Source code

Triplet

class Triplet(shape: Tuple[int, int], array: ndarray, add_extra_column: bool = False)

Bases: object

A class representing a sparse matrix in triplet (COO) format, useful for finite-difference operations.

Parameters:

• shape (tuple of int) – Shape of the matrix (rows, columns).

• array (numpy.ndarray) – A 2D array with three columns representing row indices, column indices, and values.

• add_extra_column (bool, optional) – If True, adds an extra column of ones to the array (default is False).

shape: Tuple[int, int]

array: ndarray

add_extra_column: bool = False

property index: ndarray

Return the first two columns of the array, representing the indices.

Returns:

Array of row and column indices.

Return type:

numpy.ndarray

property rows: ndarray

Return the row indices (first column).

Returns:

Array of row indices.

Return type:

numpy.ndarray

property columns: ndarray

Return the column indices (second column).

Returns:

Array of column indices.

Return type:

numpy.ndarray

property values: ndarray

Return the values (third column).

Returns:

Array of values.

Return type:

numpy.ndarray

property size: int

Return the number of entries in the triplet.

Returns:

Number of entries.

Return type:

int

remove_below_i(i_value: int) → Triplet

Remove all entries with row indices below a specified value.

Parameters:

i_value (int) – Threshold for row indices. Entries with row indices below this value are removed.

Returns:

The modified Triplet instance.

Return type:

Triplet

remove_above_i(i_value: int) → Triplet

Remove all entries with row indices above a specified value.

Parameters:

i_value (int) – Threshold for row indices. Entries with row indices above this value are removed.

Returns:

The modified Triplet instance.

Return type:

Triplet

remove_below_j(j_value: int) → Triplet

Remove all entries with column indices below a specified value.

Parameters:

j_value (int) – Threshold for column indices. Entries with column indices below this value are removed.

Returns:

The modified Triplet instance.

Return type:

Triplet

remove_above_j(j_value: int) → Triplet

Remove all entries with column indices above a specified value.

Parameters:

j_value (int) – Threshold for column indices. Entries with column indices above this value are removed.

Returns:

The modified Triplet instance.

Return type:

Triplet

delete(index: ndarray) → None

Delete entries at the given indices.

Parameters:

index (numpy.ndarray) – Indices of entries to delete.

append(other: Triplet) → None

Append another triplet to this one.

Parameters:

other (Triplet) – Another Triplet instance to append.

append_array(array: ndarray) → None

Append a NumPy array to this triplet.

Parameters:

array (numpy.ndarray) – The array to append to the triplet.

remove_duplicate() → Triplet

Remove duplicate entries by summing their values.

Returns:

A new Triplet instance with duplicate entries removed.

Return type:

Triplet

coincide_i(mask: Triplet) → None

Remove entries whose row indices do not coincide with those in the mask.

Parameters:

mask (Triplet) – The mask triplet used to filter rows.

enumerate(start: int = 0, stop: int = None)

Enumerate over the entries, yielding an index and the entry values.

Parameters:

• start (int, optional) – Starting index for enumeration (default is 0).

• stop (int, optional) – Stopping index for enumeration (default is None).

Yields:

tuple – Index and a tuple of row index, column index, and value.

merge_duplicate() → None

Merge duplicate entries by summing their values.

get_duplicate_index() → ndarray

Get indices of duplicate entries.

Returns:

Array of duplicate indices.

Return type:

numpy.ndarray

property max_i: int

Return the maximum row index.

Returns:

Maximum row index.

Return type:

int

property max_j: int

Return the maximum column index.

Returns:

Maximum column index.

Return type:

int

property min_i: int

Return the minimum row index.

Returns:

Minimum row index.

Return type:

int

property min_j: int

Return the minimum column index.

Returns:

Minimum column index.

Return type:

int

property diagonal: ndarray

Return the diagonal elements of the triplet.

Returns:

Diagonal elements.

Return type:

numpy.ndarray

shift_diagonal(value: float) → Triplet

Shift the diagonal elements by a specified value.

Parameters:

value (float) – Value to add to the diagonal elements.

Returns:

A new Triplet instance with the shifted diagonal.

Return type:

Triplet

update_elements(other_triplet: Triplet, i_range: slice) → Triplet

Update elements within a specified range.

Parameters:

• other_triplet (Triplet) – The Triplet instance whose elements will be used for updating.

• i_range (slice) – Range of rows to update.

Returns:

The updated Triplet instance.

Return type:

Triplet

to_dense() → ndarray

Convert the triplet to a dense matrix representation.

Returns:

Dense matrix representation of the triplet.

Return type:

numpy.ndarray

plot() → NoReturn

Plot the dense matrix representation of the triplet.

to_scipy_sparse() → coo_matrix

Convert the triplet to a SciPy sparse matrix.

Returns:

coo_matrix

Return type:

The scipy sparse matrix representation.

Diagonal

class Diagonal(mesh_info: object, offset: int, values: float, boundary: object)

Bases: object

Represents a diagonal element of the finite-difference method.

