SPH Kernel related constants, coefficients, and functions. More...

Data Structures
class	_forbidInvalidKernelsDict
	Modify the default dict to raise an error if a user tries to access kernels which aren't defined. More...

Functions
	_sph_kernel_eval_cubic_spline (float q)
	Evaluates the cubic spline kernel.

	_sph_kernel_eval_quartic_spline (float q)
	Evaluates the quartic spline kernel.

	_sph_kernel_eval_quartic_spline_vectorized (np.ndarray q)
	Evaluates the quartic spline kernel.

	_sph_kernel_eval_quintic_spline (float q)
	Evaluates the quintic spline kernel.

	_sph_kernel_eval_quintic_spline_vectorized (np.ndarray q)
	Evaluates the quintic spline kernel.

	_sph_kernel_eval_wendland_C2 (float q)
	Evaluates the Wendland C2 kernel.

	_sph_kernel_eval_wendland_C4 (float q)
	Evaluates the Wendland C4 kernel.

	_sph_kernel_eval_wendland_C6 (float q)
	Evaluates the Wendland C6 kernel.

	_sph_kernel_deval_cubic_spline (float q)
	Evaluates the cubic spline kernel derivative.

	_sph_kernel_deval_quartic_spline (float q)
	Evaluates the quartic spline kernel derivative.

	_sph_kernel_deval_quartic_spline_vectorized (np.ndarray q)
	Evaluates the quartic spline kernel derivative.

	_sph_kernel_deval_quintic_spline (float q)
	Evaluates the quintic spline kernel derivative.

	_sph_kernel_deval_wendland_C2 (float q)
	Evaluates the Wendland C2 kernel derivative.

	_sph_kernel_deval_wendland_C4 (float q)
	Evaluates the Wendland C4 kernel derivative.

	_sph_kernel_deval_wendland_C6 (float q)
	Evaluates the Wendland C6 kernel derivative.

	sph_kernel_W (Union[float, np.ndarray] r, Union[float, np.ndarray] h, str kernel, int ndim)
	Evaluates various kernels.

	sph_kernel_dWdr (Union[float, np.ndarray] r, Union[float, np.ndarray] h, str kernel, int ndim)
	Evaluates kernel derivatives for various kernels: returns dW/dr = dW/dq dq/dr = 1/H * dW/dq.

	sph_kernel_get_interaction_radius (Union[float, np.ndarray] h, str kernel, int ndim)
	Computes the interaction radius (compact support radius) for a given smoothing length h, SPH kernel `kernel`, and kernel dimension `ndim`.

	sph_kernel_get_H (Union[float, np.ndarray] h, str kernel, int ndim)
	Compute the compact support radius of a given kernel and given smoothing length.

	sph_kernel_get_smoothing_length_from_interaction_radius (Union[float, np.ndarray] H, str kernel, int ndim)
	Compute the smoothing length given the compact support length of a given kernel.

	sph_kernel_root (str kernel, int ndim)
	Evaluate kernel root, i.e.

Variables
list	sph_kernel_list

list	sph_vectorized_kernel_list

	sph_kernel_macro_name = _forbidInvalidKernelsDict()

list	sph_kernel_H_over_h

list	sph_kernel_normalization

	sph_kernel_eval_function = _forbidInvalidKernelsDict()

	sph_kernel_deval_function = _forbidInvalidKernelsDict()

Detailed Description

SPH Kernel related constants, coefficients, and functions.

All constants and kernel coefficients are taken from table 1 of Dehnen & Aly, MNRAS, 425, pp. 1062-1082 (2012).

Function Documentation

◆ _sph_kernel_deval_cubic_spline()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_cubic_spline ( float q )

protected

Evaluates the cubic spline kernel derivative.

Definition at line 342 of file sph_kernels.py.

◆ _sph_kernel_deval_quartic_spline()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_quartic_spline ( float q )

protected

Evaluates the quartic spline kernel derivative.

Definition at line 356 of file sph_kernels.py.

◆ _sph_kernel_deval_quartic_spline_vectorized()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_quartic_spline_vectorized ( np.ndarray q )

protected

Evaluates the quartic spline kernel derivative.

Definition at line 371 of file sph_kernels.py.

◆ _sph_kernel_deval_quintic_spline()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_quintic_spline ( float q )

protected

Evaluates the quintic spline kernel derivative.

Definition at line 396 of file sph_kernels.py.

◆ _sph_kernel_deval_wendland_C2()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_wendland_C2 ( float q )

protected

Evaluates the Wendland C2 kernel derivative.

Definition at line 417 of file sph_kernels.py.

◆ _sph_kernel_deval_wendland_C4()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_wendland_C4 ( float q )

protected

Evaluates the Wendland C4 kernel derivative.

