How can I choose powers of each variable separately and get it's value?

Hi every one I solved a equation leading to function like this f=x^a*y^b*z^c; but I don't know a,b and c.I want matlab to show me these power constants but have trouble making matlab select them. How can I choose powers of each variable separately and get it's value?

[Mahdi]

Are you trying to fit data?

[Azzi Abdelmalek]

Can you explain what how did you get f? is f symbolic class?

[behzad]

No. It was just an example.I want to do a numerical integration process using guass quadrature using equation ∫_A▒〖B_i ξ_1^(a_i ) 〗 ξ_2^(b_i ) ξ_3^(c_i )=B_i (a_i !b_i !c_i !)/((a+b+c+2)!) but the and I have a long polynomial including lots of these integrals.I want matlab to divide each term seperately term by term and identify the power constants ai,bi,ci in each term so I will be able to exert them into the right side of equation.

Answer 1

[Matt J]

If there is no error in the equations, you can take logs and turn it into a linear equation in a,b, and c

 logf=a*logx+b*logy+c*logz

[Matt J]

You can also use the linearization to develop an initial guess for the fminsearch approach (See Star Strider's answer).

Answer 2

[Star Strider]

You can do a nonlinear fit with fminsearch:

f = @(p,x,y,z) x.^p(1) .* y.^p(2) .* z.^p(3);   % Function

x = 3;                                          % Define variables
y = 5;
z = 7;

s = 13;                                         % Define f(x,y,z,) = s

objfcn = @(p) f(p,x,y,z) - s;                   % Objective function = 0 when f(x,y,z,) = s

[b, fval] = fminsearch(objfcn, [1 1 1])

produces:

b =

      11.3000    -3.0500   -25.5000

fval =

     -13.0000

[Matt J]

Should probably be

objfcn = @(p) norm(  f(p,x,y,z) - s  );

[Star Strider]

I don’t see why.

As far as we know, it’s a single-valued function. If we have a value for it for a given (x,y,z), we can accurately estimate the parameters as I described. If we don’t have these minimum conditions, it’s impossible to estimate the parameters.

If it’s part of a least-squares curve-fitting problem, a different (sum-of-squares) objective function is necessary. (The norm might be appropriate there, but since it involves the extra step of calculating the square root, usually isn’t used.)

[Matt J]

If you don't include the norm(), your error function is signed. fminsearch will then look for the 'p' that makes the error function as negative as possible.

As an example, consider the alternative data x=13,y=1,z=1, s=13. With

 objfcn = @(p) f(p,x,y,z) - s;

I obtain the false solution,

       b =

        -18.8889    6.2222    5.4278

      fval =

         -13

whereas when the norm() is included, fminsearch correctly detects that the initial point [1 1 1] is a solution,

    b =

         1     1     1

    fval =

         0

[Star Strider]

Noted. I’ve only done minimisation or least-squares curve fitting with fminsearch, so never encountered that.