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plotting.m
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plotting.m
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% PLOTTING plotting script for interp5DOF paper
%split apply & find groups
% fname = 'gitID-76fca8c_uuID-f51500cd_paper-data.mat';
% fname = 'gitID-396aaa2_uuID-6816f860_paper-data2.mat';
% fname = 'gitID-f585733_uuID-edf2fcc7_paper-data2.mat';
% fname = 'gitID-c67a123_uuID-18d21f26_set4.mat';
% fname = 'gitID-014bf70_uuID-3ed9cba0_paper-data3.mat';
% fname = 'gitID-6ede824_uuID-1cf78415_paper-data5.mat';
% fname = 'gitID-0055bee_uuID-475a2dfd_paper-data6.mat'; %bug in get_five.m with sphere sampling
% fname = 'gitID-dd6fa64_uuID-17bbadb9_paper-data9.mat'; %all runs used same rng unfortunately
fname = 'gitID-9ebfa46_uuID-34192072_paper-data10.mat';
files = dir(fullfile('**','data'));
folders = {files.folder};
ids = find(cellfun(@(x) contains(x,fullfile('interp','data')),folders));
datafolder = files(ids(1)).folder;
%assert(contains(datafolder,'interp'),'interp should be in datafolder path');
datapath = fullfile(datafolder,fname);
%%
if exist(datapath,'file') ~= 2
warning(['downloading data file because could not find at ' datapath ', May take a few minutes.'])
websave(datapath,'https://ndownloader.figshare.com/files/27540842')
end
%files = dir(fullfile('**',fname));
%fpath = fullfile(files(1).folder,files(1).name);
%load(fpath);
load(datapath)
disp('file loaded')
% slurmQ = 0;
%%
%saving
files = dir(fullfile('**','interp5DOF-paper','figures'));
figfolder = files(1).folder;
files = dir(fullfile('**','interp5DOF-paper','tables'));
tblfolder = files(1).folder;
addpath(genpath('.'))
setlatex()
%% parity plot
methodlist = {'pbary','gpr','idw','nn'};
% datatypelist = {'brk','kim'};
datatypelist = {'brk'};
sgtitleQ = false;
for datatype = datatypelist
for ninputpts = [388 10000 50000]
%extract parity and IDs
tbl3 = mdlparstbl(...
ismember(mdlparstbl.method,methodlist) & ...
ismember(mdlparstbl.datatype,datatype) & ...
mdlparstbl.ninputpts==ninputpts,:);
[G3,ID3] = findgroups(tbl3.method);
tlisttmp = cell(size(ID3));
for i = 1:size(ID3,1)
IDchar = char(ID3(i));
tlisttmp{i} = regexprep(IDchar,{'pbary','gpr','idw','nn'},{'Barycentric','GPR','IDW','NN'});
end
titlelist = categorical(tlisttmp);
parity3 = splitapply(@(x){x(1)},tbl3.parity,G3);
if strcmp(datatype,'brk') && (ninputpts == 50000)
cbnds = [1 500];
else
cbnds = [];
end
%plotting
multiparity(parity3,ID3,'hex','cbnds',cbnds,'titlelist',titlelist)
%extra
if sgtitleQ
sgtitle(['ninputpts = ' int2str(ninputpts)])
end
savefigpng(figfolder,[char(datatype) 'parity' int2str(ninputpts)]);
end
end
%% kernel scale for GPR
tbltmp = mdlparstbl(...
ismember(mdlparstbl.method,'gpr') & ...
ismember(mdlparstbl.datatype,'brk') & ...
mdlparstbl.ninputpts==50000,:);
kpars = tbltmp.KernelParameters;
kpars2 = [kpars{:}];
avgKernelScale = mean(2*rad2deg(kpars2(1,:)))
%% errors
methodlist = {'pbary','gpr','idw','nn','avg'};
xytypelbls = ['Barycentric',upper(methodlist(2:4)),'Average'];
% datatypelist = {'brk','kim'};
datatypelist = {'brk'};
ytypes = {'rmse','mae'};
ytypelbls = upper(ytypes);
for datatype = datatypelist
tbltmp = mdlparstbl(mdlparstbl.datatype==datatype,:);
multixyplots(tbltmp,methodlist,'ninputpts',ytypes,1,2,'ymin',0,...
'lgdloc','southwest','ytypelbls',ytypelbls,'xytypelbls',xytypelbls)
fig = gcf;
t1 = nexttile(1);
t1.Legend.Position = [0.299964268608805 0.516990889931764 0.163876007802576 0.229411769754747];
t2 = nexttile(2);
t2.Legend.Position = [0.774250188549525 0.509817862551335 0.163876007802575 0.229411769754747];
% fig.Children.Children(3).Position = [0.780569390710456 0.495824223265097 0.163876007802576 0.229411769754747];
%saving
savefigpng(figfolder,[char(datatype) 'error'])
end
%% timing
methodlist = {{'pbary','gpr','idw','nn'},{'pbary','gpr','idw','nn'}};
xytypelbls = {{'Barycentric','GPR','IDW','NN'},{'Barycentric','GPR','IDW','NN'}};
% methodlist = {{'pbary','gpr'},{'gpr','idw','nn'}};
% xytypelbls = {{'Barycentric','GPR'},{'GPR','IDW','NN'}};
tbl3 = mdlparstbl(mdlparstbl.ncores==12,:);
%{
whether to multiple pbary by # cores since uses parfor (although rest
might use multiple cores via vectorization..)?
