faddeeva/Faddeeva.hh

   1 /* Copyright (c) 2012 Massachusetts Institute of Technology
   2  *
   3  * Permission is hereby granted, free of charge, to any person obtaining
   4  * a copy of this software and associated documentation files (the
   5  * "Software"), to deal in the Software without restriction, including
   6  * without limitation the rights to use, copy, modify, merge, publish,
   7  * distribute, sublicense, and/or sell copies of the Software, and to
   8  * permit persons to whom the Software is furnished to do so, subject to
   9  * the following conditions:
  10  *
  11  * The above copyright notice and this permission notice shall be
  12  * included in all copies or substantial portions of the Software.
  13  *
  14  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  15  * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  16  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  17  * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
  18  * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
  19  * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
  20  * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  21  */
  22
  23 /* Available at: http://ab-initio.mit.edu/Faddeeva
  24
  25    Header file for Faddeeva.cc; see that file for more information. */
  26
  27 #ifndef FADDEEVA_HH
  28 #define FADDEEVA_HH 1
  29
  30 #include <complex>
  31
  32 namespace Faddeeva {
  33
  34 // compute w(z) = exp(-z^2) erfc(-iz) [ Faddeeva / scaled complex error func ]
  35 extern std::complex<double> w(std::complex<double> z,double relerr=0);
  36 extern double w_im(double x); // special-case code for Im[w(x)] of real x
  37
  38 // Various functions that we can compute with the help of w(z)
  39
  40 // compute erfcx(z) = exp(z^2) erfc(z)
  41 extern std::complex<double> erfcx(std::complex<double> z, double relerr=0);
  42 extern double erfcx(double x); // special case for real x
  43
  44 // compute erf(z), the error function of complex arguments
  45 extern std::complex<double> erf(std::complex<double> z, double relerr=0);
  46 extern double erf(double x); // special case for real x
  47
  48 // compute erfi(z) = -i erf(iz), the imaginary error function
  49 extern std::complex<double> erfi(std::complex<double> z, double relerr=0);
  50 extern double erfi(double x); // special case for real x
  51
  52 // compute erfc(z) = 1 - erf(z), the complementary error function
  53 extern std::complex<double> erfc(std::complex<double> z, double relerr=0);
  54 extern double erfc(double x); // special case for real x
  55
  56 // compute Dawson(z) = sqrt(pi)/2  *  exp(-z^2) * erfi(z)
  57 extern std::complex<double> Dawson(std::complex<double> z, double relerr=0);
  58 extern double Dawson(double x); // special case for real x
  59
  60 } // namespace Faddeeva
  61
  62 #endif // FADDEEVA_HH