51 lines
1.3 KiB
Mathematica
51 lines
1.3 KiB
Mathematica
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function [p,c,v] = polynomial(x,dmax,dmin)
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%POLYNOMIAL Creates parameterized polynomial
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%
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% [p,c,v] = polynomial(x,dmax,dmin)
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%
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% POLYNOMIAL is a quick way to define a parameterized polynomial p=c'*v,
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% with all monomials of dmin <= degree(p,x) <= dmax. The coefficients in
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% the polynomial are c 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
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% x = sdpvar(2,1);
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% p = polynomial(x,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 second argument should be the max degree for each variable, or a sclar');
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end
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if nargin > 2
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if (length(dmin) > 1) && (length(dmin) ~= length(x))
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error('Dimension mismatch: The second 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<3
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dmin = 0;
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end
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if any(dmin > dmax)
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error('Third 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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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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c = sdpvar(length(v),1);
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p = c'*v;
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