%}
% ids = ismember(tbl3.method,'pbary');
% tbl3(ids,'runtime') = tbl3(ids,'runtime').*tbl3(ids,'cores');
[G3,ID3] = findgroups(tbl3.method);
multixyplots(mdlparstbl,methodlist,'ninputpts',{'runtime'},1,2,'XScale','linear',...
'YScale','linear','yunits','s','lgdloc','southeast','xytypelbls',xytypelbls)
ax = gca;
% ax.YLim = [0 30];
ax.XScale = 'log';
ax.YScale = 'log';
% ax.YLim(2) = 1000;
ax.Legend.Location = 'southeast';
% stackedplot
%saving
savefigpng(figfolder,'runtime');
%% Runtime Table
% the data is too varied and a log-log plot is too misleading. Going with table instead.
methodlist = {'pbary','gpr','idw','nn'};
titlelist = {'Barycentric','GPR','IDW','NN'};
% tbltmp = tbl3(any(tbl3.method == methodlist,2),:);
[tmu,tsigma] = deal(zeros(8,length(methodlist)));
tstr = cell(8,length(methodlist));
files2 = dir(fullfile('**','interp5DOF-paper'));
folder2 = files2(1).folder;
for i = 1:length(methodlist)
%unpack
method = methodlist{i};
%extract
tbltmp = tbl3(tbl3.method == method,:);
[Gtmp,IDtmp] = findgroups(tbltmp.ninputpts);
%extract
tmu(:,i) = round(splitapply(@mean,tbltmp.runtime,Gtmp),4);
tsigma(:,i) = round(splitapply(@std,tbltmp.runtime,Gtmp),4);
%convert
tmustr = arrayfun(@(x)num2str(x,'%.4g'),tmu(:,i),'UniformOutput',false);
tsigmastr = arrayfun(@(x)num2str(x,'%.4g'),tsigma(:,i),'UniformOutput',false);
%prep
tstr(:,i) = strcat('$',tmustr,{' '},'\pm',{' '},tsigmastr,'$');
timeinfo = [titlelist; tstr];
setsizeinfo = ['\gls{vfzo} Set Size';arrayfun(@(x)['\num{' int2str(x) '}'],IDtmp,'UniformOutput',false)];
%concatenate
catinfo = [setsizeinfo,timeinfo];
%package
T = table(catinfo);
disp(T)
%write
writetable(T,fullfile(folder2,'runtime.xlsx'),'WriteVariableNames',false)
end
%% NN Mean and Standard Deviation vs. VFZO set size
tbltmp = mdlparstbl(mdlparstbl.datatype == 'brk',:);
[G,ID] = findgroups(tbltmp.ninputpts);
nnmu = splitapply(@mean,tbltmp.nnmu,G);
nnsigma = splitapply(@std,tbltmp.nnmu,G);
paperfigure();
% errorbar(ID,nnmu,nnsigma);
yyaxis left
hErr = errorbar(ID,nnmu,nnsigma);
% hold on
% x = 388:100:50000;
% f = 2.5025e-5*x-1.27396*log(x)+15.4499;
% plot(x,f,'k-');
set(gca,'XScale','log','ycolor','k');
% xlabel('VFZO Set Size','Interpreter','latex')
xlabel('Cardinality of VFZO Point Set','Interpreter','latex')
% ylabel('VFZO $\omega_{\mathrm{NN}}$ ($^{\circ}$)','Interpreter','latex')
ylabel('NN Distance ($d_\Omega\ \left[^{\circ}\right]$)','Interpreter','latex')
ylm = ylim;
yyaxis right
hCorr = plot(ID,nnmu./7.5);
hold on
xlm = xlim;
% plot(xlm,0.25*ones(size(xlm)),'k--','color',0.8*ones(1,3))
% plot(xlm,0.5*ones(size(xlm)),'k--','color',0.8*ones(1,3))
% plot(xlm,0.75*ones(size(xlm)),'k--','color',0.8*ones(1,3))
% plot(xlm,ones(size(xlm)),'k--','color',0.8*ones(1,3))
% plot(xlm,1.25*ones(size(xlm)),'k--','color',0.8*ones(1,3))
% plot(xlm,1.5*ones(size(xlm)),'k--','color',0.8*ones(1,3))
ylabel('NN Distance ($l$)','Interpreter','latex')
ylim(ylm/7.5);
set(gca,'ycolor','k')
set(hCorr,'linestyle','none')
% legend('Data','$ax-\mathrm{log}(x)b+c$','Interpreter','latex')
savefigpng(figfolder,'nndist-vs-setsize-final');
% interp1(nnmu,ID,7.5)
%%
clear mdlparstbl
%% dist-parity
seed = 10; %#ok<*UNRCH>
rng(seed);
npts = 10000;
[five,q,nA] = get_five(npts);
o = five2oct(q,nA);
pts = get_octpairs(o);
pts = normr(pts);
pd1 = pdist(pts).';
pd2 = real(pdist(pts,@get_omega).');
pd3 = real(pdist(pts,@get_alen).');
save(fullfile(figfolder,'dist-parity.mat'),'pd1','pd2','pd3')
%% arclength vs. euclidean distance parity
% addpathdir({'get_five.m','cu2qu.m','GBfive2oct.m','gmat2q.m','distance-parity.mat'})
addpathdir({'dist-parity.mat','paperfigure.m'})
fname = 'dist-parity';
load([fname,'.mat'],'pd1','pd2','pd3')
paperfigure()
parityplot(pd1,pd3,'scatter','cscale','linear','xname','Euclidean Distance',...
