diff(abs(complex function)) stays complex -- wrong result

kner

2014 12 11

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4 次查看（30 天）

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Hi, i'm a newbe. Wanted to diff the abs of a complex function, but got wrong results. The problem seems to be that diff(abs ...) stays complex and then there somthing gets weird. Thx for the help.

clear 
format compact
syms x real;
v(x)=1j*x/(1j*2*x+1.1)^2;   
re(x) = real(v(x));
im(x) = imag(v(x));
vabs(x) = sqrt(re(x)^2+im(x)^2);
vabsdiff(x) = diff(vabs(x))
x0a= solve(vabsdiff(x)==0,x); %correct
fprintf('abs of complex function correct => correct\n') ;
av(x)=abs(v(x));
fprintf('diff abs => correct\n') ;
diffav(x)=diff(abs(v(x)));
assume(x>0);
x0b= solve(diffav(x)==0,x);    %wrong
n=1001;
 t=linspace(000.1,10,n);  
 %numeric now
   %attention: diff just calculates the delta y; delta x = 1 ==> correction
   %of delta x
   diffnumeric=diff(double(vabs(t)))/((t(end)-t(1))/n);
   subplot(2,2,1);
   plot(t,double(av(t)));
   title('The original function');
   subplot(2,2,2);
   plot(t(1:end-1),double(diffnumeric));
   title('Diff numeric');
   subplot(2,2,3);
   plot(t,vabsdiff(t));  %should look like subplot 2 
   title('Diff symbolic via sqrt(re^2+im^2');
subplot(2,2,4);
   plot(t,diffav(t),'r');  %should look like subplot 2 
   % warning => treated as complex
   title('Diff symbolic via diff(abs))    W R O N G !');