has_root.m

   1 #!/usr/bin/octave --silent
   2
   3 function has_root = has_root(fa, fb)
   4   ## Use the intermediate value theorem to determine whether or not some
   5   ## function has an odd number of roots on an interval. If the function
   6   ## in question has an even number of roots, the result will be
   7   ## incorrect.
   8   ##
   9   ## Call the function whose roots we're concerned with 'f'. The two
  10   ## parameters `fa` and `fb` should correspond to f(a) and f(b).
  11   ##
  12
  13   ## If either f(a) or f(b) is zero, the product of their signs will be
  14   ## zero and either a or b is a root. If the product of their signs is
  15   ## negative, then f(a) and f(b) are non-zero and have opposite sign,
  16   ## so there must be a root on (a,b). The only case we don't want is
  17   ## when f(a) and f(b) have the same sign; in this case, the product of
  18   ## their signs would be one.
  19   if (sign(fa) * sign(fb) != 1)
  20     has_root = true;
  21   else
  22     has_root = false;
  23   end
  24 end