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Per-axis tridiagonal operators on tensor-product grids โ the building block for 1-D, 2-D and 3-D finite-difference schemes.
A discretized diffusion operator splits into one tridiagonal operator
per spatial axis (plus an explicit mixed-derivative part). Each
AxisOperator stores per-node coefficient triples, so coefficients
may vary over the whole grid โ exactly what local vol (1-D) or Heston
(2-D in spot x variance) discretizations produce. The ADI time
steppers in adi consume these directly.
Structsยง
- Axis
Operator - A tridiagonal operator along one axis of a
TensorGrid, with per-node coefficients: rowiofA ureadssub[i] * u[i - stride] + diag[i] * u[i] + sup[i] * u[i + stride]. - Tensor
Grid - A tensor-product grid: node counts per axis, flattened row-major (the last axis is contiguous). Designed and tested for 1 to 3 dimensions.