'yname','Arc Length','xunits','','yunits','rad','sz',20,'mkr','.','c',[0.6350, 0.0780, 0.1840])
%saving
% savefigpng(folder,fname);
fpath = fullfile(figfolder,fname);
print(fpath,'-dpng','-r300') %saving .fig takes too long, file is pretty big
clear pd1 pd2 pd3
% load('olm_pairwise_oct.mat','oct_new')
% t = num2cell(oct_new,3);
% t = cellfun(@(x) squeeze(x).',t.','UniformOutput',false);
% oAB = vertcat(t{:});
% oA = get_octpairs(oAB(:,1:8));
% oB = get_octpairs(oAB(:,9:16));
%% load data for octonion ensemble and fixed test
% addpathdir({'olm_octonion_list.txt','olm_pairwise_distances_cubic.mat'})
A = importdata('olm_octonion_list.txt');
olmoct = A.data;
olmoct = [qinv(olmoct(:,1:4)),qinv(olmoct(:,5:8))];
rng(5)
nptslist = [1 2 10 20];
npts = max(nptslist);
numnpts = length(nptslist);
load('olm_pairwise_distances_cubic.mat','olmpairwisedistancescubic')
pd_olmchesser = table2array(olmpairwisedistancescubic);
pd7 = rad2deg(pd_olmchesser(:));
%% octonion ensemble
[pd4c, pd5c, pd6c, errmetrics] = deal(cell(numnpts,1));
oref = zeros(numnpts,8);
% oref = get_orefs(8);
paperfigure(2,2,14.5);
j = 0;
for i = 1:npts
if i == 1
oref(i,:) = get_ocubo(1,'random',[],10);
else
oref(i,:) = get_ocubo(); %random reference octonion
% oref(i,:) = orefs(i,:);
end
olmoctsym = get_octpairs(olmoct,'oref',oref(i,:)); %symmetrize w.r.t. to oref
pd4c{i} = squareform(pdist(normr(olmoctsym)));
pd5c{i} = squareform(pdist(olmoctsym,@get_omega)); %pairwise distances
pd6c{i} = squareform(pdist(olmoctsym,@get_alen));
pd4c{i} = pd4c{i}(:);
pd5c{i} = rad2deg(pd5c{i}(:)); % flatten
pd6c{i} = pd6c{i}(:);
pd4tmp = [pd4c{:}];
pd5tmp = [pd5c{:}]; %catenate vectors of pairwise distances
pd6tmp = [pd6c{:}];
pd4 = min(pd4tmp,[],2);
pd5 = min(pd5tmp,[],2);
pd6 = min(pd6tmp,[],2);
pd4tow = 2*180/pi*pd4;
errmetrics{i} = get_errmetrics(pd4tow,pd7,'dispQ',true);
errmetrics{i}.ksize = i;
if any(i == nptslist)
j = j+1;
nexttile
yrange = ['[1,' int2str(i),']'];
yname = ['$\mathop{}_{\scriptstyle{\forall k \in' yrange '}}^{\rm{min}}2(\frac{180}{\pi})|\hat{o}_{i,k}^{sym}-\hat{o}_{j,k}^{sym}|$'];
parityplot(pd7,pd4tow,'hex','cscale','log','xname','$\omega$ (traditional)',...
'yname',yname,'xunits','$^{\circ}$','yunits','$^{\circ}$')
papertext(j,'xypos',[-0.2,1.0])
end
end
% Euclidean: '$2\frac{180}{\pi}|o_1^{sym}-o_2^{sym}|$ (this work)'
% klbls = cellfun(@char,num2cell(string(nptslist)),'UniformOutput',false);
% lbls = strcat(klbls,'-');
% lbls{end}(end) = []; %remove last '-'
lbls = lblcat(nptslist);
savefigpng(figfolder,['dist-ensemble-k' lbls])
paperfigure();
enstbl = struct2table(structvertcat(errmetrics{:})); %ensemble table
% G = findgroups(enstbl.ksize);
plot(enstbl.ksize,enstbl.rmse,'-*')
xlabel('$k_{max}$','Interpreter','latex')
ylabel('Error ($^{\circ}$)','Interpreter','latex')
hold on
plot(enstbl.ksize,enstbl.mae,'-*')
legend('RMSE','MAE','Interpreter','latex')
savefigpng(figfolder,['dist-ensemble-rmse-mae'])
%% fixed test - does holding one octonion fixed give same as both varied
tic
pd_fix = get_pd_fix(olmoct);
pdfixtime = toc;
tmp = pd_fix;
pd_fix = rad2deg(pd_fix);
pd_fix = pd_fix(:);
paperfigure();
parityplot(pd7,pd_fix,'scatter','xname','GBO distance','yname','Fixed GBO distance','xunits','deg','yunits','deg')
fixed_errmetrics = get_errmetrics(pd7,pd_fix);
savefigpng(figfolder,'pd-fix')
%% Ensemble Interpolation (Load)
fname = 'ensemble-interp';
seed = 10;
rng(seed);
ninputpts = 50000; %50000
npredpts = 10000;
[~,qm,nA] = get_five(ninputpts);
o = five2oct(qm,nA);
y = GB5DOF_setup(o(:,1:4),o(:,5:8));
[~,qm2,nA2] = get_five(npredpts);
o2 = five2oct(qm2,nA2);
ytrue = GB5DOF_setup(o2(:,1:4),o2(:,5:8));
K = 10;
method = 'gpr';
[ypred,ypredlist,interpfnlist,mdllist,mdlparslist] = ...
