How can I determine (optimize) 4 constants or parameters for an equation with 4 variables in Matlab

Hello everyone, I have got an equation with 4 variables and 4 constants as shown below: Z=c * V^-m * P^n * S^x where Z, V, P and S are variables (known data) and c, m, n and x are constants (unknown). I want to find the 4 constants. Could you please help me for this issue?

Answer 1

[Alan Weiss]

If you have no constraints (limits on your variables), use fminsearch. For an example of its use, see the documentation.

If there are constraints (such as some variables must be positive) and you have an Optimization Toolbox license, use fmincon.

Alan Weiss

MATLAB mathematical toolbox documentation

[Ahmed Hasan]

Hello Alan,

Many thanks for your response.

I tried below code,

after run the code it gives below

Function definitions are not permitted in this context.

how can I deal with this? I have limited experience in Matlab

clear; clc; close all; 

         % v  p  Sr Mv
  Data=[
  2.210023964  1.96632798  0.622109327  149.0547533
  2.196296497  2.386462852  0.628820951  152.8242102
  2.166753567  2.930816699  0.643605566  173.3434531
  2.130513499  3.489837947  0.663279316  200.357107
  2.093573729  4.058286535  0.686095512  224.3755318
  2.051858223  4.642544991  0.714181664  253.672975
  2.014818496  5.222616915  0.740872305  286.0343537
  2.006311021  5.243873893  0.747957964  298.5776738
  2.006544255  4.746250414  0.748750138  293.0350632
  2.009465229  4.245741408  0.748580469  278.3670001
  2.015040624  3.741874992  0.747291664  258.6910752
  2.022992781  3.234267866  0.744755955  237.3993754
  2.03478774  2.721358308  0.740452769  212.7082272
  2.053013285  2.298431295  0.732810432  196.4847033
  2.199857403  1.983437327  0.627812442  150.9624436
  2.249930722  0.521817469  0.843634937  150.4423024
  2.184999217  2.35849701  0.752832337  203.9696001
  2.179784486  2.595391932  0.748463977  206.7854166
  2.170807228  2.755011548  0.751670516  212.9453498
  2.154370923  3.066462125  0.755487375  226.4062671
  2.140453972  3.280966559  0.760322186  235.6738926
  2.106921271  3.816402454  0.772134151  260.1511025
  2.075137815  4.354842408  0.784947469  295.4490173
  2.043596394  4.912870738  0.797623579  329.9586459
  2.014981382  5.433358856  0.811119619  354.5100443
  2.006169147  5.445896105  0.815298702  375.4243071

];

V=Data(:,1);  % v
P=Data(:,2);  %p*
S=Data(:,3);  %Sr
M=Data(:,4);  %Mv

function b = four_var(v)
V = v(1);
P = v(2);
S = v(3);
M = v(4);

b = c * V^m * P^n * S^x

%Now find a minimum for this function using V = 1.947  
% P = 0.5127, S= 0.6105 and M = 142.534 as the starting values.

v = [1.947 0.5127 0.6105  142.534];

a = fminsearch(@three_var,v)

[Walter Roberson]

??

You have V, P, S, M in your matrix, but you said that m is a constant to be found. You do not have Z in your matrix but you said Z was known. Your function uses c without defining it.

[Walter Roberson]

http://uk.mathworks.com/matlabcentral/answers/258671-code-not-working#answer_202030