fliterPaths.md

Some contour integrals will have a negligible value compared to others. This function removes those contours from the sequence, so quadrature points are only allocated along non-negligable conoturs.

Here, information about each contour corresponds to a different quadrature ingredient stored in QuadIngredientArray. This is an array of structs, each corresponding to a steepest descent path, or straight line segment, which forms the path deformation of \(\gamma\).

Each component of QuadIngredientArray is measured at a few points to estimate its magnitude. Steepest descent paths are measured at their largest / first point, whereas straight line segments are measured at their endpoints and the stationary points of the balls that they intersect. A path is considered negligable if its estimated magnitude is sufficiently small compared with the largest estimated magnitude.

[QuadIngredientArrayOut, maxIntegrand] =...
            fliterPaths(QuadIngredientArray, phaseFunction, freq, thresh)

Inputs

• QuadIngredientArray : An array of structs, each corresponding to a steepest descent path, or straight line segment, which forms the path deformation of \(\gamma\),

• phaseFunction : The phase function \(g\) of the original integral.

• freq : The frequency \(\omega\) of the original integral.

• thresh : The threshold below which integrals are considered negligable.

Outputs

• QuadIngredientArrayOut : A subset of QuadIngredientArray, consisting only of non-negligable paths.

• maxIntegrand : The largest estimated value of all the steepest descent paths.