# StickBreakingTransform¶

Convert an unconstrained vector to the simplex with one additional dimension by the stick-breaking construction.

Examples

```import paddle

print(t.forward(x))
#        [0.47536686, 0.41287899, 0.10645414, 0.00530004])
print(t.inverse(t.forward(x)))
#        [0.99999988, 2.        , 2.99999881])
print(t.forward_log_det_jacobian(x))
#        [-9.10835075])
```
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]