Working with Values of Potentials

Visualization of Potentials

sumpy.visualization.make_field_plotter_from_bbox(bbox, h, extend_factor=0)

Parameters:

• bbox – a tuple (low, high) of points represented as 1D numpy arrays indicating the low and high ends of the extent of a bounding box.

• h – Either a number or a sequence of numbers indicating the desired (approximate) grid spacing in all or each of the dimensions. If a sequence, the length must match the number of dimensions.

• extend_factor – A floating point number indicating by what percentage the plot area should be grown compared to bbox.

class sumpy.visualization.FieldPlotter(center, extent=1, npoints=1000)

set_matplotlib_limits()

show_scalar_in_matplotlib(fld, max_val=None, func_name='imshow', **kwargs)

show_scalar_in_mayavi(fld, max_val=None, **kwargs)

write_vtk_file(file_name, data, real_only=False, overwrite=False)

Differentiation of Potentials

class sumpy.point_calculus.CalculusPatch(center, h=0.1, order=4, nodes='chebyshev')

Sets up a grid of points on which derivatives can be calculated. Useful to verify that an evaluated potential actually solves a PDE.

dim

points

shape: (dim, npoints_total)

weights()

” :returns: a vector of high-order quadrature weights on the points

basis()

Returns:

a list containing functions that realize a high-order interpolation basis on the points.

diff(axis, f_values, nderivs=1)

Return the derivative along axis of f_values.

Parameters:

f_values – an array of shape (npoints_total,)

Returns:

an array of shape (npoints_total,)

dx(f_values)

dy(f_values)

dz(f_values)

laplace(f_values)

Return the Laplacian of f_values.

Parameters:

f_values – an array of shape (npoints_total,)

Returns:

an array of shape (npoints_total,)

div(arg)

Parameters:

arg – an object array containing numpy.ndarrays with shape (npoints_total,).

curl(arg)

Take the curl of the vector quantity arg.

Parameters:

arg – an object array of shape (3,) containing numpy.ndarrays with shape (npoints_total,).

eval_at_center(f_values)

Interpolate f_values to the center point.

Parameters:

f_values – an array of shape (npoints_total,)

Returns:

a scalar.

x

y

z

norm(arg, p)

plot_nodes()

plot(f)

sumpy.point_calculus.frequency_domain_maxwell(cpatch, e, h, k)

Support for Numerical Experiments with Expansions (“Expansion toys”)

This module provides a convenient interface for numerical experiments with local and multipole expansions.

class sumpy.toys.ToyContext(cl_context: pyopencl.Context, kernel: Kernel, mpole_expn_class=None, local_expn_class=None, expansion_factory=None, extra_source_kwargs=None, extra_kernel_kwargs=None, m2l_use_fft=None)

This class functions as a container for generated code and ‘behind-the-scenes’ information.

__init__(cl_context: pyopencl.Context, kernel: Kernel, mpole_expn_class=None, local_expn_class=None, expansion_factory=None, extra_source_kwargs=None, extra_kernel_kwargs=None, m2l_use_fft=None)

class sumpy.toys.PotentialSource(toy_ctx: ToyContext)

A base class for all classes representing potentials that can be evaluated anywhere in space.

eval(targets: ndarray) → ndarray

Parameters:

targets – An array of shape (dim, ntargets).

Returns:

an array of shape (ntargets,).

Supports (lazy) arithmetic:

__neg__() → PotentialSource

__add__(other: int | float | complex | number | PotentialSource) → PotentialSource

__radd__(other: int | float | complex | number | PotentialSource) → PotentialSource

__sub__(other: int | float | complex | number | PotentialSource) → PotentialSource

__rsub__(other: int | float | complex | number | PotentialSource) → PotentialSource

__mul__(other: int | float | complex | number | PotentialSource) → PotentialSource

__rmul__(other: int | float | complex | number | PotentialSource) → PotentialSource

class sumpy.toys.ConstantPotential(toy_ctx: ToyContext, value)

Inherits from PotentialSource.

