Error Function Complex Argument Matlab
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Matlab Error Function Definitions Are Not Permitted In This Context
» Learn more 4.6 4.6 | 5 ratings Rate this file 14 Downloads matlab error function fit (last 30 days) File Size: 59.4 KB File ID: #18312 Version: 1.0 Error function of complex numbers by Marcel Leutenegger Marcel
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Leutenegger (view profile) 13 files 65 downloads 4.2475 14 Jan 2008 (Updated 14 Jan 2008) Extend the error function to the complex plane. | Watch this File File Information Description This package matlab gamma function contains two MATLAB functions e=ERF(r) and e=ERFZ(z)} as MEX-files for Windows. ERF overloads the default MATLAB error function of real-valued numbers with a much faster implementation. ERFZ enhances ERF to evaluate the error function of complex numbers too. If called with real numbers, it is identical to ERF and equally fast. ERFZ can replace ERF if no error message is required when called with complex numbers. For matlab gaussian function compatibility with operating systems other than Windows on x86 processors, ERFZ is egally implemented as a normal M-file, which relies upon the default ERF by MATLAB. Implementation details are found in the attached PDF manual. MATLAB release MATLAB 6.1 (R12.1) Other requirements x86 Windows platform (MEX-files); none (M-file). Tags for This File Please login to tag files. erferror functionmathematicsnumerical evaluation Cancel Please login to add a comment or rating. Comments and Ratings (7) 21 Aug 2015 Karan Gill Karan Gill (view profile) 0 files 0 downloads 0.0 An alternative is to use the Symbolic Math Toolbox if you have it. Ex: >> double(erf(sym(1+1i))) ans = 1.3162 + 0.1905i You could define an anonymous function to make it easier: >> erfCmplx = @(x) double(erf(sym(x))) erfCmplx = @(x)double(erf(sym(x))) >> erfCmplx(1+1i) ans = 1.3162 + 0.1905i Comment only 05 Nov 2012 Steven G. Johnson Steven G. Johnson (view profile) 1 file 25 downloads 4.75 Although this implementation is very good (and is competitive with Per's code in performance on my machine), note that it computes real(erf(z)) inaccurately near the imaginary z axis. e.g. real(erfz(1e-8 + 1i)) gives 3.1023...e-8, but the correct answer is 3.067...e-8 according to Mathematica. See http://ab-initio.mit.edu/Faddeeva for an
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PDF Documentation MuPAD Mathematics Mathematical Constants and Functions Special Functions Error and Exponential matlab normal distribution Integral Functions Symbolic Math Toolbox MuPAD Functions erfi On this page Syntax Description Environment Interactions Examples Example 1 Example 2
Imaginary Error Function Matlab
Example 3 Parameters Return Values Algorithms See Also More About This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison https://www.mathworks.com/matlabcentral/fileexchange/18312-error-function-of-complex-numbers of the page. Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Italian Japanese Korean Latvian Lithuanian Malay Maltese Norwegian Polish Portuguese Romanian Russian Slovak Slovenian Spanish Swedish Thai Turkish Ukrainian Vietnamese Welsh MathWorks Machine Translation The automated translation of this page is provided https://www.mathworks.com/help/symbolic/mupad_ref/erfi.html by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. Translate erfiImaginary error functionexpand all in page MuPAD notebooks are not recommended. Use MATLAB live scripts instead.MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.Syntaxerfi(x) Descriptionerfi(x)=−ierf(ix)=2π∫0xet2dt computes the imaginary error function.This function is defined for all complex arguments x. For floating-point arguments, erfi returns floating-point results. The implemented exact values are: erfi(0) = 0, erfi(∞) = ∞, erfi(-∞) = -∞, erfi(i∞) = i, and erfi(-i∞) = -i. For all other arguments, the error function returns symbolic function calls.For the function call erfi(x) = -i*erf(i*x) = i*(erfc(i*x) - 1) with floating-point arguments of large absolute value, internal numerical underflow or overflow can happen. If a call to erfc causes underflow or overflow, this function returns:The result truncated to 0.0 if x is a large positive real numberThe result rounded to 2.0 if x is a large negative real numberRD_NAN if x is a large complex number and MuPAD® cannot approximate the function valueThe im
toolboxes, and other File Exchange content using Add-On Explorer in MATLAB. » Watch video Highlights from Faddeeva Package: complex error functions Faddeeva_build.m Faddeeva_Dawson.m Faddeeva_erf.m Faddeeva_erfc.m Faddeeva_erfcx.m Faddeeva_erfi.m Faddeeva_w.m View all files Join the 15-year https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package--complex-error-functions community celebration. Play games and win prizes! » Learn more 4.75 4.8 | 4 ratings Rate this file 25 Downloads (last 30 days) File Size: 50.1 KB File ID: #38787 Version: 1.5 Faddeeva Package: complex error functions by Steven G. Johnson Steven G. Johnson (view profile) 1 file 25 downloads 4.75 26 Oct 2012 (Updated 17 Dec 2012) C++ MEX plugins to compute error functions error function (erf, erfc, erfi, erfcx, Faddeeva, ...) of complex args | Watch this File File Information Description C++ source code for compiled plugins (MEX files) to compute various error functions for complex arguments: ** Faddeeva_erf(z) -- the error function ** Faddeeva_erfc(z) = 1 - erf(z) -- complementary error function ** Faddeeva_erfi(z) = -i erf(iz) -- imaginary error function ** Faddeeva_erfcx(z) = exp(z^2) erfc(z) -- scaled complementary error matlab error function function ** Faddeeva_w(z) = exp(-z^2) erfc(-iz) -- Faddeeva function ** Faddeeva_Dawson(z) = 0.5 sqrt(pi) exp(-z^2) erfi(z) -- Dawson function From e.g. the Faddeeva function, one can also obtain the Voigt functions and other related functions. Assuming you have a C++ compiler (and have configured it in MATLAB with mex -setup), compile by running the included Faddeeva_build.m script in MATLAB: Faddeeva_build All of the functions have usage of the form: w = Faddeeva_w(z) or optionally Faddeeva_w(z, relerr), where relerr is a desired relative error (default: machine precision). z may be an array or matrix of complex or real numbers. This code may also be downloaded from http://ab-initio.mit.edu/Faddeeva along with documentation and other versions. As described in the source code, this implementation uses a combination of algorithms for the Faddeeva function: a continued-fraction expansion for large |z| [similar to G. P. M. Poppe and C. M. J. Wijers, "More efficient computation of the complex error function," ACM Trans. Math. Soft. 16 (1), pp. 38–46 (1990)], and a completely different algorithm for smaller |z| [Mofreh R. Zaghloul and Ahmed N. Ali, "Algorithm 916: Computing the Faddeyeva and Voigt Functions," ACM Trans. Math. Soft. 38 (2), 15 (2011).]. Given the