Asked by Abalfazl Zareei
on 10 Apr 2013

hi, I have a vector w and it is a matrix with one row and 10 columns.

>> sum(w)

ans =

-0.1563

Then, I calculate the following, which is the product of a Ones vector and w, in which in matrix algebra, this is equivalent to summation of w's elements. >> ones(1,size(w,2))*w'

ans =

1

Both results are different. Would you please let me know why?

w =

1.0e+15 *

Columns 1 through 6

-0.0497 2.4484 -3.2273 0.1944 0.1592 0.4407

Columns 7 through 10

-0.4389 0.1548 0.1592 0.1592

Answer by James Tursa
on 11 Apr 2013

Edited by James Tursa
on 11 Apr 2013

The answer is on the order of eps of the numbers you are dealing with. You have massive cancellation going on in the operation, and the order of the operation will make a difference (apparently sum and mtimes are doing the calculation in a slightly different order). The answer will have a lot of garbage bits. E.g., what do you get when you do this:

eps(max(abs(w)))

And then compare that result with your answer and you will see that they are about the same size.

Jan
on 11 Apr 2013

Exactly. Try this (insert all digits, if you have them):

w = [-0.0497e15, 2.4484e15, -3.2273e15, 0.1944e15, 0.1592e15, ...

0.4407e15, -0.4389e15, 0.1548e15, 0.1592e15, 0.1592e15];

format long g

sum(w)

sum(sort(w))

[dummy, index] = sort(abs(w));

sum(w(index))

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Answer by bym
on 10 Apr 2013

try

ones(size(w))*w.'

Cedric Wannaz
on 10 Apr 2013

Abalfazl Zareei
on 10 Apr 2013

The same answer:

>> ones(size(w))*w.'

ans =

1

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Answer by Ahmed A. Selman
on 10 Apr 2013

The line

ones(1,size(w,2))*w'

means creating a ones matrix with dimensions (1,size(w,2)) multiplied with w', and

sum(w)

means summation of the vector w.

I really don't know if it is right to compare these two, entirely different things.

So use

sum(ones(1,size(w,2))*w')

and compare :)

Jan
on 11 Apr 2013

Ahmed A. Selman
on 11 Apr 2013

Indeed it is the same. I thought w was N-by-N, my bad. Thank you for the correction.

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