beyondNoReturn.m

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beyondNoReturn.m#

This is the Matlab version of a routine which is typically run as compiled C code. The idea is based on the idea of the region of no return, which is outlined in section 3.2 of [Gibbs et al., 2024]. This subroutine identifies when a steepest descent contour has reached such a region in the complex plane, after which it can never leave.

[value, vIndex] = beyondNoReturn(h,valleys,phaseCoeffs,rStar)

The no return regions can be seen around the edges of the following image: Example

Inputs#

  • h: The steepest point that has been traced along the steepest descent path

  • valleys: Valleys of the polynomial phase function \(g\)

  • phaseCoeffs: Coefficients of the polynomial phase function \(g\).

  • rStar: A constant dependent on \(g\), stored to save repeated computations. This is the solution of a polynomial equation, details are given in section 2.4 of [Gibbs et al., 2024].

Outputs#

  • value: true if inside the region of no return, false otherwise.

  • vIndex: The index of the limiting valley of the particular segment of the no return region. This will be blank if value = false, i.e. not in the region of no return.

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