symfem.piecewise_functions

Piecewise basis function classes.

Module Contents

Classes

PiecewiseFunction

A piecewise function.

Functions

_piece_reference(tdim, shape)

Create a reference element for a single piece.

class symfem.piecewise_functions.PiecewiseFunction(pieces: Dict[symfem.geometry.SetOfPointsInput, symfem.functions.FunctionInput], tdim: int)

Bases: symfem.functions.AnyFunction

A piecewise function.

property pieces: Dict[symfem.geometry.SetOfPoints, symfem.functions.AnyFunction]

Get the pieces of the function.

Returns:

The function pieces

property shape: Tuple[int, Ellipsis]

Get the value shape of the function.

Returns:

The value shape

_pieces: Dict[symfem.geometry.SetOfPoints, symfem.functions.AnyFunction]

__len__()

Get the length of the vector.

as_sympy() → symfem.functions.SympyFormat

Convert to a sympy expression.

Returns:

A Sympy expression

as_tex() → str

Convert to a TeX expression.

Returns:

A TeX string

get_piece(point: symfem.geometry.PointType) → symfem.functions.AnyFunction

Get a piece of the function.

Parameters:

point – The point to get the piece at

Returns:

The piece of the function that is valid at that point

__getitem__(key) → PiecewiseFunction

Get a component or slice of the function.

__eq__(other: Any) → bool

Check if two functions are equal.

__add__(other: Any) → PiecewiseFunction

Add.

__radd__(other: Any) → PiecewiseFunction

Add.

__sub__(other: Any) → PiecewiseFunction

Subtract.

__rsub__(other: Any) → PiecewiseFunction

Subtract.

__truediv__(other: Any) → PiecewiseFunction

Divide.

__rtruediv__(other: Any) → PiecewiseFunction

Divide.

__mul__(other: Any) → PiecewiseFunction

Multiply.

__rmul__(other: Any) → PiecewiseFunction

Multiply.

__matmul__(other: Any) → PiecewiseFunction

Multiply.

__rmatmul__(other: Any) → PiecewiseFunction

Multiply.

__pow__(other: Any) → PiecewiseFunction

Raise to a power.

__neg__() → PiecewiseFunction

Negate.

subs(vars: symfem.symbols.AxisVariables, values: symfem.functions.ValuesToSubstitute) → PiecewiseFunction

Substitute values into the function.

Parameters:

• vars – The variables to substitute out

• values – The value to substitute in

Returns:

The substituted function

diff(variable: sympy.core.symbol.Symbol) → PiecewiseFunction

Differentiate the function.

Parameters:

variable – The variable to differentiate with respect to

Returns:

The differentiated function

directional_derivative(direction: symfem.geometry.PointType) → PiecewiseFunction

Compute a directional derivative.

Parameters:

direction – The diection

Returns:

The directional derivative

jacobian_component(component: Tuple[int, int]) → PiecewiseFunction

Compute a component of the jacobian.

Parameters:

component – The component

Returns:

The component of the jacobian

jacobian(dim: int) → PiecewiseFunction

Compute the jacobian.

Parameters:

dim – The topological dimension of the cell

Returns:

The jacobian

dot(other_in: symfem.functions.FunctionInput) → PiecewiseFunction

Compute the dot product with another function.

Parameters:

other_in – The function to multiply with

Returns:

The product

cross(other_in: symfem.functions.FunctionInput) → PiecewiseFunction

Compute the cross product with another function.

Parameters:

other_in – The function to multiply with

Returns:

The cross product

div() → PiecewiseFunction

Compute the div of the function.

Returns:

The divergence

grad(dim: int) → PiecewiseFunction

Compute the grad of the function.

Returns:

The gradient

curl() → PiecewiseFunction

Compute the curl of the function.

Returns:

The curl

norm() → PiecewiseFunction

Compute the norm of the function.

Returns:

The norm

integral(domain: symfem.references.Reference, vars: symfem.symbols.AxisVariablesNotSingle = x, dummy_vars: symfem.symbols.AxisVariablesNotSingle = t) → symfem.functions.ScalarFunction

Compute the integral of the function.

Parameters:

• domain – The domain of the integral

• vars – The variables to integrate with respect to

• dummy_vars – The dummy variables to use inside the integral

Returns:

The integral

det() → PiecewiseFunction

Compute the determinant.

Returns:

The deteminant

transpose() → PiecewiseFunction

Compute the transpose.

Returns:

The transpose

map_pieces(fwd_map: symfem.geometry.PointType)

Map the function’s pieces.

Parameters:

fwd_map – The map from the reference cell to a physical cell

Returns:

The mapped pieces

plot_values(reference: symfem.references.Reference, img: Any, value_scale: sympy.core.expr.Expr = sympy.Integer(1), n: int = 6)

Plot the function’s values.

Parameters:

• reference – The reference cell

• img – The image to plot on

• value_scale – The scale factor for the function values

• n – The number of points per side for plotting

with_floats() → symfem.functions.AnyFunction

Return a version the function with floats as coefficients.

Returns:

A version the function with floats as coefficients

abstract maximum_degree(cell: symfem.references.Reference) → int

Return the maximum degree of the function on a reference cell.

This function returns the order of the lowerst order Lagrange space on the input cell that includes this function.

Parameters:

cell – The cell

Returns:

A version the function with floats as coefficients

symfem.piecewise_functions._piece_reference(tdim, shape)

Create a reference element for a single piece.