ensembleVFZO([],[],y,[],[],K,method,'ytrue',ytrue,'o',o,'o2',o2);
fpath = fullfile(figfolder,fname);
save(fpath,'ypred','ypredlist','ytrue','qm','nA','qm2','nA2','y','o','o2')
% save(fpath,'ypred','ypredlist','ytrue','qm','nA','qm2','nA2','y','o','o2',...
% 'interpfnlist','mdllist','mdlparslist') %ran into issues with saving, maybe out of memory
% gprMdls = cellfun(@(x) x.gprMdl, mdllist, 'UniformOutput',false);
%% load Ensemble Interpolation
fname = 'ensemble-interp';
fpath = fullfile(figfolder,fname);
load(fpath,'ypred','ypredlist','ytrue','qm','nA','qm2','nA2','y','o','o2')
%% Ensemble Interpolation
paperfigure(2,2,14.509833333333333)
nexttile
parityplot(ytrue,mean([ypredlist{:}],2),'hex')
title('mean')
nexttile
parityplot(ytrue,median([ypredlist{:}],2),'hex')
title('median')
nexttile
parityplot(ytrue,min([ypredlist{:}],[],2),'hex')
title('min')
nexttile
parityplot(ytrue,max([ypredlist{:}],[],2),'hex')
title('max')
savefigpng(figfolder,'ensemble-interp')
%% Ensemble Interpolation
K = length(ypredlist);
% [errmetmean(K),errmetmed(K),errmetmin(K),errmetmax(K)] = deal([]);
clear errmetmean errmetmed errmetmin errmetmax
for i = 1:K
ypredmean = mean([ypredlist{1:i}],2);
ypredmed = median([ypredlist{1:i}],2);
ypredmin = min([ypredlist{1:i}],[],2);
ypredmax = max([ypredlist{1:i}],[],2);
errmetmean(i) = get_errmetrics(ypredmean,ytrue); %#ok<SAGROW>
errmetmed(i) = get_errmetrics(ypredmed,ytrue); %#ok<SAGROW>
errmetmin(i) = get_errmetrics(ypredmin,ytrue); %#ok<SAGROW>
errmetmax(i) = get_errmetrics(ypredmax,ytrue); %#ok<SAGROW>
end
rmse.mean = [errmetmean.rmse];
rmse.med = [errmetmed.rmse];
rmse.min = [errmetmin.rmse];
rmse.max = [errmetmax.rmse];
mae.mean = [errmetmean.mae];
mae.med = [errmetmed.mae];
mae.min = [errmetmin.mae];
mae.max = [errmetmax.mae];
rmsecat = [rmse.mean.',rmse.med.',rmse.min.',rmse.max.'];
maecat = [mae.mean.',mae.med.',mae.min.',mae.max.'];
lgdlbl = {'mean','median','min','max'};
paperfigure(1,2);
nexttile
mkr = '*-';
plot(1:K,rmsecat,mkr)
% ax = gca;
% ax.YLim(1) = 0;
xlim([1,K])
legend(lgdlbl,'Location','best')
xlabel('Ensemble Size')
ylabel('RMSE ($J/m^2$)')
nexttile
plot(1:K,maecat,mkr)
% ax = gca;
% ax.YLim(1) = 0;
xlim([1,K])
legend(lgdlbl,'Location','best')
ylabel('MAE ($J/m^2$)')
xlabel('Ensemble Size')
fname = 'ensemble-interp-rmse-mae';
savefigpng(figfolder,fname)
%% distance parity (3D)
% pts = normr(rand(388,3)-0.5);
% pts2 = normr(rand(388,3)-0.5);
% pd1 = pdist(pts);
% pd3 = pdist(pts,@get_alen);
% parityplot(pd1,pd3,'xname','euclidean','yname','arclength','units','','title','388 3D points')
% figure
% t=n2c(pts);
% scatter3(t{:})
% axis equal
%% distance histogram and knn vs. meshpoints
addpathdir({'gmat2q.m','oct50000.mat'})
% setpaperdefaults()
% distance histogram
seed = 10;
rng(seed);
npts = 50000;
[~,qm,nA] = get_five(npts);
o = five2oct(qm,nA);
pts = get_octpairs(o);
save('oct50000.mat','pts')
load('oct50000.mat','pts');
paperfigure(1,2);
nexttile
nnhist(pts,'omega');
papertext(1)
% savefigpng(folder,['nnhist',int2str(npts)])
% knn distances
nexttile
[nnpts,D,mu,sigma] = get_knn(pts,'omega',100);
% fig = figure;
% fig.Position = [460.2 245 498.4 472.8];
% paperfigure()
shadedErrorBar(1:length(mu),mu,sigma)
% errorbar(mu,sigma)
xlabel('k-th NN','Interpreter','latex','FontSize',12)
ylbl = 'average $\omega$ (deg)';
ylabel(ylbl,'Interpreter','latex','FontSize',12)
papertext(2)
