pg_utils.pg_model.expansion.SystemMatrix

class pg_utils.pg_model.expansion.SystemMatrix(*args, **kwargs)

Bases: object

System matrix

This is a wrapper for a matrix of symbolic expression (inner products) whose numerical values will be evaluated numerically. This is one of the final outcomes of the symbolic computation.

Variables:

• _row_names (List[str]) – list of names corresponding to each row (block)

• _row_idx (dict) – dict that maps row name to their index

• _col_names (List[str]) – list of names corresponding to each col (block)

• _col_idx (dict) – dict that maps col names to their index

• _matrix (array-like) – a nested list representing the matrix

__init__(*args, **kwargs) → None

Initialization

There are currently two modes of initialization.

• If the first argument is a base.LabeledCollection instance, it will be interpreted as a collection of expressions; the second argument is then interpreted as the collection of coefficients. The signaure is SystemMatrix(expressions, coefficients). The SystemMatrix will be constructed by invoking the SystemMatrix.build_matrix method

• Otherwise, the arguments will be interpreted as the row names, column names and matrix of expressions, respectively. The signature is SystemMatrix(row_names, col_names, matrix)

Methods

__init__(*args, **kwargs)	Initialization
apply(fun[, inplace, metadata])	Apply function to elements iteratively.
block_sparsity()	Give the sparsity pattern of the symbolic matrix
build_matrix(exprs, coeffs)	Build system matrix from a collection of expressions
deserialize(matrix_obj)	Construct system matrix from object
load_json(fp)	Load from json file
load_serialized_element(element)
save_json(fp)	Save to json file
serialize()	Serialize object
serialize_element(element)	Serialize an element

apply(fun: Callable, inplace: bool = False, metadata: bool = False) → SystemMatrix

Apply function to elements iteratively.

Parameters:

• fun (Callable) – function that processes the elements

• inplace (bool) – whether the change is applied in situ

• metadata (bool) – whether the name of the element is passed to fun.

block_sparsity()

Give the sparsity pattern of the symbolic matrix

Returns:

sparsity matrix. If an element of the SystemMatrix is zero or None, then it will be marked as False in the output; otherwise it will be marked as True.

Return type:

numpy.ndarray

static build_matrix(exprs: LabeledCollection, coeffs: LabeledCollection) → List

Build system matrix from a collection of expressions

Parameters:

• exprs (base.LabeledCollection) – collection of expressions each element is a sympy.Expr instance

• coeffs (base.LabeledCollection) – collection of coefficients each element is a sympy.Symbol instance

Warning

Whatever term in exprs that does not contain a coefficient included in the coeffs collection will be discarded in the process!

static deserialize(matrix_obj: List[List]) → SystemMatrix

Construct system matrix from object

static load_json(fp: TextIO) → SystemMatrix

Load from json file

save_json(fp: TextIO) → None

Save to json file

serialize() → List[List]

Serialize object

static serialize_element(element: Union[InnerProduct1D, Expr]) → Any

Serialize an element