55 lines
1.9 KiB
Mathematica
55 lines
1.9 KiB
Mathematica
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function [w,F,DefinedMonoms] = recdef(pow,F,DefinedMonoms,setinitials);
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% Recursively define monomial x(pow(1))*x(pow(2))*x(pow(3))..
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% using a set of linear variables and bilinear constraints
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switch length(pow)
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case 1
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% Just a linear variable, no constraints needed
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w = recover(pow);
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case 2
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% Quadratic
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w = sdpvar(1,1);
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xx = prod(recover(pow));
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if setinitials
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assign(w,double(xx));%prod(recover(pow))));
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end
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F = F + (xx == w);
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otherwise
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% FIX: special case x^3, implemented just to
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% speed up a particular simulation I had to run.
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% This whole file should be revised, booring
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if (nnz(diff(pow)) == 0) & length(pow) == 3
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x = recover(pow(1));
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y = sdpvar(1,1);
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w = sdpvar(1,1);
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dx = double(x);
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assign([w y],[dx^3 dx^2]);
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DefinedMonoms(end+1).power = [pow(1:2)];
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DefinedMonoms(end).variable = getvariables(y);
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DefinedMonoms(end+1).power = [pow(3) getvariables(y)];
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DefinedMonoms(end).variable = getvariables(w);
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F = F + (x*x == y) + (x*y == w);
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return
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end
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i = 1;
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found = 0;
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while ~found & i <= length(DefinedMonoms)
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if isequal(pow,DefinedMonoms(i).power)
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w = recover(DefinedMonoms(i).variable);
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return
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end
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i = i + 1;
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end
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pow1 = pow(1:floor(length(pow)/2));
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pow2 = pow(1+floor(length(pow)/2):end);
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[w1,F,DefinedMonoms] = recdef(pow1,F,DefinedMonoms,setinitials);
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[w2,F,DefinedMonoms] = recdef(pow2,F,DefinedMonoms,setinitials);
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w = sdpvar(1,1);
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w1w2 = w1*w2;
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F = F + (w1w2 == w);
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if setinitials
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assign(w,double(w1w2));
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end
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DefinedMonoms(end+1).power = pow;
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DefinedMonoms(end).variable = getvariables(w);
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end
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