trapezoidal_bin_average: Trapezoidal bin-average of a per-bin weight

In mizer: Dynamic Multi-Species Size Spectrum Modelling

Trapezoidal bin-average of a per-bin weight

Description

Internal helper for the second-order summary integrals. A summary diagnostic \int N(w) K(w)\, dw is discretised on the finite-volume grid as \sum_j N_j \bar K_j \Delta w_j, where N_j is the cell average of the density over bin [w_j, w_{j+1}]. To be second order in the bin width the point weight K(w_j) must be replaced by the bin average

\bar K_j = \frac{1}{\Delta w_j}\int_{w_j}^{w_{j+1}} K(w)\,dw \approx \tfrac12\big(K(w_j) + K(w_{j+1})\big).

The trapezoidal average \tfrac12(K_j + K_{j+1}) is uniformly second order and exact whenever K is linear in w (e.g. the first moment K = w, for which it equals (w_{j+1}^2 - w_j^2)/(2\Delta w_j)).

Usage

trapezoidal_bin_average(K)

Arguments

K	A numeric vector of weights indexed over the size grid, or a numeric array whose last dimension runs over the size grid (e.g. a species-by-size matrix or a gear-by-species-by-size array).

Details

The weight K is supplied already evaluated on the size grid (a vector indexed over the bins, or a matrix with the size dimension running along the columns). The top bin has no right-hand neighbour on the grid, so its weight is left unaveraged (one-sided); the density there is negligible, so this does not affect the second-order accuracy of the totals.

This helper is shared with the reproduction integrals (issue #376), which also need the trapezoidal bin-average of a composite weight.

Value

An object of the same shape as K containing the trapezoidal bin-averaged weights.

mizer documentation built on Aug. 24, 2026, 9:08 a.m.