Tensor

symbolica.community.spenso Class

Tensor()

A tensor class that can be either dense or sparse with flexible data types.

The tensor can store data as floats, complex numbers, or symbolic expressions. Tensors have an associated structure that defines their shape and index properties.

Examples

from symbolica.community.spenso import Tensor, TensorIndices, Representation
structure = TensorIndices(Representation.euc(4)(1))
data = [1.0, 2.0, 3.0, 4.0]
tensor = Tensor.dense(structure, data)
sparse_tensor = Tensor.sparse(structure, float)

Member details

`structure`

Method

structure() -> TensorIndices

No description is available for this member.

`sparse`

Static method

sparse(structure: TensorIndices | list[Slot], type_info: type) -> Tensor

Create a new sparse empty tensor with the given structure and data type.

Returns

Tensor

A new sparse tensor with all elements initially zero

Examples

from symbolica.community.spenso import Tensor, TensorIndices, Representation as R
structure = TensorIndices(R.euc(3)(1), R.euc(3)(2))
sparse_float = Tensor.sparse(structure, float)
sparse_sym = Tensor.sparse(structure, symbolica.Expression)

Parameters

Name	Type	Default	Description
`structure`	`TensorIndices \| list[Slot]`	`—`	The tensor structure defining shape and index properties
`type_info`	`type`	`—`	The data type - either `float` or `Expression` class

`dense`

Static method

dense(structure: TensorIndices | list[Slot], data: Sequence[Expression] | Sequence[float] | Sequence[complex]) -> Tensor

Create a new dense tensor with the given structure and data.

Returns

Tensor

A new dense tensor with the specified data

Examples

from symbolica import S
from symbolica.community.spenso import Tensor, TensorIndices, Representation as R
structure = TensorIndices(R.euc(2)(1), R.euc(2)(2))
data = [1.0, 2.0, 3.0, 4.0]
tensor = Tensor.dense(structure, data)
x, y = S("x", "y")
sym_data = [x, y, x * y, x + y]
sym_tensor = Tensor.dense(structure, sym_data)

Parameters

Name	Type	Default	Description
`structure`	`TensorIndices \| list[Slot]`	`—`	The tensor structure defining shape and index properties
`data`	`Sequence[Expression] \| Sequence[float] \| Sequence[complex]`	`—`	The tensor data in row-major order

`one`

Static method

one() -> Tensor

Create a scalar tensor with value 1.0.

Returns

Tensor

A scalar tensor containing the value 1.0

Examples

from symbolica.community.spenso import Tensor
one = Tensor.one()

`zero`

Static method

zero() -> Tensor

Create a scalar tensor with value 0.0.

Returns

Tensor

A scalar tensor containing the value 0.0

Examples

from symbolica.community.spenso import Tensor
zero = Tensor.zero()

`to_dense`

Method

to_dense() -> None

Convert this tensor to dense storage format.

Converts sparse tensors to dense format in-place. Dense tensors are unchanged. This allocates memory for all tensor elements.

Examples

from symbolica.community.spenso import Tensor, TensorIndices, Representation as R
structure = TensorIndices(R.euc(4)(2))
tensor = Tensor.sparse(structure, float)
tensor[0] = 1.0
tensor.to_dense()

`to_sparse`

Method

to_sparse() -> None

Convert this tensor to sparse storage format.

Converts dense tensors to sparse format in-place, only storing non-zero elements. This can save memory for tensors with many zero elements.

Examples

from symbolica.community.spenso import Tensor, TensorIndices, Representation as R
structure = TensorIndices(R.euc(2)(2), R.euc(2)(1))
data = [1.0, 0.0, 0.0, 2.0]
tensor = Tensor.dense(structure, data)
tensor.to_sparse()

`repr`

Method

__repr__() -> str

No description is available for this member.

`str`

Method

__str__() -> str

No description is available for this member.

`len`

Method

__len__() -> int

No description is available for this member.

`getitem`

Method

Overloads

Overload 1 #

__getitem__(item: slice | int | list[int]) -> Any

No additional description is available for this overload.

