cross (:C)/pcross

Syntax

cross(func, X, [Y])

or

X <operator>:C Y

Arguments

func is a binary function.

X and Y can be pair/vector/matrix. They can have different data forms and sizes.

Y is optional. If Y is not specified, perform cross(func, X, X) where func must be a symmetric binary function, such as corr .

Details

Apply func to the permutation of all individual elements of X and Y and return a matrix.

Assume X has m elements and Y has n elements. The template returns an m (rows) by n (columns) matrix. Below is the pseudo code for the cross template.

for(i:0~(size(X)-1)){
for(j:0~(size(Y)-1)){
    result[i,j]=<function>(X[i], Y[j]);
}
}
return result;

If X and Y are matrices, the iteration is over the columns of X and Y .

If the result of func(X[i], Y[j]) is a scalar, the result of the cross template is a matrix.

If the result of func(X[i], Y[j]) is a vector, the result of the cross template is a tuple with m elements. Each of the element is a tuple with n elements.

pcross is the parallel computing version of template function cross.

Examples

cross with two vectors:

$ x=1 2;
$ y=3 5 7;
$ x+:C y;

lable	3	5	7
1	4	6	8
2	5	7	9

$ cross(mul, x, y);

lable	3	5	7
1	3	5	7
2	6	10	14

$ cross(pow, x, y);

lable	3	5	7
1	1	1	1
2	8	32	128

cross with two matrices:

$ m = 1..6$2:3;
$ m;

clo1	col2	col3
1	3	5
2	4	6

$ n=1..4$2:2;
$ n;

clo1	col2
1	3
2	4

$ cross(**, m, n);

clo1	col2
5	11
11	25
17	39

cross with a vector and a matrix:

$ def topsum(x,n){return sum x[0:n]};
$ a=1..18$6:3;
$ a;

clo1	col2	col3
1	7	13
2	8	14
3	9	15
4	10	16
5	11	17
6	12	18

$ b=2 4;
$ a topsum :C b;

2	4
3	10
15	34
27	58

cross with tuple type results:

$ x=1 2
$ y=1..6$2:3
$ cross(add, x, y);
(([2,3],[4,5],[6,7]),([3,4],[5,6],[7,8]))

$ x=1 2
$ y=1..6$3:2
$ cross(add, x, y);
(([2,3,4],[5,6,7]),([3,4,5],[6,7,8]))