PPL  0.12.1
Parma_Polyhedra_Library::Congruence_System Class Reference

A system of congruences. More...

#include <ppl.hh>

Inherits Parma_Polyhedra_Library::Dense_Matrix.

List of all members.

Classes

class  const_iterator
 An iterator over a system of congruences. More...

Public Member Functions

 Congruence_System ()
 Default constructor: builds an empty system of congruences.
 Congruence_System (const Congruence &cg)
 Builds the singleton system containing only congruence cg.
 Congruence_System (const Constraint &c)
 If c represents the constraint $ e_1 = e_2 $, builds the singleton system containing only constraint $ e_1 = e_2 \pmod{0}$.
 Congruence_System (const Constraint_System &cs)
 Builds a system containing copies of any equalities in cs.
 Congruence_System (const Congruence_System &cgs)
 Ordinary copy constructor.
 ~Congruence_System ()
 Destructor.
Congruence_Systemoperator= (const Congruence_System &y)
 Assignment operator.
dimension_type space_dimension () const
 Returns the dimension of the vector space enclosing *this.
bool is_equal_to (const Congruence_System &y) const
 Returns true if and only if *this is exactly equal to y.
bool has_linear_equalities () const
 Returns true if and only if *this contains one or more linear equalities.
void clear ()
 Removes all the congruences and sets the space dimension to 0.
void insert (const Congruence &cg)
 Inserts in *this a copy of the congruence cg, increasing the number of space dimensions if needed.
void insert (const Constraint &c)
 Inserts in *this a copy of the equality constraint c, seen as a modulo 0 congruence, increasing the number of space dimensions if needed.
void insert (const Congruence_System &y)
 Inserts in *this a copy of the congruences in y, increasing the number of space dimensions if needed.
void recycling_insert (Congruence_System &cgs)
 Inserts into *this the congruences in cgs, increasing the number of space dimensions if needed.
bool empty () const
 Returns true if and only if *this has no congruences.
const_iterator begin () const
 Returns the const_iterator pointing to the first congruence, if *this is not empty; otherwise, returns the past-the-end const_iterator.
const_iterator end () const
 Returns the past-the-end const_iterator.
bool OK () const
 Checks if all the invariants are satisfied.
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.
memory_size_type total_memory_in_bytes () const
 Returns 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.
dimension_type num_equalities () const
 Returns the number of equalities.
dimension_type num_proper_congruences () const
 Returns the number of proper congruences.
void m_swap (Congruence_System &y)
 Swaps *this with y.
void add_unit_rows_and_columns (dimension_type dims)
 Adds dims rows and dims columns of zeroes to the matrix, initializing the added rows as in the unit congruence system.

Static Public Member Functions

static dimension_type max_space_dimension ()
 Returns the maximum space dimension a Congruence_System can handle.
static void initialize ()
 Initializes the class.
static void finalize ()
 Finalizes the class.
static const Congruence_Systemzero_dim_empty ()
 Returns the system containing only Congruence::zero_dim_false().

Protected Member Functions

bool satisfies_all_congruences (const Grid_Generator &g) const
 Returns true if g satisfies all the congruences.

Related Functions

(Note that these are not member functions.)

std::ostream & operator<< (std::ostream &s, const Congruence_System &cgs)
 Output operator.
void swap (Congruence_System &x, Congruence_System &y)
 Swaps x with y.
std::ostream & operator<< (std::ostream &s, const Congruence_System &cgs)
void swap (Congruence_System &x, Congruence_System &y)

Detailed Description

A system of congruences.

An object of the class Congruence_System is a system of congruences, i.e., a multiset of objects of the class Congruence. When inserting congruences in a system, space dimensions are automatically adjusted so that all the congruences in the system are defined on the same vector space.

In all the examples it is assumed that variables x and y are defined as follows:
  Variable x(0);
  Variable y(1);
Example 1
The following code builds a system of congruences corresponding to an integer grid in $\Rset^2$:
  Congruence_System cgs;
  cgs.insert(x %= 0);
  cgs.insert(y %= 0);
Note that: the congruence system is created with space dimension zero; the first and second congruence insertions increase the space dimension to $1$ and $2$, respectively.
Example 2
By adding to the congruence system of the previous example, the congruence $x + y = 1 \pmod{2}$:
  cgs.insert((x + y %= 1) / 2);
we obtain the grid containing just those integral points where the sum of the x and y values is odd.
Example 3
The following code builds a system of congruences corresponding to the grid in $\Zset^2$ containing just the integral points on the x axis:
  Congruence_System cgs;
  cgs.insert(x %= 0);
  cgs.insert((y %= 0) / 0);
Note:
After inserting a multiset of congruences in a congruence system, there are no guarantees that an exact copy of them can be retrieved: in general, only an equivalent congruence system will be available, where original congruences may have been reordered, removed (if they are trivial, duplicate or implied by other congruences), linearly combined, etc.

Constructor & Destructor Documentation

If c represents the constraint $ e_1 = e_2 $, builds the singleton system containing only constraint $ e_1 = e_2 \pmod{0}$.

Exceptions:
std::invalid_argumentThrown if c is not an equality constraint.

Member Function Documentation

Inserts in *this a copy of the congruence cg, increasing the number of space dimensions if needed.

The copy of cg will be strongly normalized after being inserted.

Inserts in *this a copy of the equality constraint c, seen as a modulo 0 congruence, increasing the number of space dimensions if needed.

The modulo 0 congruence will be strongly normalized after being inserted.

Exceptions:
std::invalid_argumentThrown if c is a relational constraint.

Inserts in *this a copy of the congruences in y, increasing the number of space dimensions if needed.

The inserted copies will be strongly normalized.

Adds dims rows and dims columns of zeroes to the matrix, initializing the added rows as in the unit congruence system.

Parameters:
dimsThe number of rows and columns to be added: must be strictly positive.

Turns the $r \times c$ matrix $A$ into the $(r+dims) \times (c+dims)$ matrix $\bigl(\genfrac{}{}{0pt}{}{0}{A} \genfrac{}{}{0pt}{}{B}{A}\bigr)$ where $B$ is the $dims \times dims$ unit matrix of the form $\bigl(\genfrac{}{}{0pt}{}{0}{1} \genfrac{}{}{0pt}{}{1}{0}\bigr)$. The matrix is expanded avoiding reallocation whenever possible.


Friends And Related Function Documentation

std::ostream & operator<< ( std::ostream &  s,
const Congruence_System cgs 
)
related

Output operator.

Writes true if cgs is empty. Otherwise, writes on s the congruences of cgs, all in one row and separated by ", ".

void swap ( Congruence_System x,
Congruence_System y 
)
related

Swaps x with y.

std::ostream & operator<< ( std::ostream &  s,
const Congruence_System cgs 
)
related
void swap ( Congruence_System x,
Congruence_System y 
)
related

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