PathFinder.m

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PathFinder.m#

One of the two main functions. This function takes information about the oscillatory integral

\[ I = \int_\gamma f(z)\mathrm{e}^{\mathrm{i}\omega g(z)}\mathrm{d} z \]

and returns an approximation to \(I\). This is essentially a wrapper for the quadrature rule PathFinderQuad.m, which applies it to the integral with \(f\).

I = PathFinder(a, b, f, phaseIn, freq, nPts, varargin)

Inputs#

  • a and b are the endpoints of the integration contour \(\gamma\).

  • f : A functon handle representation of \(f(z)\). If left blank f=[], then PathFinder assumes \(f(z)=1\).

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

  • freq : The frequency parameter \(\omega\).

  • nPts : The number of quadrature points per contour.

  • varargin : This function takes many optional inputs, which can modify approximation parameters, and request plots. For more information, see Usage.

Outputs#

  • z : Nodes \(z_j\).

  • w : Weights \(w_j\).

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