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2.6 Broadcasting and conformability
Two arrays need not have identical shape in order for a binary operation
between them to make perfect sense:
 y = a*x^3 + b*x^2 + c*x + d;

The obvious intent of this assignment statement is that y should
have the same shape as x, each value of y being the value of
the polynomial at the corresponding y.
Alternatively, array valued coefficients a, b, ...,
represent an array of several polynomials  perhaps Legendre
polynomials. Then, if x is a scalar value, the meaning is again
obvious; y should have the same shape as the coefficient arrays,
each y being the value of the corresponding polynomial.
A binary operation is performed once for each element, so that
a+b, say, means
for every i, j, k, l (taking a and b to be four
dimensional). The lengths of corresponding indices must match in order
for this procedure to make sense; Yorick signals a "conformability
error" when the shapes of binary operands do not match.
However, if a had only three dimensions, a+b still makes
sense as:
This sense extends to two dimensional, one dimensional, and finally
to scalar a:
which is how Yorick interpreted the monomial x^3 in the first
example of this section. The shapes of a and b are
conformable as long as the dimensions which they have in common all
have the same lengths; the shorter operand simply repeats its values
for every index of a dimension it doesn't have. This repitition is
called "broadcasting".
Broadcasting is the key to Yorick's array syntax. In practical
situations, it is just as likely for the a array to be missing the
second (j) dimension of the b array as its last (l)
dimension. To handle this case, Yorick will broadcast any unitlength
dimension in addition to a missing final dimension. Hence, if the
a array has a second dimension of length one, a+b
means:
for every i, j, k, l. The pseudoindex can be used to generate
such unit length indices when necessary (see section 2.3.5 Creating a pseudoindex).
