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

2 ビュー (過去 30 日間)
Abalfazl Zareei
Abalfazl Zareei 2013 年 4 月 10 日
hi, I have a vector w and it is a matrix with one row and 10 columns.
>> sum(w)
ans =
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 =
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

回答 (3 件)

James Tursa
James Tursa 2013 年 4 月 11 日
編集済み: James Tursa 2013 年 4 月 11 日
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:
And then compare that result with your answer and you will see that they are about the same size.
  1 件のコメント
Jan 2013 年 4 月 11 日
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
[dummy, index] = sort(abs(w));
Do you see a difference already? For a sum with error correction see FEX: XSum


bym 2013 年 4 月 10 日
  2 件のコメント
Abalfazl Zareei
Abalfazl Zareei 2013 年 4 月 10 日
The same answer:
>> ones(size(w))*w.'
ans =


Ahmed A. Selman
Ahmed A. Selman 2013 年 4 月 10 日
The line
means creating a ones matrix with dimensions (1,size(w,2)) multiplied with w', and
means summation of the vector w.
I really don't know if it is right to compare these two, entirely different things.
So use
and compare :)
  2 件のコメント
Ahmed A. Selman
Ahmed A. Selman 2013 年 4 月 11 日
Indeed it is the same. I thought w was N-by-N, my bad. Thank you for the correction.



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