Issues when multipling and summing very small values in a matrix

Hi,

So I am performing a fairly simple task, where it basically multiplies all values in a matrix by a value, then summing the matrix. The issue I am having is that when these values of the matrix becomes quite low, it just sums /rounds to 0 or something.

for count1 = 1:len1
     constant = 2*pi*count1*0.0100; 
     datamatrix = massplume_area(:, count1).*constant;
end
totalmassplume = sum(datamatrix(:));

It seems to be if the values are very small, or if there a quite a few zero values in the matrix 'massplume_area', then the act of multiplying it by the value 'constant' causes the output to be 0. If there are plenty of large values/ not many 0 values in massplume_area, then there is no issue.

Any advise?

Answer 1

[A Jenkins]

Your code as written only sums the value of the last column of massplume_area.*constant.

Did you mean

datamatrix(:, count1) = massplume_area(:, count1).*constant;

[David]

I tried this, same issue... getting nothing but 0's

Answer 2

[Roger Stafford]

I think it is likely that you are not displaying your results with sufficient accuracy to see the actual values of small quantities. The smallest value in matlab's double precision format which retains its full 53-bit precision is realmin (= 2.2251e-308,) and if the results of your multiplication are no smaller than that tiny amount, they should be precise to approximately 16 decimal places. If you display a small number by itself, even the default 'format short' will show a nonzero value:

   format short
   pi*1e-5
    = 3.1416e-5

However, if you display it along with a larger number, it may look like a zero:

   [pi,pi*1e-5]
    = 3.1416   0.0000

To display your small values accurately you should either show them alone or else use higher accuracy displays, as with 'format long', or even better, using high precision methods with 'fprintf'. For example,

   x = [pi;pi*realmin];
   fprintf('%18.16e\n',x)
   3.1415926535897931e+00
   6.9902756875809187e-308

Incidentally, you can multiply a matrix by a constant scalar without doing it column-by-column:

   datamatrisx = constant*massplume_area;

[A Jenkins]

Note his constant isn't constant, it's scaled by the loop counter, count1.

[Roger Stafford]

Yes, you're right! In that case David could do this:

   datamatrix = bsxfun(@times,1:len1,massplume_area);

(assuming 'len1' is the actual number of columns in 'massplume_area'.)

[David]

Hi, If I am correct in thinking that bsxfun(...) will times the matrix by a value, how do I correctly times it by the constant? (yes the constant changes on the loop iteration, sorry)

[Roger Stafford]

What I have written is the correct way to do the multiplication (again assuming that 'massplume_area' has 'len1' columns. The 'bsxfun' automatically expands the row vector 1:len1 in duplicated rows so as to have the same number of rows as 'massplume_area'. That means that all elements of each column of 'massplume_area' get multiplied by the same value. See the documentation for 'bsxfun' at:

   http://www.mathworks.com/help/matlab/ref/bsxfun.html

However, I think your main problem is accurately displaying small numbers, and using 'bsxfun' to avoid the for-loop will not solve that problem.