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Dawson and Fresnel integrals

beignet.special.dawson_integral_f 

dawson_integral_f(input, *, out=None)

Dawson’s integral.

Parameters:

Name Type Description Default
input Tensor

Input tensor.

 required
out Tensor

Output tensor.

 None

Returns:

Type Description
Tensor
Source code in src/beignet/special/_dawson_integral_f.py 
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def dawson_integral_f(input: Tensor, *, out: Tensor | None = None) -> Tensor:
    r"""
    Dawson’s integral.

    Parameters
    ----------
    input : Tensor
        Input tensor.

    out : Tensor, optional
        Output tensor.

    Returns
    -------
    Tensor
    """
    output = math.sqrt(torch.pi) / 2.0 * torch.exp(-(input**2)) * error_erfi(input)

    if out is not None:
        out.copy_(output)

        return out

    return output

beignet.special.faddeeva_w 

faddeeva_w(input, *, out=None)

Faddeeva function.

Parameters:

Name Type Description Default
input Tensor

Input tensor.

 required
out Tensor

Output tensor.

 None

Returns:

Type Description
Tensor
Source code in src/beignet/special/_faddeeva_w.py 
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def faddeeva_w(input: Tensor, *, out: Tensor | None = None) -> Tensor:
    r"""
    Faddeeva function.

    Parameters
    ----------
    input : Tensor
        Input tensor.

    out : Tensor, optional
        Output tensor.

    Returns
    -------
    Tensor
    """

    if not torch.is_complex(input):
        input = torch.complex(input, torch.zeros_like(input))

    # use symmetries to map to upper right quadrant of complex plane
    imag_negative = input.imag < 0.0
    input = torch.where(input.imag < 0.0, -input, input)
    real_negative = input.real < 0.0
    input = torch.where(input.real < 0.0, -input.conj(), input)

    x = input.real
    y = input.imag

    if not (((x >= 0.0) & (y >= 0.0)) | torch.isnan(x) | torch.isnan(y)).all():
        raise ValueError("failed to map input to x >= 0, y >= 0")

    output = _voigt_v(x, y, n=11) + 1j * _voigt_l(x, y, n=11)

    # compute real and imaginary parts separately to so we handle infs
    # without unnecessary nans
    expz2 = torch.complex(
        2 * torch.exp(-x.pow(2) + y.pow(2)) * torch.cos(-2 * x * y),
        2 * torch.exp(-x.pow(2) + y.pow(2)) * torch.sin(-2 * x * y),
    )
    output = torch.where(imag_negative, expz2 - output, output)
    output = torch.where(real_negative, output.conj(), output, out=out)

    if out is not None:
        out.copy_(output)
        return out
    else:
        return output