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matDICE.m
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matDICE.m
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function [Base,OptimAbatement,FullOptim] = matDICE(varargin)
% [Base,OptimAbatement,FullOptim] = matDICE(['parameter',value,'parameter',value,...])
%
% FullOptim is calculated allowing optimization of both abatement and savings rate.
% OptimAbatement is calculated allowing optimization only of abatement.
% Base is caulculated with both fixed.
%
% The switch 'doMonotonicity' requires abatement to monotonically increase.
% The parameter 'FixedAbatement' locks abatement for the first n periods at the values
% specified by the following vector.
% Other parameters are as in DICEParameters.
%
% Example: Calculation at 3% fixed discount rate
%
% [Base,OptimAbatement,FullOptim] = matDICE('elasmu',0,'prstp',.03);
% [BaseNoDamages] = matDICE('elasmu',0,'prstp',.03,'aa2',0);
%
% clf;
% subplot(2,1,1); hold on;
% plot(Base.times,Base.ppmCO2,'r');
% plot(FullOptim.times,FullOptim.ppmCO2,'b');
% plot(OptimAbatement.times,OptimAbatement.ppmCO2,'g');
% title('CO_2'); ylabel('ppm CO_2');
%
% subplot(2,1,2); hold on;
% plot(Base.times,Base.Output,'r');
% plot(FullOptim.times,FullOptim.Output,'b');
% plot(OptimAbatement.times,OptimAbatement.Output,'g');
% plot(BaseNoDamages.times,BaseNoDamages.Output,'k');
% title('GDP'); ylabel('Output (US$ trillion)');
%
% Last updated by Robert Kopp, robert-dot-kopp-at-rutgers-dot-edu, Thu Sep 03 21:46:21 EDT 2015
% Copyright (C) 2015 by Robert E. Kopp; distributed under GNU GPL v3
doMonotonicity=0;
setFixedAbatement = 0;
coarseners=0;
baseabate = [];
basesave = [];
MaxFunEvals = 8000;
incrementalemissions=[];
startabate = [];
dispmode = 'final';
useparallel = 'always';
usenlopt = 0;
TolX = 1e-4;
TolFun = 1e-6;
algorithm = 'sqp';
i=1; j=1;
spec={};
while(i<=length(varargin))
if strcmpi(varargin{i},'monotonicAbatement');
doMonotonicity=1;
i=i+1;
elseif strcmpi(varargin{i},'FixedAbatement');
FixedAbatement=varargin{i+1};
setFixedAbatement = 1;
i=i+2;
elseif strcmpi(varargin{i},'BaseAbatement');
baseabate = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'BaseSavings');
basesave = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'incrementalemissions');
incrementalemissions = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'startabatement');
startabate = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'Display');
dispmode = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'coarseners');
coarseners = varargin{i+1};
coarseners = sort(coarseners,1,'descend');
i=i+2;
elseif strcmpi(varargin{i},'MaxFunEvals');
MaxFunEvals = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'TolX');
TolX = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'TolFun');
TolFun = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'algorithm');
algorithm = varargin{i+1};
i=i+2;
elseif strcmpi(varargin{i},'nlopt')
usenlopt = 1;
