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45 lines
1.4 KiB
45 lines
1.4 KiB
3 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2020-10-29 15:04:18
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% @LastEditTime: 2021-01-11 22:00:36
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%--------------------------
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% fast version
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% dF.size() = 4 * l * m
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function dP = dPdF_fast(global_u, global_l, F, dF)
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% expand & reorder -> (4, lenout*eleNum_mi)
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lenout = size(dF,2);
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F1 = repmat(F, lenout, 1);
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F1 = permute(F1, [1,3,2]);
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F1 = reshape(F1(:), 4, []);
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dF_expand = reshape(dF, 4, []);
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dFT = dF_expand([1,3,2,4], :); % NOTE: change 2 rows to get dF^T
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Fdet = F1(1, :).*F1(4, :) - F1(2, :).*F1(3, :);
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Finv = F1([4,2,3,1], :) .* [1;-1;-1; 1] ./ Fdet;
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%% dP1 = u * dF
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mu(1,1,:) = global_u(:);
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dP1 = dF .* mu; % 4 * l * m
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%% dP2 = (mu - lambda * JJ) * Finv' * dF' * Finv';
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JJ = reshape(log(Fdet), lenout, []); % l * m
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lambda = global_l(:)'; % 1 * m
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lm_J(1,:,:) = lambda .* JJ; % 1 * l * m
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FinvT = Finv([1,3,2,4], :);
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tmp = matrix_3d_multiply(matrix_3d_multiply(FinvT, dFT), FinvT);
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tmp = reshape(tmp, size(dF));
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dP2 = mu .* tmp - lm_J .* tmp;
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%% dP3 = lambda * trace(F\dFe) * Finv'
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tmp = matrix_3d_multiply(Finv, dF_expand);
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trF = reshape(tmp(1,:)+tmp(4,:), lenout, []); % l*m
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lm_tr(1,:,:) = lambda .* trF; % 1*l*m
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dP3 = lm_tr .* reshape(FinvT, size(dF));
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dP = dP1 + dP2 + dP3; % 4 * l * m
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end
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