How to use the steepest descent method to solve a function to find the unknown parameters value

why it shows error,please fix this

ao=1;

bo=0.2;

co=0.1;

x = [0.9 1.5 13.8 19.8 24.1 28.2 35.2 60.3 74.6 81.3];

y= [455.2 428.6 124.1 67.3 43.2 28.1 13.1 -0.4 -1.3 -1.5];

Sum=0

for i=1:10

S=((y(i)-(ao.*(exp(bo.x(i))+co.x(i)).^2)));

fun = @(y,x) (a*(exp(bx))+c*x);

Sum=Sum+S

end

Initial_S=Sum

coeffi_mat=[1 0.2 0.1];

%now calculating next coefficints and then finding new S, till the value of S<0.01

j=1

while S>0.01

S_to_a=0;

S_to_b=0;

S_to_c=0;

for i=1:10

Part_1=(y(i)-(coeffi_mat(j,1)).*exp(coeffi_mat(j,2)).x(i));

S_to_a_sum_2=-1.*exp(coeffi_mat(j,2)).x(i);

S_to_a_sum= Part_1.*S_to_a_sum_2;

S_to_a= S_to_a+ S_to_a_sum;

S_to_b_sum_2=-(coeffi_mat(j,1)).*x(i).*exp(coeffi_mat(j,2)).x(i);

S_to_b_sum= Part_1.*S_to_b_sum_2;

S_to_c_sum_2=-x(i);

S_to_c=Part_1.*S_to_c_sum_2;

end

S_to_a_final=2.*S_to_a

S_to_b_final=2.*S_to_b

S_to_c_final=2.*S_to_c

%%%%%%%%%5calculating gradient%%%%%%%%5

grad=sqrt((S_to_a_final).^2+(S_to_b_final).^2+(S_to_c_final).^2)

%%%%%%%%%%%calculating unit vectoresb%%%%%%%%555

uv_a=S_to_a_final/grad

uv_b=S_to_b_final/grad

uv_c=S_to_c_final/grad

%%%%%%%%calculating new coefficient %%%%%%%

%%%del=0.02

a= coeffi_mat(i,1)-(0.02*uv_a)

b= coeffi_mat(i,2)-(0.02*uv_b)

c= coeffi_mat(i,3)-(0.02*uv_c)

%%%% Appending new coefficient in coefficient matrix %%%%%%%%%5

coeffi_mat=[coeffi_mat;a,b,c]

%%%%%%%% calculating the value of S %%%%%%%%

for i=1:10

S_1=y(i)

S_2= (coeffi_mat(i+1,1).*exp(coeffi_mat(j+1,2).*1)+coeffi_mat(j+2,3).*1)

S=((S_1)-(S_2))^2

end

end

%%whn while loop will end, final value of Swill be found thn value of a,b,c

%%will be expected as

final_a=coeffi_mat(end,1)

final_b=coeffi_mat(end,2)

final_c=coeffi_mat(end,3)

Answer 1

[Mohith Kulkarni]

You have to post the error you are facing and post the code using the editor as it is hard to read this way.

I have tried to run the code, and seems like the error is in line 9:

 S=((y(i)-(ao.*(exp(bo.x(i))+co.x(i)).^2)));
 

the bo.x(i) and co.x(i) term is invalid. If you are trying to multiply the scalar use .* instead.

  S=((y(i)-(ao.*(exp(bo.*x(i))+co.*x(i)).^2)));