i=i+1;
else
spec{j} = varargin{i};
spec{j+1} = varargin{i+1};
%eval(['p.' varargin{i} '=' num2str(varargin{i+1}) ';']);
i=i+2;
j=j+2;
end
end
p=DICEParameters(spec{:});
timesteps=length(p.t);
if ~setFixedAbatement
FixedAbatement = p.miu0;
end
if length(basesave)==0
basesavings = p.basesavings;
elseif length(basesave)==1
basesavings = basesave*ones(size(p.t));
else
basesavings = basesave;
end
if length(baseabate)==0
baseabatement = ones(size(p.t)) * p.miu0;
elseif length(baseabate)==1
baseabatement = ones(size(p.t)) * baseabate;
else
baseabatement = baseabate;
end
Nscenarios = length(p.T2xCO2);
basesavings=basesavings(:)';baseabatement=baseabatement(:)';
[EW,Base] = DICEEconomicModel(p,basesavings,baseabatement,[],incrementalemissions);
if length(startabate)==0
startabate=baseabatement;
end
Base.savings = basesavings;
%Base.abatement = baseabatement;
% Base.Population = p.L;
Base.times = p.t;
Base.p = p;
Base.SCC = SCC(p,basesavings,baseabatement,2);
Base.exitflag = 1;
for i=1:length(coarseners)
if nargout>1
Aeq=zeros(length(p.t));
if coarseners(i)>1
lockedslots = ones(size(p.t));
lockedslots(1:coarseners(i):end)=0;
if length(FixedAbatement)>1
lockedslots(1:length(FixedAbatement))=0;
end
lockedslots(end-1)=0; lockedslots(end)=0;
subunlocked=find(~lockedslots);
index=1;
for j=1:length(lockedslots)
if lockedslots(j)
pos = j-prevunlocked;
if nextunlocked<=length(p.t)
wts = [(1-pos/(nextunlocked-prevunlocked)) (pos/(nextunlocked-prevunlocked))];
Aeq(j,[prevunlocked nextunlocked]) = [wts];
else
Aeq(j,[prevunlocked]) = [1];
end
else
prevunlocked = subunlocked(index);
if index<length(subunlocked)
nextunlocked = subunlocked(index+1);
else
nextunlocked = prevunlocked+coarseners(i);
end
index=index+1;
Aeq(j,j) = 1;
end
end
else
lockedslots=zeros(size(p.t));
Aeq=eye(length(p.t));
subunlocked=find(~lockedslots);
end
% first optimize only abatement
WelfAbate = @(x) Welfare([basesavings(:) ; Aeq(:,subunlocked)*x]',p,incrementalemissions);
monotonicityA = sparse(zeros(length(subunlocked)));
if doMonotonicity
for i=1:length(subunlocked)-1
monotonicityA(i,i:i+1) = [1 -1];
end
end
monotonicityB = sparse(zeros(length(subunlocked),1));
startingPoint = [startabate(:)' ]';
% Lwr = [[p.miu_2005 zeros(1,timesteps-1)] ]';
% Upr = [[p.miu_2005 (ones(1,timesteps-1) * p.limmiu)] ]';
Lwr = [[ zeros(1,timesteps)] ]';
if length(p.limmiu)==1
Upr = [[ (ones(1,timesteps) * p.limmiu)] ]';
else
Upr = p.limmiu(:);
end
Lwr(1:length(FixedAbatement))=FixedAbatement;
Upr(1:length(FixedAbatement))=FixedAbatement;
if usenlopt
% experimental code
fitoptions.min_objective = @(x) WelfAbate(x');
fitoptions.verbose = 1;
%fitoptions.xtol_rel = 1e-3;
%fitoptions.ftol_rel = 1e-8;
fitoptions.xtol_abs = [ones(1,length(startingPoint))*1e-3];
fitoptions.maxeval = MaxFunEvals;
fitoptions.algorithm = NLOPT_LN_BOBYQA;
fitoptions.lower_bounds = Lwr(subunlocked);
fitoptions.upper_bounds = Upr(subunlocked);
[xopt,fopt,retcode] = nlopt_optimize(fitoptions,startingPoint);
