Documentation for the Package `extended_stencil`¶

Module extended_stencil.dispersion¶

class extended_stencil.dispersion.Dispersion(runinit2=True)¶

This class is used to define objects which understand the dispersion relation of a stencil. As it is an abstract base class, only its subclasses are really useful.

Note

It implements a mechanism to lazily initialize parts of the object, in order to keep the object pickleable.

The initializer should only create pickleable state.

Parameters:	runinit2 (bool) – Run second initializer `Dispersion.init2()` immediately. Default is False.

Y = 1.0¶

Z = 1.0¶

coefficients¶: This read-only property returns the full list of coefficients defining the numerical dispersion relation

dim = 0¶

dt_multiplier = 1.0¶

dt_ok(parameters)¶

This function represents the optimization constraint that the time step must fulfil the CFL condition

Parameters:	parameters (numpy.ndarray) – Array containing the parameters.

dx = 1.0¶

init2()¶: Second initializer which must be used to create unpickleable state on lazy initialization.

norm(parameters)¶

This method returns the norm of the dispersion relation with the given parameters.

Parameters:	parameters (numpy.ndarray) – Array containing the parameters.

omega(parameters)¶

This function returns the function \(\omega(\vec{k})\)

Parameters:	parameters (numpy.ndarray) – Array containing the parameters.

omega_output(fname, parameters)¶

This method writes the dispersion relation to the file fname.

Parameters:	fname (string) – Filename parameters (numpy.ndarray) – Array containing the parameters.

parameters¶

This read/write-property manages the parameters to the numerical dispersion relation. Setting the property requires an array of the correct length.

Parameters:	parameters (numpy.ndarray) – Array containing the parameters.

sqrtarg¶: This read-only property represents the term under the square-root on the right hand side of \(s_\omega=\sqrt{\sum_i s_i^2 A_i}\).

sqrtres¶: This read-only property represents the right hand side of \(s_\omega=\sqrt{\sum_i s_i^2 A_i}\).

stencil = None¶

stencil_ok(parameters)¶

This function represents the optimization constraint that \(s_\omega=\sqrt{\sum_i s_i^2 A_i}\leq 1\).

Parameters:	parameters (numpy.ndarray) – Array containing the parameters.

w = 1.0¶

class extended_stencil.dispersion.Dispersion2D(Y, N, stencil, **kwargs)¶

This class is a specialisation of the class Dispersion for the two-dimensional case.

dim = 2¶

init2()¶

sqrtarg¶

stencil_ok(parameters)¶

class extended_stencil.dispersion.Dispersion3D(Y, Z, N, stencil)¶

This class is a specialisation of the class Dispersion for the three-dimensional case.

dim = 3¶

init2()¶

sqrtarg¶

stencil_ok(parameters)¶

Module extended_stencil.optimize¶

class extended_stencil.optimize.Optimize(args)¶

Class that contains the main optimization logic.

Parameters:	args (namespace) – Namespace object containing all the arguments.

omega_output(fname, x)¶: Write resulting dispersion relation through extended_stencil.dispersion.Dispersion.omega_output().

optimize()¶

Execute the optimization.

This will loop through the grid of starting values and return the best optimization result.

class extended_stencil.optimize.make_single_max_constraint(index, maxval)¶

Class representing upper bounds for parameters.

Parameters:	index (int) – Index of the parameter which is to be bounded maxval (float) – Upper bound

__call__(p)¶

class extended_stencil.optimize.make_single_min_constraint(index, minval)¶

Class representing lower bounds for parameters.

Parameters:	index (int) – Index of the parameter which is to be bounded maxval (float) – Lower bound

__call__(p)¶

Module extended_stencil.stencil¶

class extended_stencil.stencil.Stencil¶

Parent class representing all Stencils

Coefficients = None¶

Parameters = None¶

coefficients(args)¶

Method that converts the given parameters into the stencil coefficients.

Parameters:	args (iterable) – iterable of parameters

dof¶: Read-only property giving the number of the degrees of freedom.

classmethod get_stencil(args)¶

This method will do two things:

Interpret the given args in order to determine the set of flags that the user wants
Find and instantiate a Stencil subclass that has the requested flags

Parameters:	args (namespace) – Namespace object containing all the arguments.
Returns:	Object of a subclass of `Stencil`
Return type:	`Stencil`

classmethod register_subclasses(sub=None)¶

This method will walk the tree of subclasses of Stencil and fill Stencil.stencils. This method runs recursively.

Parameters:	sub (`Stencil`) – Start from thus subclass

stencils = {}¶

class extended_stencil.stencil.StencilCylinder3D¶

Three dimensional stencil that is the same on two out of three axes.

Flags = frozenset({<StencilFlags.DIM3: 1>, <StencilFlags.CYLINDERSYM: 4>})¶

class extended_stencil.stencil.StencilCylinderDivFree3D¶

Three dimensional stencil that is the same on two out of three axes and preserves \(\operatorname{div}\vec{B}=0\).

Flags = frozenset({<StencilFlags.DIM3: 1>, <StencilFlags.DIVFREE: 2>, <StencilFlags.CYLINDERSYM: 4>})¶

class extended_stencil.stencil.StencilDivFree2D¶

Two dimensional stencil that preserves \(\operatorname{div}\vec{B}=0\).

