sum(w) and ones(1,size(w,2))*w' results totally different numbers

조회 수: 1(최근 30일)
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

답변(3개)

James Tursa
James Tursa 2013년 4월 11일
편집: James Tursa 2013년 4월 11일
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.
  댓글 수: 1
Jan
Jan 2013년 4월 11일
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))
Do you see a difference already? For a sum with error correction see FEX: XSum

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bym
bym 2013년 4월 10일
try
ones(size(w))*w.'
  댓글 수: 2
Abalfazl Zareei
Abalfazl Zareei 2013년 4월 10일
The same answer:
>> ones(size(w))*w.'
ans =
1

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Ahmed A. Selman
Ahmed A. Selman 2013년 4월 10일
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 :)
  댓글 수: 2
Ahmed A. Selman
Ahmed A. Selman 2013년 4월 11일
Indeed it is the same. I thought w was N-by-N, my bad. Thank you for the correction.

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