relative error: Error using ==> mtimes

Hello I am trying to get the relative error for sinx=sqrt(1-cos^2(x) and getting error with this matlab code:

 clear
clc
x=logspace(-1,-10,10);
lhs=sin(x);
t=cos(x);
rhs=sqrt(1-cos(x)*cos(x)); 
abserr=abs(lhs-rhs);
Rel=abs((lhs-rhs)/lhs);
disp('x  error   rel.error')
disp('--------------------')
for i=1:10
    disp(sprintf('%22.15e %22.15e %22.15e\n',x(i),abserr(i),Rel(i)))
end
  end

??? Error using ==> mtimes Inner matrix dimensions must agree.

Error in ==> Q at 6 rhs=sqrt(1-cos(x)*cos(x));

any idea? thanks

Answer 1

[Jan]

rhs = sqrt(1 - cos(x) .* cos(x))

While * performs the matrix multiplication, .* multiplies elementwise.

Answer 2

[NH]

thank you thats solved the problem. Now after i run it i get this new error:

?? Attempted to access Rel(2); index out of bounds because numel(Rel)=1.

Error in ==> Q at 11 disp(sprintf('%22.15e %22.15e %22.15e/n',x(i),abserr(i),Rel(i)))

clear
clc
x=logspace(-1,-10,10);
lhs=sin(x);
rhs=sqrt(1-cos(x).*cos(x)); 
abserr=abs(lhs-rhs);
Rel=abs((lhs-rhs)/lhs);
disp('x  error   rel.error')
disp('--------------------')
for i=1:10
    disp(sprintf('%22.15e %22.15e %22.15e\n',x(i),abserr(i),Rel(i)))
end
  end

[Jan]

1. Please post a new thread for a new problem.
2. Use the debugger to find the reasons for the size of Rel: Set a breakpoint in the line Rel=abs((lhs-rhs)/lhs) to find out, that exactly the same argument of matrix versus elementwise operations concerns the division also. Therefore you need ./ instead of / . Surprised?

[NH]

1. Thank you, next time I will. 2. Wow! thank you fore your advice exactly what I needed.