% savefigpng(folder,['knnhist',int2str(npts)])
savefigpng(figfolder,['nnhist-knn-',int2str(npts)])
%% barycentric methods
proj_down_test(1)
savefigpng(figfolder,'bary-remove-deg',[130.5 19.5 1886 572])
proj_down_test(2)
savefigpng(figfolder,'bary-delaunay',[131.5 7.5 1872 432])
%% voronoi example
addpathdir('PGnames.mat')
toBPFZ_test(1)
% nexttile
% toBPFZ_test(1)
% nexttile
% toBPFZ_test(4)
fname = 'voronoi';
savefigpng(figfolder,fname)
% savefigpng(folder,'voronoi-4NN')
%% bary interp
sphbary_test()
fname = 'bary-interp';
savefigpng(figfolder,fname,[242.5 351.5 609 393])
% fpath = fullfile(folder,[fname,'.png']);
% I = imread(fpath);
% imshow(I)
% Icropped = imcrop(I,[242.5 351.5 609 393]);
% imwrite(Icropped,fpath)
%% Prior Work Error Summary
S = load('prior-work-error-summary.mat');
ypred = S.lobpcg.ypred;
ytrue = S.lobpcg.ytrue;
rmse = 0.0277;
rmse2 = 0.0076;
f1 = nnz(ytrue < 0.9)/90000;
f2 = 1-f1;
f1*rmse+f2*rmse2
%% Arbitrary path through GB space
%tunnelplot()
%% Kim GPR Mixture Interpolation, Teaching
rng(10)
[ypred,ysd,ytrue,ci,covmat,kfntmp,kfntmp2,mdl,gprMdl2] = gprmix_test();
savefigpng(figfolder,'kim-interp-teach')
%% Kim GPR Mixture Final Result
rng(10);
% paperfigure(2,2,13.6843);
paperfigure(1,2,7.46983333333333);
nexttile
parityplot(ytrue,ypred);
papertext(1);
n = 300;
nexttile
mdl.method = 'gprmix';
[~,~,~,~,A,B] = tunnelplot(mdl,[],[],n,'brkQ',false,'nnQ',false,'nnQ2',false,'tpredlist',ypred,...
'kfntmp',kfntmp,'kfntmp2',kfntmp2,'gprMdl2',gprMdl2);
legend('GPR mixture model','Location','best','Interpreter','latex')
papertext(2);
disp(A)
disp(B)
[qm1,nA1] = oct2five(A);
disp(qm1)
disp(nA1)
[qm2,nA2] = oct2five(B);
disp(qm2)
disp(nA2)
% nsamp = 10;
% gprsamples = mvnrnd(ypred,covmat,nsamp);
savefigpng(figfolder,'kim-interp')
fpath = fullfile(figfolder,'kimAB');
save(fpath,'A','B')
%%
fpath = fullfile(figfolder,'kimAB');
load(fpath,'A','B')
[qm1,nA1] = oct2five(A);
disp(qm1)
disp(nA1)
[qm2,nA2] = oct2five(B);
disp(qm2)
disp(nA2)
dm1 = disorientation(qm1(1,:));
dm2 = disorientation(qm2(1,:));
r1 = q2rod(dm1);
r2 = q2rod(dm2);
paperfigure();
plotFZrodriguez()
scl = 0.1;
x = [1,0,0]*scl;
y = [0,1,0]*scl;
z = [0,0,1]*scl;
w = [0,0,0];
hold on
quiver3(w,w,w,x,y,z,1,'linewidth',1)
text(x(1),x(2)+0.01,x(3),'$d_1$','FontWeight','bold','Interpreter','latex')
text(y(1),y(2),y(3)+0.01,'$d_2$','FontWeight','bold','Interpreter','latex')
text(z(1)+0.01,z(2),z(3),'$d_3$','FontWeight','bold','Interpreter','latex')
hold on
t = n2c(r1);
ax = cell(1,3);
ax{1} = scatter3(t{:},'b');
t = n2c(r2);
ax{2} = scatter3(t{:},'r');
t = n2c([r1; r1(1:2) 0; r1(1) 0 0]);
ax{3} = plot3(t{:},'k:');
t = n2c([r2; r2(1:2) 0; r2(1) 0 0]);
ax{4} = plot3(t{:},'k:');
legend([ax{1:2}],'A','B','Location',[0.190232753462038 0.576379005936667 0.180441240026672 0.110647062492371]);
savefigpng(figfolder,'ABrod-kim')
%% Kim (non-mix) results
load('gpr46883_gitID-5e6bd14_puuID-2e34b447_kim-paper-data3_meta.mat','errmetrics')
format long
errmetrics
format short
%% Kim Tunnel Plots and Posterior Sampling
paperfigure(2,2,13.6843);
rng(10)
i = 0;
nexttile
i = i+1;
npts = size(ytrue,1);
rids = randperm(npts,npts);
parityplot(ytrue(rids),ypred(rids),'scatter','c',ysd(rids),'cblbl','$\sigma_{\mathrm{pred}} (J m^{-2})$')
papertext(i);
nexttile
i = i+1;
mdl.method = 'gprmix';
tunnelplot(mdl,A,B,n,'brkQ',false,'nnQ',true,'nnQ2',true,'tpredlist',ypred,...
