Steepest descent method n shows error 'Index exceeds matrix dimensions.', how to fix this

clc
clear all
%%%%%%%%%%%%%%%%Steepest Descent %%%%%%%%%%%%%%%5
ao=1;
bo=0.2;
co=0.1;
x = [0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8];
y= [1.196 1.379 1.581 1.79 2.013 2.279 2.545 2.842 3.173 3.5];
Sum=0
for i=1:10
 S=((y(i)-(ao.*(exp(bo*x(i))+co*x(i)).^2)));
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
%%when while loop will end, final value of S will be found then 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

[Cris LaPierre]

The error means that somewhere in your code you are trying to access an element that doesn't exist. For example, if a variable has 10 values in it, you are trying to use the 11th.

When I run your code, the error appears here: a= coeffi_mat(i,1)-(0.02*uv_a)

Here, i has a value of 10 (final value from the for loop in lines 22-31), but coeffi_mat=[1 0.2 0.1]

[Cris LaPierre]

Please share the full error message along with your code.

I see this message: Index in position 1 exceeds array bounds (must not exceed 2).

This is the same underliying cause as your first error. Specifically, it is this part of your equation (j=1):

coeffi_mat(j+2,3)

[Sarvjeet Singh]

This error message -

Index exceeds matrix dimensions.

Error in Steepest_descent (line 51)

S_2=(coeffi_mat(i+1,1).*exp(coeffi_mat(j+1,2).*1)+coeffi_mat(j+2,3).*1) %(ao.*(exp(bo*x(i))+co*x(i)).^2);

This is the code-

clc

clear all

%%%%%%%%%%%%%%%%Steepest Descent %%%%%%%%%%%%%%%

ao=1;

bo=0.2;

co=0.1;

x = [0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8];

y= [1.196 1.379 1.581 1.79 2.013 2.279 2.545 2.842 3.173 3.5];

Sum=0;

for i=1:10

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

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= ao-(0.02*uv_a) %5coeffi_mat(i,1)-(0.02*uv_a)

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

c= co-(0.02*uv_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) %(ao.*(exp(bo*x(i))+co*x(i)).^2); %

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

end

end

%%when while loop will end, final value of S will be found then 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)