Placeholder

In pyinduct.placeholder you find placeholders for symbolic Term definitions.

class FieldVariable(function_label, order=(0, 0), weight_label=None, location=None, exponent=1, raised_spatially=False)

Bases: pyinduct.placeholder.Placeholder

Class that represents terms of the systems field variable .

Note

Use TemporalDerivedFieldVariable and SpatialDerivedFieldVariable if no mixed derivatives occur.

Parameters:

• function_label (str) – Label of shapefunctions to use for approximation, see register_base() for more information about how to register an approximation basis.
• tuple of int (order) – Tuple of temporal_order and spatial_order derivation order.
• weight_label (str) – Label of weights for which coefficients are to be calculated (defaults to function_label).
• location – Where the expression is to be evaluated.
• exponent – Exponent of the term.

Examples

Assuming some shapefunctions have been registered under the label "phi" the following expressions hold:

• 

>>> x_dtdz = FieldVariable("phi", order=(1, 1))

• 

>>> x_ddt_at_3 = FieldVariable("phi", order=(2, 0), location=3)

• 

>>> x_dt_squared = FieldVariable("phi", order=(1, 0), exponent=2)

class TestFunction(function_label, order=0, location=None)

Bases: pyinduct.placeholder.SpatialPlaceholder

Class that works as a placeholder for test-functions in an equation.

Parameters:

• function_label (str) –
• order (int) –
• location –

class EquationTerm(scale, arg)

Bases: object

Base class for all accepted terms in a weak formulation.

Parameters:

• scale –
• arg –

class Input(function_handle, index=0, order=0, exponent=1)

Bases: pyinduct.placeholder.Placeholder

Class that works as a placeholder for the input of a system.

Parameters:

• function_handle (callable) –
• index – If input is a vector, which element shall be used.
• order – See Placeholder.
• exponent – See FieldVariable.

class IntegralTerm(integrand, limits, scale=1.0)

Bases: pyinduct.placeholder.EquationTerm

Class that represents an integral term in a weak equation.

Parameters:

• integrand –
• limits (tuple) –
• scale –

class Placeholder(data, order=(0, 0), location=None)

Bases: object

Base class that works as a placeholder for terms that are later parsed into a canonical form.

Parameters:

• data (arbitrary) – Data to store in the placeholder.
• order (tuple) – (temporal_order, spatial_order) derivative orders that are to be applied before evaluation.
• location (numbers.Number) – Location to evaluate at before further computation.

derive(temp_order=0, spat_order=0)

Mimics a copy constructor and adds the given derivative orders.

Note

The desired derivative orders temp_order and spat_order are added to the original orders.

Parameters:

• temp_order – Temporal derivative order to be added.
• spat_order – Spatial derivative order to be added.

Returns:

New Placeholder instance with the desired derivative order.

class Product(a, b=None)

Bases: object

Represents a product.

Parameters:

• a –
• b –

get_arg_by_class(cls)

Extract element from product that is an instance of cls.

Parameters:cls – Returns: Return type:list

class ScalarFunction(function_label, order=0, location=None)

Bases: pyinduct.placeholder.SpatialPlaceholder

Class that works as a placeholder for spatial-functions in an equation such as spatial dependent coefficients.

Parameters:

• function_label (str) –
• order (int) –
• location –

class ScalarTerm(argument, scale=1.0)

Bases: pyinduct.placeholder.EquationTerm

Class that represents a scalar term in a weak equation.

Parameters:

• argument –
• scale –

class Scalars(values, target_term=None, target_weight_label=None)

Bases: pyinduct.placeholder.Placeholder

Placeholder for scalars that will be replaced later.

Parameters:

• values – Iterable object containing the scalars for every n-th equation.
• target_term (dict) – Coefficient matrix to add_to().
• target_weight_label (str) – Desired weight label.

class SpatialDerivedFieldVariable(function_label, order, weight_label=None, location=None)

Bases: pyinduct.placeholder.FieldVariable

class SpatialPlaceholder(data, order=0, location=None)

Bases: pyinduct.placeholder.Placeholder

Base class for all spatially-only dependent placeholders. The deeper meaning of this abstraction layer is to offer an easier to use interface.

derive(order=0)

class TemporalDerivedFieldVariable(function_label, order, weight_label=None, location=None)

Bases: pyinduct.placeholder.FieldVariable

get_common_target(scalars)

Extracts the common target from list of scalars while making sure that targets are equivalent.

Parameters:scalars (Scalars) – Returns:Weight label as string and common target as dict. Return type:tuple