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hplc_gra_sim.m
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hplc_gra_sim.m
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function samples2 = hplc_gra_sim(samples,datastruct,hplcparam_design)
nObs = size(hplcparam_design,1);
nSamples= size(samples.logkwHat,1);
nAnalytes=datastruct.nAnalytes;
hplcparam=hplcparam_design;
mod=hplcparam(:,7);
steps=hplcparam(:,13);
nDiss=datastruct.R;
chargesA=datastruct.chargesA;
chargesB=datastruct.chargesB;
samples2.trHatCond=zeros(nSamples, nAnalytes, nObs);
samples2.trHatPred=zeros(nSamples, nAnalytes, nObs);
samples2.trObsCond=zeros(nSamples, nAnalytes, nObs);
samples2.trObsPred=zeros(nSamples, nAnalytes, nObs);
for z = 1:nSamples
z
dlogkT=samples.dlogkT(z,:);
logkwx=squeeze(samples.logkwx(z,:,:));
S1mx=squeeze(samples.S1mx(z,:,:));
S1ax=squeeze(samples.S1ax(z,:,:));
pKaw =squeeze(samples.pKaw(z,:,:));
alpham =squeeze(samples.alpham(z,:,:));
alphaa =squeeze(samples.alphaa(z,:,:));
S2mHat =samples.S2mHat(z,:);
S2aHat =samples.S2aHat(z,:);
nu = 3;
apH =squeeze(samples.apH(z,:));
sigma =samples.sigma(z,:);
dlogkTPred=samples.dlogkTPred(z,:);
logkwxPred=squeeze(samples.logkwxPred(z,:,:));
S1mxPred=squeeze(samples.S1mxPred(z,:,:));
S1axPred=squeeze(samples.S1axPred(z,:,:));
pKawPred=squeeze(samples.pKawPred(z,:,:));
alphamPred=squeeze(samples.alphamPred(z,:,:));
alphaaPred=squeeze(samples.alphaaPred(z,:,:));
sigmaPred =samples.sigmaPred(z,:);
trHatCond=zeros(nAnalytes,nObs);
trHatPred=zeros(nAnalytes,nObs);
for j=1:nAnalytes
for i=1:nObs
if (mod(i)==1)
y_hat_Cond = chromgratrapz(steps(i), ...
logkwx(j,:) + dlogkT(j)*hplcparam(i,11), ...
S1mx(j,:), ...
pKaw(j,:), ...
alpham(j,:), ...
S2mHat, ...
apH,...
chargesA(j,:), ...
chargesB(j,:), ...
nDiss(j), ...
hplcparam(i,:));
end
if (mod(i)==2)
y_hat_Cond = chromgratrapz(steps(i), ...
logkwx(j,:) + dlogkT(j)*hplcparam(i,11), ...
S1ax(j,:), ...
pKaw(j,:), ...
alphaa(j,:), ...
S2aHat, ...
apH,...
chargesA(j,:), ...
chargesB(j,:), ...
nDiss(j), ...
hplcparam(i,:));
end
trHatCond(j,i) = hplcparam(i,3) + hplcparam(i,4) + y_hat_Cond;
end
for i=1:nObs
if (mod(i)==1)
y_hat_Pred = chromgratrapz(steps(i), ...
logkwxPred(j,:) + dlogkTPred(j)*hplcparam(i,11), ...
S1mxPred(j,:), ...
pKawPred(j,:), ...
alphamPred(j,:), ...
S2mHat, ...
apH,...
chargesA(j,:), ...
chargesB(j,:), ...
nDiss(j), ...
hplcparam(i,:));
end
if (mod(i)==2)
y_hat_Pred = chromgratrapz(steps(i), ...
logkwxPred(j,:) + dlogkTPred(j)*hplcparam(i,11), ...
S1axPred(j,:), ...
pKawPred(j,:), ...
alphaaPred(j,:), ...
