Error Function In Fortran 90
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type shall
Error Function In Fortran 95
be REAL. Return value:The return value is of type REAL, of the same kind inverse error function fortran as X and lies in the range -1 \leq erf (x) \leq 1 . Example: program test_erf real(8) :: x = 0.17_8 x = erf(x) end program test_erf Specific names: Name Argument Return type Standard DERF(X) REAL(8) X REAL(8) GNU extension
erf(x)=2π∫ 0 xe −t 2dt. \text{erf}(x) = complementary error function \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt. Standard Fortran 2008 and later Class Elemental function Syntax result = erf(x) https://gcc.gnu.org/onlinedocs/gfortran/ERF.html Arguments x - The type shall be real. Return value The return value is of type real, of the same kind as x and lies in the range −1≤erf(x)≤1-1 \leq erf http://fortranwiki.org/fortran/show/erf (x) \leq 1 . Example program test_erf real(8) :: x = 0.17_8 x = erf(x) end program test_erf category: intrinsics Revised on June 2, 2009 17:17:59 by Jason Blevins (152.3.10.27) (586 characters / 0.0 pages) Edit | Back in time (2 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: Intrinsic procedures, Fortran 2008 This site is running on Instiki 0.19.7(MML+) Powered by Ruby on Rails 2.3.18
arbitrary positive integer order N, or for any positive non-integer order (an unusual feature). Routines are also available for the Gamma function, the logarithm of the Gamma function, the https://people.sc.fsu.edu/~jburkardt/f_src/specfun/specfun.html exponential integrals, the error function, the Psi function, and Dawson's integral. The original, true, https://en.wikipedia.org/wiki/Inverse_error_function correct (FORTRAN77) version of SPECFUN is available through NETLIB: http://www.netlib.org/specfun/index.html". Licensing: The computer code and data files described and made available on this web page are distributed under the GNU LGPL license. Languages: SPECFUN is available in a FORTRAN77 version and a FORTRAN90 version. Related Data and Programs: CORDIC, a FORTRAN90 library which error function use the CORDIC method to compute certain elementary functions. FN, a FORTRAN90 library which evaluates elementary and special functions, by Wayne Fullerton. G95_INTRINSICS, FORTRAN90 programs which demonstrate the use of intrinsic functions peculiar to the G95 FORTRAN compiler, which include Bessel J and Y functions, ERF and GAMMA. GSL, a C++ library which evaluates many special functions. MACHAR, a FORTRAN90 library which is used to compute function in fortran machine arithmetic parameters. POLPAK, a FORTRAN90 library which evaluates certain mathematical functions, especially some recursive polynomial families. SLATEC, a FORTRAN90 library which evaluates many special functions. SPECIAL_FUNCTIONS, a FORTRAN90 library which computes the Beta, Error, Gamma, Lambda, Psi functions, the Airy, Bessel I, J, K and Y, Hankel, Jacobian elliptic, Kelvin, Mathieu, Struve functions, spheroidal angular functions, parabolic cylinder functions, hypergeometric functions, the Bernoulli and Euler numbers, the Hermite, Laguerre and Legendre polynomials, the cosine, elliptic, exponential, Fresnel and sine integrals, by Shanjie Zhang, Jianming Jin; TEST_VALUES, a FORTRAN90 library which contains a few test values of many functions. TOMS644, a FORTRAN77 library which evaluates the Bessel I, J, K, Y functions, the Airy functions Ai and Bi, and the Hankel function, for complex argument and real order. TOMS715, a FORTRAN90 library which evaluates special functions, including the Bessel I, J, K, and Y functions of order 0, of order 1, and of any real order, Dawson's integral, the error function, exponential integrals, the gamma function, the normal distribution function, the psi function. This is a version of ACM TOMS algorithm 715. Author: The original FORTRAN77 version is by William Cody and Laura Stoltz. Reference: Donald Amos, C
function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion. It is defined as:[1][2] erf ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0 x e − t 2 d t . {\displaystyle {\begin − 6\operatorname − 5 (x)&={\frac − 4{\sqrt {\pi }}}\int _{-x}^ − 3e^{-t^ − 2}\,\mathrm − 1 t\\&={\frac − 0{\sqrt {\pi }}}\int _ 9^ 8e^{-t^ 7}\,\mathrm 6 t.\end 5}} The complementary error function, denoted erfc, is defined as erfc ( x ) = 1 − erf ( x ) = 2 π ∫ x ∞ e − t 2 d t = e − x 2 erfcx ( x ) , {\displaystyle {\begin 2\operatorname 1 (x)&=1-\operatorname 0 (x)\\&={\frac Φ 9{\sqrt {\pi }}}\int _ Φ 8^{\infty }e^{-t^ Φ 7}\,\mathrm Φ 6 t\\&=e^{-x^ Φ 5}\operatorname Φ 4 (x),\end Φ 3}} which also defines erfcx, the scaled complementary error function[3] (which can be used instead of erfc to avoid arithmetic underflow[3][4]). 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 ) = 2 π ∫ 0 π / 2 exp ( − x 2 sin 2 θ ) d θ . {\displaystyle \operatorname 0 (x|x\geq 0)={\frac Φ 9{\pi }}\int _ Φ 8^{\pi /2}\exp \left(-{\frac Φ 7}{\sin ^ Φ 6\theta }}\right)d\theta \,.} The imaginary error function, denoted erfi, is defined as erfi ( x ) = − i erf ( i x ) = 2 π ∫ 0 x e t 2 d t = 2 π e x 2 D ( x ) , {\displaystyle {\begin Φ 0\operatorname − 9 (x)&=-i\operatorname − 8 (ix)\\&={\frac − 7{\sqrt {\pi }}}\int _ − 6^ − 5e^ − 4}\,\mathrm − 3 t\\&={\frac − 2{\sqrt {\pi }}}e^ − 1}D(x),\end − 0}} where D(x) is the Dawson function (which can be used instead of erfi to avoid arithmetic overflow[3]). Despite the name "imaginary error function", erfi ( x ) {\displaystyle \operatorname 8 (x)} is real when x is real. When the error function is evaluated for arbitrary complex arguments z, the resulting complex error function is usually discussed in scaled form as the Faddeeva function: w ( z ) = e − z 2 erfc ( − i z ) = erfcx ( − i z ) . {\displaystyle w(z)=e^{-z^ 6}\operatorname 5 (-iz)=\operatorname 4 (-iz).} Contents 1 The name "error functi