200;5.4140;7.1710; 4.5820;6.5400;6.8220;5.6220;8.0110;8.6600; 3.4010;3.7460;4.7180;2.9260;3.4290;4.2780;2.2480;3.8900;4.359]; options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt'); f = @(x,vec_x)(1/sqrt(2))*erfc(x(1)+(x(2)*vec_x/sqrt(2))); lsqcurvefit(f,-2,vec_x,vec_y); % the approximation will starts from -2 Here i got an error (after executing the above code): Index exceeds matrix dimensions. Error in @(x,fmpd_dinosaur)(1/sqrt(2))*erfc(x(1)+ (x(2)*fmpd_dinosaur/sqrt(2))) Error in lsqcurvefit (line 199) initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:}); Caused by: Failure in initial user-supplied objective function evaluation. LSQCURVEFIT cannot continue. I don't understand where this error comes from. Any ideas ? matlab share|improve this question edited Dec 23 '15 at 21:51 asked Dec 23 '15 at 16:47 Anass 257 Please share some reproducible and legible code. You can use newline followed by four consecutive spaces to format as code. It will look much cleaner that way. –Some Guy Dec 23 '15 at 17:02 i Edited the