Puzzler: Market Days 
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 Puzzler: Market Days

Here's my APL solution to the Market Days puzzle:

     {del} Z{<-}A DAYSPLUS B;I;M;R;S;Y;#IO

[2]    #IO{<-}0







     {del}

{del}.    CIY{<-}1994 1995

{del}.    CID{<-}2 12 31{rho}'WWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDD{+
+}DDDWWHDDDDWWDXXXDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDHWWDDDDDWWDDDDDWWDDDDDWWDDH{+
+}DDWXWDDDDDWWDDDDDWWDDDDDWWDDDDDWWHDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDXDWWHDDDD{+
+}WWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWHDDDDWWDDDDDWWDD{+
+}DDDWWDDDDDXWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDHDWWDDDXD{+
+}DWWDDDDDWWDDDDDWWDDDDDWWHDDDDWWHDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWD{+
+}DDDDWWHDDDDWWDDXXXDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDHWWDDDDDWWDD{+
+}DDDWWXDDDDDWWDDDDDWWDDDDDWWDDDDDWWHDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDXWWDHDD{+
+}DWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWHDDDDWWDDDDDWWD{+
+}DDDDWWDDDDDWXWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDDDWWDDDHDWWDDDD{+
+}XDWWDDDDDWWDDDDDWWDDDDDWWHDDDDWW'

(Note: If you pass this message to DEFINEFNS in the APLASCII v1.3
workspace, it will define both DAYSPLUS and the variables CIY and CID.)

   This is essentially the same algorithm as Roger Hui's J solution of
6 Sep 1995, with a slight variation in the origin shifting.  I convert
years, months, and days to zero-origin indices by subtracting the scalar
19940101 instead of subtracting 1994 1 1 from each column of the
unpacked date matrix.  The dual Roger mentions is on line [8] of this
function: indexing through M is "inverted" by lookup in M.  Quite a lot
of duals for such a small function; I count four of them.

   The algorithm assumes that CIY contains consecutive years in
ascending order.  CIY and CID should be sorted beforehand if this is not
the case.

   I saw Roger's solution before I started working on this problem, and
I must admit that figuring out his program was a more interesting puzzle
than developing the APL solution.  Maybe I'll find time to write an
explanation of Roger's function, but for now I'd just like to point out
something that made my jaw drop: the phrase "efd^:_1" is used to compute
the inverse of efd, a rather nontrivial user-defined function.  Roger
has pointed out that tacit definitions are amenable to formal
manipulation, and this is an impressive example.  But I suspect that few
many J users would know that J could invert efd.  From my study of the
manual and readme files, I would have expected J to invert {&cenum (part
of efd) by linear approximation, but it seems to know that cenum&i. is a
suitable inverse.

ObTimings:

The execution times below were measured on a 66MHz 486, running Windows
3.1 (for +III and J2).  The left argument was 5000{rho}19950906; the
right argument was 5000{rho}{neg}11+{iota}21 (in 1-origin APL; _10+i.21
in 0-origin J).

        APL*PLUS/PC v7.1        1.81   secs

        APL*PLUS II v5.2        0.177

        APL*PLUS III v1.2       0.153

        J2 v2.06                0.64

The J2 figure is for Roger's daysplus function, which avoids a bit of
work by precomputing cenum.  When I put all of his solution (including
the cenum=.) in an explicit function, the execution time was .66
seconds.  I don't know what's slowing up the J program.  It isn't the
computation of efd^:_1, which seems to run just as fast as efd itself.

   While I prefer the monolithic form of DAYSPLUS, Roger's EFD function
(and its inverse DFE) are handy for defining the other market day
utilities that Roger gave in his posting.  Here are APL versions,
expressed using direct definition:

   CENUM {<-} +\,CID='D'

   CORG  {<-} 0 100 100{basevalue}(1{take}CIY),1 1

   EFD:  CENUM[#IO+0 12 31{basevalue}0 100 100{represent}{omega}-CORG]

   DFE:  CORG+0 100 100{basevalue}0 12 31{represent}(CENUM{iota}{omega})-#IO

DAYSPLUS and the other utilities are asily expressed in terms of EFD and
DFE:

   DAYSPLUS:  DFE {omega}+EFD{alpha}

   BETWEEN:   (EFD{omega})-EFD{alpha}

   MARKETDAY: {omega}=DFE EFD{omega}

I wonder if there's a clever algebraic way of expressing EFD and DFE.

                                                Jim



Sun, 01 Mar 1998 03:00:00 GMT  
 
 [ 1 post ] 

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