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	zero = 0.0_dp
real(kind=dp), parameter	one = 1.0_dp
real(kind=dp), parameter	two = 2.0_dp
real(kind=dp), parameter	half = 0.5_dp
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
real(kind=dp), parameter	one_sqrt_pi = one/SQRT(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 76 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 284 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 300 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 474 of file erf_complex.F.

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Variable Documentation

zero

real(kind=dp), parameter erf_complex::zero = 0.0_dp

Definition at line 57 of file erf_complex.F.

one

real(kind=dp), parameter erf_complex::one = 1.0_dp

Definition at line 57 of file erf_complex.F.

two

real(kind=dp), parameter erf_complex::two = 2.0_dp

Definition at line 57 of file erf_complex.F.

half

real(kind=dp), parameter erf_complex::half = 0.5_dp

Definition at line 57 of file erf_complex.F.

rmin

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

Definition at line 57 of file erf_complex.F.

eps0

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

Definition at line 57 of file erf_complex.F.

sqrt_log_rmin

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

Definition at line 57 of file erf_complex.F.

pi2

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

Definition at line 57 of file erf_complex.F.

one_sqrt_pi

real(kind=dp), parameter erf_complex::one_sqrt_pi = one/SQRT(pi)

Definition at line 57 of file erf_complex.F.

cmplxj

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

Definition at line 61 of file erf_complex.F.

cmplx0

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

Definition at line 61 of file erf_complex.F.