X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=bisect.m;fp=bisect.m;h=0000000000000000000000000000000000000000;hp=3570e57442caf428f5cf22afe75a25b509214dca;hb=437324f2edf6b26c772080f8cbe3b321dda8d70f;hpb=f32a60e5aceefce5b4b7497b9d295c8175297110

diff --git a/bisect.m b/bisect.m
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--- a/bisect.m
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-function [root,iterations] = bisect(f, a, b, epsilon)
-  ## Find a root of the function `f` on the closed interval [a,b].
-  ##
-  ## It is assumed that there are an odd number of roots within [a,b].
-  ## The intermediate value theorem is used to determine whether or not
-  ## there is a root on a given interval. So, for example, cos(-2) and
-  ## cos(2) are both less than zero; the I.V.T. would not conclude that
-  ## cos(x) has a root on -2<=x<=2.
-  ##
-  ## If `f` has more than one root on [a,b], the smallest root will be
-  ## returned. This is an implementation detail.
-  ##
-  ##
-  ## INPUTS:
-  ##
-  ##   * ``f`` - The function whose root we seek.
-  ##
-  ##   * ``a`` - The "left" endpoint of the interval in which we search.
-  ##
-  ##   * ``b`` - The "right" endpoint of the interval in which we search.
-  ##
-  ##   * ``epsilon`` - How close we should be to the actual root before we
-  ##     halt the search and return the current approximation.
-  ##
-  ## OUTPUTS:
-  ##
-  ##   * ``root`` - The root that we found.
-  ##
-  ##   * ``iterations`` - The number of bisections that we performed
-  ##     during the search.
-  ##
-
-  ## Store these so we don't have to recompute them.
-  fa = f(a);
-  fb = f(b);
-
-  ## We first check for roots at a,b before bothering to bisect the
-  ## interval.  
-  if (fa == 0)
-    root = a;
-    iterations = 0;
-    return;
-  end
-
-  if (fb == 0)
-    root = b;
-    iterations = 0;
-    return;
-  end
-
-  ## Bisect the interval.
-  c = (a+b)/2;
-  iterations = 1;
-  
-  ## If we're within the prescribed tolerance, we're done.
-  if (b-c < epsilon)
-    root = c;
-    return;
-  end
-
-  if (has_root(fa,f(c)))
-    [root,subiterations] = bisect(f,a,c,epsilon);
-    iterations = iterations + subiterations;
-  else
-    [root,subiterations] = bisect(f,c,b,epsilon);
-    iterations = iterations + subiterations;
-  end
-end