111 lines
2.3 KiB
Mathematica
111 lines
2.3 KiB
Mathematica
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function dfdx = shadowjacobian(f,x)
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% See SDPVAR/jacobian
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if isa(f,'double')
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dfdx = zeros(size(f,1),length(x));
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return
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end
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if ~isempty(intersect(deepdepends(f),depends(x)))
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% Under development
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end
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if nargin==1
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if isa(f,'sdpvar')
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x = recover(depends(f));
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else
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x = 0;
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end
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else
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if length(getvariables(x))<length(x)
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error('x should be a vector of scalar independant variables');
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end
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end
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[n,m]=size(f);
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if m>1
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error('Jacobian only defined for column vectors.')
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end
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if n*m==1
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dfdx = scalar_jacobian(f,x);
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% Argh, fix this (sorts inside scalar_jacobian
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for i = 1:length(x)
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var(i,1)=getvariables(x(i));
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end
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[i,j]=sort(var);
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dfdx = dfdx(1,j);
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return
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else
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dfdx = [];
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AllVars = recover(unique([depends(f) getvariables(x)]));
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for i = 1:length(f)
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dfdx = [dfdx;scalar_jacobian(f(i),x,AllVars)];
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end
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% Argh, fix this (sorts inside scalar_jacobian
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for i = 1:length(x)
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var(i,1)=getvariables(x(i));
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end
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[i,j]=sort(var);
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dfdx = dfdx(:,j);
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end
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function [dfdx,dummy] = scalar_jacobian(f,x,AllVars)
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if isa(f,'double')
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dfdx = zeros(1,length(x));
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return
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end
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if nargin==2
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AllVars = recover(uniquestripped([depends(f) getvariables(x)]));
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%AllVars = recover(uniquestripped([deepdepends(f) depends(f) getvariables(x)]));
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end
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exponent_p = exponents(f,AllVars);
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coefficients = getbase(f);
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coefficients = coefficients(2:end);
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coefficients = coefficients(:);
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if nnz(exponent_p(1,:))==0
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exponent_p=exponent_p(2:end,:);
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end
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x_variables = getvariables(x);
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AllVars_variables = getvariables(AllVars);
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%AllDeriv = [];
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AllDeriv2 = [];
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for k = 1:length(x)
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wrt = find(ismembc(AllVars_variables,x_variables(k)));
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deriv = exponent_p;
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deriv(:,wrt) = deriv(:,wrt)-1;
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keep{k} = find(deriv(:,wrt)~=-1);
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AllDeriv2 = [AllDeriv2;deriv(keep{k},:)];
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end
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if size(AllDeriv2,1)==0
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dummy = 1;
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else
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dummy = recovermonoms(AllDeriv2,AllVars);
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end
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top = 1;
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dfdx=[];
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for k = 1:length(x)
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wrt = find(ismembc(AllVars_variables,x_variables(k)));
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m = length(keep{k});
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if m>0
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poly = sum((coefficients(keep{k}(:)).*exponent_p(keep{k}(:),wrt)).*dummy(top:top+m-1),1);
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top = top + m;
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else
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poly = 0;
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end
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dfdx = [dfdx ; poly];
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end
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dfdx = dfdx';
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