# 4.1.3. pde.fields.scalar module¶

Defines a scalar field over a grid

class ScalarField(grid, data='zeros', *, label=None, dtype=None, with_ghost_cells=False)[source]

Bases: DataFieldBase

Scalar field discretized on a grid

Parameters
• grid (GridBase) – Grid defining the space on which this field is defined.

• data (Number or ndarray, optional) – Field values at the support points of the grid. The flag with_ghost_cells determines whether this data array contains values for the ghost cells, too. The resulting field will contain real data unless the data argument contains complex values. Special values are “zeros” or None, initializing the field with zeros, and “empty”, just allocating memory with unspecified values.

• label (str, optional) – Name of the field

• dtype (numpy dtype) – The data type of the field. If omitted, it will be determined from data automatically.

• with_ghost_cells (bool) – Indicates whether the ghost cells are included in data

classmethod from_expression(grid, expression, *, label=None, dtype=None)[source]

create a scalar field on a grid from a given expression

Warning

This implementation uses exec() and should therefore not be used in a context where malicious input could occur.

Parameters
• grid (GridBase) – Grid defining the space on which this field is defined

• expression (str) – Mathematical expression for the scalar value as a function of the position on the grid. The expression may contain standard mathematical functions and it may depend on the axes labels of the grid. More information can be found in the expression documentation.

• label (str, optional) – Name of the field

• dtype (numpy dtype) – The data type of the field. If omitted, it will be determined from data automatically.

Return type

ScalarField

classmethod from_image(path, bounds=None, periodic=False, *, label=None)[source]

create a scalar field from an image

Parameters
• path (Path or str) – The path to the image file

• bounds (tuple, optional) – Gives the coordinate range for each axis. This should be two tuples of two numbers each, which mark the lower and upper bound for each axis.

• periodic (bool or list) – Specifies which axes possess periodic boundary conditions. This is either a list of booleans defining periodicity for each individual axis or a single boolean value specifying the same periodicity for all axes.

• label (str, optional) – Name of the field

Return type

ScalarField

apply gradient operator and return result as a field

Parameters
• bc (Optional[BoundariesData]) – The boundary conditions applied to the field. Boundary conditions are generally given as a list with one condition for each axis. For periodic axis, only periodic boundary conditions are allowed (indicated by ‘periodic’ and ‘anti-periodic’). For non-periodic axes, different boundary conditions can be specified for the lower and upper end (using a tuple of two conditions). For instance, Dirichlet conditions enforcing a value NUM (specified by {‘value’: NUM}) and Neumann conditions enforcing the value DERIV for the derivative in the normal direction (specified by {‘derivative’: DERIV}) are supported. Note that the special value ‘natural’ imposes periodic boundary conditions for periodic axis and a vanishing derivative otherwise. More information can be found in the boundaries documentation. If the special value None is given, no boundary conditions are enforced. The user then needs to ensure that the ghost cells are set accordingly.

• out (VectorField, optional) – Optional vector field to which the result is written.

• label (str, optional) – Name of the returned field

Returns

result of applying the operator

Return type

VectorField

apply squared gradient operator and return result as a field

This evaluates $$|\nabla \phi|^2$$ for the scalar field $$\phi$$

Parameters
• bc (Optional[BoundariesData]) – The boundary conditions applied to the field. Boundary conditions are generally given as a list with one condition for each axis. For periodic axis, only periodic boundary conditions are allowed (indicated by ‘periodic’ and ‘anti-periodic’). For non-periodic axes, different boundary conditions can be specified for the lower and upper end (using a tuple of two conditions). For instance, Dirichlet conditions enforcing a value NUM (specified by {‘value’: NUM}) and Neumann conditions enforcing the value DERIV for the derivative in the normal direction (specified by {‘derivative’: DERIV}) are supported. Note that the special value ‘natural’ imposes periodic boundary conditions for periodic axis and a vanishing derivative otherwise. More information can be found in the boundaries documentation. If the special value None is given, no boundary conditions are enforced. The user then needs to ensure that the ghost cells are set accordingly.

• out (ScalarField, optional) – Optional vector field to which the result is written.

• label (str, optional) – Name of the returned field

• central (bool) – Determines whether a central difference approximation is used for the gradient operator or not. If not, the squared gradient is calculated as the mean of the squared values of the forward and backward derivatives, which thus includes the value at a support point in the result at the same point.

Returns

the squared gradient of the field

Return type

ScalarField

property integral: Union[int, float, complex]

integral of the scalar field over space

Type

Number

laplace(bc, out=None, **kwargs)[source]

apply Laplace operator and return result as a field

Parameters
• bc (Optional[BoundariesData]) – The boundary conditions applied to the field. Boundary conditions are generally given as a list with one condition for each axis. For periodic axis, only periodic boundary conditions are allowed (indicated by ‘periodic’ and ‘anti-periodic’). For non-periodic axes, different boundary conditions can be specified for the lower and upper end (using a tuple of two conditions). For instance, Dirichlet conditions enforcing a value NUM (specified by {‘value’: NUM}) and Neumann conditions enforcing the value DERIV for the derivative in the normal direction (specified by {‘derivative’: DERIV}) are supported. Note that the special value ‘natural’ imposes periodic boundary conditions for periodic axis and a vanishing derivative otherwise. More information can be found in the boundaries documentation. If the special value None is given, no boundary conditions are enforced. The user then needs to ensure that the ghost cells are set accordingly.

• out (ScalarField, optional) – Optional scalar field to which the result is written.

• label (str, optional) – Name of the returned field

• backend (str) – The backend (e.g., ‘numba’ or ‘scipy’) used for this operator.

Returns

the Laplacian of the field

Return type

ScalarField

project(axes, method='integral', label=None)[source]

project scalar field along given axes

Parameters
• axes (list of str) – The names of the axes that are removed by the projection operation. The valid names for a given grid are the ones in the GridBase.axes attribute.

• method (str) – The projection method. This can be either ‘integral’ to integrate over the removed axes or ‘average’ to perform an average instead.

• label (str, optional) – The label of the returned field

Returns

The projected data in a scalar field with a subgrid of the original grid.

Return type

ScalarField

rank: int = 0
slice(position, *, method='nearest', label=None)[source]

slice data at a given position

Parameters
• position (dict) – Determines the location of the slice using a dictionary supplying coordinate values for a subset of axes. Axes not mentioned in the dictionary are retained and form the slice. For instance, in a 2d Cartesian grid, position = {‘x’: 1} slices along the y-direction at x=1. Additionally, the special positions ‘low’, ‘mid’, and ‘high’ are supported to reference relative positions along the axis.

• method (str) – The method used for slicing. nearest takes data from cells defined on the grid.

• label (str, optional) – The label of the returned field

Returns

The sliced data in a scalar field with a subgrid of the original grid.

Return type

ScalarField

to_scalar(scalar='auto', *, label=None)[source]

return a modified scalar field by applying method scalar

Parameters
• scalar (str or callable) – Determines the method used for obtaining the scalar. If this is a callable, it is simply applied to self.data and a new scalar field with this data is returned. Alternatively, pre-defined methods can be selected using strings. Here, abs and norm denote the norm of each entry of the field, while norm_squared returns the squared norm. The default auto is to return a (unchanged) copy of a real field and the norm of a complex field.

• label (str, optional) – Name of the returned field

Returns

Scalar field after applying the operation

Return type

ScalarField