50 lines
1.0 KiB
Matlab
50 lines
1.0 KiB
Matlab
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% solves a*x+b*x*c=d
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function x=sylvester3(a,b,c,d)
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n = size(a,1);
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m = size(c,1);
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if n == 1
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x=d./(a*ones(1,m)+b*c);
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return
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end
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if m == 1
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x = (a+c*b)\d;
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return;
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end
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x=zeros(n,m);
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[u,t]=schur(c);
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[aa,bb,qq,zz]=qz(full(a),full(b),'real'); % available in Matlab version 6.0
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d=qq*d*u;
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i = 1;
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while i < m
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if t(i+1,i) == 0
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if i == 1
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c = zeros(n,1);
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else
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c = bb*(x(:,1:i-1)*t(1:i-1,i));
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end
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x(:,i)=(aa+bb*t(i,i))\(d(:,i)-c);
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i = i+1;
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else
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if i == n
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c = zeros(n,1);
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c1 = zeros(n,1);
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else
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c = bb*(x(:,1:i-1)*t(1:i-1,i));
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c1 = bb*(x(:,1:i-1)*t(1:i-1,i+1));
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end
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z = [aa+bb*t(i,i) bb*t(i+1,i); bb*t(i,i+1) aa+bb*t(i+1,i+1)]...
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\[d(:,i)-c;d(:,i+1)-c1];
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x(:,i) = z(1:n);
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x(:,i+1) = z(n+1:end);
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i = i + 2;
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end
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end
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if i == m
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c = bb*(x(:,1:m-1)*t(1:m-1,m));
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x(:,m)=(aa+bb*t(m,m))\(d(:,m)-c);
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end
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x=zz*x*u';
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% 01/25/03 MJ corrected bug for i==m (sign of c in x determination)
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% 01/31/03 MJ added 'real' to qz call
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