Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Prepared by Ibrahim Mesecan.
Covariance Matrix
In probability theory and statistics, covariance
is a measure of how much two random variables
change together.
e.g. if you have the following 6 rows and
2 cols series, covariance matrix can be calculated
as follows: First you calculate the average of
every columns (4.5; 5)
Then, you calculate residuals by subtracting the
average from every element of series:
Residual of every row is multiplied with
its transpose (rotated 90o).
Then, the results are summed up and divided by
(n-1) (5).
Question:
Write a program that reads n rows m columns series.
And then, it calculates and shows the covariance matrix.
Input specification
You will be given two numbers (n and m) in the beginning
where 1 ≤ n ≤ 1000 and 1 ≤ m ≤ 50. Then
Then in the following n lines you will be given
m integers where the given numbers are integers between
0 and 1000.
Output specification
Show the covriance matrix with two digits precision.
Sample Input I
6 2
3 2
2 4
3 4
6 5
6 7
7 8
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Sample Input II
6 3
11 9 8
5 11 9
9 7 8
1 0 4
5 10 7
10 11 2
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Sample Output I
4.3 3.8
3.8 4.8
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Sample Output II
14.57 9.80 0.87
9.80 17.60 3.00
0.87 3.00 7.47
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Для отправки решений необходимо выполнить вход.
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