# AbsTransform¶

Absolute transformation with formula \(y = f(x) = abs(x)\), element-wise.

This non-injective transformation allows for transformations of scalar distributions with the absolute value function, which maps `(-inf, inf)` to `[0, inf)` .

• For `y` in `(0, inf)` , `AbsTransform.inverse(y)` returns the set invese `{x  in (-inf, inf) : |x| = y}` as a tuple, `-y, y` .

• For `y` equal `0` , `AbsTransform.inverse(0)` returns `0, 0`, which is not the set inverse (the set inverse is the singleton {0}), but “works” in conjunction with `TransformedDistribution` to produce a left semi-continuous pdf.

• For `y` in `(-inf, 0)` , `AbsTransform.inverse(y)` returns the wrong thing `-y, y`. This is done for efficiency.

Examples

```>>> import paddle

[1., 0., 1.])

[1.]))

>>> # The |dX/dY| is constant 1. So Log|dX/dY| == 0
0.))

>>> #Special case handling of 0.
[0.]))
0.))
```
forward ( x )

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

Useful for turning one random outcome into another.

Parameters

x (Tensos) – 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]