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60 lines
2.2 KiB
60 lines
2.2 KiB
3 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-05-18 19:11:25
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% @LastEditTime: 2021-05-18 21:54:48
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%--------------------------
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% fast version
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% dF.size() = 9 * 24 * m
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function dP = dPdF_fast_nonlinear(global_u, global_l, F, dF)
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% expand & reorder -> (9, 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(:), 9, []);
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dFT = dF([1:3:9,2:3:9,3:3:9], :); % 9,24
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Fdet = det_3rank(F1); % 1,m*v
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Finv = inv_3rank(F1); % 9,m*v
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%% dP1 = u * dF
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mu(1,1,:) = global_u(:);
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dP1 = dF .* mu; % 9 * v * m
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%% dP2 = (mu - lambda * JJ) * Finv' * dF' * Finv';
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JJ = reshape(log(Fdet), lenout, []); % v * m
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lambda = global_l(:)'; % 1 * m
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lm_J(1,:,:) = lambda .* JJ; % 1 * v * m
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FinvT = Finv([1:3:9,2:3:9,3:3:9], :);
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tmp = matrix_3d_multiply_3rank(matrix_3d_multiply_3rank(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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dF1 = reshape(dF, 9, []);
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tmp = matrix_3d_multiply_3rank(Finv, dF);
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trF = reshape(tmp(1,:)+tmp(5,:)+tmp(9,:), 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; % 9 * l * m
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end
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function c = matrix_3d_multiply_3rank(a, b)
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% [ a1*b1 + a4*b2 + a7*b3, a1*b4 + a4*b5 + a7*b6, a1*b7 + a4*b8 + a7*b9]
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% [ a2*b1 + a5*b2 + a8*b3, a2*b4 + a5*b5 + a8*b6, a2*b7 + a5*b8 + a8*b9]
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% [ a3*b1 + a6*b2 + a9*b3, a3*b4 + a6*b5 + a9*b6, a3*b7 + a6*b8 + a9*b9]
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c = [a(1,:) .* b(1,:) + a(4,:) .* b(2,:) + a(7, :) .* b(3, :);
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a(2,:) .* b(1,:) + a(5,:) .* b(2,:) + a(8, :) .* b(3, :);
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a(3,:) .* b(1,:) + a(6,:) .* b(2,:) + a(9, :) .* b(3, :);
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a(1,:) .* b(4,:) + a(4,:) .* b(5,:) + a(7, :) .* b(6, :);
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a(2,:) .* b(4,:) + a(5,:) .* b(5,:) + a(8, :) .* b(6, :);
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a(3,:) .* b(4,:) + a(6,:) .* b(5,:) + a(9, :) .* b(6, :);
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a(1,:) .* b(7,:) + a(4,:) .* b(8,:) + a(7, :) .* b(9, :);
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a(2,:) .* b(7,:) + a(5,:) .* b(8,:) + a(8, :) .* b(9, :);
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a(3,:) .* b(7,:) + a(6,:) .* b(8,:) + a(9, :) .* b(9, :)];
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end
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