'kfntmp',kfntmp,'kfntmp2',kfntmp2,'gprMdl2',gprMdl2);
ax = nexttile(i);
ch = ax.Children([1,2]);
legend(ch,'GPR mixture','1st (input) NN','Location','southwest','Interpreter','latex')
papertext(i);
nexttile
i = i+1;
mdl.method = 'gprmix';
tunnelplot(mdl,A,B,n,'brkQ',false,'nnQ',false,'nnQ2',false,'tpredlist',ypred,...
'kfntmp',kfntmp,'kfntmp2',kfntmp2,'gprMdl2',gprMdl2,'nsamp',5);
papertext(i);
nexttile
i = i+1;
mdl.method = 'gprmix';
tunnelplot(mdl,[],[],n,'brkQ',true,'nnQ',false,'nnQ2',false,'tpredlist',ypred,...
'kfntmp',kfntmp,'kfntmp2',kfntmp2,'gprMdl2',gprMdl2);
legend('Ni BRK','Fe GPR mixture','Location','southwest','Interpreter','latex')
papertext(i);
savefigpng(figfolder,'kim-interp-posterior')
%% GPR Mixture Sigmoid Function
paperfigure();
thr = 1.1;
scl = 30;
sigfn = @(x,scl,xshift) 1./(1+exp(-scl*(x-xshift)));
x = 0.5:0.01:1.5;
plot(x,sigfn(x,scl,thr),'LineWidth',1.5);
ylim([0 1])
xlabel('GBE ($J m^{-2}$)','Interpreter','latex')
ylabel('Mixing fraction (f)','Interpreter','latex')
axis square
savefigpng(figfolder,'gprmix-sigmoid')
%% tunnel plot (full)
ninputpts = 50000; %1000, 50000
n = 150;
rng(10)
paperfigure();
[tpredlist,tsdlist,propList,methodlist,A,B] = tunnelplot_test(2,ninputpts,n,'extend',0);
fname = ['tunnel-',int2str(ninputpts)];
fpath = fullfile(figfolder,fname);
save(fpath,'tpredlist','tsdlist','propList','methodlist','A','B')
savefigpng(figfolder,fname)
%%
fname = ['tunnel-',int2str(50000)];
fpath = fullfile(figfolder,fname);
load(fpath,'A','B')
disp(A)
disp(B)
[qm1,nA1] = oct2five(A);
disp(qm1)
disp(nA1)
[qm2,nA2] = oct2five(B);
disp(qm2)
disp(nA2)
dm1 = disorientation(qm1(1,:));
dm2 = disorientation(qm2(1,:));
r1 = q2rod(dm1);
r2 = q2rod(dm2);
paperfigure();
plotFZrodriguez()
scl = 0.1;
x = [1,0,0]*scl;
y = [0,1,0]*scl;
z = [0,0,1]*scl;
w = [0,0,0];
hold on
quiver3(w,w,w,x,y,z,1,'linewidth',1)
text(x(1),x(2)+0.01,x(3),'$d_1$','FontWeight','bold','Interpreter','latex')
text(y(1),y(2),y(3)+0.01,'$d_2$','FontWeight','bold','Interpreter','latex')
text(z(1)+0.01,z(2),z(3),'$d_3$','FontWeight','bold','Interpreter','latex')
hold on
t = n2c(r1);
ax = cell(1,3);
ax{1} = scatter3(t{:},'b');
t = n2c(r2);
ax{2} = scatter3(t{:},'r');
t = n2c([r1; r1(1:2) 0; r1(1) 0 0]);
ax{3} = plot3(t{:},'k:');
t = n2c([r2; r2(1:2) 0; r2(1) 0 0]);
ax{4} = plot3(t{:},'k:');
legend([ax{1:2}],'A','B','Location',[0.190232753462038 0.576379005936667 0.180441240026672 0.110647062492371]);
savefigpng(figfolder,'ABrod')
%% tunnel plot (shortcut)
ninputpts = 1000;
n = 150;
fname = ['tunnel-' int2str(ninputpts)];
fpath = fullfile(figfolder,fname);
load(fpath,'tpredlist','tsdlist','propList','methodlist','A','B')
paperfigure();
tunnelplot_test(2,ninputpts,n,tpredlist,tsdlist,propList,methodlist,A,B);
disp(A)
disp(B)
savefigpng(figfolder,fname)
%% Kim Interp Degeneracy Info
fname = 'kim-interp-degeneracy'; % produced in Kim2oct.m
fpath = fullfile(figfolder,fname);
load(fpath,'errmetrics')
paperfigure(2,2);
i = 0;
nexttile
i = i+1;
e = errmetrics.e;
ecat = vertcat(e{:});
nprops = errmetrics.nprops;
ids = nprops <= 4;
e1 = e(ids);
ecat1 = vertcat(e1{:});
nprops = errmetrics.nprops;
histogram(ecat1);
axis square
% set(gca,'YScale','log');
xlabel({'Error relative to (1-4 degeneracy)','set average ($J/m^2$)'},'Interpreter','latex')
ylabel('counts','Interpreter','latex')
min(ecat)
max(ecat)
papertext(i);
nexttile
i=i+1;
propavg = vertcat(errmetrics.propavg{ids});
props = vertcat(errmetrics.propsets{ids});
parityplot(propavg,props)
xlabel('Average set-wise GBE ($J/m^2$)','Interpreter','latex')
