# Parma_Polyhedra_Library::Grid_Generator Class Reference
[C++ Language Interface]

A grid line, parameter or grid point. More...

`#include <ppl.hh>`

Inherits Parma_Polyhedra_Library::Generator.

List of all members.

## Public Types
enum | Type { LINE, PARAMETER, POINT }
| The generator type. More...
## Public Member Functions
| Grid_Generator (const Grid_Generator &g)
| Ordinary copy constructor.
| ~Grid_Generator ()
| Destructor.
Grid_Generator & | operator= (const Grid_Generator &g)
| Assignment operator.
Grid_Generator & | operator= (const Generator &g)
| Assignment operator.
dimension_type | space_dimension () const
| Returns the dimension of the vector space enclosing `*this`.
Type | type () const
| Returns the generator type of `*this`.
bool | is_line () const
| Returns `true` if and only if `*this` is a line.
bool | is_parameter () const
| Returns `true` if and only if `*this` is a parameter.
bool | is_line_or_parameter () const
| Returns `true` if and only if `*this` is a line or a parameter.
bool | is_point () const
| Returns `true` if and only if `*this` is a point.
bool | is_parameter_or_point () const
| Returns `true` if and only if `*this` row represents a parameter or a point.
Coefficient_traits::const_reference | coefficient (Variable v) const
| Returns the coefficient of `v` in `*this`.
Coefficient_traits::const_reference | divisor () const
| Returns the divisor of `*this`.
memory_size_type | total_memory_in_bytes () const
| Returns a lower bound to the total size in bytes of the memory occupied by `*this`.
memory_size_type | external_memory_in_bytes () const
| Returns the size in bytes of the memory managed by `*this`.
bool | is_equivalent_to (const Grid_Generator &y) const
| Returns `true` if and only if `*this` and `y` are equivalent generators.
bool | is_equal_to (const Grid_Generator &y) const
| Returns `true` if `*this` is exactly equal to `y`.
bool | is_equal_at_dimension (dimension_type dim, const Grid_Generator &gg) const
| Returns `true` if `*this` is equal to `gg` in dimension `dim`.
bool | all_homogeneous_terms_are_zero () const
| Returns `true` if and only if all the homogeneous terms of `*this` are .
void | ascii_dump () const
| Writes to `std::cerr` an ASCII representation of `*this`.
void | ascii_dump (std::ostream &s) const
| Writes to `s` an ASCII representation of `*this`.
void | print () const
| Prints `*this` to `std::cerr` using `operator<<`.
bool | ascii_load (std::istream &s)
| Loads from `s` an ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets `*this` accordingly. Returns `true` if successful, `false` otherwise.
bool | OK () const
| Checks if all the invariants are satisfied.
void | swap (Grid_Generator &y)
| Swaps `*this` with `y`.
void | coefficient_swap (Grid_Generator &y)
| Swaps `*this` with `y`, leaving `*this` with the original capacity.
## Static Public Member Functions
static Grid_Generator | grid_line (const Linear_Expression &e)
| Returns the line of direction `e`.
static Grid_Generator | parameter (const Linear_Expression &e=Linear_Expression::zero(), Coefficient_traits::const_reference d=Coefficient_one())
| Returns the parameter of direction `e` and size `e/d`.
static Grid_Generator | grid_point (const Linear_Expression &e=Linear_Expression::zero(), Coefficient_traits::const_reference d=Coefficient_one())
| Returns the point at `e` / `d`.
static dimension_type | max_space_dimension ()
| Returns the maximum space dimension a Grid_Generator can handle.
static void | initialize ()
| Initializes the class.
static void | finalize ()
| Finalizes the class.
static const Grid_Generator & | zero_dim_point ()
| Returns the origin of the zero-dimensional space .
## Related Functions
(Note that these are not member functions.)
std::ostream & | operator<< (std::ostream &s, const Grid_Generator &g)
| Output operator.
void | swap (Parma_Polyhedra_Library::Grid_Generator &x, Parma_Polyhedra_Library::Grid_Generator &y)
| Specializes `std::swap`.
bool | operator== (const Grid_Generator &x, const Grid_Generator &y)
| Returns `true` if and only if `x` is equivalent to `y`.
bool | operator!= (const Grid_Generator &x, const Grid_Generator &y)
| Returns `true` if and only if `x` is not equivalent to `y`.
std::ostream & | operator<< (std::ostream &s, const Grid_Generator::Type &t)
| Output operator.

