mm.physics.gaussian_integrals.real_gaussian_integral

mrmustard.physics.gaussian_integrals.real_gaussian_integral(Abc, idx)

Computes the Gaussian integral of the exponential of a real quadratic form. The integral is defined as (note that in general we integrate over a subset of m dimensions):

where

\(F(x) = \textrm{exp}(0.5 x^T A x + b^T x)\)

Here, x is an n-dim real vector, A is an n x n real matrix, b is an n-dim real vector, c is a real scalar. The integral indices are specified by idx.

Parameters:

• Abc (tuple) – the (A,b,c) triple

• idx (tuple[int, ...]) – the tuple of indices of the x variables

Returns:

The (A,b,c) triple of the result of the integral.

code/api/mrmustard.physics.gaussian_integrals.real_gaussian_integral

 

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