`INTERVAL_VECTOR`

.
**Data Type:**`INTERVAL_VECTOR`

`Variable`[(`Dimension`)]- Declares
`Variable`as interval vector. The optional parameter`Dimension`denotes the initial dimension of the vector. If`Dimension`is missing, no memory is allocated for the vector elements (this will be done after the vector is resized or after the first assignment to the vector).

The basic operations `+`, `-`, `*`, and `/`, the unary operators
`+` and `-` as well as `+=`, `-=`, `*=`, and `/=` are
defined for interval vectors. `REAL`

or `VECTOR`

operands may also be used
instead of interval operands, as long as one operand is an `INTERVAL`

type.

Comparisons of interval vectors are possible with `==` and `!=`.
Inclusion properties may be tested with `<=` and `<` where the latter tests
for inclusion in the interior. For example:

a <= b

returns `TRUE`

, if the interval vector `a`

is contained in the interval
vector `b`

.
All comparisons are performed componentwise and the result of a
vector comparison is true, if it is true for all components. Otherwise the result is
`FALSE`

.

If `i` is an `INT`

expression and `v` an interval vector, ` v`(

Additionally, the following functions are provided:

**Function:**`INT Dimension (INTERVAL_VECTOR`

`v`)- Returns the current dimension of
`v`.

**Function:**`void Resize (INTERVAL_VECTOR`

`v`, INT`i`)- Discards the old elements of
`v`and resizes`v`to contain`i`elements.

**Function:**`void MakeTemporary (INTERVAL_VECTOR`

`v`)- Defines
`v`to be a temporary variable. This is only important when the improved memory management is used.See section Vector Operations ---

`Vector.h`, function`MakeTemporary`

for more information.

**Function:**`void MakePermanent (INTERVAL_VECTOR`

`v`)- Changes the temporary variable
`v`into a permanent one.See section Configuration, for details.

**Function:**`void Clear (INTERVAL_VECTOR`

`v`)- Initializes all elements of
`v`with 0.

**Function:**`void Initialize (INTERVAL_VECTOR`

`v`, INTERVAL`a`)- Initializes all elements of
`v`with the interval`a`.

**Function:**`INTERVAL_VECTOR AddBounds (VECTOR`

`v`, VECTOR`w`)- Returns an interval vector containing an enclosure of the true sum of
`v`and`w`.

**Function:**`INTERVAL_VECTOR SubBounds (VECTOR`

`v`, VECTOR`w`)- Returns an interval vector containing an enclosure of the true difference between
`v`and`w`.

**Function:**`INTERVAL_VECTOR MulBounds (REAL`

`r`, VECTOR`v`)- Returns an interval vector containing an enclosure of the true product of
`r`and`v`.

**Function:**`INTERVAL_VECTOR MulBounds (VECTOR`

`v`, VECTOR`w`)- Returns an interval containing an enclosure of the true product of
`v`and`w`.

**Function:**`INTERVAL_VECTOR DivBounds (VECTOR`

`v`, REAL`r`)- Returns an interval vector containing an enclosure of the true quotient between
`v`and`r`.

**Function:**`VECTOR Inf (INTERVAL_VECTOR`

`v`)- Returns a vector containing the lower bounds of the interval vector
`v`.

**Function:**`VECTOR Sup (INTERVAL_VECTOR`

`v`)- Returns a vector containing the upper bounds of the interval vector
`v`.

**Function:**`INTERVAL_VECTOR Hull (VECTOR`

`v`)- Returns the point interval vector [
`v`,`v`].

**Function:**`INTERVAL_VECTOR Hull (`

`v`,`w`)- Returns the convex hull of
`v`and`w`. The expressions`v`and`w`may be either of type`VECTOR`

or`INTERVAL_VECTOR`

.

**Function:**`INTERVAL_VECTOR SymHull (VECTOR`

`v`)- Returns the interval vector [-
`v`,`v`].

**Function:**`VECTOR Mid (INTERVAL_VECTOR`

`v`)- Returns the midpoint of the interval vector
`v`.

**Function:**`VECTOR Diam (INTERVAL_VECTOR`

`v`)- Returns the diameter of the interval vector
`v`.

**Function:**`VECTOR Abs (INTERVAL_VECTOR`

`v`)- Returns the absolute value of the interval vector
`v`.

**Function:**`BOOL Intersection (INTERVAL_VECTOR`

`u`, INTERVAL_VECTOR`v`, INTERVAL_VECTOR`w`)- If
`v`and`w`intersect, the value`TRUE`

is returned and`u`contains the intersection. Otherwise`FALSE`

is returned and the contents of`u`are undefined.

**Function:**`INTERVAL Sqr (INTERVAL_VECTOR`

`v`)- Returns the scalar product of
`v`with itself, i.e. a faster form of*`v``v`.

**Function:**`INTERVAL Norm (INTERVAL_VECTOR`

`v`)- Returns the 2-Norm of
`v`.