# PNS toy example

Example of horizontal analysis using PNS

## Contents

- 1. Set up
- 2. Make data
- 3. Fisher-Rao curve registration
- 4. PNS on the warping functions

## 1. Set up

To make this example work, please first download J. S. Marron's softwares AllMatlab7Combined.zip on http://www.unc.edu/depts/stat-or/miscellaneous/marron/Matlab7Software/ and unzip it. The softwares we need are 'General' and 'Smoothing'. Then, add 'General','Smoothing' and 'SRVF' to your search path. One way to do it is: Click on 'Set Path' -> 'Add with Subfolders', select 'General', 'Smoothing' and 'SRVF', then all these three and their subfolders will be added to the search path.

## 2. Make data

    d = 300;
    n = 21;
    sig = 0.1;
    m = 1;
    warpRange = 5;
    b = 3;
    randn('seed',0);

    gamO = zeros(d,n);
    a = linspace(-warpRange,warpRange,n+1); a = a(a~=0);
    t = linspace(-b,b,d);
    m=1;
    f = zeros(d,n);
    for i = 1:n;
        if a(i)~=0;
            gamO(:,i) = ((2*b)*(exp(a(i)*(t+b)/(2*b))-1)/(exp(a(i))-1)-b);
        else gamO(:,i) = t;
        end;
    end;
    t = (t+b)/(2*b);
    gamO = (gamO+b)/(2*b);
    for i = 1:n;
        f(:,i) = normrnd(m,sig) * betapdf(gamO(:,i),6,12)+ ... # 6,12
            normrnd(m,sig) * betapdf(gamO(:,i),12,6);
    end;

    mycolor = hsvcolmapQY(n); % rainbow color

    clf ;
    hold on;
    for i = 1:n
        plot(t, f(:,i),'color',mycolor(i,:))
    end
    hold off;

## 3. Fisher-Rao curve registration

    [fn,qn,q0,fmean,mqn,gam,psi,stats]=time_warping_oneplot(f,t',mycolor);

     lambda =   0.0

    Initializing...
    Computing Karcher mean of 21 functions in SRVF space...
    updating step: r=1
    updating step: r=2

## 4. PNS on the warping functions

    inputstruct = struct( 'gam',gam,...
        'meanf',fmean,...
        't',t,...
        'colmap',mycolor, ...
        'plotType',2,...
        'npns',3);

    curvepnsLXS(inputstruct);

    Message from PNSmain.m; dataset is on 298-sphere.
     .. found null space of dimension 278,to be trivially reduced.
     .. then narrow down to 20-sphere

      (c)  Qunqun Yu, Xiaosun Lu  2015