__init__(toy_ctx: ToyContext, value)

class sumpy.toys.PointSources(toy_ctx: ToyContext, points: ndarray, weights: ndarray, center: ndarray | None = None)

Inherits from PotentialSource.

points

[ndim, npoints]

__init__(toy_ctx: ToyContext, points: ndarray, weights: ndarray, center: ndarray | None = None)

These functions manipulate these potentials:

sumpy.toys.multipole_expand(psource: PotentialSource, center: ndarray, order: int | None = None, rscale: float = 1, **expn_kwargs) → MultipoleExpansion

sumpy.toys.local_expand(psource: PotentialSource, center: ndarray, order: int | None = None, rscale: int | float | complex | number = 1, **expn_kwargs) → LocalExpansion

sumpy.toys.logplot(fp: FieldPlotter, psource: PotentialSource, **kwargs) → None

sumpy.toys.combine_inner_outer(psource_inner: PotentialSource, psource_outer: PotentialSource, radius: float | None, center: ndarray | None = None) → PotentialSource

sumpy.toys.combine_halfspace(psource_pos: PotentialSource, psource_neg: PotentialSource, axis: int, center: ndarray | None = None) → PotentialSource

sumpy.toys.combine_halfspace_and_outer(psource_pos: PotentialSource, psource_neg: PotentialSource, psource_outer: PotentialSource, axis: int, radius: float | None = None, center: ndarray | None = None) → PotentialSource

sumpy.toys.l_inf(psource: PotentialSource, radius: float, center: ndarray | None = None, npoints: int = 100, debug: bool = False) → number

These functions help with plotting:

sumpy.toys.draw_box(el, eh, **kwargs)

sumpy.toys.draw_circle(center, radius, **kwargs)

sumpy.toys.draw_annotation(to_pt, from_pt, label, arrowprops=None, **kwargs)

Parameters:

• to_pt – Head of arrow

• from_pt – Tail of arrow

• label – Annotation label

• arrowprops – Passed to arrowprops

• kwargs – Passed to annotate

sumpy.toys.draw_schematic(psource, **kwargs)

These are created behind the scenes and are not typically directly instantiated by users:

class sumpy.toys.OneOnBallPotential(toy_ctx: ToyContext, center: ndarray, radius: float)

A potential that is the characteristic function on a ball.

Inherits from PotentialSource.

__init__(toy_ctx: ToyContext, center: ndarray, radius: float) → None

class sumpy.toys.HalfspaceOnePotential(toy_ctx: ToyContext, center: ndarray, axis: int, side: int = 1)

A potential that is the characteristic function of a halfspace.

__init__(toy_ctx: ToyContext, center: ndarray, axis: int, side: int = 1) → None

class sumpy.toys.ExpansionPotentialSource(toy_ctx, center, rscale, order, coeffs, derived_from, radius=None, expn_style=None, text_kwargs=None)

Inherits from PotentialSource.

radius

Not used mathematically. Just for visualization, purely advisory.

text_kwargs

Passed to matplotlib.pyplot.annotate(). Used for customizing the expansion label. Changing the label text is supported by passing the kwarg s. Just for visualization, purely advisory.

__init__(toy_ctx, center, rscale, order, coeffs, derived_from, radius=None, expn_style=None, text_kwargs=None)

class sumpy.toys.MultipoleExpansion(toy_ctx, center, rscale, order, coeffs, derived_from, radius=None, expn_style=None, text_kwargs=None)

Inherits from ExpansionPotentialSource.

class sumpy.toys.LocalExpansion(toy_ctx, center, rscale, order, coeffs, derived_from, radius=None, expn_style=None, text_kwargs=None)

Inherits from ExpansionPotentialSource.

class sumpy.toys.PotentialExpressionNode(psources: Sequence[PotentialSource])

Inherits from PotentialSource.

__init__(psources: Sequence[PotentialSource]) → None

class sumpy.toys.Sum(psources: Sequence[PotentialSource])

Inherits from PotentialExpressionNode.

class sumpy.toys.Product(psources: Sequence[PotentialSource])

Inherits from PotentialExpressionNode.

class sumpy.toys.SchematicVisitor(default_expn_style='circle')