4.1.5. pde.fields.vectorial module¶
Defines a vectorial field over a grid
- class VectorField(grid, data='zeros', *, label=None, dtype=None, with_ghost_cells=False)[source]¶
Bases:
DataFieldBase
Vector 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
- divergence(bc, out=None, **kwargs)[source]¶
apply divergence 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
**kwargs – Additional arguments affecting how the operator behaves.
- Returns
result of applying the operator
- Return type
- dot(other, out=None, *, conjugate=True, label='dot product')[source]¶
calculate the dot product involving a vector field
This supports the dot product between two vectors fields as well as the product between a vector and a tensor. The resulting fields will be a scalar or vector, respectively.
- Parameters
other (VectorField or Tensor2Field) – the second field
out (ScalarField or VectorField, optional) – Optional field to which the result is written.
conjugate (bool) – Whether to use the complex conjugate for the second operand
label (str, optional) – Name of the returned field
- Returns
ScalarField
orVectorField
: result of applying the operator- Return type
- classmethod from_expression(grid, expressions, *, label=None, dtype=None)[source]¶
create a vector field on a grid from given expressions
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 definedexpressions (list of str) – A list of mathematical expression, one for each component of the vector field. The expressions determine the values as a function of the position on the grid. The expressions may contain standard mathematical functions and they 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
- classmethod from_scalars(fields, *, label=None, dtype=None)[source]¶
create a vector field from a list of ScalarFields
Note that the data of the scalar fields is copied in the process
- Parameters
- Returns
the resulting vector field
- Return type
- get_vector_data(transpose=False, max_points=None, **kwargs)[source]¶
return data for a vector plot of the field
- Parameters
- Returns
Information useful for plotting an vector field
- Return type
- gradient(bc, out=None, **kwargs)[source]¶
apply vector gradient operator and return result as a field
The vector gradient field is a tensor field \(t_{\alpha\beta}\) that specifies the derivatives of the vector field \(v_\alpha\) with respect to all coordinates \(x_\beta\).
- Parameters
bc (Optional[BoundariesData]) – The boundary conditions applied to the field. Boundary conditions need to determine all components of the vector 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
**kwargs – Additional arguments affecting how the operator behaves.
- Returns
result of applying the operator
- Return type
- laplace(bc, out=None, **kwargs)[source]¶
apply vector Laplace operator and return result as a field
The vector Laplacian is a vector field \(L_\alpha\) containing the second derivatives of the vector field \(v_\alpha\) with respect to the coordinates \(x_\beta\):
\[L_\alpha = \sum_\beta \frac{\partial^2 v_\alpha}{\partial x_\beta \partial x_\beta}\]- 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
**kwargs – Additional arguments affecting how the operator behaves.
- Returns
result of applying the operator
- Return type
- make_dot_operator(backend='numba', *, conjugate=True)[source]¶
return operator calculating the dot product involving vector fields
This supports both products between two vectors as well as products between a vector and a tensor.
Warning
This function does not check types or dimensions.
- Parameters
- Returns
function that takes two instance of
ndarray
, which contain the discretized data of the two operands. An optional third argument can specify the output array to which the result is written. Note that the returned function is jitted with numba for speed.- Return type
- make_outer_prod_operator(backend='numba')[source]¶
return operator calculating the outer product of two vector fields
Warning
This function does not check types or dimensions.
- Parameters
backend (str) – The backend (e.g., ‘numba’ or ‘scipy’) used for this operator.
- Returns
function that takes two instance of
ndarray
, which contain the discretized data of the two operands. An optional third argument can specify the output array to which the result is written. Note that the returned function is jitted with numba for speed.- Return type
- outer_product(other, out=None, *, label=None)[source]¶
calculate the outer product of this vector field with another
- Parameters
other (
VectorField
) – The second vector fieldout (
Tensor2Field
, optional) – Optional tensorial field to which the result is written.label (str, optional) – Name of the returned field
- Returns
result of the operation
- Return type
- to_scalar(scalar='auto', *, label='scalar `{scalar}`')[source]¶
return a scalar field by applying method
- Parameters
scalar (str) – Choose the method to use. Possible choices are norm, max, min, squared_sum, norm_squared, or an integer specifying which component is returned (indexing starts at 0). The default value auto picks the method automatically: The first (and only) component is returned for real fields on one-dimensional spaces, while the norm of the vector is returned otherwise.
label (str, optional) – Name of the returned field
- Returns
the scalar field after applying the operation
- Return type