This class constructs a diagonal with parameters such as its offset and boundary condition.

Parameters:

• mesh_info (object) – Instance describing the meta information on the mesh to be considered.

• offset (int) – Offset of the column index for the diagonal.

• values (float) – Value associated with the diagonal.

• boundary (object) – Instance of the boundary used for the diagonal.

mesh_info: object

offset: int

values: float

boundary: object

property triplet: Triplet

Return the Triplet instance of the diagonal.

Returns:

A Triplet instance representing the non-zero values in the diagonal.

Return type:

Triplet

compute_triplet() → None

Compute the diagonal indices and generate a Triplet instance out of it.

The value of the third column in the triplet depends on the boundary condition.

apply_symmetry() → None

Apply boundary symmetry conditions to the diagonal.

If the boundary is symmetric, the value stays the same. If it is anti-symmetric, a negative sign is added. If it is zero, the value becomes zero.

validate_index() → None

Remove all negative indices from the diagonal.

plot() → None

Plot the Triplet instance representing the diagonal.

class ConstantDiagonal(offset: int, value: float, mesh_info: list, boundary: object)

Bases: Diagonal

Represents a diagonal with constant values.

This subclass of Diagonal is initialized with constant values for the entire diagonal.

apply_symmetry() → None

Apply boundary symmetry conditions to the diagonal.

If the boundary is symmetric, the value stays the same. If it is anti-symmetric, a negative sign is added. If it is zero, the value becomes zero.

compute_triplet() → None

Compute the diagonal indices and generate a Triplet instance out of it.

The value of the third column in the triplet depends on the boundary condition.

plot() → None

Plot the Triplet instance representing the diagonal.

property triplet: Triplet

Return the Triplet instance of the diagonal.

Returns:

A Triplet instance representing the non-zero values in the diagonal.

Return type:

Triplet

validate_index() → None

Remove all negative indices from the diagonal.

mesh_info: object

offset: int

values: float

boundary: object

FiniteDifference1D

class Boundary(name: str, value: BoundaryValue | None, mesh_info: object)

Bases: object

Class representing a boundary with a specific name, value, and mesh information.

Parameters:

• name (str) – The name of the boundary.

• value (Optional[BoundaryValue]) – The value associated with the boundary, such as BoundaryValue.SYMMETRIC, BoundaryValue.ANTI_SYMMETRIC, BoundaryValue.ZERO, or BoundaryValue.NONE.

• mesh_info (object) – The mesh information object containing information about the mesh size and structure.

get_factor() → float

Get the factor associated with the boundary value.

Returns:

The factor corresponding to the boundary value.

Return type:

float

Raises:

ValueError – If the boundary value is unexpected.

get_shift_vector(offset: int) → ndarray | None

Calculate the shift vector based on the boundary name and offset.

Parameters:

offset (int) – The offset value to be used in the shift vector calculation.

Returns:

The shift vector as a numpy array, or None if the boundary name is ‘center’.

Return type:

Optional[numpy.ndarray]

Raises:

ValueError – If the boundary name is unexpected.

class FiniteDifference(n_x: int, dx: float = 1, derivative: int = 1, accuracy: int = 2, boundaries: ~PyFinitDiff.finite_difference_1D.boundaries.Boundaries = <factory>, x_derivative: bool = True)

Bases: object

Represents a specific finite difference configuration, including the discretization of the mesh, derivative order, accuracy, and boundary conditions.

Parameters:

• n_x (int) – Number of points in the x direction.

• dx (float, optional) – Infinitesimal displacement in the x direction (default is 1).

• derivative (int, optional) – Order of the derivative to convert into a finite-difference matrix (default is 1).

• accuracy (int, optional) – Accuracy of the derivative approximation (error is inversely proportional to the power of this value, default is 2).

• boundaries (PyFinitDiff.finite_difference_1D.boundaries.Boundary, optional) – Values of the four possible boundaries of the system (default is an empty Boundaries object).

• x_derivative (bool, optional) – Whether to add the x derivative (default is True).

mesh_info

Contains information about the mesh, such as the number of points and spacing.

Type:

MeshInfo

boundaries

Boundary conditions applied to the system.

Type:

PyFinitDiff.finite_difference_1D.boundaries.Boundary

finit_coefficient

Coefficients used for finite difference calculation.

Type:

FiniteCoefficients

_triplet

The triplet representation of the finite-difference matrix, initialized to None.

Type:

tuple or None

n_x: int

dx: float = 1

derivative: int = 1

accuracy: int = 2

boundaries: Boundaries

x_derivative: bool = True

property shape

Tuple representing the shape of the finite-difference system.

Returns:

The shape of the system, represented by the number of points in the x direction.

Return type:

tuple

property triplet

Returns the triplet representation of the non-zero values of the finite-difference configuration. Constructs the triplet if it has not been initialized.

Returns:

The triplet representation of the finite-difference matrix.

Return type:

tuple

iterate_central_coefficient(coefficients: str, offset_multiplier: int)

Iterates through the given type of coefficients to provide the offset, value, and boundary type.

