Fortran Error Function
Contents |
it shall be scalar. Return value:The return value is a scalar of type REAL(*) and it is positive ( - 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 Option DERF(X) REAL(8) X REAL(8) gnu
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 ∞ https://gcc.gnu.org/onlinedocs/gcc-4.1.0/gfortran/ERF.html 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 https://en.wikipedia.org/wiki/Inverse_error_function ) {\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
LearningModern CodeNetworkingOpen SourceStorageToolsDeveloper TypeEmbedded SystemsGame DevMediaTechnical, Enterprise, HPCWebOSAll ToolsAndroid*HTML5Linux*OS X*Windows*ResourcesCode SamplesContact SupportDocumentationFree SoftwareIntel Registration CenterProduct ForumsSDKsResourcesPartner with IntelAcademic ProgramPartner SpotlightBlack Belt DeveloperDeveloper MeshInnovator ProgramSuccess StoriesLearnBlogBusiness TipsEventsVideosSupportContact SupportDeveloper EvangelistsFAQsForums Search form Search You are hereHome › Forums › Intel® Software Development Products › Intel® https://software.intel.com/en-us/forums/intel-visual-fortran-compiler-for-windows/topic/509357 Visual Fortran Compiler for Windows* FacebookLinkedInTwitterDiggDeliciousGoogle Plus No Inverse Error function? No Inverse Error function? William S. Tue, 04/15/2014 - 13:14 The Fortran Math library has ERF for the error function, but I http://www.ibm.com/support/knowledgecenter/SS2MB5_14.1.0/com.ibm.xlf141.bg.doc/language_ref/erf.html have not been able to find the Inverse. Its a statistical function based upon the Gaussian Normal distribution. Strangely enough, it does exist for VECTOR ELEMENTS, but I don't see why error function they would not include it for regular usage. Every other math library on other processors has this function. If it is in the library, searching for it produces no results. How do we use vector elements - what are they referring to? (in case I get desperate) ' RSS Top 12 posts / 0 new Last post For more complete information about compiler fortran error function optimizations, see our Optimization Notice. pbkenned1 Tue, 04/15/2014 - 13:35 The IMSL package add-on has ERFI, but I don't think it is a part of standard Intel Fortran. Can you expand on 'it does exist for VECTOR ELEMENTS'? Patrick Top Steve Lionel (Intel) Tue, 04/15/2014 - 13:40 What you've found is entries for erfinv in Intel MKL. Fortran does not define the erfinv intrinsic. You can use this from MKL but it is defined on arrays only. You could pass a single-element array if you wanted. Ask over in the MKL forum if you need more help. 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 functions have been added to the Fortran 2008 standard and I think these are available in the latest Intel Fortran compiler version: What exactly is the inverse error function? Is it the same as the complementary error function (erfc(x)) explained above? 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),