Parameters

Name	Type	Default	Description
`item`	`slice \| int \| list[int]`	`—`	—

Overload 2 #

__getitem__(item: slice) -> list[Expression | complex | float]

Get tensor elements at the specified range of indices.

Returns

list of float, complex, or Expression

The tensor elements at the specified range

Parameters

Name	Type	Default	Description
`item`	`slice`	`—`	Slice object defining the range of indices

Overload 3 #

__getitem__(item: Sequence[int] | int) -> Expression | complex | float

Get tensor element at the specified index or indices.

Returns

float, complex, or Expression

The tensor element at the specified index

Parameters

Name	Type	Default	Description
`item`	`Sequence[int] \| int`	`—`	Index specification (int for flat index, list of int for coordinates)

`setitem`

Method

Overloads

Overload 1 #

__setitem__(item: Any, value: Any) -> None

Set tensor element(s) at the specified index or indices.

Examples

from symbolica.community.spenso import Tensor, TensorIndices, Representation as R
structure = TensorIndices(R.euc(2)(2), R.euc(2)(1))
tensor = Tensor.sparse(structure, float)
tensor[0] = 4.0
tensor[1, 1] = 1.0

Parameters

Name	Type	Default	Description
`item`	`Any`	`—`	Index specification (int for flat index, list of int for coordinates)
`value`	`Any`	`—`	The value to set

Overload 2 #

__setitem__(item: int | Sequence[int], value: Expression | complex | float) -> None

Set tensor element at the specified index.

Examples

from symbolica.community.spenso import Tensor, TensorIndices, Representation
rep = Representation.euc(2)
structure = TensorIndices(rep(1), rep(2))
tensor = Tensor.sparse(structure, float)
tensor[0] = 1.0
tensor[1, 1] = 2.0

Parameters

Name	Type	Default	Description
`item`	`int \| Sequence[int]`	`—`	Index specification (int for flat index, list of int for coordinates)
`value`	`Expression \| complex \| float`	`—`	The value to set

`evaluator`

Method

evaluator(constants: Mapping[Expression, Expression], funs: Mapping[tuple[Expression, str, Sequence[Expression]], Expression], params: Sequence[Expression], iterations: int = 100, n_cores: int = 4, verbose: bool = False) -> TensorEvaluator

Create an optimized evaluator for symbolic tensor expressions.

Compiles the symbolic expressions in this tensor into an optimized evaluation tree that can efficiently compute numerical values for different parameter inputs.

Returns

TensorEvaluator

An optimized evaluator for efficient numerical evaluation

Examples

from symbolica import S
from symbolica.community.spenso import Tensor, TensorIndices, Representation as R
x, y = S("x", "y")
structure = TensorIndices(R.euc(2)(1))
tensor = Tensor.dense(structure, [x * y, x + y])
evaluator = tensor.evaluator(constants={}, funs={}, params=[x, y], iterations=50)
results = evaluator.evaluate_complex([[1.0, 2.0], [3.0, 4.0]])

Parameters

Name	Type	Default	Description
`constants`	`Mapping[Expression, Expression]`	`—`	Dict mapping symbolic expressions to their constant numerical values
`funs`	`Mapping[tuple[Expression, str, Sequence[Expression]], Expression]`	`—`	Dict mapping function signatures to their symbolic definitions
`params`	`Sequence[Expression]`	`—`	List of symbolic parameters that will be varied during evaluation
`iterations`	`int`	`100`	Number of optimization iterations for Horner scheme (default: 100)
`n_cores`	`int`	`4`	Number of CPU cores to use for optimization (default: 4)
`verbose`	`bool`	`False`	Whether to print optimization progress (default: False)

`scalar`

Method

scalar() -> Expression

Extract the scalar value from a rank-0 (scalar) tensor.

Returns

Expression

The scalar expression contained in this tensor

Raises

RuntimeError: If the tensor is not a scalar

Examples

from symbolica.community.spenso import Tensor
scalar_tensor = Tensor.one()
value = scalar_tensor.scalar()

`iter`

Method

__iter__() -> Iterator[Any]

Iterator

View generated signature source: docs/api/python/spynso3.pyi:594