Re: Multiple > and < calculations [great than & less than]

*To*: mathgroup at smc.vnet.net*Subject*: [mg55334] Re: [mg55271] Multiple > and < calculations [great than & less than]*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sat, 19 Mar 2005 04:46:14 -0500 (EST)*References*: <200503181033.FAA14605@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Geezer wrote: > USING EXCEL > I need a simple formula.............. > > I want to give a set value to a number within a given range > e.g cell value is 1038 > - the look up range is below > - so the formula should return the value 'A' > - because the example cell value is between 1000 and 1500 > > Value Range Result > <999 > 1000-1500 A > 1501-2500 B > 2501-3500 C > 3501-4500 D > 4501-5500 E > 5501-7000 F > 7001-10000 G > 10001-15000 H > 15001-20000 I > 20001-30000 J > >>30001 K > > > There are over 10,000 cells to run the formula through > > Help Please you can reply directly if you wish > Many Thanks > G This comes up from time to time. One method that will use a fast divide-and-conquer behind the scenes is evaluation of an InterpolatingFunction, which we create with InterpolatingOrder->0 to make it piecewise constant. We use numbers 1,2,... for the second value. You then need a fast method to convert these to your own values e.g. A,B,... but this only requires a constant time table lookup. To indicate speed we make a test function below. points[n_,hi_] := Union[Table[Random[Integer,{1,hi-1}],{n}]] lookup[n_,hi_] := Module[{pts=points[n,hi],len}, len = Length[pts]; Interpolation[ Transpose[{Prepend[Append[pts,hi],0],Range[len+2]}], InterpolationOrder->0] ] Create a lookup table with around 10^4 entries with random values from 1 to 10^7-1, augmented by the endpoints (the actual size is a bit less as per the birthday paradox). ltab10k = lookup[10^4,10^7]; Now we look up 10^4 random values in this range. In[13]:= Timing[Do[ltab10k[Random[Integer,10^7]], {10^5}]] Out[13]= {1.65 Second, Null} We do the same, but for a table with 10^5 entries in that range. ltab100k = lookup[10^5,10^7]; In[15]:= Timing[Do[ltab100k[Random[Integer,10^7]], {10^5}]] Out[15]= {1.84 Second, Null} Similar ideas show up in notes at the URLs below, and others in their respective threads. http://forums.wolfram.com/mathgroup/archive/2000/Nov/msg00342.html http://forums.wolfram.com/mathgroup/archive/2002/Sep/msg00277.html http://forums.wolfram.com/mathgroup/archive/2003/Feb/msg00375.html Daniel Lichtblau Wolfram Research

**References**:**Multiple > and < calculations [great than & less than]***From:*"Geezer" <clive@gemnet.co.uk>