Differentiating gives wrong result

Question

Richárd Tóth 2019-8-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/475809-differentiating-gives-wrong-result

回答： Alex Mcaulley 2019-8-12

Hello

One of my functions returns this symbolic expression

(10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1

If I use the diff function(by x1) on it, it gives wrong result(ignores the variables or I don't know):

(20000*cos((9*pi)/40)*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40)))/9801 + (20000*sin((9*pi)/40)*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40)))/9801

Instead of:

(50706024009129175657667733171308125*x1)/24848487065673752728138376231780352

If I simply run this code, it works, so something is probably wrong with my returned expression from the function

syms x1 x2
f=(10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1;
diff(f,x1)

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Alex Mcaulley 2019-8-12

Can you show the complete code that generates the symbolic expression? As you say, it works just executing your code.

Richárd Tóth 2019-8-12

Yes, it's not the same code, that code is much longer but gives the same result.

The function:

function expr = testfunc()
syms x1 x2 d1 d2 d3 center1 center2
expr = (cos(d3)*(center1 - x1) - sin(d3)*(center2 - x2))^2/d1^2 + (cos(d3)*(center2 - x2) + sin(d3)*(center1 - x1))^2/d2^2 - 1;

and the code:

syms x1 x2 lambda d1 d2 d3 center1 center2
d1=0.9900;d2=0.9900;d3=9*pi/40;
center1=0;center2=0;
ell = testfunc;
ell = subs(ell);
g = ell;
diff(g,x1)

Running this displays the wrong value I mentioned in previous post.

If you try this, it works:

syms x1 x2
f = (10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1;
diff(f,x1)

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Answer 1

Alex Mcaulley 2019-8-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/475809-differentiating-gives-wrong-result#answer_387245

I don't know why the result is presented in different way depending on the case, but the result is allways the same:

%Case 1
syms x1 x2
f = (10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1;
sol = diff(f,x1)
sol =
    (50706024009129175657667733171308125*x1)/24848487065673752728138376231780352
    
double(subs(sol,x1,1))
ans =
    2.0406
    
%Case 2
syms x1 x2 lambda d1 d2 d3 center1 center2
d1=0.9900;d2=0.9900;d3=9*pi/40;
center1=0;center2=0;
ell = testfunc;
ell = subs(ell);
g = ell;
sol = diff(g,x1)
sol = 
(20000*cos((9*pi)/40)*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40)))/9801 + (20000*sin((9*pi)/40)*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40)))/9801
sol = simplify(sol)
sol =
(20000*x1)/9801
double(subs(sol,x1,1))
ans =
    2.0406