Index in position 2 exceeds array bounds (must not exceed 2

Background : I am writing a MATLAB algorithm LinearReg that takes as an input the vectors x and y and solves the linear regression problem associated with the data stored in x and y using a version decomposition that I wrote and then plots the data and the obtained line using plot(x,y,’bo’,x,ysol,’g-’). It should output ysol, the vector of y coordinates of the obtained line at the x points.

• First, I wrote the modified algorithm as follow :

function x=QRQ(A,b,n)
[Q1,R1]=qr(A);
c1=Q1'*b;
n=length(c1);
x=backward(R1,c1,n);
end
function x=backward(U,y,n)
x=zeros(n,1);
x(n)=y(n)/U(n,n);
for i=n -1 : -1 : 1
      x(i)=(y(i)-U(i,i+1 : n)*x(i+1 : n))/U(i,i);
end
end

• The second and vital part is writing the MATLAB function LinearReg that should solve and plot the graph of the linear function :

function ysol = LinearReg(x,y)
A=[x ones(21,1)];
z=QRQ(A,y,2);
ysol=z(1)*x+z(2);
plot(x,y,'bo',x,ysol,'g-');
end

Running this code using the following data points :

x=[0;0.25;0.5;0.75;1;1.25;1.5;1.75;2;2.25;2.5;2.75;3;3.25;3.5;3.75;4;4.25;4.5;4.75;5];
y=[4;3;7;7;1;4;4;6;7;7;2;6;6;1;1;4;9;3;5;2;7];

have resulted in an error stating that Index in position 2 exceeds array bounds (must not exceed 2). I am afraid that my mistake is something trivial or stupid. I hope someone assists me in functioning this code. Thank you very much!

Answer 1

[Cris LaPierre]

The full error message is

Index in position 2 exceeds array bounds (must not exceed 2).

Error in untitled>backward (line 12)

x(n)=y(n)/U(n,n);

Error in untitled>QRQ (line 8)

x=backward(R1,c1,n);

Error in untitled>LinearReg (line 20)

z=QRQ(A,y,2);

The line causing the error is x(n)=y(n)/U(n,n);

• the only variable with an index in position 2 is U. Apparently U only has 2 columns, and n is a value >2, hence the error.

Using the debugger, I see that U is a 21x2 array, and n has a value of 21.

U = rand(21,2);
U(3,3)

Index in position 2 exceeds array bounds (must not exceed 2).

[Tarek Hajj Shehadi]

Thank you very much!