Added remaining documentation

Author: AndrewGibbs

docs/guide/api/matlab/Dijkstra.md

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+# `Dijkstra.m`
+
+This code and associated function was written by Dimas Aryo. Full documentation can be found [here, on the Mathworks file exchange](https://www.mathworks.com/matlabcentral/fileexchange/36140-dijkstra-algorithm).
+
+PathFinder uses [Dijkstra's shortest path algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) to find the shortest path as part of [shortestInfinitePath.m](shortestInfinitePath.md).

docs/guide/api/matlab/PathFinder.md

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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](PathFinderQuad.md), which applies it to the integral with $f$.
+
+```matlab
+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](../../usage/index.md).
+
+## Outputs
+* `z` : Nodes $z_j$.
+* `w` : Weights $w_j$.

docs/guide/api/matlab/PathFinderQuad.md

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+# `PathFinderQuad.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 weights $w_j$ and nodes $z_j$ such that
+$$
+I \approx \sum_{j=1}^N f(z_j)w_j
+$$
+
+```matlab
+[z,w] = PathFinderQuad(a, b, phaseIn, freq, nPts, varargin)
+```
+
+## Inputs
+* `a` and `b` are the endpoints of the integration contour $\gamma$.
+* `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](../../usage/index.md).
+
+## Outputs
+* `z` : Nodes $z_j$.
+* `w` : Weights $w_j$.

docs/guide/api/matlab/addPaths.md

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+# `addPaths.m`
+
+This function should be run before PathFinder, and adds all necessary subdirectories to the Matlab search path.
+
+```matlab
+addPaths()
+```

docs/guide/api/matlab/compileAll.md

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+# `compileAll.m`
+
+This is a Matlab script which compiles all MEX functions required by PathFinder. For more information, see [Installation](../../setup/index.md).

docs/guide/api/matlab/files.yaml

@@ -4,3 +4,8 @@ files:
   - getRStar.md
   - getSteepestExitsOnBall.md
   - planBisection.md
+  - shortestInfinitePath.md
+  - PathFinder.md
+  - PathFinderQuad.md
+  - compileAll.md
+  - addPaths.md

docs/guide/api/matlab/shortestInfinitePath.md

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+# `shortestInfinitePath.m`
+
+Chooses a suitable sequence of steepest descent and straight line contours, which correspond to a deformation of the original integration contour from $a$ to $b$. This is done by representing the key topological properties of known quantities as a graph, and then solving a shortest
+ path problem.
+
+Specifically, for this graph:
+balls, exits, entrances, endpoints and valleys are interpreted as nodes. Steepest descent contours (finite or infinite), and straight line contours connecting points inside balls, are represented as edges.
+ The approach in this code is to create multiple adjacency matrices corresponding to the connections between different types of points (or
+ valleys). These adjacency matrices are then combined, and we keep track
+ of the different meanings of the different indices. This adjacency matrix
+ is used to solve the shortest path problem.
+
+ For more information, see {cite:p}`PFpaper`.
+
+```matlab
+[Q, graphData] = shortestInfinitePath(a, b, contours, balls, valleys, params)
+```
+
+## Inputs
+
+* `a` and `b` : The enepoindts of the original contour.
+* `contours` : An array of type [ContourSD.m](ContourSD.md)
+* `balls` : An array of type [Ball.m](Ball.md)
+* `valleys` : An array of valleys.
+* `params` : A struct of approximation parameters.
+
+## Outputs
+
+* `Q` : Struct of quadrature ingredients, which contains all of the information about the chosen path deformation. From this, quadrature points are subsequently constructed.
+* `graphData` : Simplified struct, used for plotting,.