A vector is a one dimension array of double precision real numbers. A vector can be thought of as a list of numbers. There is no maximum length for vectors.
A literal vector can be a list of numbers, such as,
[3;4.2;.456;-8]
, or a range of numbers, such as,
[3:21:2]
, or an expression that results in a list of
numbers, such as 3*[2:5]^2
.
Elements of a list are separated
by semicolons, ;
, while the colon, :
, is used as
the range element separator.
The following table shows the possible ways that variables can be considered to be equivalent to vectors, that is, can be used wherever vectors are expected.
Let a
be a scalar and let x
be a vector.
Suppose that M
is a matrix and V
is a vector.
V | = | V[i] | for i = 1, ..., LEN(V) |
V[x] | = | V[i] |
for i = x[1], x[2], ..., x[#] |
M[x,b] | = | M[i,a] |
for i = x[1], x[2], ..., x[#] |
M[a,x] | = | M[a,j] |
for j = x[1], x[2], ..., x[#] |
All vectors have an order property. Vectors are either in ascending order,
descending order, or un-ordered. The type is displayed in the
SHOW
command, where +O
means ascending
order, -O
means descending order, and no symbol means
un-ordered. For now, being ordered only has an affect on the vector
union, /|
, and the vector
intersection, /&
, operators.
These operations are much faster if the vector operands are ordered. The
WHERE
function produces an ascending order vector, as does the
SORT/UP
command. The
SORT/DOWN
command produces a descending order vector.