| function [Lall, omegaall, thetaall, hall, v, pall, vall] = solveh(s, Whinterp, Wrinterp, p, pti, type, At, Y, znow, hnow, tnow)
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| ns = size(s, 1);
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| if strcmp(type, 'r')
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| Lall = zeros(ns, 3);
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| omegaall = zeros(ns, 3);
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| thetaall = zeros(ns, 3);
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| hall = zeros(ns, 3);
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| vall = zeros(ns, 3);
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| for branch = 1 : 1 : 3
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| if branch == 1
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| Lall(:, branch) = At + Y;
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| omegaall(:, branch) = 0;
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| thetaall(:, branch) = 0;
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| hall(:, branch) = 0;
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| vall(:, branch) = Wrinterp(Lall(:, branch), znow);
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| elseif branch == 2
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| vtemp = zeros(ns, p.nh) - 1e12;
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| Ltemp = zeros(ns, p.nh);
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| Cash = At + Y;
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| for i = 1 : p.nh
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| Ltemp(:,i) = Cash - p.hgrid(i);
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (i - 1)*p.no*p.nt + (1 - 1) *p.no + 1;
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| good = Ltemp(:, i) >= p.lgrid(1);
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| if any(good)
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| vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
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| end
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| end
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| [vall(:, branch), htemp] = max(vtemp, [], 2);
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| hind = sub2ind([ns, p.nh], (1 : 1 : ns)', htemp);
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| Lall(:, branch) = Ltemp(hind);
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| omegaall(:, branch) = 0;
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| thetaall(:, branch) = 0;
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| hall(:, branch) = p.hgrid(htemp);
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| elseif branch == 3 % Purchase New Home with Mortgage
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| % create a grid of possible houses and initial LTVs
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| ht = gridmake((1 : 1 : p.nh)', (1 : 1 : p.nt)');
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| vtemp = zeros(ns, p.nh*p.nt) - 1e12;
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| Ltemp = zeros(ns, p.nh*p.nt);
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| Cash = At + Y;
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| for i = 1 : p.nh*p.nt
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| ttilde = (p.tgrid(ht(i, 2)) - p.F0m/p.hgrid(ht(i, 1)))/(1 + p.F1m);
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| Ltemp(:, i) = Cash - (1 - ttilde).*p.hgrid(ht(i, 1)); % liquidity after housing choice
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (ht(i, 1) - 1)*p.no*p.nt + (ht(i, 2) - 1) *p.no + p.no;
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| good = (ttilde <= min(p.thetam, pti*Y/p.mbar/p.hgrid(ht(i, 1)))) & (Ltemp(:,i) > p.lgrid(1));
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| if any(good)
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| vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
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| end
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| end
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| [vall(:, branch), htemp] = max(vtemp, [], 2);
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| hind = sub2ind([ns, p.nh*p.nt], (1 : 1 : ns)', htemp);
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| Lall(:, branch) = Ltemp(hind);
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| omegaall(:, branch) = 1;
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| thetaall(:, branch) = p.tgrid(ht(htemp, 2));
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| hall(:, branch) = p.hgrid(ht(htemp, 1));
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| end
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| end
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| [vn, in] = max(vall(:, 1 : 2), [], 2);
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| vb = vall(:,3);
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| pb = (1 - exp(-p.nu*max(vb - vn, 0))).*(vb >= vn);
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| pall = zeros(ns, 3);
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| pall(:, 1) = (1 - pb).*(in == 1);
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| pall(:, 2) = (1 - pb).*(in == 2);
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| pall(:, 3) = pb;
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| v = vn.*(vb < vn) + (vb - pb/p.nu).*(vb >= vn);
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| else
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| Lall = zeros(ns, 5);
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| omegaall = zeros(ns, 5);
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| thetaall = zeros(ns, 5);
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| hall = zeros(ns, 5);
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| vall = zeros(ns, 5);
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| for branch = 1 : 1 : 5
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| if branch == 1
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| Lall(:, branch) = At + Y + (1 - p.Fs)*s(:,4) - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4);
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| omegaall(:, branch) = 0;
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| thetaall(:, branch) = 0;
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| hall(:, branch) = 0;
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| vall(:, branch) = Wrinterp(Lall(:, branch), znow);
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| elseif branch == 2
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| vtemp = zeros(ns, p.nh) - 1e12;
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| Ltemp = zeros(ns, p.nh);
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| Cash = At + Y + (1 - p.Fs)*s(:,4) - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4);
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| for i = 1 : p.nh
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| Ltemp(:,i) = Cash - p.hgrid(i);
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (i - 1)*p.no*p.nt + (1 - 1) *p.no + 1;
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| good = Ltemp(:, i) >= p.lgrid(1);
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| if any(good)
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| vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
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| end
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| end
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| [vall(:, branch), htemp] = max(vtemp, [], 2);
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| hind = sub2ind([ns, p.nh], (1 : 1 : ns)', htemp);
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| Lall(:, branch) = Ltemp(hind);
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| omegaall(:, branch) = 0;
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| thetaall(:, branch) = 0;
