has_root.m

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