$ \DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}} $

List of helper functions

create a debug functional for algorithms
1
% createDebugFct(M,F,modIter) - creates a debug functional for algorithms

For all algorithms, i.e. CPP, gradient, and subgradient can all call a debug function. This function returns a handle @8x,xold,iter) to display the function value of the current iterate, the current iterate as well as the last maximal change of and .

Conditional display
1
% dispIf(condition,str) display string if condition is true.

Computes the remainder of a value in , which is mostly used for phase data, i.e. the manifold and .

export points, curves and tangents on the sphere \(\mathbb S^2\) to asymptote
1
% fileStr = exportSphereSignals2Asymptote(pts,curves,xi,colors)

Export arrays (sorted in cell arrays) of points, curves, and tangent vectors to Asymptote, where they are plotted on a sphere.

plot data on the Sphere $\mathbb S^2$
1
% plotS2 - plot a signal on the sphere

Plot a set of points on the sphere .

step size rule based on the Armijo rule
1
% stepSizeAsrmijo(M,F,x,descentDir) compute the step size by Armijo's rule

Determines a step size such that

where is a descent direction, e.g. . where the search is performed by , and is a constant.

more
Create a maxiteration or minimal change stopping criterion
1
% stopCritMaxIterEpsilonCreator(M,maxIter,epsilon) a maxIt minEps criterion

Given a manifold , a maximal number of iterates and a minimal change , this small helper returns a function handle suitable for -valued data of any dimension that returns true when in the current iterate

This criterion is evaluated after running the th iteration and hence stops after iterations.

Compute the remainder in $\bigl[-\tfrac{T}{2},\frac{T}{2}\bigr)$
1
% symMod(v,T) compute the modulus with respect to [-T/2, T/2)

Computes the remainder of a value in , which is mostly used for phase data, i.e. the manifold and .