# Working with Values of Potentials#

## Visualization of Potentials#

sumpy.visualization.make_field_plotter_from_bbox(bbox, h, extend_factor=0)[source]#
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)[source]#
set_matplotlib_limits()[source]#
show_scalar_in_matplotlib(fld, max_val=None, func_name='imshow', **kwargs)[source]#
show_scalar_in_mayavi(fld, max_val=None, **kwargs)[source]#
write_vtk_file(file_name, data, real_only=False, overwrite=False)[source]#

## Differentiation of Potentials#

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

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()[source]#

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

basis()[source]#
Returns:

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

diff(axis, f_values, nderivs=1)[source]#

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)[source]#
dy(f_values)[source]#
dz(f_values)[source]#
laplace(f_values)[source]#

Return the Laplacian of f_values.

Parameters:

f_values – an array of shape `(npoints_total,)`

Returns:

an array of shape `(npoints_total,)`

div(arg)[source]#
Parameters:

arg – an object array containing `numpy.ndarray`s with shape `(npoints_total,)`.

curl(arg)[source]#

Take the curl of the vector quantity arg.

Parameters:

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

eval_at_center(f_values)[source]#

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)[source]#
plot_nodes()[source]#
plot(f)[source]#
sumpy.point_calculus.frequency_domain_maxwell(cpatch, e, h, k)[source]#

## 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)[source]#

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)[source]#
class sumpy.toys.PotentialSource(toy_ctx: ToyContext)[source]#

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

eval(targets: ndarray) [source]#
Parameters:

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

Returns:

an array of shape `(ntargets,)`.

Supports (lazy) arithmetic:

__neg__() [source]#
__sub__(other: ) [source]#
__rsub__(other: ) [source]#
__mul__(other: ) [source]#
__rmul__(other: ) [source]#
class sumpy.toys.ConstantPotential(toy_ctx: ToyContext, value)[source]#

Inherits from `PotentialSource`.

__init__(toy_ctx: ToyContext, value)[source]#
class sumpy.toys.PointSources(toy_ctx: ToyContext, points: ndarray, weights: ndarray, center: = None)[source]#

Inherits from `PotentialSource`.

points#

`[ndim, npoints]`

__init__(toy_ctx: ToyContext, points: ndarray, weights: ndarray, center: = None)[source]#

These functions manipulate these potentials:

sumpy.toys.multipole_expand(psource: PotentialSource, center: ndarray, order: = None, rscale: float = 1, **expn_kwargs) [source]#
sumpy.toys.local_expand(psource: PotentialSource, center: ndarray, order: = None, rscale: Number = 1, **expn_kwargs) [source]#
sumpy.toys.logplot(fp: FieldPlotter, psource: PotentialSource, **kwargs) None[source]#
sumpy.toys.combine_inner_outer(psource_inner: PotentialSource, psource_outer: PotentialSource, radius: , center: = None) [source]#
sumpy.toys.combine_halfspace(psource_pos: PotentialSource, psource_neg: PotentialSource, axis: int, center: = None) [source]#
sumpy.toys.combine_halfspace_and_outer(psource_pos: PotentialSource, psource_neg: PotentialSource, psource_outer: PotentialSource, axis: int, radius: = None, center: = None) [source]#
sumpy.toys.l_inf(psource: PotentialSource, radius: float, center: = None, npoints: int = 100, debug: bool = False) [source]#

These functions help with plotting:

sumpy.toys.draw_box(el, eh, **kwargs)[source]#
sumpy.toys.draw_annotation(to_pt, from_pt, label, arrowprops=None, **kwargs)[source]#
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)[source]#

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)[source]#

A potential that is the characteristic function on a ball.

Inherits from `PotentialSource`.

__init__(toy_ctx: ToyContext, center: ndarray, radius: float) None[source]#
class sumpy.toys.HalfspaceOnePotential(toy_ctx: ToyContext, center: ndarray, axis: int, side: int = 1)[source]#

A potential that is the characteristic function of a halfspace.

__init__(toy_ctx: ToyContext, center: ndarray, axis: int, side: int = 1) None[source]#
class sumpy.toys.ExpansionPotentialSource(toy_ctx, center, rscale, order, coeffs, derived_from, radius=None, expn_style=None, text_kwargs=None)[source]#

Inherits from `PotentialSource`.

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

Inherits from `ExpansionPotentialSource`.

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

Inherits from `ExpansionPotentialSource`.

class sumpy.toys.PotentialExpressionNode(psources: )[source]#

Inherits from `PotentialSource`.

__init__(psources: ) None[source]#
class sumpy.toys.Sum(psources: )[source]#

Inherits from `PotentialExpressionNode`.

class sumpy.toys.Product(psources: )[source]#

Inherits from `PotentialExpressionNode`.

class sumpy.toys.SchematicVisitor(default_expn_style='circle')[source]#