S2aHat, ...
apH,...
chargesA(j,:), ...
chargesB(j,:), ...
nDiss(j), ...
hplcparam(i,:));
end
trHatPred(j,i) = hplcparam(i,3) + hplcparam(i,4) + y_hat_Pred;
end
samples2.trHatCond(z,:,:)=trHatCond;
samples2.trHatPred(z,:,:)=trHatPred;
samples2.trObsCond(z,:,:)=trHatCond+(sigma(:)*ones(1,nObs)).*trnd(nu,size(trHatCond));
samples2.trObsPred(z,:,:)=trHatPred+(sigmaPred(:)*ones(1,nObs)).*trnd(nu,size(trHatPred));
end
end
function sol = gra_state(t, hplcparam)
tg = hplcparam(1);
td = hplcparam(2);
fio = hplcparam(5);
fik = hplcparam(6);
pHo = hplcparam(8);
alpha1 = hplcparam(9);
alpha2 = hplcparam(10);
fi = fio+(fik-fio)/tg*(t-td);
if (t<td)
fi = fio;
end
if (t>tg+td)
fi = fik;
end
sol(1)=fi;
sol(2)=pHo+alpha1*fi+alpha2*fi.^2;
function logki=funlogki(logkwx, S1, pKaw, alpha, S2, apH, nDiss, chargesA, chargesB, fipH)
fi = fipH(1);
pH = fipH(2);
logkix = logkwx-S1*fi/(1+S2*fi)+ chargesA*apH(1)*(pH-7) + chargesB*apH(2)*(pH-7);
pHmpKa = pH-(pKaw+alpha*fi);
logki = NaN;
if (nDiss==0)
logki = logkix(1);
end
if (nDiss==1)
logki = logkix(1) + ...
log1p_exp(log(10)*(pHmpKa(1)+logkix(2)-logkix(1)))/log(10)- ...
log1p_exp(log(10)*(pHmpKa(1)))/log(10);
end
if (nDiss==2)
logki = logkix(1) + ...
log1p_exp(log(10)*(pHmpKa(1)+logkix(2)-logkix(1)) + ...
log1p_exp(log(10)*(pHmpKa(2)+logkix(3)-logkix(2))))/log(10)- ...
log1p_exp(log(10)*(pHmpKa(1)) + ...
log1p_exp(log(10)*(pHmpKa(2))))/log(10);
end
function cki_b = areaandslope(time1, time2, invki1, invki2)
if (invki2>1.001*invki1)
bo = (log(invki2)-log(invki1))/(time2-time1);
cki = (invki2-invki1)/bo;
else
bo = 0.001/(time2-time1);
cki = (time2-time1)*(invki2+invki1)/2;
end
cki_b(1) = cki;
cki_b(2) = bo;
function tr = chromgratrapz(steps, logkwx, logkmx, pKaw, alpha, S2mHat, apH, chargesA, chargesB, nDiss, hplcparam)
tg = hplcparam(1);
td = hplcparam(2);
to = hplcparam(3);
dt = tg/steps;
time1 = 0;
time2 = td;
fipH1 = gra_state(time1, hplcparam);
% fipH2 = fipH1;
logki1 = funlogki(logkwx, ...
logkmx, ...
pKaw, ...
alpha,...
S2mHat,...
apH, ...
nDiss,...
chargesA, chargesB, ...
fipH1);
% logki2 = logki1;
invki1 = 1/to/10^logki1;
invki2 = invki1;
cumki1 = 0;
cumki2 = td*invki1;
bo = 0.001/td;
for x=1:steps
if (cumki2<1)
time1 = time2;
time2 = time2+dt;
% fipH1 = fipH2;
fipH2 = gra_state(time2, hplcparam);
% logki1 = logki2;
logki2 = funlogki(logkwx, ...
logkmx, ...
pKaw, ...
alpha,...
S2mHat,...
apH, ...
nDiss,...
chargesA, chargesB, ...
fipH2);
invki1 = invki2;
invki2 = 1/to/10^logki2;
cki_b = areaandslope(time1, time2, invki1, invki2);
cumki1 = cumki2;
cumki2 = cumki2 + cki_b(1);
bo = cki_b(2);
end
end
if (cumki2>=1)
tr = time1+log1p((1-cumki1)*bo/invki1)/bo;
elseif (cumki2<1)
tr = time2 + (1-cumki2)/invki2;
else
end
function y = log1p_exp(x)
y=log(1+exp(x));
function y = log1p(x)
y=log(1+x);