All arrays in LISP must be declared before they are used.

LISP    ARRAY(x) — LISP function that takes three or more arguments of type name, type, and dimnsions, and creates an array of that name, type, and dimensions.

    (ARRAY TWODIMENSIONS FIXNUM 1024 1024)

    The example creates a LISP array named TWODIMENSIONS that can contain fixed point numbers. The array elements are numbered by two indices, both in the range of 0 to 1,023.

order of multi-dimensional arrays

    The storage of a signle dimension array in memory is obvious: a linear sequence of memory locations (possibly with padding for instruction alignment purposes).

    When an array has two or more dimensions, it is still ultimately stored in a linear sequence of memory locations (possibly with padding for instruction alignment purposes), but the dimensions must be lined up sequentially as well.

    The two major choices are either row major (rows are stored one after another) or column major (columns are stored one after another). These either group the linear representation of the array by the row or by the column.

    Ada uses a row-major order.

    ALGOL 60 does not specify an order, but many ALGOL 60 compilers use row-major order.

    C uses a row-major order.

    C++ uses a row-major order.

    COBOL uses a row-major order.

    FORTRAN explicitly requires a column-major order.

    Java uses a row-major order.

    Matlab uses a column-major order.

    Modula-2 uses a row-major order.

    Pascal implicitly requires a row-major order.

    PL/I uses a row-major order.

C

matrix operations in APL

functions

PostScript    aload(x) — PosScript array operator that places on the stack all of the elements of an array followed by the array itself.
LISP    ARRAY(x) — LISP function that takes three or more arguments of type name, type, and dimnsions, and creates an array of that name, type, and dimensions.

PL/I    DIM(x, n) — Pl/I built-in function that returns the size of an array. The data item x is the name of the array to be examined. The data item n is the number of the dimension of the specififed array for which the extent is to be returned. The function is most efficient if data item n is of type FIXED BINARY (15). It is an error if the array has less than n dimensions or if n is zero or less or if the array x is not currently allocated. For a matrix the value of n should be either 1 or 2.

PL/I    LBOUND(x, n) — Pl/I built-in function that returns the lower bound for the specififed dimension of an array. The data item x is the name of the array to be examined. The data item n is the number of the dimension of the specififed array for which the extent is to be returned. The function is most efficient if data item n is of type FIXED BINARY (15). It is an error if the array has less than n dimensions or if n is zero or less or if the array x is not currently allocated. For a matrix, the value of n should be 1 or 2.

PL/I    HBOUND(x, n) — Pl/I built-in function that returns the upper bound for the specififed dimension of an array. The data item x is the name of the array to be examined. The data item n is the number of the dimension of the specififed array for which the extent is to be returned. The function is most efficient if data item n is of type FIXED BINARY (15). It is an error if the array has less than n dimensions or if n is zero or less or if the array x is not currently allocated. For a matrix, the value of n should be 1 or 2.

PL/I    SUM(x) — Pl/I built-in function that returns the total sum of all of the values of the elements in an arithmetic array x. Note that the IBM PL/I-F compiler converts all array values to floating point to perform the operation and returns a result in floating point. This may create small rounding errors for commercial programmers needing dollar and cents accuracy.

PL/I    PROD(x) — Pl/I built-in function that returns the total product of all of the values of the elements in an arithmetic array x. The PROD function is always carried out in floating point arithmetic. This may create small rounding errors for commercial programmers needing dollar and cents accuracy.

other

   “Ah, variable names.ÊLength is not a virtue in a name; clarity of expression is.ÊA global variable rarely used may deserve a long name, maxphysaddr say.ÊAn array index used on every line of a loop needn’t be named any more elaborately than i.Ê Saying index or elementnumber is more to type (or calls upon your text editor) and obscures the details of the computation.ÊWhen the variable names are huge, it’s harder to see what’s going on.ÊThis is partly a typographic issue; consider
        for(i=0 to 100)
            array[i]=0 ;
   “vs.
        for(elementnumber=0 to 100)
            array[elementnumber]=0;
   “The problem gets worse fast with real examples.ÊIndices are just notation, so treat them as such.” —Rob Pike, Notes on Programming in C, February 21, 1989