Variance reduction

Generate MAGIC weight windows and sample source voxels with alias tables.

The vr-tools crate provides two variance-reduction primitives used with MCNP mesh tallies: MAGIC weight-window generation and Walker/Vose alias-table source sampling.

MAGIC weight windows

Given a mesh tally, MAGIC produces lower weight-window bounds:

\text{ww}[ve][g] = \begin{cases} \text{null\_value} & \text{if rel\_error}[ve][g] > \text{tolerance} \\ \dfrac{\phi[ve][g]}{2 \, \max_{ve'} \phi[ve'][g]} & \text{otherwise} \end{cases}

You can run it on energy-integrated totals or per energy group. After generating bounds, the energy upper-bound structure is plotted as a step line.

Alias-table sampling

AliasTable implements Walker’s method with Vose’s construction. Given a non-negative PDF and two uniform random numbers in $[0, 1)$ , it returns a bin index in $O(1)$ time. MeshSourceSampler applies this to a mesh tally, supporting analog, uniform, and user-biased modes (the browser demo below exposes the analog and uniform modes).

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Variance reduction

MAGIC weight windows

Alias-table sampling

See also