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Inverse Error Function Fortran 90

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Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). This function is already present in the standard C math library, but its inverse function is missing. Softw., 19 (1): 22–32, doi:10.1145/151271.151273 ^ Zaghloul, M. M.; Petersen, Vigdis B.; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008). http://auctusdev.com/error-function/inverse-error-function-fortran.html

Negative integer values of Im(ƒ) are shown with thick red lines. Top billsincl Tue, 04/15/2014 - 15:20 That thing that mecej4 sent me doesn't work either. ErfInv Family Functions Relationship Useful relations for these functions: Special Values for Real Function v?ErfInv(x)Argument Result VML Error Status Exception +0 +0 -0 -0 +1 +∞ VML_STATUS_SING Handbook of Continued Fractions for Special Functions. see it here

Error Function In Fortran 90

I don't see any useful purpose in that, unless it has to do with optimization of the results. 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. Taylor series[edit] The error function is an entire function; it has no singularities (except that at infinity) and its Taylor expansion always converges. It's not in typical C libraries.

  1. For example: program xinverf implicit none include 'mkl_vml.f90' integer,parameter :: n=1 integer*8 mode real a(1),v(1) a(1) = 0.4 call vserfcinv(n, a, v) write(*,*)v(1) end program xinverf With this program we get
  2. Just like you could use the Newton_Raphson technique to get an ARC Tangent if you didn't already have one.   The C++ library routine it appears uses a set of polynomials,
  3. What is the 'dot space filename' command doing in bash?
  4. Why did Moody eat the school's sausages?
  5. Also has erfi for calculating i erf ⁡ ( i x ) {\displaystyle i\operatorname {erf} (ix)} Maple: Maple implements both erf and erfc for real and complex arguments.
  6. The imaginary error function has a very similar Maclaurin series, which is: erfi ⁡ ( z ) = 2 π ∑ n = 0 ∞ z 2 n + 1 n
  7. LCCN65-12253.
  8. C: Pointer to an array that contains the output vector y.

Skip to main content Developer Zone Join today Log in DevelopmentOSAndroid*Chrome*HTML5Windows*Device2-in-1 & Ultrabook™Business ClientEmbedded SystemsIoTServer, Workstation, HPCTechnologyBig DataDual ScreenGame DevIntel® RealSense™ISA ExtensionsMachine LearningModern CodeNetworkingOpen SourceStorageToolsDeveloper TypeEmbedded SystemsGame DevMediaTechnical, Enterprise, HPCWebOSAll ToolsAndroid*HTML5Linux*OS Despite the name "imaginary error function", erfi ⁡ ( x ) {\displaystyle \operatorname ⁡ 8 (x)} is real when x is real. Join them; it only takes a minute: Sign up Need code for Inverse Error Function up vote 5 down vote favorite 4 Does anyone know where I could find code for Complementary Error Function Standard:Fortran 2008 and later Class:Elemental function Syntax:RESULT = ERF(X) Arguments: X The type shall be REAL.

For any complex number z: erf ⁡ ( z ¯ ) = erf ⁡ ( z ) ¯ {\displaystyle \operatorname − 0 ({\overline ⁡ 9})={\overline {\operatorname ⁡ 8 (z)}}} where z C++: C++11 provides erf() and erfc() in the header cmath. Matlab provides both erf and erfc for real arguments, also via W. https://gcc.gnu.org/onlinedocs/gfortran/ERF.html Both functions are overloaded to accept arguments of type float, double, and long double.

Note that for it to work well, you also need a good implementation of erf(). Q : (1.0-Q); double T = sqrt( -2.0*log(QF)); double X = T - ((NORX_C2*T + NORX_C1)*T + NORX_C0) /(((NORX_D3*T + NORX_D2)*T + NORX_D1)*T + 1.0); double SPI2 = sqrt( 2.0 * So far as I can tell that one is rubbish for x near to 0 (IIRC). Comp. 23 (107): 631–637.

