Signature

Derivative table representation utilities

ndmap.signature.apply(table: list, function: Callable) → None

Apply function to all bottom elements

Parameters:

• table (Table) – input derivative table representation

• function (Callable) – function to apply

Return type:

None

Examples

>>> import torch
>>> from ndmap.derivative import derivative
>>> def fn(x, y):
...    x1, x2 = x
...    y1, y2 = y
...    return (x1 + x2 + x1**2 + x1*x2 + x2**2)*(1 + y1 + y2)
>>> x = torch.tensor([0.0, 0.0])
>>> y = torch.zeros_like(x)
>>> t = derivative((2, 1), fn, x, y)
>>> apply(t, torch.norm)
>>> t
[[tensor(0.), tensor(0.)],
 [tensor(1.4142), tensor(2.)],
 [tensor(3.1623), tensor(4.4721)]]

ndmap.signature.chop(table: list, *, threshold: float = 1e-09, value: float = 0.0, replace: bool = False) → None

Chop tensor elements in a table below a given threshold

Parameters:

• table (Table) – input derivative table representation

• threshold (float, default=1.0E-9) – threshold value

• value (float, default=0.0) – set value

• replace (bool, default=False) – flag to replace zero tensors

Return type:

None

Examples

>>> import torch
>>> from ndmap.derivative import derivative
>>> def fn(x, y):
...    x1, x2 = x
...    y1, y2 = y
...    return (x1 + x2 + x1**2 + x1*x2 + x2**2)*(1 + y1 + y2)
>>> x = torch.tensor([0.0, 0.0])
>>> y = torch.zeros_like(x)
>>> t = derivative((0, 1), fn, x, y)
>>> apply(t, lambda x: x + 1.0E-10)
>>> chop(t)
>>> t
[[tensor(0.), tensor([0., 0.])]]

ndmap.signature.get(table: list, index: tuple[int, ...]) → torch.Tensor | list

Get derivative table element at a given (bottom) element signature

Note, index can correspond to a bottom element or a subtable

Parameters:

• table (Table) – input derivative table representation

• index (tuple[int, ...]) – element signature

Returns:

element value

Return type:

Union[Tensor, Table]

Examples

>>> import torch
>>> from ndmap.derivative import derivative
>>> def fn(x, y):
...    x1, x2 = x
...    y1, y2 = y
...    return (x1 + x2 + x1**2 + x1*x2 + x2**2)*(1 + y1 + y2)
>>> x = torch.tensor([0.0, 0.0])
>>> y = torch.zeros_like(x)
>>> t = derivative((2, 1), fn, x, y)
>>> get(t, (1, 1))
tensor([[1., 1.],
    [1., 1.]])

ndmap.signature.set(table: list, index: tuple[int, ...], value: torch.Tensor | list) → None

Set derivative table element at a given (bottom) element signature

Note, index can correspond to a bottom element or a subtable

Parameters:

• table (Table) – input derivative table representation

• index (tuple[int, ...]) – element signature

• value (Union[Tensor, Table]) – element value

Return type:

None

Examples

>>> import torch
>>> from ndmap.derivative import derivative
>>> def fn(x, y):
...    x1, x2 = x
...    y1, y2 = y
...    return (x1 + x2 + x1**2 + x1*x2 + x2**2)*(1 + y1 + y2)
>>> x = torch.tensor([0.0, 0.0])
>>> y = torch.zeros_like(x)
>>> t = derivative((2, 1), fn, x, y)
>>> set(t, (1, 1), 1 + get(t, (1, 1)))
>>> get(t, (1, 1))
tensor([[2., 2.],
        [2., 2.]])

ndmap.signature.signature(index: list[int], table: torch.Tensor, *, factor: bool = False)

(auxiliary)

ndmap.signature.to(table: list, *args: tuple, **kwargs: dict) → None

Perform dtype and/or device conversion for all bottom table element elements (tensors)

Parameters:

• *args (tuple) – passed to torch.to function

• **kwargs (dict) – passed to torch.to function

Return type:

None

Examples

>>> import torch
>>> from ndmap.derivative import derivative
>>> x = torch.tensor(0.0)
>>> y = torch.tensor(0.0)
>>> t = derivative((1, 1), lambda x, y: x + y, x, y)
>>> to(t, torch.float64)
>>> t
[[tensor(0., dtype=torch.float64), tensor(1., dtype=torch.float64)],
[tensor(1., dtype=torch.float64), tensor(0., dtype=torch.float64)]]
    [[tensor(0.), tensor([0., 0.])]]