C7: transforming a truncated gaussian with regular and irregular spacing

We first transform a regularly-spaced sampled Gaussian using the inverse transform.

%%% prelim

l1=@(xprime) 1./xprime; Ebase=-10.5:10.5; Tbase=-10:10;

Lt=length(Tbase); t=linspace(Ebase(1),Ebase(end),450);

load pfnfile

pt=out.p(t); mt=out.p(Tbase);

Tshift=Tbase+15; Eshift=Ebase+15; tshift=t+15;

%%% plot original Gaussian

figure(5); clf; hold on

plot(tshift,pt,'-','Color',.7*[1 1 1],'LineWidth',2.2)

plot(Eshift(1)*[1 1],[0 mt(1)],'k--','LineWidth',.75);

for n=1:(Lt),

try plot((Eshift(n+1))*[1 1],[0 max(mt(n:n+1))],'k--','LineWidth',.75); end

plot((Eshift(n:n+1)),mt(n)*[1 1],'k-','LineWidth',2.25);

plot((Tshift(n)),mt(n),'ko','MarkerFaceColor','k','MarkerSize',9); end

axis([3 27 0 .03]);

%%% plot transformed Gaussian

figure(6); clf; hold on

%mt=mt./max(mt);

%plot(l1(Tshift),mt,'ko','MarkerFaceColor','k','MarkerSize',7);

[PCout]=pTX(tshift,pt,l1); PCout(:,1)=PCout(:,1)/max(PCout(:,1));

plot(PCout(:,2),PCout(:,1),'-','Color',.7*[1 1 1],'LineWidth',4)

[PCout]=pTX(Tshift,mt,l1); PCout(:,1)=PCout(:,1)/max(PCout(:,1));

for n=1:(Lt),

plot(l1(Eshift(n:n+1)),PCout(end-n+1,1)*[1 1],'k-','LineWidth',2.25); end

plot(l1(Eshift(1))*[1 1],[0 mt(1)],'k--','LineWidth',.75);

for n=1:(Lt),

try plot(l1(Eshift(n+1))*[1 1],[0 max(PCout(end-[n:n+1]+1,1))],'k--','LineWidth',.75); end, end

axis([0.03 .24 0 1.05]);

Then we perform this transform with an irregularly-spaced sampling of the same Gaussian.

%%% prelim

t=[-10.5 10.5];

ts=linspace(t(1),t(2),450); tplot=ts+15;

Lt=11; dmean=diff(t)/Lt;

dEprime=rand(Lt-1,1)*dmean+dmean/2;

Eprime=[t(1); t(1)+cumsum(dEprime); t(2)]; Eplot=Eprime+15;

Xprime=[]; m=[]; for n=2:length(Eprime),

Xprime(n-1)=mean(Eprime(n-1:n));

m(n-1)=out.p(Xprime(n-1))*diff(Eprime(n-1:n)); end

Xplot=Xprime+15;

%%% plot original Gaussian

figure(5); clf; hold on

plot(Xplot,m,'ko','MarkerFaceColor','k','MarkerSize',11)

plot(tplot,out.p(ts),'-','Color',[.7 .7 .7],'LineWidth',2.6)

for n=1:length(Xprime),

plot(Xplot(n)*[1 1],[0 m(n)],'k-')

plot(Eprime(n:n+1)+15,out.p(Xprime(n))*[1 1],'k-','LineWidth',2.1); end

%%% transform

l1=@(xprime) 1./xprime; m=m/max(m);

pmx=pTX(Xplot,m,l1); pmx=pmx/max(pmx); pex=pTX(Eplot,out.p(Eprime),l1); pex(:,1)=pex(:,1)/max(pex(:,1));

%%% plot transformed Gaussian

figure(6); clf; hold on

PCout=pTX(tplot,out.p(ts),l1); PCout(:,1)=PCout(:,1)/max(PCout(:,1));

plot(PCout(:,2),PCout(:,1),'-','Color',[.7 .7 .7],'LineWidth',2.6)

PCout=pTX(Xplot,out.p(Xprime),l1); PCout(:,1)=PCout(:,1)/max(PCout(:,1));

for n=1:length(Xplot),

plot(l1(Xplot(n))*[1 1],[0 m(n)],'k-'); plot(l1(Xplot(n)),m(n),'ko','MarkerFaceColor','k','MarkerSize',11);

plot(l1(Eplot(n))*[1 1],[0 PCout(end-n+1,1)],'k:','LineWidth',.05);

plot(l1(Eplot(n+1))*[1 1],[0 PCout(end-n+1,1)],'k:','LineWidth',.05);

plot(l1(Eplot(n:n+1)),PCout(end-n+1,1)*[1 1],'k-','LineWidth',2.1); end

axis([0.03 .24 0 1.05]);