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| hall(:, branch) = p.hgrid(htemp);
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| elseif branch == 3 % Purchase home with mortgage
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| ht = gridmake((1 : 1 : p.nh)', (1 : 1 : p.nt)');
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| vtemp = zeros(ns, p.nh*p.nt) - 1e12;
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| Ltemp = zeros(ns, p.nh*p.nt);
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| Cash = At + Y + (1 - p.Fs)*s(:, 4) - (1 + p.rm)*s(:, 2).*s(:, 3).*s(:, 4);
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| for i = 1 : p.nh*p.nt
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| ttilde = (p.tgrid(ht(i, 2)) - p.F0m/p.hgrid(ht(i, 1)))/(1 + p.F1m);
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| Ltemp(:, i) = Cash - (1 - ttilde).*p.hgrid(ht(i, 1));
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| good = (ttilde <= min(p.thetam, pti*Y/p.mbar/p.hgrid(ht(i, 1)))) & Ltemp(:, i) >= p.lgrid(1);
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (ht(i, 1) - 1)*p.no*p.nt + (ht(i, 2) - 1) *p.no + p.no;
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| if any(good)
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| vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
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| end
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| end
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| [vall(:, branch), htemp] = max(vtemp, [], 2);
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| hind = sub2ind([ns, p.nh*p.nt], (1 : 1 : ns)', htemp);
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| Lall(:, branch) = Ltemp(hind);
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| omegaall(:, branch) = 1;
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| thetaall(:, branch) = p.tgrid(ht(htemp, 2));
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| hall(:, branch) = p.hgrid(ht(htemp, 1));
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| elseif branch == 4
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| vtemp = zeros(ns, p.nt) - 1e12;
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| Ltemp = zeros(ns, p.nt);
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| Cash = At + Y - (1 + p.rm)*s(:, 2).*s(:, 3).*s(:, 4);
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| for i = 1 : p.nt
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| ttilde = (p.tgrid(i) - p.F0m./s(:,4))/(1 + p.F1m);
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| Ltemp(:, i) = Cash + ttilde.*s(:, 4);
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| good = (ttilde <= min(p.thetam, pti*Y/p.mbar./s(:,4))) & Ltemp(:, i) >= p.lgrid(1);
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (i - 1)*p.no + p.no;
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| if any(good)
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| vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
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| end
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| end
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| [vall(:, branch), htemp] = max(vtemp, [], 2);
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| hind = sub2ind([ns, p.nt], (1 : 1 : ns)', htemp);
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| Lall(:, branch) = Ltemp(hind);
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| omegaall(:, branch) = 1;
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| thetaall(:, branch) = p.tgrid(htemp);
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| hall(:, branch) = s(:, 4);
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| elseif branch == 5 % Stay inactive
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| vtemp = zeros(ns, p.no + 1) - 1e12;
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| Ltemp = zeros(ns, p.no + 1);
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| % Pay more than required
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| Cash = At + Y - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4);
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| for i = 1 : p.no
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| Ltemp(:, i) = Cash + p.ogrid(i).*s(:,3).*s(:,4);
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| good = (p.ogrid(i) < max((1 + p.rm)*s(:,2) - p.mbar, 0)) & (Ltemp(:, i) >= p.lgrid(1));
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (tnow - 1)*p.no + i;
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| if any(good)
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| vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
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| end
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| end
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| % Pay minimum required
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| otemp = max((1 + p.rm)*s(:,2) - p.mbar, 0);
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| Ltemp(:, p.no + 1) = At + Y - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4) + otemp.*s(:,3).*s(:,4);
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| good = (Ltemp(:, p.no + 1) >= p.lgrid(1));
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| if any(good)
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| % Interpolate
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| otempind = lookup1(p.ogrid, otemp, 3);
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| w = (p.ogrid(otempind + 1) - otemp)./(p.ogrid(otempind + 1) - p.ogrid(otempind));
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (tnow - 1)*p.no + otempind;
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| vtemp(good, p.no + 1) = w(good).*Whinterp(Ltemp(good, p.no + 1), ind2(good));
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| ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (tnow - 1)*p.no + otempind + 1;
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| vtemp(good, p.no + 1) = vtemp(good, p.no + 1) + (1 - w(good)).*Whinterp(Ltemp(good, p.no + 1), ind2(good));
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| end
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| [vall(:, branch), htemp] = max(vtemp, [], 2);
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| hind = sub2ind([ns, p.no + 1], (1 : 1 : ns)', htemp);
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| Lall(:, branch) = Ltemp(hind);
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| omegaall(htemp <= p.no, branch) = p.ogrid(htemp(htemp <= p.no));
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| omegaall(htemp > p.no, branch) = otemp(htemp > p.no);
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| thetaall(:, branch) = p.tgrid(tnow);
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| hall(:, branch) = s(:,4);
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| end
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| end
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| [vn, in] = max(vall(:, [1, 2, 5]), [], 2);
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| [vb, ib] = max(vall(:, [3, 4]), [], 2);
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| pb = (1 - exp(-p.nu*max(vb - vn, 0))).*(vb >= vn);
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| pall = zeros(ns, 5);
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| pall(:, 1) = (1 - pb).*(in == 1);
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| pall(:, 2) = (1 - pb).*(in == 2);
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| pall(:, 5) = (1 - pb).*(in == 3);
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| pall(:, 3) = pb.*(ib == 1);
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| pall(:, 4) = pb.*(ib == 2);
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| v = vn.*(vb < vn) + (vb - pb/p.nu).*(vb >= vn);
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| end
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