# SigmoidTransform¶

Sigmoid transformation with mapping $$y = \frac{1}{1 + \exp(-x)}$$ and $$x = \text{logit}(y)$$.

Examples

>>> import paddle

>>> print(t.forward(x))
[[0.73105860, 0.73105860, 0.73105860],
[0.73105860, 0.73105860, 0.73105860]])
>>> print(t.inverse(t.forward(x)))
[[1.00000012, 1.00000012, 1.00000012],
[1.00000012, 1.00000012, 1.00000012]])
>>> print(t.forward_log_det_jacobian(x))
[[-1.62652326, -1.62652326, -1.62652326],
[-1.62652326, -1.62652326, -1.62652326]])

forward ( x )

Forward transformation with mapping $$y = f(x)$$.

Useful for turning one random outcome into another.

Parameters

x (Tensor) – Input parameter, generally is a sample generated from Distribution.

Returns

Outcome of forward transformation.

Return type

Tensor

forward_log_det_jacobian ( x )

The log of the absolute value of the determinant of the matrix of all first-order partial derivatives of the inverse function.

Parameters

x (Tensor) – Input tensor, generally is a sample generated from Distribution

Returns

The log of the absolute value of Jacobian determinant.

Return type

Tensor

forward_shape ( shape )

Infer the shape of forward transformation.

Parameters

shape (Sequence[int]) – The input shape.

Returns

The output shape.

Return type

Sequence[int]

inverse ( y )

Inverse transformation $$x = f^{-1}(y)$$. It’s useful for “reversing” a transformation to compute one probability in terms of another.

Parameters

y (Tensor) – Input parameter for inverse transformation.

Returns

Outcome of inverse transform.

Return type

Tensor

inverse_log_det_jacobian ( y )

Compute $$log|det J_{f^{-1}}(y)|$$. Note that forward_log_det_jacobian is the negative of this function, evaluated at $$f^{-1}(y)$$.

Parameters

y (Tensor) – The input to the inverse Jacobian determinant evaluation.

Returns

The value of $$log|det J_{f^{-1}}(y)|$$.

Return type

Tensor

inverse_shape ( shape )

Infer the shape of inverse transformation.

Parameters

shape (Sequence[int]) – The input shape of inverse transformation.

Returns

The output shape of inverse transformation.

Return type

Sequence[int]