ylabel('Input GBE ($J/m^2$)','Interpreter','latex')
ids2 = nprops > 4;
e2 = e(ids2);
ecat2 = vertcat(e2{:});
papertext(i);
nexttile
i = i+1;
histogram(ecat2)
axis square
xlabel({'Error relative to (5+ degeneracy)','set average ($J/m^2$)'},'Interpreter','latex')
ylabel('counts','Interpreter','latex')
papertext(i);
nexttile
i = i+1;
propavg = vertcat(errmetrics.propavg{ids2});
props = vertcat(errmetrics.propsets{ids2});
parityplot(propavg,props)
xlabel('Average set-wise GBE ($J/m^2$)','Interpreter','latex')
ylabel('Input GBE ($J/m^2$)','Interpreter','latex')
papertext(i);
fname = 'kim-interp-degeneracy-results';
savefigpng(figfolder,fname)
paperfigure()
histogram(errmetrics.nprops)
axis square
xlabel('Number of degenerate GBs per set','Interpreter','latex')
ylabel('Number of sets','Interpreter','latex')
fname = 'kim-interp-degeneracy-sets';
savefigpng(figfolder,fname)
%
% nexttile
% histogram(nprops(ids))
disp(['wtrmse: ' num2str(errmetrics.wtrmse)])
disp(['wtmae: ' num2str(errmetrics.wtmae)])
%% Olmsted Ni Dataset Comparison
%see also interp5DOF_setup.m
rng(10)
A = importdata('olm_octonion_list.txt');
o = A.data;
o = [qinv(o(:,1:4)),qinv(o(:,5:8))];
o = get_octpairs(o);
B = importdata('olm_properties.txt');
y = B.data(:,1);
[qm,nA] = oct2five(o);
qm2 = qm;
nA2 = nA;
ytrue = y;
[ypred,interpfn,mdl,mdlpars] = interp5DOF(qm,nA,y,qm2,nA2,'ytrue',ytrue);
[ypred_lowSig,interpfn_lowSig,mdl_lowSig,mdlpars_lowSig] = interp5DOF(qm,nA,y,qm2,nA2,'ytrue',ytrue,...
'mygpropts',{'PredictMethod','exact','Sigma',1e-4,'ConstantSigma',true,'SigmaLowerBound',5e-5});
y_brk = GB5DOF_setup(o(:,1:4),o(:,5:8));
gpr_errmetrics = get_errmetrics(ytrue,ypred);
gpr_lowSig_errmetrics = get_errmetrics(ytrue,ypred_lowSig);
brk_errmetrics = get_errmetrics(ytrue,y_brk);
parity{1} = struct('ytrue',ytrue,'ypred',y_brk);
parity{2} = struct('ytrue',ytrue,'ypred',ypred);
parity{3} = struct('ytrue',ytrue,'ypred',ypred_lowSig);
strs={'BRK','GPR','low-noise-GPR'};
for i = 1:3
paperfigure();
str = strs{i};
parityplot(parity{i}.ypred,parity{i}.ytrue,'xname','Olmsted Ni','yname',['predicted ' str]);
str = lower(str);
savefigpng(figfolder,['resubloss-ni-' str])
end
%% Fitted Parameters
% kim = load('gpr46883_gitID-b473165_puuID-50ffdcf6_kim-rng11.mat','mdl');
kim = load('gpr58604_gitID-1cb3232_puuID-2bf8308c_kim-Fe-train-all-data.mat','mdl');
S = structvertcat(mdlpars,mdlpars_lowSig);
KernelParameters = [S.KernelParameters,kim.mdl.gprMdl.KernelInformation.KernelParameters];
SigmaL = 2*rad2deg(KernelParameters(1,:)).';
SigmaF = KernelParameters(2,:).';
KernelParameterNames = S.KernelParameterNames;
Beta = vertcat(S.Beta,kim.mdl.gprMdl.Beta);
Sigma = vertcat(S.Sigma,kim.mdl.gprMdl.Sigma);
ConstantSigma = {'no';'yes';'no'};
datasets = {'Ni';'Ni';'Fe'};
% numGBs = [388;388;46883];
R = @(x) round(x,4,'decimals');
T = table(datasets,ConstantSigma,R(SigmaL),R(SigmaF),R(Beta),R(Sigma),'VariableNames',...
{'element',...
'constant-sigma (yes/no)','sigma-L (deg)',...
'sigma-F (J m^-2)',...
'beta (J m^-2)',...
'sigma (J m^-2)'});
writetable(T,fullfile(tblfolder,'resubloss-ni-pars.csv'))
% caption = ['Fitted parameters for two \gls{gpr} models fitted to the 388 '...
% 'simulated Ni \glspl{gbe} by \citet{olmstedSurveyComputedGrain2009a}. '...
% 'The first model allows $\sigma$ to vary, whereas the second constrains '...
% '$\sigma$ to be fixed. $\sigma_L$, $\sigma_F$, $\beta$, and $\sigma$ are '...
% 'the kernel length scale, signal standard deviation, constant basis function, '...
% 'and input property standard deviation, respectively. See '...
