Matlab Code For Error Function
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Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation Toggle navigation Trial Software Product complementary error function Updates Documentation Home MATLAB Examples Functions Release Notes PDF Documentation erfc matlab Mathematics Elementary Math Special Functions MATLAB Functions erf On this page Syntax Description Examples Find Error erf function calculator 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
Inverse Erf
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 error function table 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 (CD
Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation matlab erf Toggle navigation Trial Software Product Updates Documentation Home MATLAB
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Erf(1)
Functions error On this page Syntax Description Examples Throw Error Throw Error with Formatted Message Throw Error Using Structure Related Examples Input Arguments msg https://www.mathworks.com/help/matlab/ref/erf.html msgID A1,...,An errorStruct More About 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 https://www.mathworks.com/help/matlab/ref/error.html 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 errorThrow error and display messagecollapse all in page Syntaxerror(msg) exampleerror(msg,A1,...,An)error(msgID,___)error(errorStruct) exampleDescription exampleerror(msg
) throws an error and displays an error message. error(msg
,A1,...,An) displays an error message that contains formatting conversion characters, such as those used with the MATLAB® sprintf function. Each conversion character in msg is converted to one of the values A1,...,An. error(msgID
,___) includes
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 http://math.stackexchange.com/questions/615065/complementary-error-function-in-matlab complementary error function erfc(X) is defined as: The scaled complementary error function erfcx(X) is defined 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) matlab code for 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 Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Complementary error function in matlab up vote 1 down vote favorite Please I really want to know how to verify the following relation in MatLAB $\text{erfc}(x)\overset{x\rightarrow\infty}{\longrightarrow}\dfrac{e^{-x^2}}{x\sqrt{\pi}}$ limits special-functions matlab share|cite|improve this question asked Dec 21 '13 at 19:48 YYG 347214 1 It would be more accurate to use $\sim_{x \to \infty}$ instead of $\overset{x\rightarrow\infty}{\longrightarrow}$ since $\to$ usually denotes a limit being taken (in this context). Also, could you be more specific about what kind of verification you're looking for? It's simple to verify this by hand using L'Hopital's rule, for instance. –Antonio Vargas Dec 21 '13 at 19:53 Isn't the expression about limit? What do you mean by $\sim_{x \to \infty}$ anyway? –YYG Dec 21 '13 at 20:01 By definition $f(x) \sim_{x \to \infty} g(x)$ means $$\lim_{x \to \infty} \frac{f(x)}{g(x)} = 1.$$ See here for some more info. This is the standard way to write the type of relationship you're interested in (the one between $\operatorname{erfc}(x)$ and $e^{-x^2}/x\sqrt{\pi}$). –Antonio Vargas Dec 21 '13 at 20:03 I checked the link but doesn't help me, I just want to prove the relation in Matlab, anyway it is verified is okay for me. –YYG Dec 21 '13 at 20:08 I'm not sure Matlab can prove this type of statement. I would be interested to see if it could. As I said, it is straightforward to verify it by hand using L'Hopital's rule instead. –Antonio Vargas Dec 21 '13 at 20:08 | show 7 more comments 2 Answers 2 active oldest votes up vote 3 down vote accepted That is not the limit of the complementary error function for $x \rightarrow \infty$ (that's zero). It is also not the asymptotic series expansion of the function. Rather, it is just the first term in the the asymptotic series expansion, but it's a very good approximation. To find the limit using Matlab, you can use the limit function in the Symbolic Math