How do I calculate a mean value of a vector and ignore from the "0" when appears inside the vectors?

Hello.

I need to calculate a mean value of a velocity vector. The vector contains a damaged cells which appears as "0" inside the vector. How do I calculate a mean value of a vector and ignore from the "0" when appears inside the vectors?

Answer 1

[Star Strider]

If you have a recent release (I don’t remember when the 'omitnan' option appeared) or the Statistics and Machine Learning Toolbox nanmean function you can change the zeros to NaN and use those functions:

V = randi([0 9], 5)
V(V==0)= NaN
Out_1 = nanmean(V)
Out_2 = mean(V, 'omitnan')

V =
     0     4     6     0     4
     1     5     1     9     3
     6     2     3     7     5
     7     7     6     4     5
     6     1     7     4     8

V =
   NaN     4     6   NaN     4
     1     5     1     9     3
     6     2     3     7     5
     7     7     6     4     5
     6     1     7     4     8

Out_1 =
            5          3.8          4.6            6            5

Out_2 =
            5          3.8          4.6            6            5

The problem with the logical indexing approach is that it defaults to ‘linear indexing’ because the rows and columns are no longer equal. That produces a vector argument to the mean function, and the mean of the vector.

[Tzahi Shukrun]

Hi! First, thank you for your help!

Second, the command, as you exampled gives me outputs the same mean value as it with "0". so, in that case I can calculate it easly with with "mean(MAT)" and with the "0" values.

[Star Strider]

My pleasure!

Actually, not.

Looking at the first column of ‘V’ with the NaN values, the mean with nanmean, or mean with 'omitnan', the mean is:

(1 + 6 + 7 + 6)/4 = 20/4 = 5

the desired result.

With the ‘0’, the mean of that column is:

(0 + 1 + 6 + 7 + 6)/5 = 20/5 = 4

which is not the result you said you want.

So substituting the ‘0’ with NaN and using the appropriate functions produces the correct result.

[Tzahi Shukrun]

PERFECT! THANKS!

[Star Strider]

My pleasure!

Answer 2

[George]

Replacing the 0s with NaN and using the 'omitnan' flag should do what you want.

>> A

A =

         NaN       NaN   11.6780       NaN       NaN       NaN       NaN  -23.3560  -35.0340  -42.8200
         NaN       NaN       NaN       NaN       NaN       NaN       NaN   -7.7850   -7.7850  -15.5710
         NaN       NaN       NaN       NaN       NaN       NaN    3.8930       NaN   -3.8930  -15.5710
         NaN       NaN       NaN       NaN       NaN       NaN   -3.8930       NaN       NaN   15.5710
         NaN       NaN       NaN       NaN       NaN       NaN       NaN   -3.8930  -11.6780  -15.5710
         NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN
         NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN
         NaN       NaN       NaN       NaN       NaN       NaN       NaN  -19.4630  -35.0340  -54.4980
         NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   -3.8930  -15.5710
         NaN       NaN       NaN       NaN       NaN       NaN       NaN    3.8930    7.7850   11.6780
         NaN       NaN       NaN       NaN       NaN       NaN       NaN   -3.8930  -11.6780  -19.4630
         NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   -3.8930       NaN
         NaN       NaN       NaN       NaN       NaN       NaN       NaN   -3.8930   -3.8930  -11.6780
         NaN       NaN       NaN       NaN       NaN       NaN       NaN   -3.8930   -3.8930   -7.7850
         NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   -7.7850  -15.5710
         NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN    7.7850

Trial>> meanCols = mean(A, 'omitnan')

meanCols =

         NaN       NaN   11.6780       NaN       NaN       NaN         0   -7.7854  -10.0562  -13.7742

>>

[Tzahi Shukrun]

Hi! Thank you for your help. This command gives me the mean value of the entire matrix. I do i get the mean value of each vector in the matrix?

[Tzahi Shukrun]

PERFECT!

THANK YOU VERY MUCH!

Answer 3

[Image Analyst]

Try this

meanVelocity = mean(allVelocities(allVelocities ~= 0))

[Tzahi Shukrun]

Hi! Thank you for your help. This command gives me the mean value of the entire matrix. I do i get the mean value of each vector in the matrix?

[Image Analyst]

No it doesn't. It gives the means of only the non-zero elements of your vector. But now you've changed your question. Now you're saying that you have a matrix, NOT a vector. In that case, I'd use mean with the omitnan option after you've set 0's to nans, exactly what Star showed.

allVelocities(allVelocities == 0) = nan;
meanVelocity = mean(allVelocities, 'omitnan')

Note, in the above, allVelocities is a matrix (as in your comment), not a vector as you originally said. And meanVelocity is the column over rows (that is, going down columns) so you have one mean for every column.

[Tzahi Shukrun]

yeah... you are right, I didnt write my question well. Thanks to you, I have my answer!

Answer 4

[Jan]

You do not have to replace the zeros by NaNs, because the zeros are neutral for the SUM already:

sum(A, 1) ./ sum(A ~= 0, 1)

[Thorsten]

For the sum, but not for the mean.

[Jan]

@Thorsten: Exactly. Therefore you divide by the number of non-zeros and not by the number of elements. The posted code does exactly this.

Answer 5

[Suraj Sudheer Menon]

All non zero elements can be stored in another location using logical indexing and mean operation can be performed.

temp=A(A~=0); %stores the non zero values in temp.

ans=sum(temp)/nnz(A) ; %nnz returns number of non zero elements.

[Image Analyst]

But since the sum of any number of zeros is still zero, the sum of A will be the sum of temp. So temp is not necessary, and you'd get the same thing from

ans=sum(A(:))/nnz(A) ;