Yorick
2.3.8: Marking an index for matrix multiplication
Yorick has a special syntax for matrix multiplication, or, more generally, inner product:
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A(,+)*B(+,) B(+,)*A(,+) x(+)*y(+) P(,+,,)*Q(,,+)
In the first example, A would be an L-by-M array, B would be an M-by-N array, and the result would be the L-by-N matrix product. In the second example, the result would be the N-by-L transpose of the first result. The general rule is that all of the ``spectator'' dimensions of the left operand precede the spectator dimensions of the right operand in the result.
The third example shows how to form the inner product of two vectors x and y of equal length. The fourth example shows how to contract the second dimension of a 4-D array P with the third dimension of the 3-D array Q. If P were 2-by-3-by-4-by-5 and Q were 6-by-7-by-3, the result array would be 2-by-4-by-5-by-6-by-7.
Unlike all of the other special subscript symbols (nil, -, .., and * so far), the + sign marking an index for use in an inner product is actually treated specially by the Yorick parser. The + subscript is a parse error unless the array (or expression) being subscripted is the left or right operand of a binary * operator, which is then parsed as matrix multiplication instead of Yorick's usual element-by-element multiplication. A parse error will also result if only one of the operands has a dimension marked by +. Both operands must have exactly one marked dimension, and the marked dimensions must turn out to be of equal length at run time.
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