76 lines
2.0 KiB
Mathematica
76 lines
2.0 KiB
Mathematica
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function keep = newtonpolytope(exponent_m,exponent_p)
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%NEWTONPOLYTOPE Internal function to remove monimials in SOS programs using Newton polytope
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% Author Johan L<EFBFBD>fberg
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% $Id: newtonpolytope.m,v 1.1 2006-03-30 13:27:20 joloef Exp $
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% WARNING : THIS CODE SUCKS AND IS ONLY USED AS A BACK UP PLAN
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% IF EVERYTHING ELSE FAILS (CRASHING LP SOLVERS ETC)
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% *************************************
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% TRY TO CALCULATE CONVEX HULL
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% *************************************
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try
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cnvhull = convhulln(full(exponent_p));
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catch
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keep = 1:size(exponent_m,1);
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return
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end
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% ***************************************
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% GET THE UNIQUE POINTS OF IN CONVEX HULL
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% ***************************************
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unique_points = unique(cnvhull);
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% ***************************************
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% CALCULATE A POINT IN INTERIOR
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% ***************************************
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p_c = sum(exponent_p(unique_points,:),1)'/length(unique_points);
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% ***************************************
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% CALCULATE HYPER-PLANES Ai^T(x-bi)=0
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% ***************************************
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j = 1;
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A = [];
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for i = 1:size(cnvhull,1)
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X = exponent_p(cnvhull(i,:),:)';
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y = X(:,1);
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dX = X(:,2:end)-repmat(X(:,1),1,size(X,2)-1);
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Atemp = null(full(dX'));
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% Is this a full-dimensional facet
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if size(Atemp,2)==1
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direction = (p_c-y)'*Atemp;
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if direction > 0
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A{j}=-Atemp;
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else
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A{j}=Atemp;
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end
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b{j}=y;
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j=j+1;
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end
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end
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% ***************************************
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% CHECK IF MONOMIAL IS IN NEWTON POLYTOPE
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% ***************************************
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if ~isempty(A)
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keep = [];
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for j = 1:size(exponent_m,1)
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inside = 1;
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y = exponent_m(j,:)';
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if isempty(findrows(exponent_p,y)) % Numerically safe on border
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i = 1;
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while inside & (i<=length(A))
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inside = inside & ((A{i}'*(y-b{i}))<=1e-9);
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i = i+1;
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end
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end
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if inside
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keep = [keep j];
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end
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end
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else
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keep = 1:size(exponent_m,1);
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end
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