erf_complex Module Reference

Module to compute the error function of a complex argument. More...

Functions/Subroutines
elemental complex(kind=dp) function, public	faddeyeva_accurate (z, err)
	Computes the Faddeyeva function w(z) = exp(-z**2) * erfc(-i*z).
elemental complex(kind=dp) function, public	erfz_accurate (z, err)
	Computes the error function of a complex argument using the Zaghloul and Ali algorithm.
elemental complex(kind=dp) function, public	faddeyeva_fast (z)
	Computes the Faddeyeva function w(z) = exp(-z**2) * erfc(-i*z).
elemental complex(kind=dp) function, public	erfz_fast (z)
	Computes the error function of a complex argument using the Poppe and Wijers algorithm.

Variables
real(kind=dp), parameter	rmin = TINY(one)
real(kind=dp), parameter	eps0 = EPSILON(one)
real(kind=dp), parameter	sqrt_log_rmin = SQRT(-LOG(rmin))
real(kind=dp), parameter	pi2 = pi*pi
complex(kind=dp), parameter	cmplxj = CMPLX(zero, one, kind=dp)
complex(kind=dp), parameter	cmplx0 = CMPLX(zero, zero, kind=dp)

Detailed Description

Module to compute the error function of a complex argument.

History

08.2025 Adapted to use CP2K intrinsics and constants

Author

Stefano Battaglia

Function/Subroutine Documentation

faddeyeva_accurate()

elemental complex(kind=dp) function, public erf_complex::faddeyeva_accurate	(	complex(kind=dp), intent(in)	z,
		real(kind=dp), intent(in)	err )

Computes the Faddeyeva function w(z) = exp(-z**2) * erfc(-i*z).

Parameters

z	complex argument
err	desired accuracy (positive)

Returns

Faddeyeva function w(z)

Definition at line 80 of file erf_complex.F.

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erfz_accurate()

elemental complex(kind=dp) function, public erf_complex::erfz_accurate	(	complex(kind=dp), intent(in)	z,
		real(kind=dp), intent(in)	err )

Computes the error function of a complex argument using the Zaghloul and Ali algorithm.

Parameters

z	complex argument
err	desired accuracy (positive)

Returns

error function of z

Definition at line 288 of file erf_complex.F.

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faddeyeva_fast()

elemental complex(kind=dp) function, public erf_complex::faddeyeva_fast

(

complex(kind=dp), intent(in)

z

)

Computes the Faddeyeva function w(z) = exp(-z**2) * erfc(-i*z).

Parameters

z	complex argument

Returns

Faddeyeva function w(z)

Definition at line 304 of file erf_complex.F.

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erfz_fast()

elemental complex(kind=dp) function, public erf_complex::erfz_fast

(

complex(kind=dp), intent(in)

z

)

Computes the error function of a complex argument using the Poppe and Wijers algorithm.

Parameters

z	complex argument

Returns

error function of z

Definition at line 478 of file erf_complex.F.

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Variable Documentation

rmin

real(kind=dp), parameter erf_complex::rmin = TINY(one)

Definition at line 62 of file erf_complex.F.

eps0

real(kind=dp), parameter erf_complex::eps0 = EPSILON(one)

Definition at line 62 of file erf_complex.F.

sqrt_log_rmin

real(kind=dp), parameter erf_complex::sqrt_log_rmin = SQRT(-LOG(rmin))

Definition at line 62 of file erf_complex.F.

pi2

real(kind=dp), parameter erf_complex::pi2 = pi*pi

Definition at line 62 of file erf_complex.F.

cmplxj

complex(kind=dp), parameter erf_complex::cmplxj = CMPLX(zero, one, kind=dp)

Definition at line 65 of file erf_complex.F.

cmplx0

complex(kind=dp), parameter erf_complex::cmplx0 = CMPLX(zero, zero, kind=dp)

Definition at line 65 of file erf_complex.F.