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function [res,A,info] = ep_problem_2(y,x,pm)
info = 0;
res = [];
A = [];
dynamic_model = pm.dynamic_model;
ny = pm.ny;
params = pm.params;
steady_state = pm.steady_state;
order = pm.order;
nodes = pm.nodes;
nnodes = pm.nnodes;
weights = pm.weights;
h_correction = pm.h_correction;
dimension = pm.dimension;
world_nbr = pm.world_nbr;
nnzA = pm.nnzA;
periods = pm.periods;
i_rows = pm.i_rows';
i_cols = pm.i_cols;
nyp = pm.nyp;
nyf = pm.nyf;
hybrid_order = pm.hybrid_order;
i_cols_1 = pm.i_cols_1;
i_cols_j = pm.i_cols_j;
icA = pm.icA;
i_cols_T = pm.i_cols_T;
eq_index = pm.eq_index;
i_cols_p = i_cols(1:nyp);
i_cols_s = i_cols(nyp+(1:ny));
i_cols_f = i_cols(nyp+ny+(1:nyf));
i_cols_A = i_cols;
i_cols_Ap0 = i_cols_p;
i_cols_As = i_cols_s;
i_cols_Af0 = i_cols_f - ny;
i_hc = i_cols_f - 2*ny;
nzA = cell(periods,world_nbr);
res = zeros(ny,periods,world_nbr);
Y = zeros(ny*(periods+2),world_nbr);
Y(1:ny,1) = pm.y0;
Y(end-ny+1:end,:) = repmat(steady_state,1,world_nbr);
Y(pm.i_upd_y) = y;
offset_r0 = 0;
for i = 1:order+1
i_w_p = 1;
for j = 1:(1+(nnodes-1)*(i-1))
innovation = x;
if i <= order && j == 1
% first world, integrating future shocks
if nargout > 1
A1 = sparse([],[],[],i*(1+(nnodes-1)*(i-1))*ny,dimension,nnzA*world_nbr);
end
for k=1:nnodes
if nargout > 1
if i == 2
i_cols_Ap = i_cols_Ap0;
elseif i > 2
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes- ...
1)*(i-2)*(i-3)/2);
end
if k == 1
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2);
else
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2+(i-1)*(nnodes-1) ...
+ k - 1);
end
end
if i > 1
innovation(i+1,:) = nodes(k,:);
end
if k == 1
k1 = 1;
else
k1 = (nnodes-1)*(i-1)+k;
end
if hybrid_order == 2 && (k > 1 || i == order)
z = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)+h_correction(i_hc)];
else
z = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)];
end
if nargout > 1
[d1,jacobian] = dynamic_model(z,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(eq_index,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(eq_index,i_cols_j);
end
else
d1 = dynamic_model(z,innovation,params,steady_state,i+1);
end
res(:,i,1) = res(:,i,1)+weights(k)*d1(eq_index);
end
if nargout > 1
[ir,ic,v] = find(A1);
nzA{i,j} = [ir,ic,v]';
end
elseif j > 1 + (nnodes-1)*(i-2)
% new world, using previous state of world 1 and hit
% by shocks from nodes
if nargout > 1
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
end
k = j - (nnodes-1)*(i-2);
innovation(i+1,:) = nodes(k,:);
z = [Y(i_cols_p,1);
Y(i_cols_s,j);
Y(i_cols_f,j)];
if nargout > 1
[d1,jacobian] = dynamic_model(z,innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
[ir,ic,v] = find(jacobian(eq_index,i_cols_j));
nzA{i,j} = [i_rows(ir),i_cols_A(ic), v]';
else
d1 = dynamic_model(z,innovation,params,steady_state,i+1);
end
res(:,i,j) = d1(eq_index);
if nargout > 1
i_cols_Af = i_cols_Af + ny;
end
else
% existing worlds other than 1
if nargout > 1
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2+j-1);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
end
z = [Y(i_cols_p,j);
Y(i_cols_s,j);
Y(i_cols_f,j)];
if nargout > 1
[d1,jacobian] = dynamic_model(z,innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
[ir,ic,v] = find(jacobian(eq_index,i_cols_j));
nzA{i,j} = [i_rows(ir),i_cols_A(ic),v]';
i_cols_Af = i_cols_Af + ny;
else
d1 = dynamic_model(z,innovation,params,steady_state,i+1);
end
res(:,i,j) = d1(eq_index);
end
i_rows = i_rows + ny;
if mod(j,nnodes) == 0
i_w_p = i_w_p + 1;
end
if nargout > 1 && i > 1
i_cols_As = i_cols_As + ny;
end
offset_r0 = offset_r0 + ny;
end
i_cols_p = i_cols_p + ny;
i_cols_s = i_cols_s + ny;
i_cols_f = i_cols_f + ny;
end
for j=1:world_nbr
i_rows_y = i_cols+(order+1)*ny;
offset_c = ny*(order+(nnodes-1)*(order-1)*order/2+j-1);
offset_r = offset_r0+(j-1)*ny;
for i=order+2:periods
if nargout > 1
[d1,jacobian] = dynamic_model(Y(i_rows_y,j),x,params, ...
steady_state,i+1);
if i < periods
[ir,ic,v] = find(jacobian(eq_index,i_cols_j));
else
[ir,ic,v] = find(jacobian(eq_index,i_cols_T));
end
nzA{i,j} = [offset_r+ir,offset_c+icA(ic), v]';
else
d1 = dynamic_model(Y(i_rows_y,j),x,params, ...
steady_state,i+1);
end
res(:,i,j) = d1(eq_index);
i_rows_y = i_rows_y + ny;
offset_c = offset_c + world_nbr*ny;
offset_r = offset_r + world_nbr*ny;
end
end
if nargout > 1
iA = [nzA{:}]';
A = sparse(iA(:,1),iA(:,2),iA(:,3),dimension,dimension);
end
res = res(pm.i_upd_r);
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