kwantam/resgrad

-- Copyright (C) 2010 Riad S Wahby <rsw@jfet.org>
-- 
-- This file is part of resgrad
--
--  resgrad is free software.  It comes without any warranty, to
--  to the extent permitted by applicable law.  You can redistribute it
--  and/or modify it under the terms of the Do What The Fuck You Want To
--  Public License, Version 2, as published by Sam Hocevar.  See
--  the COPYING file or http://sam.zoy.org/wtfpl/COPYING for more details
--

{-
 - When attempting to make a pair of resistors with a large ratio, it is
 - optimal to devote equivalent area to each resistor.  As such, the most
 - obviously ideal ratios are those which are perfect squares; this allows
 - one string of sqrt(R) in series, and one string of sqrt(R) in parallel,
 - devoting equal area to each resistor and resulting in a ratio R.
 -
 - Unfortunately, laying out such resistors to be gradient insensitive is
 - not as simple as when matching two resistors of equal value: after some
 - thought it should be obvious that common centroiding does not work to
 - cancel the effect of gradients, since one resistor accumulates errors
 - linearly and the other as 1/delta.  As a result, the "correct" layout for
 - a given set of resistors can be very nonintuitive.
 -
 - This software performs 2d optimization of a resistor pack in the presence
 - of linear gradients in X and Y of specified magnitude.  It is assumed
 - that the resistor ratio is equal to nUnits^2, i.e., the resistors will be
 - nUnits in parallel and in series.  The results are written to the present
 - directory in the form of the nOut best configurations.
 -
 - Usage:
 -
 - resgrad <nUnits> <nRows> <deltaY> <deltaX> <nOut>
 -   nUnits : the number of units per resistor
 -   nRows  : the number of rows into which to split
 -     NOTE: nRows must evenly divide 2*nUnits!
 -   deltaY : deltaRho/Rho between top-most and bottom-most row
 -   deltaX : deltaRho/Rho between left-most and right-most row
 -   nOut   : output the nOut best configurations
 -}