Definition at line 428 of file sph_kernels.py.

◆ _sph_kernel_deval_wendland_C6()

exaparty.api.sphtools.sph_kernels._sph_kernel_deval_wendland_C6 ( float q )

protected

Evaluates the Wendland C6 kernel derivative.

Definition at line 446 of file sph_kernels.py.

◆ _sph_kernel_eval_cubic_spline()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_cubic_spline ( float q )

protected

Evaluates the cubic spline kernel.

Definition at line 169 of file sph_kernels.py.

◆ _sph_kernel_eval_quartic_spline()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_quartic_spline ( float q )

protected

Evaluates the quartic spline kernel.

Definition at line 183 of file sph_kernels.py.

◆ _sph_kernel_eval_quartic_spline_vectorized()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_quartic_spline_vectorized ( np.ndarray q )

protected

Evaluates the quartic spline kernel.

Definition at line 198 of file sph_kernels.py.

◆ _sph_kernel_eval_quintic_spline()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_quintic_spline ( float q )

protected

Evaluates the quintic spline kernel.

Definition at line 225 of file sph_kernels.py.

◆ _sph_kernel_eval_quintic_spline_vectorized()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_quintic_spline_vectorized ( np.ndarray q )

protected

Evaluates the quintic spline kernel.

Definition at line 251 of file sph_kernels.py.

◆ _sph_kernel_eval_wendland_C2()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_wendland_C2 ( float q )

protected

Evaluates the Wendland C2 kernel.

Definition at line 287 of file sph_kernels.py.

◆ _sph_kernel_eval_wendland_C4()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_wendland_C4 ( float q )

protected

Evaluates the Wendland C4 kernel.

Definition at line 299 of file sph_kernels.py.

◆ _sph_kernel_eval_wendland_C6()

exaparty.api.sphtools.sph_kernels._sph_kernel_eval_wendland_C6 ( float q )

protected

Evaluates the Wendland C6 kernel.

Definition at line 321 of file sph_kernels.py.

◆ sph_kernel_dWdr()

exaparty.api.sphtools.sph_kernels.sph_kernel_dWdr	(	Union[float, np.ndarray]	r,
		Union[float, np.ndarray]	h,
		str	kernel,
		int	ndim
	)

Evaluates kernel derivatives for various kernels: returns dW/dr = dW/dq dq/dr = 1/H * dW/dq.

The kernels are scaled such that W(q > 1) = 0. Currently implemented: cubic_spline, quartic_spline, quintic_spline, wendland_C2, wendland_C4, [not with ndim=1] wendland_C6, [not with ndim=1]

Parameters

r: float or ndarray particle distance(s)

h: float or ndarray smoothing length(s)

kernel: str which kernel to use

ndim: int what dimension to use. [1-3]

Returns

dWdr: float or ndarray evaluated kernel derivative

Definition at line 535 of file sph_kernels.py.

◆ sph_kernel_get_H()

exaparty.api.sphtools.sph_kernels.sph_kernel_get_H	(	Union[float, np.ndarray]	h,
		str	kernel,
		int	ndim
	)

Compute the compact support radius of a given kernel and given smoothing length.

The kernels defined above are defined and scaled to support a region <= H.

Parameters

h: float or np.ndarray smoothing length

kernel: str which kernel to use.

ndim: int how many dimensions we're working with

Returns

H: float or np.dnarray compact support radii.

Definition at line 594 of file sph_kernels.py.

◆ sph_kernel_get_interaction_radius()

exaparty.api.sphtools.sph_kernels.sph_kernel_get_interaction_radius	(	Union[float, np.ndarray]	h,
		str	kernel,
		int	ndim
	)

Computes the interaction radius (compact support radius) for a given smoothing length h, SPH kernel kernel, and kernel dimension ndim.

Definition at line 584 of file sph_kernels.py.

◆ sph_kernel_get_smoothing_length_from_interaction_radius()

exaparty.api.sphtools.sph_kernels.sph_kernel_get_smoothing_length_from_interaction_radius	(	Union[float, np.ndarray]	H,
		str	kernel,
		int	ndim
	)

Compute the smoothing length given the compact support length of a given kernel.

The kernels defined above are defined and scaled to support a region <= H.

Parameters

H: float or np.ndarray compact support radii.

kernel: str which kernel to use.

ndim: int how many dimensions we're working with

Returns

h: float or np.dnarray smoothing lengt(s)

Definition at line 623 of file sph_kernels.py.

◆ sph_kernel_root()

exaparty.api.sphtools.sph_kernels.sph_kernel_root	(	str	kernel,
		int	ndim
	)

Evaluate kernel root, i.e.

