Attachments: AttachmentSize Download ErrorFunctions.png31.58 KB Top mecej4 Tue, 04/15/2014 - 13:45 FortranFan: if y = erf(x), x = inverf(y); if y = erfc(x), x = inverfc(y), as is usual in mathematics Licensing: The computer code and data files described and made available on this web page are distributed under the GNU LGPL license. Real error function ERF(x). ! ! *** Details: ! ! Fortran 77 implementations are available in SLATEC.

Mathematica: erf is implemented as Erf and Erfc in Mathematica for real and complex arguments, which are also available in Wolfram Alpha. Basically, I recently changed from s.p. Anyway, thanks again as always Mat..... Haskell: An erf package[18] exists that provides a typeclass for the error function and implementations for the native (real) floating point types.

Never understood why it isn't renamed for the year it's actually approved... 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. Another form of erfc ( x ) {\displaystyle \operatorname 2 (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc ( x | x ≥ 0 ERF_VALUES returns some values of the ERF or "error" function.

I'm struggling to understand whether the VS2012/2013 implementation is for Nvidia accelerator only. Math. Ask over in the MKL forum if you need more help. This integral can not be solved in terms of standard transcendental and algebraic functions, so a new special function called the error function is introduced: (1) The next few worksheets

Error function and Fresnel Integrals, EQN. 7.1.28. ! Example: program test_erf real(8) :: x = 0.17_8 x = erf(x) end program test_erf Specific names: Name Argument Return type Option DERF(X) REAL(8) X REAL(8) gnu Fortran Wiki erf Skip Rob. Matlab provides both erf and erfc for real arguments, also via W.

Option:gnu Class:elemental function Syntax:X = ERF(X) Arguments: X The type shall be REAL(*), and it shall be scalar. I usually never forget to put implicit none in. Mat, Does PGI support the F2008* erf yet? Stegun, Dover Publications, Inc., New York, 1965. ! !

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 Example program test_erf real(8) :: x = 0.17_8 x = erf(x) end program Next:ERFC, Previous:EPSILON, Up:Intrinsic Procedures 9.88 ERF — Error function Description:ERF(X) computes the error function of X. Tue, 04/15/2014 - 13:14 The Fortran Math library has ERF for the error function, but I have not been able to find the Inverse.

Valid to |E(x)| <= 3e-7. TIMESTAMP prints the current YMDHMS date as a time stamp. Continued fraction expansion[edit] A continued fraction expansion of the complementary error function is:[11] erfc ( z ) = z π e − z 2 1 z 2 + a 1 This series diverges for every finite x, and its meaning as asymptotic expansion is that, for any N ∈ N {\displaystyle N\in \mathbb Γ 2 } one has erfc (

TEST_ABORT demonstrates the ABORT routine. 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 TEST_DBESJN checks DBESJN against BESSEL_JN_VALUES. Tue, 04/15/2014 - 17:08 I did "kluge" up an inverse error function, for those that are interested.

Asymptotic expansion[edit] A useful asymptotic expansion of the complementary error function (and therefore also of the error function) for large real x is erfc ( x ) = e − Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007), "Section 6.2. Intermediate levels of Re(ƒ)=constant are shown with thin red lines for negative values and with thin blue lines for positive values. Other compilers may implicitly declare these functions for you but this would be an extension and not part of the Fortran Standard.

TEST_GAMMA checks GAMMA against GAMMA_VALUES. Irene A. As any statistician will tell you - just ask ! ! ! for example you would use the inverse when you know the probability of an outcome, and you want William S.

You can use this from MKL but it is defined on arrays only. GAMMA_LOG_VALUES returns some values of the Log Gamma function. This allows one to choose the fastest approximation suitable for a given application. Then another question - perhaps for Steve or other folks more familiar with the Fortran standards development and/or those who are more mathematically inclined: If the Fortran standard now includes the error function (erf(x)), any idea

TEST_BESY0 checks BESY0 against BESSEL_Y0_VALUES. BESSEL_J0_VALUES returns some values of the J0 Bessel function. I'm not sure how "new" the DERF function is in PGI fortran. Indeed, Φ ( x ) = 1 2 π ∫ − ∞ x e − t 2 2 d t = 1 2 [ 1 + erf ( x 2

If you add 'implicit none' in the erf_test program all compilers should let you know that they aren't declared. The error function and its approximations can be used to estimate results that hold with high probability. TEST_SYSTEM tests SYSTEM. gfortran_intrinsics_output.txt, the output file; List of Routines: MAIN is the main program for GFORTRAN_INTRINSICS_PRB.

This usage is similar to the Q-function, which in fact can be written in terms of the error function. Call my function version of ERF(x): result = erf_stegun(x) print*, 'Returned result : ', result ! to d.p. (hence code used to work) - I did change my function from ERF to DERF and assumed that was all I needed to do. TEST_FDATE tests FDATE.

After division by n!, all the En for odd n look similar (but not identical) to each other. MATH_INTRINSICS, a JAVA program which illustrates the use of the intrinsic functions in the Java Math package. Almost there though. doi:10.1109/TCOMM.2011.072011.100049. ^ Numerical Recipes in Fortran 77: The Art of Scientific Computing (ISBN 0-521-43064-X), 1992, page 214, Cambridge University Press. ^ DlangScience/libcerf, A package for use with the D Programming language.

Apologies if I'm doing something silly - any advice/info would be greatly appreciated.... ISBN 978-0-486-61272-0. TEST_ERFC checks ERFC against ERFC_VALUES. Steve - Intel Developer Support Top William S.

in gpu precision. ! !------------------------------------------------------------------------------ implicit none real*8 :: x real*8 :: erf_x real*8 However, it can be extended to the disk |z| < 1 of the complex plane, using the Maclaurin series erf − 1 ( z ) = ∑ k = 0 TEST_GETCWD tests GETCWD. TEST_DBESJ1 checks DBESJ1 against BESSEL_J1_VALUES.