Parameters:

• coefficients (str) – The type of coefficients to iterate over.

• offset_multiplier (int) – Multiplier applied to the coefficient offset.

Yields:

tuple – A tuple containing the offset, value, and corresponding boundary type.

get_diagonal_set_full(offset_multiplier: int, delta: float) → DiagonalSet

Constructs and returns a complete set of diagonals, including central, forward, and backward coefficients.

Parameters:

• offset_multiplier (int) – Multiplier applied to the coefficient offset.

• delta (float) – Scaling factor for the coefficient values.

Returns:

A set of diagonals representing the finite-difference configuration, including adjustments for boundaries.

Return type:

DiagonalSet

construct_triplet() → None

Constructs the triplet representation of the finite-difference matrix for the x direction.

FiniteDifference2D

class Boundary(name: str, value: BoundaryValue | None, mesh_info: object)

Bases: object

Represents a boundary with a specific name, value, and mesh information.

Parameters:

• name (str) – The name of the boundary.

• value (Optional[BoundaryValue]) – The value associated with the boundary (e.g., BoundaryValue.SYMMETRIC, BoundaryValue.ANTI_SYMMETRIC).

• mesh_info (object) – Mesh information object, used to determine mesh-related properties.

get_factor() → float

Gets the factor associated with the boundary value.

Returns:

The factor corresponding to the boundary value. Possible values are: - 1.0 for BoundaryValue.SYMMETRIC - -1.0 for BoundaryValue.ANTI_SYMMETRIC - 0.0 for BoundaryValue.ZERO - numpy.nan for BoundaryValue.NONE

Return type:

float

get_shift_vector(offset: int) → ndarray | None

Calculates the shift vector based on the boundary name and offset.

Parameters:

offset (int) – The offset value to be used in the shift vector calculation.

Returns:

The shift vector as a numpy array, or None if the boundary is ‘center’.

Return type:

Optional[numpy.ndarray]

class FiniteDifference(n_x: int, n_y: int, dx: float = 1, dy: float = 1, derivative: int = 1, accuracy: int = 2, boundaries: ~PyFinitDiff.finite_difference_2D.boundaries.Boundaries = <factory>, x_derivative: bool = True, y_derivative: bool = True)

Bases: object

Represents a specific finite difference configuration, defined by the discretization of the mesh, derivative order, accuracy, and boundary conditions.

Parameters:

• n_x (int) – Number of points in the x direction.

• n_y (int) – Number of points in the y direction.

• dx (float, optional) – Infinitesimal displacement in the x direction (default is 1).

• dy (float, optional) – Infinitesimal displacement in the y direction (default is 1).

• derivative (int, optional) – Order of the derivative to convert into a finite-difference matrix (default is 1).

• accuracy (int, optional) – Accuracy of the derivative approximation (error is inversely proportional to the power of this value, default is 2).

• boundaries (PyFinitDiff.finite_difference_2D.boundaries.Boundary, optional) – Values of the four possible boundaries of the system (default is an empty Boundaries object).

• x_derivative (bool, optional) – Whether to add the x derivative (default is True).

• y_derivative (bool, optional) – Whether to add the y derivative (default is True).

mesh_info

Contains information about the mesh, such as the number of points and spacing.

Type:

MeshInfo

boundaries

Boundary conditions applied to the system.

Type:

PyFinitDiff.finite_difference_2D.boundaries.Boundary

finite_coefficient

Coefficients used for finite difference calculations.

Type:

FiniteCoefficients

_triplet

The triplet representation of the finite-difference matrix, initialized to None.

Type:

Triplet or None

n_x: int

n_y: int

dx: float = 1

dy: float = 1

derivative: int = 1

accuracy: int = 2

boundaries: Boundaries

x_derivative: bool = True

y_derivative: bool = True

property shape

Returns the shape of the mesh as a tuple.

Returns:

The shape of the system, represented by the number of points in the x and y directions.

Return type:

tuple

property triplet

Returns the triplet representation of the non-null values of the finite-difference configuration. Constructs the triplet if it has not been initialized.

Returns:

The Triplet instance containing the array and shape.

Return type:

Triplet

iterate_central_coefficient(coefficients: str, offset_multiplier: int)

Iterates through the given type of coefficients to provide the offset, value, and boundary type.

Parameters:

• coefficients (str) – The type of coefficients to iterate over.

• offset_multiplier (int) – Multiplier applied to the coefficient offset.

Yields:

tuple – A tuple containing the offset, value, and corresponding boundary type.

get_diagonal_set_full(offset_multiplier: int, delta: float) → DiagonalSet

Constructs and returns a complete set of diagonals, including central, forward, and backward coefficients.

Parameters:

• offset_multiplier (int) – Multiplier applied to the coefficient offset.

• delta (float) – Scaling factor for the coefficient values.

Returns:

A set of diagonals representing the finite-difference configuration, including adjustments for boundaries.

Return type:

DiagonalSet

construct_triplet() → None

Constructs the Triplet instance for the finite-difference configuration.