HOC CODE TO COLLAPSE A DENDRITIC TREE
	=====================================

   Collapse a dendritic tree into 3 compartments "proximal", "middle"
   and "distal".  

   The collapse is made such as the collapsed dendritic structure
   preserves the axial resistance of the original structure. 
   The algorithm works by merging successive pairs of dendritic 
   branches into an equivalent branch (a branch that preserves the 
   axial resistance of the two original branches).
   This merging of branches can be done according to different methods
   selectable in the present code:

   AREABYLONG

	The code rejects the smallest original branch if it is more than
	5 times smaller than the long orginal branch.  If AREABYLONG is
	set to 1, then the small branch is rescaled to the longest one 
	(a new diameter is assigned such that the small branch conserves
	its axial resistance).  This minimizes errors for dendritic 
	structures where branches have a large range of possible lengths.
	AREABYLONG = 0 is the default.


   AVGLENGTH, AVGLENGTHWDIAM, AVGLENGTHWSURF

	During the merging of two branches, the length of the equivalent 
	branch is calculated by one out of three possible methods.  

	First, a simple average of the two branch length:

		L = (L1+L2)/2

	This is the method originally used by Bush and Sejnowski
	(J. Neurosci. Methods 46: 159-166, 1993).
	It is selected by setting AVGLENGTH=1.

	Second, by weighting this average with the diameters of each branch

		L = (diam1*L1 + diam2*L2)/(diam1+diam2)

	This algorithm produces more fair merging in the case two branches of
	very different diameters are to be merged.  It is selected by setting
	AVGLENGTHWDIAM=1.

	Third, by weighting the average with membrane area:

		L = (area1*L1 + area2*L2)/(area1+area2)

	This algorithm is better in the case two branches of very different
	areas are to be merged.  It is selected by setting AVGLENGTHWSURF=1.


   CUTOFF1, CUTOFF2

	The dendritic branches are assigned to one of the three compartments
	("proximal", "middle" or "distal") based on their path axial 
	resistance (in Meg-Ohms) to the soma.  The cutoff values (CUTOFF1
	and CUTOFF2) determine these cut-offs.  For example, CUTOFF1=10 means
	that all branches laying within 10 Meg-Ohm of axial resistance from 
	the soma will be merged together into the same ("proximal") section.
	

   Written by M. Neubig & A. Destexhe
   Laval University, 1997; CNRS 2000




The run this example, enter:

  nrniv collapse.hoc -

it should give the following output:

Section Length (um)     Diameter (um)
1       70.69612        7.9574464 
2       28.123442       8.0002892 
3       12.49237        10.281249