Erfinv Approximation

H. https://en.wikipedia.org/wiki/Inverse_error_function C: Pointer to an array that contains the output vector y. Error Function In Fortran 90 Output ParametersName Type Description y FORTRAN 77: REAL for vserfinv, vmserfinv DOUBLE PRECISION for vderfinv, vmderfinv Fortran 90: REAL, INTENT(OUT) for vserfinv, vmserfinv DOUBLE PRECISION, INTENT(OUT) for vderfinv, vmderfinv C: float* Inverse Error Function C++ Code But you may not get the full REAL*8 accuracy.

function erfc(const x: Double): Double; var t,z,ans: Double; begin z := abs(x); t := 1.0/(1.0+0.5*z); ans := t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+ t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+ t*(-0.82215223+t*0.17087277))))))))); if x>=0.0 then begin Result := ans; end else begin Result http://auctusdev.com/error-function/inverse-error-function-in-r.html Another approximation is given by erf ⁡ ( x ) ≈ sgn ⁡ ( x ) 1 − exp ⁡ ( − x 2 4 π + a x 2 1 By using this site, you agree to the Terms of Use and Privacy Policy. Retrieved 2011-10-03. ^ Chiani, M., Dardari, D., Simon, M.K. (2003). Erfinv C++

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 more hot questions question feed lang-pascal about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation For iterative calculation of the above series, the following alternative formulation may be useful: erf ⁡ ( z ) = 2 π ∑ n = 0 ∞ ( z ∏ k http://auctusdev.com/error-function/inverse-error-function-c.html In order of increasing accuracy, they are: erf ⁡ ( x ) ≈ 1 − 1 ( 1 + a 1 x + a 2 x 2 + a 3 x

where Φ-1(x) and erf-1(x) are the inverses to Φ(x) and erf(x) respectively. SyntaxFORTRAN:call vserfinv( n, a, y )call vmserfinv( n, a, y, mode )call vderfinv( n, a, y )call vmderfinv( n, a, y, mode )C:vsErfInv( n, a, y );vmsErfInv( n, a, y, mode The inverse means x = erfinv(y) satisfies y = erf(x).

share|improve this answer answered May 12 '11 at 0:05 lhf 43.2k54686 Great, thanks.

mode FORTRAN 77: INTEGER*8 Fortran 90: INTEGER(KIND=8), INTENT(IN) C: const MKL_INT64 Overrides global VML mode setting for this function call. Want to make things right, don't know with whom What is the exchange interaction? where is the cumulative normal distribution function. is the double factorial: the product of all odd numbers up to (2n–1).

Math. The denominator terms are sequence A007680 in the OEIS. See vmlSetMode for possible values and their description. weblink The system returned: (22) Invalid argument The remote host or network may be down.

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. C: Pointer to an array that contains the input vector a. a FORTRAN 77: REAL for vserfinv, vmserfinv DOUBLE PRECISION for vderfinv, vmderfinv Fortran 90: REAL, INTENT(IN) for vserfinv, vmserfinv DOUBLE PRECISION, INTENT(IN) for vderfinv, vmderfinv C: const float* for vsErfInv, vmsErfInv After all, one can get the same answers by using a DO LOOP.   And why they did that for the Error function and its complement, and not for their inverses,

But anyway, see below –Marco van de Voort May 13 '11 at 20:28 add a comment| up vote 1 down vote The math is pretty complex, but there's a decent approximation Tue, 04/15/2014 - 17:08 I did "kluge" up an inverse error function, for those that are interested. maybe it and its coefficients can help you: http://w3eos.whoi.edu/12.747/mfiles/lect07/erfinv.m Another PDF here: http://people.maths.ox.ac.uk/~gilesm/files/gems_erfinv.pdf Relevant snippet: Table 1: Pseudo-code to compute y = erfinv(x) , with p1(t)..p6(t) representing a 1st through 6th Again, the definition of Error Function Complement is 1-ErrF, not ErrF^-1, but this has got to be getting you close: http://infohost.nmt.edu/~es421/pascal/list11-3.pas I found this interesting implementation (language unknown, I'm guessing it's

Cody, Math. IEEE Transactions on Wireless Communications, 4(2), 840–845, doi=10.1109/TWC.2003.814350. ^ Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". 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