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92 lines
2.7 KiB
92 lines
2.7 KiB
4 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2020-12-03 22:31:02
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% @LastEditTime: 2021-01-08 16:02:26
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% optimize n to get a ideal macro shape function
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% vdofs_ma: idx in micro-ndofs which matches to macro-vars
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%--------------------------
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function n_opt = optNH(u_mi, u_ma, vdofs_ma, microx, harm_u, edofMat, dNh, opt_harmonic)
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%% yalmip init
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ops = sdpsettings('solver', 'mosek');
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ops.showprogress = 0;
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ops.verbose = 0;
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ops.debug = 1;
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ops.warning = 1;
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% ops.removeequalities = 1; % removes equality constraints using a QR decomposition and reformulates the problem using a smaller set of variables
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num_v = length(vdofs_ma)/2;
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num_dofs_mi = 2*(microx+1)^2;
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harm_num = size(harm_u, 2);
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n = sdpvar(num_v*2, num_dofs_mi); % [2v, 2n]
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% n = reshape(1:num_v*2*num_dofs_mi, [], num_dofs_mi);
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%% obj
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tmp_mat = edofMat';
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n_reorder = n(:, tmp_mat(:))'; % [2v,8m]'
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n1 = reshape(n_reorder, 8, []); % [8,m*2v]
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obj = 0;
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for gp = 1:4
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dNh_g = dNh{gp}; % [4,8]
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dNH = dNh_g * n1; % [4,m*2v]
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dNH2 = reshape(dNH, [], 2*num_v); % [4*m,2v]
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% dNH1 = reshape(dNH, 4, [], 2*num_v); % [4,m,2v]
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% dNH2 = squeeze(sum(dNH1, 2)); % [4,2v]
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obj = obj + trace(dNH2 * dNH2');
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end
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%% cons
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% cons1: \sum_i n_ij = I
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I = eye(2);
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R1 = repmat(I, 1, num_v); % [2, 2v]
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C1 = repmat(eye(2),1,num_dofs_mi/2);
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cons1 = [R1 * n == C1];
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% freedofs_num = size(R12,2);
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% C1 = repmat(I, 1, freedofs_num/2); % [2, 2n]
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% cons1 = [R1 * n * R12 == C1];
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% cons2: n_ij = \delta_ij * I, for all X_i^H, X_j^H
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R2 = zeros(num_dofs_mi, 2*num_v); % [2n, 2v]
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R2(vdofs_ma, :) = eye(2*num_v);
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C2 = eye(num_v*2);
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cons2 = [n * R2 == C2];
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% tmp = (n*R2 - C2)';
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% load ttt
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% max(tmp(:) - ttt(:))
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if opt_harmonic
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% cons3: harmonic deformation
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cons3 = [];
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for i = 1:harm_num
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C3 = harm_u(:, i); % [2n, 1]
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R3 = harm_u(vdofs_ma, i); % [2v, 1]
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cons3 = [cons3, R3' * n == C3']; % [1,2v] * [2v,2n] = [1,2n]
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end
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cons = [cons1, cons2, cons3];
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else
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% cons3: micro deformation
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cons4 = u_ma' * n == u_mi';
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cons = [cons1, cons2, cons4];
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end
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%% opt
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sol = optimize(cons, obj, ops);
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% % Analyze error flags
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if sol.problem == 0
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n_opt = value(n);
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% % Extract and display value
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% u_opt = value(u_var);
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% obj_opt = value(obj)
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%
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% err = sum((u_opt-u_obj(:)).^2) / sum(u_obj(:).^2)
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else
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sol.info
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yalmiperror(sol.problem)
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end
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end
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