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Author: rahulvigneswaran

Chebyshev Approximation/comp_residual.m

@@ -0,0 +1,49 @@
+
+function F = comp_residual(x)
+
+global params truss_data samples f
+
+
+
+matB = truss_data.matB;
+matG = truss_data.matG;
+vec_f = truss_data.vec_f;
+
+nm = size(matB,1);
+nd = size(matB,2);
+ns = length(samples.eps);
+
+%%%%% x = [vec_u; vec_e; vec_s];
+vec_u = x(1:nd);
+vec_e = x((nd+1):(nd+nm));
+vec_s = x((nd+nm+1):end);
+
+%%%%% Compatibility relation
+res_compatibility = 10^(3) * ((matB * vec_u) - vec_e);
+
+%%%%% Force-balance equation
+res_force_balance = (matG * vec_s) - vec_f;
+
+%%%%% Regression
+res_regression = zeros(nm,1);
+for i=1:nm
+S = f.s(vec_e(i));
+%S = neural(vec_e(i));
+
+%     numer = 0;
+%     denom = 0;
+%     for j=1:ns
+%         numer = numer +...
+%             exp( -params.alpha * ((vec_e(i) - samples.eps(j))^2) ) * samples.sig(j);
+%         denom = denom +...
+%             exp( -params.alpha * ((vec_e(i) - samples.eps(j))^2) );
+%     end
+     res_regression(i) = S - vec_s(i);
+%       res_regression(i) = (numer/denom) - vec_s(i);
+end
+
+%%%%% Assemblage
+F = [res_compatibility; res_force_balance; 10^(1)*res_regression];
+
+
+

Chebyshev Approximation/member.m

@@ -0,0 +1,86 @@
+
+function [dll,matH,coord_x,ir,irr,ird] = member(nx,ny)
+%
+dx = 360.0;
+dy = 360.0;
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% coord_x (nk, 2)
+% --->
+for i=1:(ny+1)
+    for j=1:(nx++1)
+        pp = ((i-1) * (nx+1)) + j;
+        coord_x(pp,1) = (j-1) * dx;
+        coord_x(pp,2) = (i-1) * dy;
+    end
+end
+nk = size(coord_x,1);
+
+%%%% irr(nm, 2)
+irr = [...
+    4  5;
+    5  6;
+    1  2;
+    2  3;
+    2  5;
+    3  6;
+    2  4;
+    1  5;
+    3  5;
+    2  6;
+    ];
+nm = size(irr,1);
+%
+%%%% ird(nk, 2)
+ird = ones(nk,2);
+for j=1:(ny+1)
+    pp = ((nx+1) * (j-1)) + 1;
+    ird(pp,:) = zeros(1,2);
+    clear pp
+end
+nd = sum(sum(ird));
+%
+ii = 0;
+for j=1:nk
+    for k=1:2
+        if ird(j,k) == 1
+            ii = ii + 1;
+            ird(j,k) = ii;
+        else
+            ird(j,k) = nd +1;
+        end
+    end
+end
+%
+%%%% ir(nm, 4)
+ir = zeros(nm,4);
+for i=1:nm
+    for j=1:2
+        ir(i,j)   = ird(irr(i,1), j);
+        ir(i,j+2) = ird(irr(i,2), j);
+    end
+end
+%
+%%%% matH(nd, nm)
+dll = zeros(nm,1);
+matH = sparse(zeros(nd+1,nm));
+for i=1:nm
+    j1 = irr(i,1);
+    j2 = irr(i,2);
+    dx = coord_x(j2,1) - coord_x(j1,1);
+    dy = coord_x(j2,2) - coord_x(j1,2);
+    dll(i) = norm([dx; dy], 2);
+    dir_cos(1) =-dx/dll(i);
+    dir_cos(2) =-dy/dll(i);
+    dir_cos(3) = dx/dll(i);
+    dir_cos(4) = dy/dll(i);
+    for j=1:4
+        if abs(dir_cos(j)) < 10^(-16)
+            dir_cos(j) = 0;
+        end
+        matH(ir(i,j),i) = dir_cos(j);
+    end
+end
+%
+matH = matH(1:nd,:);
+

Chebyshev Approximation/obj_fun_entropy.m

@@ -0,0 +1,29 @@
+
+function f = obj_fun_entropy(x)
+
+global params truss_data samples
+
+nm = size(truss_data.matB,1);
+nd = size(truss_data.matB,2);
+ns = length(samples.eps);
+vec_vol = truss_data.vol;
+
+%%%%% x = [vec_u; vec_e; vec_s];
+vec_e = x((nd+1):(nd+nm));
+vec_s = x((nd+nm+1):end);
+
+power_num = zeros(ns,1);
+for j=1:ns
+    for i=1:nm
+        power_num(j) = power_num(j) +...
+            ( (params.c_value/2) * vec_vol'...
+            * ( (vec_e - samples.eps(j)) .* (vec_e - samples.eps(j)) ) )...
+            + ( (1/(2*params.c_value)) * vec_vol'...
+            * ( (vec_s - samples.sig(j)) .* (vec_s - samples.sig(j)) ) );
+    end
+end
+
+f = 0;
+for j=1:ns
+    f = f - exp(-(params.beta/2) * power_num(j));
+end