W(0, h). We don't actually need h here, because the quantity used in the kernels, q = r/h is also zero by construction.

Parameters

kernel: str which kernel to use

ndim: int what dimension to use. [1-3]

Returns

W: float evaluated kernel

Definition at line 655 of file sph_kernels.py.

◆ sph_kernel_W()

exaparty.api.sphtools.sph_kernels.sph_kernel_W	(	Union[float, np.ndarray]	r,
		Union[float, np.ndarray]	h,
		str	kernel,
		int	ndim
	)

Evaluates various kernels.

The kernels are scaled such that W(q > 1) = 0. Currently implemented: cubic_spline, quartic_spline, quintic_spline, wendland_C2, wendland_C4, [not with ndim=1] wendland_C6, [not with ndim=1]

Parameters

r: float or ndarray particle distance(s)

h: float or ndarray smoothing length(s)

kernel: str which kernel to use

ndim: int what dimension to use. [1-3]

Returns

W: float evaluated kernel

Definition at line 487 of file sph_kernels.py.

Variable Documentation

◆ sph_kernel_deval_function

exaparty.api.sphtools.sph_kernels.sph_kernel_deval_function = _forbidInvalidKernelsDict()

Definition at line 84 of file sph_kernels.py.

◆ sph_kernel_eval_function

exaparty.api.sphtools.sph_kernels.sph_kernel_eval_function = _forbidInvalidKernelsDict()

Definition at line 81 of file sph_kernels.py.

◆ sph_kernel_H_over_h

list exaparty.api.sphtools.sph_kernels.sph_kernel_H_over_h

Initial value:

=  [
    _forbidInvalidKernelsDict(blocked_keys=("wendland_C4", "wendland_C6"), ndim=1),
    _forbidInvalidKernelsDict(ndim=2),
    _forbidInvalidKernelsDict(ndim=3),
]

Definition at line 66 of file sph_kernels.py.

◆ sph_kernel_list

list exaparty.api.sphtools.sph_kernels.sph_kernel_list

Initial value:

=  [
    "cubic_spline",
    "quartic_spline",
    "quintic_spline",
    "wendland_C2",
    "wendland_C4",
    "wendland_C6",
]

Definition at line 15 of file sph_kernels.py.

◆ sph_kernel_macro_name

exaparty.api.sphtools.sph_kernels.sph_kernel_macro_name = _forbidInvalidKernelsDict()

Definition at line 63 of file sph_kernels.py.

◆ sph_kernel_normalization

list exaparty.api.sphtools.sph_kernels.sph_kernel_normalization

Initial value:

=  [
    _forbidInvalidKernelsDict(blocked_keys=("wendland_C4", "wendland_C6"), ndim=1),
    _forbidInvalidKernelsDict(ndim=2),
    _forbidInvalidKernelsDict(ndim=3),
]

Definition at line 74 of file sph_kernels.py.

◆ sph_vectorized_kernel_list

list exaparty.api.sphtools.sph_kernels.sph_vectorized_kernel_list

Initial value:

=  [
    "quartic_spline_vectorized",
]

Definition at line 24 of file sph_kernels.py.

Data Structures

Functions

Variables

Detailed Description

Function Documentation

◆ _sph_kernel_deval_cubic_spline()

◆ _sph_kernel_deval_quartic_spline()

◆ _sph_kernel_deval_quartic_spline_vectorized()

◆ _sph_kernel_deval_quintic_spline()

◆ _sph_kernel_deval_wendland_C2()

◆ _sph_kernel_deval_wendland_C4()

◆ _sph_kernel_deval_wendland_C6()

◆ _sph_kernel_eval_cubic_spline()

◆ _sph_kernel_eval_quartic_spline()

◆ _sph_kernel_eval_quartic_spline_vectorized()

◆ _sph_kernel_eval_quintic_spline()

◆ _sph_kernel_eval_quintic_spline_vectorized()

◆ _sph_kernel_eval_wendland_C2()

◆ _sph_kernel_eval_wendland_C4()

◆ _sph_kernel_eval_wendland_C6()

◆ sph_kernel_dWdr()

Parameters

Returns

◆ sph_kernel_get_H()

Parameters

Returns

◆ sph_kernel_get_interaction_radius()

◆ sph_kernel_get_smoothing_length_from_interaction_radius()

Parameters

Returns

◆ sph_kernel_root()

Parameters

Returns

◆ sph_kernel_W()

Parameters

Returns

Variable Documentation

◆ sph_kernel_deval_function

◆ sph_kernel_eval_function

◆ sph_kernel_H_over_h

◆ sph_kernel_list

◆ sph_kernel_macro_name

◆ sph_kernel_normalization

◆ sph_vectorized_kernel_list