I want to use integral&fzero to solve the equation but I could't debug by myself

Hello, I have written some code below but I could't debug by myself. Does anyone can give me some advice? Thanks!

n = 100; Cpk_hat = 1.5; r = 0.95; zzz = 1.00;
fun = @(t,C)chi2cdf(((n-1)*((3*C+abs(zzz)*sqrt(n))-t).^2/(9*n*Cpk_hat.^2)),n-1)*...
    (normpdf(t+zzz*sqrt(n))+normpdf(t-zzz*sqrt(n)));
C_guess = 1;
fzero(@(C) integral(@(t) fun(t,C),0,((3*C+abs(zzz))*sqrt(n)))-(1-r),C_guess);

error message:
Error using fzero (line 306)
FZERO cannot continue because user-supplied function_handle ==>
@(C)integral(@(t)fun(t,C),0,((3*C+abs(strange_hat))*sqrt(n)))-(1-r) failed with the error
below.

Inner matrix dimensions must agree.

[Adam]

Simplest debugging option would be to move your complicated function into its own file, split into variables across multiple lines rather than all on one line, then just create a simple function handle to that to pass in. Then you will be able to debug it with the 'stop on errors' option from the breakpoints menu.

At a glance all your inputs are scalar so I can't see simply where your error would be.

[Louis Liu]

Thanks! I will try it!

Answer 1

[Matt J]

Define fun() with element-wise operators

 fun=@(t,C)chi2cdf(((n-1).*((3.*C+abs(zzz).*sqrt(n))-t).^2./(9.*n.*Cpk_hat.^2)),n-1).*(normpdf(t+zzz.*sqrt(n))+normpdf(t-zzz.*sqrt(n)))

[Louis Liu]

Hello @Matt J I can get some value now. But the standard answer of this equation is 1.315, and the matlab retuns me 13.1470 now. I am very sure that the value of n = 100; Cpk_hat = 1.5; r = 0.95; zzz = 1.00 are correct. Could you guess the reason why the value doesn't match the answer? Thanks!

[Matt J]

Louis,

If 1.315 is definitely the right answer, then you've definitely provided the wrong equation to fzero. You can verify by direct substitution that 13.1470 satisfies the equation much better than 1.315

>> g=@(C) integral(@(t) fun(t,C),0 ((3*C+abs(zzz))*sqrt(n)))-(1-r);

>> g(1.315)

 ans =

   -0.0500

 >> g(13.147)

 ans =

   3.6488e-06

It is noteable however that your desired answer is exactly a factor of 10 different from what fzero gave you. A missing coefficient somewhere, perhaps?

[Louis Liu]

@Matt J Thanks! I will check it again!

[Louis Liu]

@Matt J Hello, I have found the mistake and get the right value 1.3147 now. Thank for your help!