When argument B is a multidimensional array, the [I] index entry is used to specify
the coordinate acted on. If the index entry is omitted, the last coordinate (columns)
is acted on. If thm fB lform is used, the first coordinate is acted on. Indexing along a
nonexistent coordinate will result in INDEX ERROR.
When argument B is a multidimensional array, the coordinate of argument B that is
acted on is eliminated:
x.:i 4.. 2 3 p :I. 2 3 1.1. 5 4)
B
:I. 2 3
1.1 5 6
.4 ,/ E
4. / I:: 2 ::I b
4. / M
+ ,' I:: 1. ::I I4
B 4- 2 9 14. (3 1. 2 I)
E{
2 3 4
5 0 '7 €1
9 1. I) :I. 1. 1.2 123
6 :I. 5 -The last coordinate (columns) is assumed;
l) :I. 5
5 '7 9
5 '7 '9
therefore, the reduction is between columns:
1+2+3=6
The second coordinate (in this case, columns)
is specified.
The first coordinate (rows) is specified;
therefore, the reduction is between rows:
L
1
13 1.14 1. 5 :L 6
1. 7 :L 8 :I. 9 2 (1
2 1. 22 23 24
456
579
22 24. 26 2ti3 (planes) is specified;
therefore, the reduction
is between planes.
If argument B is an array that has a coordinate whose dimension is zero, then reduc-
tion along that coordinate yields an array whose elements are equal to .the identity
element for the function. The identity element for each function is given in the
preceding table.
112

<.I
Inner Product Operator ( .) 0
The symbol for the innerproducr operator is . (period). The inner product opera-
tor is used to combine any two primitive scalar dyadic functions and cause them to
operate on an array. An example of its use would be in matrix algebra, in finding
the matrix product of two matrices. The form for inner product is: A@ .@,
first and then 8 f reduction is applied between the results of function@.
are any primitive scalar dyadic functions. Functionais performed
The result is an array; the shape of the array is all but the last coordinate of
argument A catenated to all but the first coordinate of argument B (-1 G pA),(I G pB).
If argument A and argument B are matrices, the elements in each row of argument A
are acted on by the elements in each column of argument B:
Ai-2 2p1. 2 3 4
Bi-2 2pS 6 7 8
A
34
H
= 19
c.
The above example is the same as doing the following for each element in the result:
113