Estimating a function in matlab using different values of parameters froma matrix/dataset

THE SITUATION

I have the following function:

(2*(r - 1))/(90 - x)^r - (4*(r - 1))/(2*x + 90)^r + (a*(r - 1))/(2*(90 - x)^r) - (a*(r - 1))/(2*x + 90)^r =0

I have a dataset/matrix with different values of r and x and I wish to estimate "a"

I tried the following:

a) generate a function:

function [x] =Model_b(x,r,a,j)

f=@(x) ((2*(r - 1))/(90 - x)^r - (4*(r - 1))/(2*x + 90)^r...
    + (a*(r - 1))/(2*(90 - x)^r) - (a*(r - 1))/(2*x + 90)^r ==0);
    a =  solve(f, a )
    end

b) try to run a loop:

for i=1:N
    r=dataset2(i,3);
    x=dataset2(i,2);
   a(i)=Model_b(r,x,a);
 end 

RESULT

1) If I have the "==0"

I get the following error

f =

  function_handle with value:

    @(x)(2*(r-1))/(90-x)^r-(4*(r-1))/(2*x+90)^r+(a*(r-1))/(2*(90-x)^r)-(a*(r-1))/(2*x+90)^r==0

Error using solve (line 266)
Specify the variable to solve for.

Error in FSdydx_b (line 8)
a =  solve(f,a)

2) If I remove "==0" I get the following sequence of errors:

Undefined operator '*' for input arguments of type 'struct'.

Error in Model_b>@(x)((2*(r-1))/(90-x)^r-(4*(r-1))/(2*x+90)^r+(a*(r-1))/(2*(90-x)^r)-(a*(r-1))/(2*x+90)^r) (line 7)
   (2*(r - 1))/(90 - x)^r - (4*(r - 1))/(2*x + 90)^r + (a*(r - 1))/(2*(90 - x)^r) - (a*(r - 1))/(2*x + 90)^r...

Error in sym>funchandle2ref (line 1291)
    S = x(S{:});

Error in sym>tomupad (line 1204)
    x = funchandle2ref(x);

Error in sym (line 211)
                S.s = tomupad(x);

Error in solve>getEqns (line 402)
        a = sym(a);

Error in solve (line 226)
[eqns,vars,options] = getEqns(varargin{:});

Error in model_b (line 10)
a =  solve(f, a )

ADDITIONAL COMMENTS

Note that if my function was of the simpler form:

 function [x] = Model_y_(x,r,b,j)
     b =  -(4*x - (90 - x)^r + (2*x + 90)^r - 90)/(90 - x)^r
 end

I can do the estimation without a problem. My problem stems from the fact that I cannot initially create such a format so I need to say to Matlab to input the values of r and x and solve for b. Any idea what I am doing wrong?

Answer 1

[Stephan]

Hi,

no datasets needed i think, a=-4.

syms r x a
fun = (2*(r - 1))/(90 - x)^r - (4*(r - 1))/(2*x + 90)^r + (a*(r - 1))/(2*(90 - x)^r) - (a*(r - 1))/(2*x + 90)^r ==0;
result = isolate(fun,a)

Best regards

Stephan

[Alex Karakostas]

HI Stephan!

Thanks for the quick reply! You are right. It seems that -4 is the solution. Let me generalize the question, as I anticipate I will run to this again.

How do I write a function which says, for function x solve(x,a). I think that the error comes from the way I define the function, as otherwise I should receive the answer -4 in my dataset for all observations.

Best regards,

Alex

PS: Happy New Year!

[Stephan]

A very good answer to this consecutive question is given by Madhan below. But sometimes Symbolic Toolbox fails if things are getting to complicated, then you should try to solve numeric - for example by using fzero.

Answer 2

[madhan ravi]

solve is a part of symbolic math toolbox so the variables have to be defined as of symbolic class so remove @(x) and define it as syms at the beginning as Stephen showed in his answer.

[Alex Karakostas]

Hi Madhan,

Following your point and Stephan answer I did the following:

Changed the function to:

    function [x] = Model_b(x,r,a,j)
        syms r x a
        f=(2*(r - 1))/(90 - x)^r - (4*(r - 1))/(2*x + 90)^r + (a*(r - 1))/(2*(90 - x)^r) - (a*(r - 1))/(2*x + 90)^r
        a = solve(f,a)
    end 

and then run my loop from before. I now get a calculation.

f =
 
(2*r - 2)/(90 - x)^r - (4*r - 4)/(2*x + 90)^r + (a*(r - 1))/(2*(90 - x)^r) - (a*(r - 1))/(2*x + 90)^r
 
 
a =
 
-4
 
The following error occurred converting from sym to double:
Unable to convert expression into double array.

However, there is still something wrong as it does not pass this information in to the a0 matrix.

[madhan ravi]

Please upload the script your trying also I have no clue why your function requires input when you have defined everything inside the function.

[Stephan]

dont use a in double sense as a numric variable to save result in and as a symbolic variable at the same time - try:

res_a = double(solve(f,a))

or when using isolate:

res_a = double(rhs(isolate(f,a)))

[madhan ravi]

oh, or lookup vpasolve()

vpasolve(f,a)