65 lines
1.9 KiB
Mathematica
65 lines
1.9 KiB
Mathematica
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function F = nnz_internal(z,x,direction)
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switch direction
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case 0
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[nx,mx] = size(x);
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if issymmetric(x)
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d = binvar(nx,nx); % d == 1 means x(i,j) can be non-zero
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else
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d = binvar(nx,mx,'full');
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end
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x = reshape(x,nx*mx,1);
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d = reshape(d,nx*mx,1);
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[M,m] = derivebounds(x);
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F = (m.*d <= x <= M.*d) + (z == sum(sum(d)));
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F = F + (0 <=z <= nx*mx);
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case 1
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[nx,mx] = size(x);
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if issymmetric(x)
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du = binvar(nx,nx); % du == 1 means x(i,j) > 0
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dd = binvar(nx,nx); % dd == 1 means x(i,j) < 0
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else
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du = binvar(nx,mx,'full');
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dd = binvar(nx,mx,'full');
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end
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x = reshape(x,nx*mx,1);
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du = reshape(du,nx*mx,1);
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dd = reshape(dd,nx*mx,1);
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[M,m] = derivebounds(x);
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fixedzeros = find(M==m & m==0);
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positive = find(m>0);
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negative = find(M<0);
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left = setdiff(1:nx*mx,[fixedzeros;positive;negative]);
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m = m(left);
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M = M(left);
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x = x(left);
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du = du(left);
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dd = dd(left);
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du(M<=0) = 0;
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dd(m>=0) = 0;
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F = [];
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eps=1e-3;
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F = F + (sum([du dd],2) <= 1);
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F = F + (z == length(negative)+length(positive) + ((sum(du) + sum(dd))));
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F = F + (x >= eps+(m-eps).*(1-du));
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F = F + (x <= eps+(M-eps).*du);
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F = F + (x <=-eps+(M+eps).*(1-dd));
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F = F + (x >= -eps+(m+eps).*dd);
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F = F + (m.*(du+dd) <= x <= M.*(dd+du));
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F = F + (0 <= z <=nx*mx);
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%F = F + (x > 0+(m-0).*(1-du));
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% F = F + (x < -0+(0+M).*(1-dd));
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%F = F + (0 <= z <=nx*mx);
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% F = (m.*(du+dd) <= x <= M.*(du+dd)) + (sum([du dd],2) <= 1);
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% F = F + (z == ((sum(du) + sum(dd))));
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% F = F + (x > 1e-5+(-1+m).*(1-du));
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% F = F + (x < -1e-5+(1+M).*(1-dd));
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% F = F + (0 <= z <=nx*mx);
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otherwise
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end
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