CorrCholeskyTransform

class tensorplay.distributions.CorrCholeskyTransform(cache_size: int = 0)[source]

Transforms an unconstrained real vector $x$ with length $D*(D-1)/2$ into the Cholesky factor of a D-dimension correlation matrix. This Cholesky factor is a lower triangular matrix with positive diagonals and unit Euclidean norm for each row. The transform is processed as follows:

1. First we convert x into a lower triangular matrix in row order.

2. For each row $X_i$ of the lower triangular part, we apply a signed version of class StickBreakingTransform to transform $X_i$ into a unit Euclidean length vector using the following steps: - Scales into the interval $(-1, 1)$ domain: $r_i = \tanh(X_i)$. - Transforms into an unsigned domain: $z_i = r_i^2$. - Applies $s_i = StickBreakingTransform(z_i)$. - Transforms back into signed domain: $y_i = sign(r_i) * \sqrt{s_i}$.

property inv: Transform

Returns the inverse Transform of this transform. This should satisfy t.inv.inv is t.

property sign: int

Returns the sign of the determinant of the Jacobian, if applicable. In general this only makes sense for bijective transforms.