abacus-develop/source/source_base/math_erf_complex.h at develop · pplab/abacus-develop · GitHub

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#ifndef MATH_ERF_COMPLEX_H

#define MATH_ERF_COMPLEX_H

#include <complex>

#include <vector>

namespace ModuleBase

{

class ErrorFunc

{

public:

ErrorFunc();

~ErrorFunc();

/**

* @brief A class of the error function of complex arguments based on Faddeeva algorithm.

* More information please refer to http://ab-initio.mit.edu/Faddeeva

* @author jiyy on 2025-05-18

// compute w(z) = exp(-z^2) erfc(-iz) [ Faddeeva / scaled complex error func ]

static std::complex<double> scaled_w(std::complex<double> z, double relerr);

static double scaled_w_im(double x); // special-case code for Im[w(x)] of real x

// compute erfcx(z) = exp(z^2) erfc(z)

static std::complex<double> erfcx(std::complex<double> z, double relerr = 0);

static double erfcx(double x); // special case for real x

// compute erf(z), the error function of complex arguments

static std::complex<double> erf(std::complex<double> z, double relerr = 0);

// compute erfi(z) = -i erf(iz), the imaginary error function

static std::complex<double> erfi(std::complex<double> z, double relerr = 0);

static double erfi(double x); // special case for real x

// compute erfc(z) = 1 - erf(z), the complementary error function

static std::complex<double> erfc(std::complex<double> z, double relerr = 0);

private:

static double w_im_y100(double y100, double x);

static inline double sinc(double x, double sinx)

{

return fabs(x) < 1e-4 ? 1 - (0.1666666666666666666667) * x * x : sinx / x;

}

static inline double copysign(double x, double y)

{

return x < 0 != y < 0 ? -x : x;

}

static const std::vector<double> expa2n2;

};

} // namespace ModuleBase

#endif // MATH_ERF_H

abacus-develop/source/source_base/math_erf_complex.h at develop · pplab/abacus-develop · GitHub

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