Inverse Error Function Algorithm
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Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue Sep inverse error function calculator 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special inverse error function excel Functions>Erf> Calculus and Analysis>Calculus>Integrals>Definite Integrals> History and Terminology>Wolfram Language Commands> Inverse Erf The inverse erf function erf(2) is the inverse function of the erf function such that (1) (2) with the first identity holding for and the second for . It is implemented in the
Inverse Error Function C++
Wolfram Language as InverseErf[x]. It is an odd function since (3) It has the special values (4) (5) (6) It is apparently not known if (7) (OEIS A069286) can be written in closed form. It satisfies the equation (8) where is the inverse erfc function. It has the derivative (9) and its integral is (10) inverse error function matlab (which follows from the method of Parker 1955). Definite integrals are given by (11) (12) (13) (14) (OEIS A087197 and A114864), where is the Euler-Mascheroni constant and is the natural logarithm of 2. The Maclaurin series of is given by (15) (OEIS A002067 and A007019). Written in simplified form so that the coefficient of is 1, (16) (OEIS A092676 and A092677). The th coefficient of this series can be computed as (17) where is given by the recurrence equation (18) with initial condition . SEE ALSO: Confidence Interval, Erf, Inverse Erfc, Probable Error RELATED WOLFRAM SITES: http://functions.wolfram.com/GammaBetaErf/InverseErf/, http://functions.wolfram.com/GammaBetaErf/InverseErf2/ REFERENCES: Bergeron, F.; Labelle, G.; and Leroux, P. Ch.5 in Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, 1998. Carlitz, L. "The Inverse of the Error Function." Pacific J. Math. 13, 459-470, 1963. Parker, F.D. "Integrals of Inverse Functions." Amer. Math. Monthly 62, 439-440, 1955. Sloane, N.J.A. Sequences A002067/M4458, A007019/M3126, A069286, A087197, A092676, A092677, A114859, A114860, and A114864 in "The On-Line Encyclopedia
documentation home page. Error Function Inverses Synopsis #include
Inverse Error Function Approximation
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Inverse Complementary Error Function
functions is computed using the result type calculation rules: the return type is double if T is an integer type, and T otherwise. The final Policy argument is optional and http://mathworld.wolfram.com/InverseErf.html can be used to control the behaviour of the function: how it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. Description template
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 http://stackoverflow.com/questions/12556685/is-there-a-javascript-implementation-of-the-inverse-error-function-akin-to-matl 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 is there a JavaScript implementation of the Inverse Error Function, akin to error function MATLAB erfinv()? up vote 3 down vote favorite 1 is there a JavaScript implementation of the Inverse Error Function? This would implement the Gauss inverse error function. Approximations are ok. javascript share|improve this question asked Sep 23 '12 at 22:10 ptmalcolm 14110 "Approximations are ok" the other option being... :) –Bluefire Apr 4 at 11:17 add a comment| 2 Answers 2 active oldest votes up vote 4 inverse error function down vote accepted Why yes. There is. The following code uses built-in JavaScript functions and implments Abramowitz and Stegun's algorithm as described here: function erfinv(x){ var z; var a = 0.147; var the_sign_of_x; if(0==x) { the_sign_of_x = 0; } else if(x>0){ the_sign_of_x = 1; } else { the_sign_of_x = -1; } if(0 != x) { var ln_1minus_x_sqrd = Math.log(1-x*x); var ln_1minusxx_by_a = ln_1minus_x_sqrd / a; var ln_1minusxx_by_2 = ln_1minus_x_sqrd / 2; var ln_etc_by2_plus2 = ln_1minusxx_by_2 + (2/(Math.PI * a)); var first_sqrt = Math.sqrt((ln_etc_by2_plus2*ln_etc_by2_plus2)-ln_1minusxx_by_a); var second_sqrt = Math.sqrt(first_sqrt - ln_etc_by2_plus2); z = second_sqrt * the_sign_of_x; } else { // x is zero z = 0; } return z; } share|improve this answer answered Sep 23 '12 at 22:13 ptmalcolm 14110 add a comment| up vote 0 down vote function provided earlier in this post did not work for me... NaN result on a 33meter circle with confidence 65% represented as 65.0 ... I wrote the following based on an equation listed here https://en.wikipedia.org/wiki/Error_function#Inverse_functions and it worked fine: var _a = ((8*(Math.PI - 3)) / ((3*Math.PI)*(4 - Math.PI))); function erfINV( inputX ) { var _x = parseFloat(inputX); var signX = ((_x < 0) ? -1.0 : 1.0 ); var oneMinusXsquared = 1.0 - (_x * _x); var LNof1min
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