## Detailed Description

A grid line, parameter or grid point.

An object of the class Grid_Generator is one of the following:

- a grid_line ;

- a parameter ;

- a grid_point ;

where is the dimension of the space and, for grid_points and parameters, is the divisor.

How to build a grid generator.
  Each type of generator is built by applying the corresponding function (`grid_line`, `parameter` or `grid_point`) to a linear expression; the space dimension of the generator is defined as the space dimension of the corresponding linear expression. Linear expressions used to define a generator should be homogeneous (any constant term will be simply ignored). When defining grid points and parameters, an optional Coefficient argument can be used as a common divisor for all the coefficients occurring in the provided linear expression; the default value for this argument is 1.

  In all the following examples it is assumed that variables `x`, `y` and `z` are defined as follows:

        Variable x(0);
        Variable y(1);
        Variable z(2);

Example 1
  The following code builds a grid line with direction and having space dimension :

        Grid_Generator l = grid_line(x - y - z);

  By definition, the origin of the space is not a line, so that the following code throws an exception:

        Grid_Generator l = grid_line(0*x);

Example 2
  The following code builds the parameter as the vector which has the same direction as the line in Example 1:

        Grid_Generator q = parameter(x - y - z);

  Note that, unlike lines, for parameters, the length as well as the direction of the vector represented by the code is significant. Thus `q` is not the same as the parameter `q1` defined by

        Grid_Generator q1 = parameter(2x - 2y - 2z);

  By definition, the origin of the space is not a parameter, so that the following code throws an exception:

        Grid_Generator q = parameter(0*x);

Example 3
  The following code builds the grid point :

        Grid_Generator p = grid_point(1*x + 0*y + 2*z);

  The same effect can be obtained by using the following code:

        Grid_Generator p = grid_point(x + 2*z);

  Similarly, the origin can be defined using either one of the following lines of code:

        Grid_Generator origin3 = grid_point(0*x + 0*y + 0*z);
        Grid_Generator origin3_alt = grid_point(0*z);

  Note however that the following code would have defined a different point, namely :

        Grid_Generator origin2 = grid_point(0*y);

  The following two lines of code both define the only grid point having space dimension zero, namely . In the second case we exploit the fact that the first argument of the function `point` is optional.

        Grid_Generator origin0 = Generator::zero_dim_point();
        Grid_Generator origin0_alt = grid_point();

Example 4
  The grid point specified in Example 3 above can also be obtained with the following code, where we provide a non-default value for the second argument of the function `grid_point` (the divisor):

        Grid_Generator p = grid_point(2*x + 0*y + 4*z, 2);

  Obviously, the divisor can be used to specify points having some non-integer (but rational) coordinates. For instance, the grid point can be specified by the following code:

        Grid_Generator p1 = grid_point(-15*x + 32*y + 21*z, 10);

  If a zero divisor is provided, an exception is thrown.

Example 5
  Parameters, like grid points can have a divisor. For instance, the parameter can be defined:

        Grid_Generator q = parameter(2*x + 0*y + 4*z, 2);

  Also, the divisor can be used to specify parameters having some non-integer (but rational) coordinates. For instance, the parameter can be defined:

        Grid_Generator q = parameter(-15*x + 32*y + 21*z, 10);

  If a zero divisor is provided, an exception is thrown.

How to inspect a grid generator
  Several methods are provided to examine a grid generator and extract all the encoded information: its space dimension, its type and the value of its integer coefficients and the value of the denominator.

Example 6
  The following code shows how it is possible to access each single coefficient of a grid generator. If `g1` is a grid point having coordinates , we construct the parameter `g2` having coordinates .

        if (g1.is_point()) {
          cout << "Grid point g1: " << g1 << endl;
          Linear_Expression e;
          for (dimension_type i = g1.space_dimension(); i-- > 0; )
            e += (i + 1) * g1.coefficient(Variable(i)) * Variable(i);
          Grid_Generator g2 = parameter(e, g1.divisor());
          cout << "Parameter g2: " << g2 << endl;
        }
        else
          cout << "Grid Generator g1 is not a grid point." << endl;

  Therefore, for the grid point

        Grid_Generator g1 = grid_point(2*x - y + 3*z, 2);

  we would obtain the following output:

        Grid point g1: p((2*A - B + 3*C)/2)
        Parameter g2: parameter((2*A - 2*B + 9*C)/2)

  When working with grid points and parameters, be careful not to confuse the notion of coefficient with the notion of coordinate: these are equivalent only when the divisor is 1.

