matlab showing 0 for small number values product

I have matrix with elements have small values. I am taking product of some elements of matrix for 100 times. If I take matrix 10*10 then it shows output but when I take matrix 100*100 then it shows 0. I think it shows 0 because product appears very small value. so how to take product so this small value should display.

Answer 1

[John D'Errico]

help format

Specifically, I'd suggest one of these:

format long g
format short g

[Jay Hanuman]

10*10 matrix product value shows 1.42185374673164e-108. format long g also not works i.e. output shows 0.

[Jay Hanuman]

matlab showing approximately upto 2.835313878787100e-314 but not below this.

[John D'Errico]

Sigh. If something did not work, then show what you think is wrong, and I can try to help.

A = rand(5);
A =
      0.81472      0.09754      0.15761      0.14189      0.65574
      0.90579       0.2785      0.97059      0.42176     0.035712
      0.12699      0.54688      0.95717      0.91574      0.84913
      0.91338      0.95751      0.48538      0.79221      0.93399
      0.63236      0.96489      0.80028      0.95949      0.67874
>> A.^500
ans =
   3.2002e-45            0            0            0   2.3231e-92
   3.2676e-22  2.5776e-278   3.3001e-07  3.4147e-188            0
            0  8.8435e-132   3.1178e-10   7.6742e-20   3.0684e-36
   2.1123e-20   3.7234e-10  1.0939e-157   2.6268e-51   1.4855e-15
  3.0334e-100   1.7321e-08   4.1794e-49    1.049e-09   7.0823e-85

As far as MATLAB is concerned, those numbers ARE zero. They underflowed.

Below realmmin, MATLAB double precision underflows. It is truly zero as far as MATLAB is concerned.

realmin('double')
ans =
  2.2251e-308

Although MATLAB also supports denormalized numbers that go down another 16 digits or so.

realmin/1000000000000000
ans =
  2.4703e-323

realmin/10000000000000000
ans =
     0

If you really need more than that, then you need to use a higher precision. Thus either sym or HPF.

[Jay Hanuman]

yes I want more than e-323, so how to use sym or HPF

[Walter Roberson]

A = rand(5);   %start with your standard floating point number
Asym = sym(A);  %convert them to symbolic
B = Asym .^ 500;  %raise them individually to the 500th power
num_digits = 50;  %number of digits you want to see the result to
vpa(B, num_digits)