How can I count the sum of inverse value of each non zero elements of a matrix?

Suppose,

x=[2 1 0 0

0 1 1 1

0 1 1 1

1 0 3 1]

How can I count the sum of inverse value of each non zero elements?

The answer would be = sum (1/2 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/3 + 1/1) = 9.83

How can I count the sum of inverse value of each non zero elements when x also contains NaN?

e.g.,

x=[2 1 0 NaN

0 1 1 1

0 1 1 1

1 0 3 1]

Answer 1

[Image Analyst]

x=[2 1 0 0
    0 1 1 1
    0 1 1 1
    1 0 3 1]

x = 4×4

2 1 0 0 0 1 1 1 0 1 1 1 1 0 3 1

numNonZeros = nnz(x)

numNonZeros = 11

Not sure what you want for the second question since your sum does not include all 16 elements.

x2=x;
x2(x==0) = 1

x2 = 4×4

2 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1

s = sum(1./x2(:))

s = 14.8333

 % Sum 11 of the 16 -- only some of them for some reason.  
 % Not sure which to take and which to exclude.
 thesum = (1/2 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/3 + 1/1) % 11 of the 16

thesum = 9.8333

  % Now sum all 16
  thesum = (1/2 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/3 + 1/1) 

thesum = 14.8333

If this is your homework, you're most likely not allowed to turn my code in as your own. And please tag it as homework if it is.

Regarding your edit, to sum up only elements where x is not zero:

x2=x(:); % Make a copy as a column vector.
x2(x==0) = [] % Remove the zeros.

x2 = 11×1

2 1 1 1 1 1 1 3 1 1

s = sum(1./x2(:))

s = 9.8333

[Image Analyst]

Regarding your edit: remove nans prior to using x

x = x(~isnan(x)); % Extract only non-nan values.

[Md. Asadujjaman]

I want to do the following sum:

thesum = (1/2 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/1 + 1/3 + 1/1) = 9.8333

% 11 (non zero elements) of the 16

Note: This is not my homework.

I got my answer. Thank you.

[Image Analyst]

OK, thanks for Accepting. If you have a newer version of MATLAB you can use the 'omitnan' option like Matt showed below.

Answer 2

[Matt J]

sum(1./nonzeros(x),'omitnan')

[Md. Asadujjaman]

Excellent.

Thank you.

Answer 3

[Jan]

x = [2 1 0 0; ...
     0 1 1 1; ...
     0 1 1 1; ...
     1 0 3 1];
r = sum(1 ./ x(x ~= 0))

r = 9.8333

x = [2 1 0 NaN; ...
     0 1 1 1; ...
     0 1 1 1; ...
     1 0 3 1];
r = sum(1 ./ x(x ~= 0 & ~isnan(x)))

r = 9.8333

[Md. Asadujjaman]

Very good. Thanks.