% '\url{https://www.mathworks.com/help/stats/fitrgp.html} for additional details.'];
% savetblstr(T,'resubloss-ni-pars',tblfolder,caption)
%% Low-Sigma 1D slices
fname = 'olm-oct-Sigma-3-5-7-9-11.mat';
files = dir(fullfile('**','interp','data','**',fname));
fpath = fullfile(files(1).folder,files(1).name);
load(fpath,'oolmABCDE','yolmABCDE','olm_ids') %generated in fz_proj.mlx
fname = 'kim-oct-Sigma-3-5-7-9-11';
load(fullfile(files(1).folder,fname),'kimABCDE','ykimABCDE','kim_ids');
n = 150;
Slist = [5 7 9 11];
A1 = oolmABCDE{1};
A2 = get_octpairs(kimABCDE{1});
% paperfigure(2,2);
% fname = 'gpr388_gitID-57857cd_puuID-abf7948f_olmsted-Ni-rng11-Sigma-1e-2.mat';
% fname = 'gpr388_gitID-57857cd_puuID-d2476f08_olmsted-Ni-rng11-Sigma-5e-2.mat';
% fname = 'gpr388_gitID-57857cd_puuID-67702aca_olmsted-Ni-rng10.mat';
% fname = 'gpr388_gitID-57857cd_puuID-e9c787cd_olmsted-Ni';
% fnames = {'gpr46883_gitID-b473165_puuID-50ffdcf6_kim-rng11.mat',...
% 'gpr388_gitID-57857cd_puuID-e9c787cd_olmsted-Ni'};
% fnames = {'gpr58604_gitID-1cb3232_puuID-2bf8308c_kim-Fe-train-all-data.mat',...
% 'gpr388_gitID-57857cd_puuID-e9c787cd_olmsted-Ni'};
fnames = {'gpr58604_gitID-3b7183c_puuID-ce759533_kim-Fe-train-all-data-fic.mat',...
'gpr388_gitID-57857cd_puuID-e9c787cd_olmsted-Ni'};
datatypes = {'kim','olmsted'};
mats = {'Fe','Ni'};
for j = 1:2
fname = fnames{j};
datatype = datatypes{j};
mat = mats{j};
load(fname,'mdl','mdlpars')
mdl.mixQ = false;
mdl.K = 1;
mdl.thr = [];
mdl.scl = [];
mdl.mdls(1) = mdl;
mdl.cgprMdls2 = [];
mdl.oreflist = [];
for i = 1:4
S = Slist(i);
switch datatype
case 'olmsted'
A = A1;
B = get_octpairs(oolmABCDE{i+1},'oref',get_ocubo(1,'random',[],10));
case 'kim'
A = A2;
B = get_octpairs(kimABCDE{i+1},'oref',get_ocubo(1,'random',[],10));
end
fname = ['path-3-' int2str(S) '-' datatype];
% paperfigure();
% if j == 2
% tunneltri(mdl,'line',A,B,'olm',true,'mkr','r.','disptxt',false,...
% 'extend',0,'uncertainty',true);
% else
% tunneltri(mdl,'line',A,B,'mkr','r.',...
% 'txt',{'$\Sigma3$',['$\Sigma' int2str(S) '$']},...
% 'extend',0,'uncertainty',true);
% end
% hold on
% if j == 2
% tunneltri([],'line',A,B,'brk',true,'txt',{'$\Sigma3$',['$\Sigma' int2str(Slist(i)) '$']},'extend',0); %note, tunneltri() is in the egprm repo, not the interp repo (2021-04-20)
% end
% if j == 2
% legend('Ni-GPR','Ni-BRK','location','south')
% else
% legend('Fe-GPR','location','south')
% end
% savefigpng(figfolder,fname)
paperfigure(1,1,11.5);
if strcmp(datatype,'olmsted')
brkQ = true;
else
brkQ = false;
end
tunnelplot({mdl},A,B,100,'lgdloc','northoutside','brkQ',brkQ,'K',6);
xlabel(['$\overline{\Sigma3,\Sigma' int2str(S) '}(t) (^\circ{})$'])
fig = gcf;
ax = gca;
switch datatype
case 'olmsted'
chnum = 3;
case 'kim'
chnum = 2;
end
ax.Children(1).DisplayName=[mat '-GPR($\pm$CI)'];
ax.Children(chnum).DisplayName=['$\overline{\Sigma3,\Sigma' int2str(S) '}$ 1st-NN'];
cb = colorbar;
cb.Label.Interpreter = 'latex';
cb.Label.String = ['GBO distance to $\overline{\Sigma3,\Sigma' int2str(S) '} (^\circ{})$'];
fname = ['tunnel-3-' int2str(S) '-' datatype];
savefigpng(figfolder,fname)
end
end
%% largest minimum (symmetrized) distance between any 2 GBs
load('oct50000.mat','pts')
npts = 20000;
pts = pts(1:npts,:);
K = 20;
fpath = fullfile(datafolder,['pd' int2str(npts) '-K' int2str(K)]);
%%
pd = ensembleGBdist(pts,[],K, "squareform", true);
save(fpath,'pd','npts','K','-v7.3')
%%
load(fpath,'pd')
%%
mpd = 2*max(pd,[],'all');
disp(['max pd (degrees):' num2str(mpd)])
pd2 = ensembleGBdist(sqrt2norm(pts),[],1, "squareform", true);
mpd2 = 2*max(pd2,[],'all');
%% PCA
[coeff,score,latent,tsquared,explained,mu] = pca(pts,'NumComponents',5);
sum(explained(1:5))
tbl = table((1:8).',round(explained,4,'significant'),'VariableNames',{'Dimension','Explained Variance (%)'});
writetable(tbl,fullfile(tblfolder,'pca-explained.csv'))
%% USV matrices
load('oct50000.mat','pts')