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Oblique m/.  u/. _ _ _ Key

u/.y applies u to each of the oblique lines of a table y . For example:
   i.3 4
0 1  2  3
4 5  6  7
8 9 10 11

   </. i.3 4
+-+---+-----+-----+----+--+
|0|1 4|2 5 8|3 6 9|7 10|11|
+-+---+-----+-----+----+--+
In general, u/.y is the result of applying u to the oblique lines of _2-cells of y . If the rank of y is less than two, y is treated as the table ,.y .

m/.y applies successive verbs from the gerund m to the oblique lines of _2-cells of y, extending m cyclically as required. Thus:
   <`(<@|.) /. i.3 4
+-+---+-----+-----+----+--+
|0|4 1|2 5 8|9 6 3|7 10|11|
+-+---+-----+-----+----+--+
  x u/.y « (=x) u@# y , that is, items of x specify keys for corresponding items of y and u is applied to each collection of y having identical keys. For example:
   1 2 3 1 3 2 1 </. 'abcdefg'
+---+--+--+
|adg|bf|ce|
+---+--+--+
x m/.y applies successive verbs from the gerund m to the collections of y, extending m cyclically as required.

The application of a function to diagonals of a table is commonly useful, as in correlation, in convolution, and in products of polynomial coefficients (or, equivalently, products of numbers in a fixed base). For example:
   t=: p */ q [ p=: 1 2 1 [ q=: 1 3 3 1

   t ; (+//.t) ; 1 1 &(+//.@(*/)) ^: (i.6) 1
+-------+-------------+-------------+
|1 3 3 1|1 5 10 10 5 1|1 0  0  0 0 0|
|2 6 6 2|             |1 1  0  0 0 0|
|1 3 3 1|             |1 2  1  0 0 0|
|       |             |1 3  3  1 0 0|
|       |             |1 4  6  4 1 0|
|       |             |1 5 10 10 5 1|
+-------+-------------+-------------+

   ((10#.p)*10#.q), 10 #. +//. p */ q
161051 161051
Unlike polynomial coefficients, the diagonal sums of a multiplication table of digits should be "normalized" if any equal or exceed the radix.




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