cyjax.ml.cholesky_decode

cyjax.ml.cholesky_decode(diag, upper)

Construct hermitian matrix from Cholesky decomposition.

From diag and upper, first a matrix \(M\) is initialized as

\[\begin{split}M = \begin{bmatrix} \mathrm{diag}_1 & & \text{upper}_{ij}\\ & \ddots & \\ 0 & & \mathrm{diag}_n \end{bmatrix}\end{split}\]

The output of this function is then \(M M^\dagger\), which is Hermitian and positive-definite. Indexing of the 1d diag array with respect to the upper triangular is done as in np.triu_indices() (i.e. row-major).

Parameters:

• diag (Union[Array, ndarray, bool_, number]) – Real 1d-array of diagonal entries.

• upper (Union[Array, ndarray, bool_, number]) – Complex 1d-array of upper diagonal entries.

Returns:

Hermitian, positive-definite matrix constructed by the Cholesky decomposition.