Flags = frozenset({<StencilFlags.DIVFREE: 2>, <StencilFlags.DIM2: 0>})¶

class extended_stencil.stencil.StencilDivFree3D¶

Three dimensional stencil that preserves \(\operatorname{div}\vec{B}=0\).

Flags = frozenset({<StencilFlags.DIM3: 1>, <StencilFlags.DIVFREE: 2>})¶

class extended_stencil.stencil.StencilFlags¶

An enumeration representing various flags a Stencil can carry.

CYLINDERSYM = 4¶

DIM2 = 0¶

DIM3 = 1¶

DIVFREE = 2¶

ISOTROPIC = 3¶

SYMMETRICBETA = 5¶

class extended_stencil.stencil.StencilFree2D¶

Most general two-dimensional stencil

Coefficients = namedarray(['dt', 'alphax', 'alphay', 'betaxy', 'betayx', 'deltax', 'deltay'])¶

Flags = frozenset({<StencilFlags.DIM2: 0>})¶

class extended_stencil.stencil.StencilFree3D¶

Most general three-dimensional stencil

Coefficients = namedarray(['dt', 'alphax', 'alphay', 'alphaz', 'betaxy', 'betaxz', 'betayx', 'betayz', 'betazx', 'betazy', 'deltax', 'deltay', 'deltaz'])¶

Flags = frozenset({<StencilFlags.DIM3: 1>})¶

class extended_stencil.stencil.StencilIsotropic2D¶

A two dimensional stencil that is the same on all axis.

Flags = frozenset({<StencilFlags.SYMMETRICBETA: 5>, <StencilFlags.ISOTROPIC: 3>, <StencilFlags.DIM2: 0>})¶

class extended_stencil.stencil.StencilIsotropic3D¶

Three dimensional stencil with symmetric \(\beta_{ij}\) that is the same on all axes.

Flags = frozenset({<StencilFlags.SYMMETRICBETA: 5>, <StencilFlags.DIM3: 1>, <StencilFlags.ISOTROPIC: 3>})¶

class extended_stencil.stencil.StencilIsotropicDivFree2D¶

A two dimensional stencil that is the same on each axis and preserves \(\operatorname{div}\vec{B}=0\).

Flags = frozenset({<StencilFlags.SYMMETRICBETA: 5>, <StencilFlags.ISOTROPIC: 3>, <StencilFlags.DIVFREE: 2>, <StencilFlags.DIM2: 0>})¶

class extended_stencil.stencil.StencilIsotropicDivFree3D¶

Three dimensional stencil with symmetric \(\beta_{ij}\) that is the same on all axes and preserves \(\operatorname{div}\vec{B}=0\).

Flags = frozenset({<StencilFlags.SYMMETRICBETA: 5>, <StencilFlags.DIM3: 1>, <StencilFlags.DIVFREE: 2>, <StencilFlags.ISOTROPIC: 3>})¶

class extended_stencil.stencil.StencilSymmetric2D¶

Two dimensional stencil with symmetric \(\beta_{ij}\).

Flags = frozenset({<StencilFlags.SYMMETRICBETA: 5>, <StencilFlags.DIM2: 0>})¶

class extended_stencil.stencil.StencilSymmetric3D¶

Three dimensional stencil with symmetric \(\beta_{ij}\).

Flags = frozenset({<StencilFlags.SYMMETRICBETA: 5>, <StencilFlags.DIM3: 1>})¶

extended_stencil.stencil.get_stencil(args)¶: Module level function that will call Stencil.get_stencil().

class extended_stencil.stencil.namedarray(field_names)¶

Class representing a set of field names such that any list or array of numbers can be casted into a numpy.recarray

Parameters:	field_names (list) – List of field names

__call__(args)¶

Convert a list or an array into a numpy.recarray

Parameters:	args (iterable) – List or Array to be converted

convert(other)¶

Convert a numpy.recarray to a numpy.recarray with additional fields, filling the additional fields with 0.

Parameters:	other (`numpy.recarray`) – The `numpy.recarray` to be converted.

Module extended_stencil.weight¶

extended_stencil.weight.weight_xaxis()¶: Factory function that returns a function set_weight_xaxis which acts on an object of extended_stencil.dispersion.Dispersion and applies a weight function that only cares about the \(k_x\)-axis

extended_stencil.weight.weight_xaxis_soft(width=0.1)¶: Factory function that returns a function set_weight_xaxis_soft which acts on an object of extended_stencil.dispersion.Dispersion and applies a weight function that only cares about a region close to the \(k_x\)-axis

Documentation for the Package `extended_stencil`¶

Module extended_stencil.dispersion¶

Module extended_stencil.optimize¶

Module extended_stencil.stencil¶

Module extended_stencil.weight¶

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Related Topics

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Documentation for the Package extended_stencil¶

Module extended_stencil.dispersion¶

Module extended_stencil.optimize¶

Module extended_stencil.stencil¶

Module extended_stencil.weight¶

Documentation for the Package `extended_stencil`¶