## Member Enumeration Documentation

enum Parma_Polyhedra_Library::Grid_Generator::Type

The generator type.

Enumerator:

  LINE | The generator is a grid line.
  PARAMETER | The generator is a parameter.
  POINT | The generator is a grid point.

Reimplemented from Parma_Polyhedra_Library::Generator.

## Member Function Documentation

Grid_Generator grid_line | ( | const Linear_Expression & | e | ) | `[inline, static]`

Returns the line of direction `e`.

Shorthand for Grid_Generator Grid_Generator::grid_line(const Linear_Expression& e).

Exceptions:

  | std::invalid_argument | Thrown if the homogeneous part of `e` represents the origin of the vector space.

Grid_Generator parameter | ( | const Linear_Expression & | e = `Linear_Expression::zero()`,
|  | Coefficient_traits::const_reference | d = `Coefficient_one()` |
| ) |  |  | `[inline, static]`

Returns the parameter of direction `e` and size `e/d`.

Shorthand for Grid_Generator Grid_Generator::parameter(const Linear_Expression& e, Coefficient_traits::const_reference d).

Both `e` and `d` are optional arguments, with default values Linear_Expression::zero() and Coefficient_one(), respectively.

Exceptions:

  | std::invalid_argument | Thrown if `d` is zero.

Grid_Generator grid_point | ( | const Linear_Expression & | e = `Linear_Expression::zero()`,
|  | Coefficient_traits::const_reference | d = `Coefficient_one()` |
| ) |  |  | `[inline, static]`

Returns the point at `e` / `d`.

Shorthand for Grid_Generator Grid_Generator::grid_point(const Linear_Expression& e, Coefficient_traits::const_reference d).

Both `e` and `d` are optional arguments, with default values Linear_Expression::zero() and Coefficient_one(), respectively.

Exceptions:

  | std::invalid_argument | Thrown if `d` is zero.

Coefficient_traits::const_reference Parma_Polyhedra_Library::Grid_Generator::coefficient | ( | Variable | v | ) | const`[inline]`

Returns the coefficient of `v` in `*this`.

Exceptions:

  | std::invalid_argument | Thrown if the index of `v` is greater than or equal to the space dimension of `*this`.

Reimplemented from Parma_Polyhedra_Library::Generator.

Coefficient_traits::const_reference Parma_Polyhedra_Library::Grid_Generator::divisor | ( |  | ) | const`[inline]`

Returns the divisor of `*this`.

Exceptions:

  | std::invalid_argument | Thrown if `*this` is a line.

Reimplemented from Parma_Polyhedra_Library::Generator.

bool Parma_Polyhedra_Library::Grid_Generator::is_equivalent_to | ( | const Grid_Generator & | y | ) | const

Returns `true` if and only if `*this` and `y` are equivalent generators.

Generators having different space dimensions are not equivalent.

void Parma_Polyhedra_Library::Grid_Generator::coefficient_swap | ( | Grid_Generator & | y | ) |

Swaps `*this` with `y`, leaving `*this` with the original capacity.

All elements up to and including the last element of the smaller of `*this` and `y` are swapped. The parameter divisor element of `y` is swapped with the divisor element of `*this`.

## Friends And Related Function Documentation

std::ostream & operator<< | ( | std::ostream & | s,
|  | const Grid_Generator & | g |
| ) |  |  | `[related]`

Output operator.

void swap | ( | Parma_Polyhedra_Library::Grid_Generator & | x,
|  | Parma_Polyhedra_Library::Grid_Generator & | y |
| ) |  |  | `[related]`

Specializes `std::swap`.

bool operator== | ( | const Grid_Generator & | x,
|  | const Grid_Generator & | y |
| ) |  |  | `[related]`

Returns `true` if and only if `x` is equivalent to `y`.

bool operator!= | ( | const Grid_Generator & | x,
|  | const Grid_Generator & | y |
| ) |  |  | `[related]`

Returns `true` if and only if `x` is not equivalent to `y`.

std::ostream & operator<< | ( | std::ostream & | s,
|  | const Grid_Generator::Type & | t |
| ) |  |  | `[related]`

Output operator.

The documentation for this class was generated from the following file:

- ppl.hh