Concepts of Programming Languages

6.5 Array Types 267

APL includes a collection of unary operators for vectors and matrices,

some of which are as follows (where V is a vector and M is a matrix):

V reverses the elements of V

M reverses the columns of M

M reverses the rows of M

o\M transposes M (its rows become its columns and vice versa)

÷M inverts M

APL also includes several special operators that take other operators as

operands. One of these is the inner product operator, which is specified with

a period (.). It takes two operands, which are binary operators. For example,

+.×

is a new operator that takes two arguments, either vectors or matrices. It first

multiplies the corresponding elements of two arguments, and then it sums the

results. For example, if A and B are vectors,

A × B

is the mathematical inner product of A and B (a vector of the products of the

corresponding elements of A and B). The statement

A +.× B

is the sum of the inner product of A and B. If A and B are matrices, this expres-

sion specifies the matrix multiplication of A and B.

The special operators of APL are actually functional forms, which are

described in Chapter 15.

6.5.6 Rectangular and Jagged Arrays

A rectangular array is a multidimensioned array in which all of the rows have

the same number of elements and all of the columns have the same number of

elements. Rectangular arrays model rectangular tables exactly.

A jagged array is one in which the lengths of the rows need not be the

same. For example, a jagged matrix may consist of three rows, one with 5 ele-

ments, one with 7 elements, and one with 12 elements. This also applies to the

columns and higher dimensions. So, if there is a third dimension (layers), each

layer can have a different number of elements. Jagged arrays are made possible

when multidimensioned arrays are actually arrays of arrays. For example, a

matrix would appear as an array of single-dimensioned arrays.

C, C++, and Java support jagged arrays but not rectangular arrays. In those

languages, a reference to an element of a multidimensioned array uses a sepa-

rate pair of brackets for each dimension. For example,

myArray[3][7]