xopt = Aeq(:,subunlocked)*xopt;
xopt = xopt(:)';
else
% fitoptions=optimset('Display',dispmode,'TolX',TolX,'TolFun',abs(1e-8*Base.ExpectedWelfare),'MaxFunEval',MaxFunEvals,'Algorithm',algorithm);
fitoptions=optimset('Display',dispmode,'MaxFunEval',MaxFunEvals,'Algorithm',algorithm,'UseParallel',useparallel,'TolX',TolX,'TolFun',TolFun);
[optm1.coeffs,optm1.fval,optm1.exitflag,optm1.output,optm1.lambda,optm1.grad] = fmincon(WelfAbate,startingPoint(subunlocked),full(monotonicityA),full(monotonicityB),[],[],Lwr(subunlocked),Upr(subunlocked),[],fitoptions);
xopt = Aeq(:,subunlocked)*optm1.coeffs;
xopt = xopt(:)';
end
[EW,OptimAbatement] = DICEEconomicModel(p,basesavings(:)',xopt,[],incrementalemissions);
%OptimAbatement.abatement=optm1.coeffs;
OptimAbatement.savings=basesavings;
OptimAbatement.times = p.t;
OptimAbatement.p = p;
OptimAbatement.SCC = SCC(p,OptimAbatement.savings,OptimAbatement.abatement,2);
OptimAbatement.exitflag = optm1.exitflag;
baseabatement = xopt;
end
if nargout > 2
Aeq2 = [Aeq Aeq*0 ; Aeq*0 Aeq];
subunlocked2 = [subunlocked subunlocked+length(p.t)];
% then optimize savings and abatement
Welfare2 = @(x) Welfare([Aeq2(:,subunlocked2) * x(:)]',p,incrementalemissions);
monotonicityA2 = sparse(zeros(length(subunlocked2)));
monotonicityA2(length(subunlocked)+1:end,length(subunlocked)+1:end)=monotonicityA;
monotonicityB2 = sparse(zeros(length(subunlocked2),1));
basesavings=basesavings(:)';
startingPoint = [basesavings(subunlocked) optm1.coeffs(:)' ]';
Lwr = [[basesavings(1) ones(1,timesteps-1)*.01] [p.miu0 zeros(1,timesteps-1)] ]';
if length(p.limmiu)==1
Upr = [[basesavings(1) ones(1,timesteps-1)*.9] [p.miu0 (ones(1,timesteps-1) * p.limmiu)] ]';
else
Upr = [[basesavings(1) ones(1,timesteps-1)*.9] [p.miu0 p.limmiu(2:end)] ]';
end
% fitoptions=optimset('Display',dispmode,'TolX',1e-4,'TolFun',abs(1e-8*Base.ExpectedWelfare),'MaxFunEval',MaxFunEvals,'Algorithm',algorithm);
% fitoptions=optimset('Display',dispmode,'TolX',1e-6,'TolFun',1e-8,'MaxFunEval',MaxFunEvals,'Algorithm',algorithm);
[optm2.coeffs,optm2.fval,optm2.exitflag,optm2.output,optm2.lambda,optm2.grad] = fmincon(Welfare2,startingPoint,full(monotonicityA2),full(monotonicityB2),[],[],Lwr(subunlocked2),Upr(subunlocked2),[],fitoptions);
optm2.coeffs = Aeq2(:,subunlocked2)*optm2.coeffs;
optm2.coeffs = optm2.coeffs(:)';
[EW,FullOptim] = DICEEconomicModel(p,optm2.coeffs(1:timesteps),optm2.coeffs(timesteps+1:end),[],incrementalemissions);
%FullOptim.abatement = [optm2.coeffs(timesteps+1:end)];
FullOptim.savings = [optm2.coeffs(1:timesteps)];
% FullOptim.Population = p.L;
FullOptim.times = p.t;
FullOptim.p = p;
FullOptim.SCC = SCC(p,FullOptim.savings,FullOptim.abatement,2);
FullOptim.exitflag = optm2.exitflag;
basesavings = FullOptim.savings;
baseabatement = optm2.coeffs;
end
end
end
function wlf=Welfare(x,p,incrementalemissions)
x=x(:)';
lentime = length(p.t);
wlf = (-1 * DICEEconomicModel(p,x(1:lentime),x(lentime+1:end),[],incrementalemissions));
end