mm.math.hermite_renormalized_binomial

math.hermite_renormalized_binomial(B, C, shape, max_l2, global_cutoff)

Renormalized multidimensional Hermite polynomial given by the “exponential” Taylor series of \(exp(C + Bx + 1/2*Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\). The computation fills a tensor of given shape up to a given L2 norm or global cutoff, whichever applies first. The max_l2 value, if not provided, is set to the default value of the AUTOCUTOFF_PROBABILITY setting.

Parameters:

• A (ndarray) – The A matrix.

• B (ndarray) – The B vector.

• C (ndarray) – The C scalar.

• shape (Tuple[int]) – The shape of the final tensor (local cutoffs).

• max_l2 (float) – The maximum squared L2 norm of the tensor.

• global_cutoff (optional int) – The global cutoff.

Return type:

ndarray

Returns:

The renormalized Hermite polynomial of given shape.

code/api/mrmustard.math.hermite_renormalized_binomial

 

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