# StackTransform¶

class paddle.distribution. StackTransform ( transforms, axis=0 ) [source]

`StackTransform` applies a sequence of transformations along the specific axis.

Parameters
• transforms (Sequence[Transform]) – The sequence of transformations.

• axis (int, optional) – The axis along which will be transformed. default value is 0.

Examples

```>>> import paddle

...     1
>>> )
>>> print(t.forward(x))
[[2.71828175 , 1.         ],
[7.38905621 , 4.         ],
[20.08553696, 9.         ]])

>>> print(t.inverse(t.forward(x)))
[[1., 1.],
[2., 2.],
[3., 3.]])

>>> print(t.forward_log_det_jacobian(x))
[[1.        , 0.69314718],
[2.        , 1.38629436],
[3.        , 1.79175949]])
```
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]