From 84f7b410dbc8a62a473e720b3a7309763773006f Mon Sep 17 00:00:00 2001 From: Eric J Alexandrescu Date: Mon, 6 Aug 2018 01:12:52 -0400 Subject: [PATCH] Add files via upload --- muon.m | 214 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ muon.xlsx | Bin 0 -> 434863 bytes 2 files changed, 214 insertions(+) create mode 100644 muon.m create mode 100644 muon.xlsx diff --git a/muon.m b/muon.m new file mode 100644 index 0000000..fcb899e --- /dev/null +++ b/muon.m @@ -0,0 +1,214 @@ +num=xlsread('muon.xlsx'); +x=(num(:,1)); +x=x./1000; +step=0.4; +X=0:step:max(x); +figure(1) +h=histogram(x,X); +xlabel('Decay Time (us)') +ylabel('Observed Counts') +hold on +y=h.Values; +XX=(step/2):step:max(x); +XX=XX(1:end-1); +errorbar(XX,y,sqrt(y),'o') + + +%linear and nonlinear fit before background subtraction +%plot(XX,log(y),'o') +fun1=@(v) v(1)*exp(-v(2)*XX)-y; +x0=[4000,1]; +[v,resnorm,residual,exitflag,output,lambda,jacobian]=lsqnonlin(fun1,x0); + + +Jacobian = full(jacobian); +varv=resnorm*inv(Jacobian'*Jacobian)/length(XX); +stdv=sqrt(diag(varv)); + + +Y1=v(1)*exp(-v(2)*XX); +plot(XX,Y1,'g') +legend('Observed Decays','Uncertainty','Best Fit Without Background Subtraction') +title('Nonlinear Regression with no Consideration of Bacground Effects') +ylabel('Bin Count') +xlabel('Decay Time (microseconds)') +%hold on +%plot(XX,y) + + + +%% +%linear and nonlinear fit after background subtraction +clearvars v resnorm residual stdv jacobian + +figure(2) +count=sum(y(XX>12)); +avg=count/(length(y(XX>12))); +Y=y-avg; +Y(Y<0)=0; +%plot(XX,log(Y),'o') +h=histogram(x,X); +xlabel('Decay Time (us)') +ylabel('Observed Counts') +hold on +y=h.Values; +errorbar(XX,y,sqrt(y),'o') + + + + +%fun2=@(v) v(1)*exp(-v(2)*XX)+v(3);%-y; +%v=[50,5,1]; +%fun2=@(v,x) (v(1)*exp(-v(2)*x)+v(3)); +%nlinfit(XX,y,fun2,X0) + +fun2=@(v) v(1)*exp(-v(2)*XX)+v(3)-y; +X0=[4000,5,10]; + +[v,resnorm,residual,exitflag,output,lambda,jacobian]=lsqnonlin(fun2,X0); +ci=nlparci(v,residual,'Jacobian',jacobian); +v=v'; + + +Jacobian = full(jacobian); +varv=resnorm*inv(Jacobian'*Jacobian)/length(XX); +stdv=sqrt(diag(varv)); + + + + + +Y=v(1)*exp(-v(2)*XX)+v(3); +YY=log(v(1))-v(2)*XX+log(v(3)); +plot(XX,Y,'g') +legend('Observed Decays','Uncertainty','Best Fit With Background Subtraction') +title('Nonlinear Regression with Consideration of Bacground Effects') +ylabel('Bin Count') +xlabel('Decay Time (microseconds)') +%hold on +%plot(XX,y) + + + + + +%% Maximum likelihood +%without background subtraction +lambda=0.275:0.0001:0.282; +%lambda=0.1:0.01:0.6; +P=zeros(length(lambda),length(x)); +mP=zeros(1,length(lambda)); +for i=1:length(lambda) + for j=1:length(x) + P(i,j)=lambda(i)*exp(-lambda(i)*x(j)); + end +end +P=log(P); + +for i=1:length(lambda) + mP(i)=sum(P(i,:)); +end + +figure(5) +plot(lambda,mP) +hold on +yy=(max(mP(:))-0.5)*ones(1,length(lambda)); +plot(lambda,yy) +vs=(mP((mP-yy>-0.04 & mP-yy<0.04))); +Vs=zeros(1,2); +for i=1:length(vs) + Vs(i)=lambda(mP==vs(i)); +end +plot(Vs,yy(1:2),'o') + + +lambda1=lambda(mP==max(mP)); +siga=abs(lambda1-Vs(1)); +sigb=abs(lambda1-Vs(2)); +yy1=get(gca,'ylim'); +plot([lambda1,lambda1],yy1); +title('Maximum Likelihood Approach with no Consideration of Background') +xlabel('Lambda (s^-1)') +ylabel('Sum of log of Probabilities') +legend('Sum of log of Probabilities','Maximum-0.5') + + + +%% with background subtraction +lambda=0.48:0.0002:0.50; +b=0.0095:0.00002:0.0101; + +P=zeros(length(lambda),length(b),length(x)); +mP=zeros(length(lambda),length(b)); +for i=1:length(lambda) + for j=1:length(b) + for k=1:length(x) + P(i,j,k)=lambda(i)*(1-b(j)*20)*exp(-lambda(i)*x(k))+b(j); + end + end +end +P=log(P); + +for i=1:length(lambda) + for j=1:length(b) + mP(i,j)=sum(P(i,j,:)); + end +end + +figure(6) +[XXX,YYY]=meshgrid(b,lambda); +surf(XXX,YYY,mP) +xlabel('Background') +ylabel('Lambda (s^-1)') +zlabel('Sum of log of Probabilities') +hold on + +M=max(mP(:)); +[row,col]=find(mP==M); + + 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