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LCCN65-12253. However, it can be extended to the disk |z| < 1 of the complex plane, using the Maclaurin series erf − 1 ( z ) = ∑ k = 0 Notice that the argument of the error function can be a complex number, in which case the integral needs to be done in the complex plane. Basically, I recently changed from s.p. Check This Out

Schöpf and P. To use these approximations for negative x, use the fact that erf(x) is an odd function, so erf(x)=−erf(−x). Steve - Intel Developer Support Top FortranFan Tue, 04/15/2014 - 13:45 As explained by John Reid in his 2014 report, "The New Features of Fortran 2008", the following 3 new intrinsic Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.

Math. IDL: provides both erf and erfc for real and complex arguments. This usage is similar to the Q-function, which in fact can be written in terms of the error function. H.

This is useful, for example, in determining the bit error rate of a digital communication system. The error function is a special case of the Mittag-Leffler function, and can also be expressed as a confluent hypergeometric function (Kummer's function): erf ( x ) = 2 x The second thing that's wrong is the double precision intrinsic DERF function, which is clearly producing junk. Back to top **mkcolgJoined: 30** Jun 2004Posts: 6764Location: The Portland Group Inc.

Now, if I compile with PGI fortran: pgfortran -o a.out erf_test.f90, I get this output: Code: erf_stegun (subroutine) : 1.000000000000000 0.8427010463338918 Returned result : For large enough values of x, only the first few terms of this asymptotic expansion are needed to obtain a good approximation of erfc(x) (while for not too large values of If L is sufficiently far from the mean, i.e. μ − L ≥ σ ln k {\displaystyle \mu -L\geq \sigma {\sqrt {\ln {k}}}} , then: Pr [ X ≤ L Irene A.

Bit annoying that intel declares DERF for you as a non standard feature. The error function is related to the cumulative distribution Φ {\displaystyle \Phi } , the integral of the standard normal distribution, by[2] Φ ( x ) = 1 2 + 1 Calculation in double precision, result returned ! See [2]. ^ http://hackage.haskell.org/package/erf ^ Commons Math: The Apache Commons Mathematics Library ^ a b c Cody, William J. (1969). "Rational Chebyshev Approximations for the Error Function" (PDF).

The error function at +∞ is exactly 1 (see Gaussian integral). If you add 'implicit none' in the erf_test program all compilers should let you know that they aren't declared. Fortran Derf That would be like having a SINE function but no ARCSINE, or a TAN function, but no ARC Tangent. Erfc is the double factorial: the product of all odd numbers up to (2n–1).

All generalised error functions for n>0 look similar on the positive x side of the graph. his comment is here Related functions[edit] The error function is **essentially identical to the** standard normal cumulative distribution function, denoted Φ, also named norm(x) by software languages, as they differ only by scaling and translation. For complex

Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Level of Im(ƒ)=0 is shown with a thick green line. Every other math library on other processors has this function. this contact form Craig, A new, simple and exact result for calculating the probability of error for two-dimensional signal constellaions, Proc. 1991 IEEE Military Commun.

Excel: Microsoft Excel provides the erf, and the erfc functions, nonetheless both inverse functions are not in the current library.[17] Fortran: The Fortran 2008 standard provides the ERF, ERFC and ERFC_SCALED Steve - Intel Developer Support Top William S. Join today Support Terms of Use *Trademarks Privacy Cookies Publications Intel® Developer Zone Newsletter Intel® Parallel Universe Magazine Look for us on: FacebookTwitterGoogle+LinkedInYouTube English简体中文EspañolPortuguês Rate Us Technology PGI Unified Binary MPI

For any complex number z: erf ** ( z ¯** ) = erf ( z ) ¯ {\displaystyle \operatorname − 0 ({\overline 9})={\overline {\operatorname 8 (z)}}} where z N ! ∫ x ∞ t − 2 N e − t 2 d t , {\displaystyle R_ − 7(x):={\frac {(-1)^ − 6}{\sqrt {\pi }}}2^ − 5{\frac {(2N)!} − 4}\int _ Other compilers may implicitly declare these functions for you but this would be an extension and not part of the Fortran Standard. doi:10.1090/S0025-5718-1969-0247736-4. ^ Error Function and Fresnel Integrals, SciPy v0.13.0 Reference Guide. ^ R Development Core Team (25 February 2011), R: The Normal Distribution Further reading[edit] Abramowitz, Milton; Stegun, Irene Ann, eds.

The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3. Generalized error functions[edit] Graph of generalised error functions En(x): grey curve: E1(x) = (1−e−x)/ π {\displaystyle \scriptstyle {\sqrt {\pi }}} red curve: E2(x) = erf(x) green curve: E3(x) blue curve: E4(x) J. navigate here J.

The denominator terms are sequence A007680 in the OEIS. if y = erf(x), x = inverf(y); if y = erfc(x), x = inverfc(y), as is usual in mathematics .. Thanks mecej4. Applications[edit] When the results of a series of measurements are described by a normal distribution with standard deviation σ {\displaystyle \textstyle \sigma } and expected value 0, then erf ( a p.297.

Back to top mkcolgJoined: 30 Jun 2004Posts: 6764Location: The Portland Group Inc. Both functions are overloaded to accept arguments of type float, double, and long double. These generalised functions can equivalently be expressed for x>0 using the Gamma function and incomplete Gamma function: E n ( x ) = 1 π Γ ( n ) ( Γ Edited by Milton Abramowitz and !

Not a member? Softw., 19 (1): 22–32, doi:10.1145/151271.151273 ^ Zaghloul, M. Real error function ERF(x). ! ! *** Details: ! ! Haskell: An erf package[18] exists that provides a typeclass for the error function and implementations for the native (real) floating point types.