In A2_trail (line 16) Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN

I'm Trying to solve matrix multiplications involing 500 by 4 size...but I'm getting that warning and final ans as : a= NaN + iNaN

NaN + iNaN

NaN + iNaN

NaN + iNaN

Could someone please tell me where its going wrong and why..!

load HW2_Prob2_data
z=log(z_train);       %z_train is 500 by 1 matrix,similarly x_train and y_train    
y=log(y_train);        % train data is already available
x=x_train;
a=[1; 1; 1; 1];
r=rand(100,1);
for k=1:50
    J=rand(500,4);
    for i=1:500
        J(i,4)=double(1/a(1));
        J(i,3)=double(a(2)*(log(x(i)+a(3))));
        J(i,2)=double(a(2)/(log(x(i)+a(3))));
        J(i,1)=double(y(i));
        r(i)=double(z(i)-(log(a(1))+a(2)*log(x(i)+a(3))+a(4)*y(i)));
    end
    a_new=double(inv(J'*J)*J'*r);
    if norm(a_new)<0.0001
        break
    end
    a=a+a_new;
end
disp(a)   

[David Goodmanson]

Hello ND,

This code works if x,y and z are random positive numbers, so something is going on with your data. The most likely possibility is that x contains at least one entry xi that equals 0, so that log(xi) = inf.

Even if the data were OK, it is bad practice to solve the equation

J*a_new = r

by the old fashioned method

a_new = inv(J'*J)*J'*r .

(The 'double' isn't required since J is already a double).

Instead, take advantage of Matlab's capabilities and use

a_new = J\r . 

p.s. it woud be better and faster if the entire r vector were preallocated with r = rand(500,1). That way Matlab doesn't have to resize the r vector for every value of i between 101 and 500.