numeric solve issue for an equation involving a logarithm

8 次查看（过去 30 天）

Mac Sampson 2012-9-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/48772-numeric-solve-issue-for-an-equation-involving-a-logarithm

I am trying to solve an equation involving a common logorithm within a loop. I first solve an equation to get r(i). then I take that r(i) value and plug it into an equation to solve for b(i).The second equation is:

b(i)=solve('r(i)=.5*Log10(b(i)) + .5*b(i)')

It is having a lot of trouble solving this. This is the error message:

Warning: Could not find an exact (case-sensitive) match for 'Log10'.
/Applications/MATLAB_R2009aSV.app/toolbox/matlab/elfun/log10.m is a
case-insensitive match and will be used instead.
You can improve the performance of your code by using exact
name matches and we therefore recommend that you update your
usage accordingly. Alternatively, you can disable this warning using
warning('off','MATLAB:dispatcher:InexactCaseMatch').
This warning will become an error in future releases. 
> In testloopwithgraph at 6
??? Error using ==> mupadengine.mupadengine>mupadengine.feval at 162
Error: no indeterminate(s) [numeric::solve]
Error in ==> solve>mupadSolve at 232
    list = feval(symengine,'mlfsolve',eqns,vars);
Error in ==> solve at 93
[R,symvars,order] = mupadSolve(eqns,vars);
Error in ==> testloopwithgraph at 7
    b(i)=solve('r(i)=.5*Log10(b(i)) + .5*b(i)');

I can numericaly solve this equation in mathematica with just a warning about how the output might not cover all values, but it does give me values. In my matlab code it won't give me values at all. Is there a way around this?

4 个评论
显示 2更早的评论隐藏 2更早的评论

Azzi Abdelmalek 2012-9-21

在 MATLAB Online 中打开

(2:1:((n/2)-2)/1) % why /1 ?

Mac Sampson 2012-9-21

thanks for catching that. that was a typo

请先登录，再进行评论。

请先登录，再回答此问题。

回答（4 个）

Azzi Abdelmalek 2012-9-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/48772-numeric-solve-issue-for-an-equation-involving-a-logarithm#answer_59617

编辑：Azzi Abdelmalek 2012-9-21

在 MATLAB Online 中打开

use

log10

not

Log10

6 个评论
显示 4更早的评论隐藏 4更早的评论

Azzi Abdelmalek 2012-9-21

编辑：Azzi Abdelmalek 2012-9-21

在 MATLAB Online 中打开

do you want to use symbolic toolbox. In your case, implicit solution could'nt be found, unless you use just

syms b

%with r known

syms b 
sol=solve(-r(1)+0.5*log10(b)+0.5*b,b)

Mac Sampson 2012-9-21

so this code would go within the loop and without noting r and b as r(i) and b(i)?

请先登录，再进行评论。

Matt Tearle 2012-9-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/48772-numeric-solve-issue-for-an-equation-involving-a-logarithm#answer_59619

在 MATLAB Online 中打开

If I understand your intent correctly, you're trying to solve the equation

r_i = (Log10(b) + b)/2

for b, given a (numeric?) value of r_i. Then you want to store that b value as b_i. (Repeat for i+1)

If so, then (1) you don't need to do this symbolically and (2) you are getting the error because solve can't figure out what the variable is.

I'd suggest using fzero:

for i = 2:n
  % get r(i)
  % solve for b(i) using b(i-1) as an initial guess
  b(i) = fzero(@(b) (log10(b) + b)/2 - r(i),b(i-1));
end

4 个评论
显示 2更早的评论隐藏 2更早的评论

Mac Sampson 2012-9-21

i don't want to use previous values of b. the first equation gives me a value for r(i). I then want to plug in r(i) into the next equation to solve for b. this gives me one value for r(i) at that iteration and one value for b(i) at that iteration. I then want it to return to the beginning of the loop and do it all over again with i+1, giving me two new values for r(i+1) and b(i+10

Matt Tearle 2012-9-21

Yes, I understand that, but fzero is a numerical solver, so it requires an initial guess for the solution. When doing stuff like this in a loop, it's not uncommon to use the previous solution as the starting point for the next solution. If r(i) varies somewhat slowly and smoothly with i, that would make sense. But it looks like maybe that's not the case here.

So, see my new answer...

请先登录，再进行评论。

Matt Tearle 2012-9-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/48772-numeric-solve-issue-for-an-equation-involving-a-logarithm#answer_59621

编辑：Matt Tearle 2012-9-21

在 MATLAB Online 中打开

Didn't see your comment with your code. This works:

imax = (n/2)-2;
r = zeros(imax,1);
syms b
for i = 2:imax;
      r(i)=.5*log10((2*p)^((1 - 2*(i - 2))/(n - 4))*(t/2)^((2*(i - 2))/(n - 4)))+(i - 2)*(((n - 4)*p-2*p-.5*t)/(n - 4));
      bsolve(i)=solve((log10(b) + b)/2 == r(i),b);
end
bnum = double(bsolve);

8 个评论
显示 6更早的评论隐藏 6更早的评论

Mac Sampson 2012-9-22

no. r(i)=0.5*log10(b)+0.5*b is the equation i am using. I know r(i) from the previous equation in the loop. I want to solve for b. When I try to invert the function and get b(i) in terms of r(i), it spits out the wrong values.

Walter Roberson 2012-9-22

b(i) in terms of r(i) is the formula I show above, involving LambertW .

I tested in Maple and the results appear to be correct. However, in cases where r(i) is complex, there can be multiple solutions.

请先登录，再进行评论。

Mac Sampson 2012-9-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/48772-numeric-solve-issue-for-an-equation-involving-a-logarithm#answer_59640

Thanks so much to all of you. I believe with your help I have found what is wrong and will embark on tracking down and fixing the problem. Thanks again for all your help!