Partial Derivative and its roots

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Ali Akber
Ali Akber 2015-10-28
评论： @Johannes 2015-10-28
Dear Matlab Gurus
I want to calculate the symbolic partial derivative of a function w.r.t to 'a' and 'b'. The function is
f=n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2)
Further more I also want to simplify and calculate the roots of both variable 'a' and 'b'. Actually I want to find the optimal point expression for both 'a' and 'b'. My code is
syms a
syms b
syms n
syms p
syms h
syms g
syms d
syms e
syms r
syms s
f=inline('(n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2)','a','b');
diff(diff(f(a,b),a),b)
however, the above code generates the following errors
Error using inlineeval (line 15)
Error in inline expression ==> (n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2)
Undefined function or variable 'n'.
Error in inline/subsref (line 24)
INLINE_OUT_ = inlineeval(INLINE_INPUTS_, INLINE_OBJ_.inputExpr, INLINE_OBJ_.expr);
Error in test (line 12)
diff(diff(f(a,b),a),b)
Any kind of help is highly appreciated.
P.S: I have the symbolic math toolbox installed.
Regards

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采纳的回答

@Johannes
@Johannes 2015-10-28
Hi Ali,
instead of the inline function you should use Anonymus Functions because inline will be removed in future releases.
syms a b n p h g d e r s
f=@(n,a,b,p,h,g,d,r,e,s) (n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2);
diff(diff(f,a),b)
Best regards,
Johannes
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Ali Akber
Ali Akber 2015-10-28
Thank you Johannes I deleted and reinstalled my Matlab and now the above code is working fine.
>> syms a b n p h g d e r s
>> f=@(n,a,b,p,h,g,d,r,e,s) (n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2);
>> derivative=diff(diff(f,a),b)
derivative =
(a*b*g^2*h^2*n*p*(b*d*n*g^2*r^2 + d*e*(b - 1)*s^2))/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2)^2 - (b*g^2*h^2*n*p)/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2) - (g^2*h^2*n*p*(b - 1))/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2) + (b*g^2*h^2*n*p*(a*d*n*g^2*r^2 + d*e*(a - 1)*s^2)*(b - 1))/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2)^2 + (a*g^2*h^2*n*p*(b*d*n*g^2*r^2 + d*e*(b - 1)*s^2)*(b - 1))/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2)^2 + (a*b*g^2*h^2*n*p*(d*n*g^2*r^2 + d*e*s^2)*(b - 1))/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2)^2 - (2*a*b*g^2*h^2*n*p*(a*d*n*g^2*r^2 + d*e*(a - 1)*s^2)*(b*d*n*g^2*r^2 + d*e*(b - 1)*s^2)*(b - 1))/(a*b*d*n*g^2*r^2 + d*e*(a - 1)*(b - 1)*s^2)^3
since the output is very long and it will take my lots of time to solve it manually, can you help me on how to find the roots of 'a' and 'b' using matlab?. I tried this but it didn't work.
>> [sola, solb] = solve([derivative == 0, derivative == 0], [a, b])
Once again thank you so much.
Regards
Ali
@Johannes
@Johannes 2015-10-28
Once again code:
syms a b n p h g d e r s
f=@(n,a,b,p,h,g,d,r,e,s) (n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2);
derivative_a=diff(f,a);
derivative_b=diff(f,b);
[sol_a,sol_b]=solve([derivative_a==0,derivative_b==0],[a,b])
You can type for example " doc solve " in your Matlab command window and the documentation of solve will appear.
Regards, Johannes

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更多回答（1 个）

Torsten
Torsten 2015-10-28
Why do you calculate diff(diff(f,a),b) ? Just for testing ?
syms a b n p h g d e r s
[sol_a,sol_b]=solve([diff(n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2,a)==0,diff(n*a*b*(1-b)*p*h^2*g^2)/(n*a*b*g^2*d*r^2+(1-a)*(1-b)*d*e*s^2,b)==0],[a,b])
Best wishes
Torsten.
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Ali Akber
Ali Akber 2015-10-28
Didn't work, generates these errors.
Error using char
Conversion to char from logical is not possible.
Error in solve>getEqns (line 245)
vc = char(v);
Error in solve (line 141)
[eqns,vars,options] = getEqns(varargin{:});
Something wrong with my Matlab? Can you execute and post your results?
Regards
Ali
Torsten
Torsten 2015-10-28
Consult your documentation on how to use the solve-command in release 2011b.
Best wishes
Torsten.

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