63 lines
1.4 KiB
Mathematica
63 lines
1.4 KiB
Mathematica
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function [p,c,v] = matrixpolynomial(x,n,dmax,dmin)
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%MATRIXPOLYNOMIAL Creates parameterized polynomial
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%
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% [p,c,v] = matrixpolynomial(x,n,dmax,dmin)
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%
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% MATRIXPOLYNOMIAL is a quick way to define a parameterized polynomial
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% p=sum C_i v_i(x) with all monomials of dmin <= degree(p,x) <= dmax. The
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% coefficients in the polynomial are C_i while v is the monomial basis.
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%
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% Example:
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%
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% Paramterized quartic 2x2 matrix
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% x = sdpvar(2,1);
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% p = matrixpolynomial(x,2,4);
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%
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% See also MONOLIST, COEFFICIENTS
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if (length(dmax) > 1) && (length(dmax) ~= length(x))
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error('Dimension mismatch: The third argument should be the max degree for each variable, or a sclar');
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end
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if nargin > 3
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if (length(dmin) > 1) && (length(dmin) ~= length(x))
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error('Dimension mismatch: The third argument should be the max degree for each variable, or a sclar');
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end
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end
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if any(dmax < 0)
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error('Only non-negative polynomial degrees possible')
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end
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if nargin<4
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dmin = 0;
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end
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if any(dmin > dmax)
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error('Fourth argument (dmin) should not be larger than second argument (dmax)');
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end
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if any(dmin < 0)
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error('Only non-negative polynomial degrees possible')
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end
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if length(n)==1
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n = [n n];
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end
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v = monolist(x,dmax);
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if dmin <= dmax & dmin>0
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s = nchoosek(length(x) + dmin-1,dmin-1);
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v = extsubsref(v,s+1:length(v));
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end
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p = 0;
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c = [];
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for i = 1:length(v)
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Ci = sdpvar(n(1),n(2));
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c = [c reshape(Ci,[],1)];
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end
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p = reshape(c*v,n(1),n(2));
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