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+--- Thread: (48G,50g) ConvOffs Transform (/thread-12514.html)
(48G,50g) ConvOffs Transform - John Keith - 02-27-2019 02:22 PM
These strangely named integer transforms are generalizations of the method used to create Pascal's triangle and similar number triangles. More information in this thread. The first program takes a list of integers and returns the transformed list, which will be one term longer than the input list.
Updated 1/20/2020 with a shorter and faster version using DOLIST.
Code:
\<< DUP SIZE
IF DUP 1. >
THEN
IF DUP 3. >
THEN DUP 2. / IP SWAP 1. + 2. / IP
ELSE 0.
END \-> m t
\<< 1 SWAP DUP 1. m SUB SWAP REVLIST 1. m SUB 2.
\<< PICK3 * SWAP /
\>> DOLIST + DUP 1. t SUB REVLIST +
\>>
ELSE 1. SAME { HEAD DUP 2. \->LIST } { DROP { 1 } } IFTE
END
\>>For example, given the input list { 1 2 3 4 5 } the program will return row 5 of Pascal's triangle.
The next program implements the ConvOffsStoT transform. It calls the program above. This program is basically the same but returns a list of lists which are transforms of sublists of the input list. Given a list of length n, the program will return lists of length 1 through n+1.
Code:
\<< DUP SIZE \-> n
\<< 0. n
FOR k DUP 1. k SUB ConvOffs SWAP
NEXT DROP n 1. + \->LIST
\>>
\>>As an example, with an input list of { 1 2 3 4 5 } the program will return the first 6 rows (rows 0 through 5) of Pascals triangle.