Inherits Parma_Polyhedra_Library::Linear_Row.
Public Types |
enum | Type { EQUALITY,
NONSTRICT_INEQUALITY,
STRICT_INEQUALITY
} |
| The constraint type. More...
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Public Member Functions |
| Constraint (const Constraint &c) |
| Ordinary copy constructor.
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| Constraint (const Congruence &cg) |
| Copy-constructs from equality congruence cg .
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| ~Constraint () |
| Destructor.
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Constraint & | operator= (const Constraint &c) |
| Assignment operator.
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dimension_type | space_dimension () const |
| Returns the dimension of the vector space enclosing *this .
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Type | type () const |
| Returns the constraint type of *this .
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bool | is_equality () const |
| Returns true if and only if *this is an equality constraint.
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bool | is_inequality () const |
| Returns true if and only if *this is an inequality constraint (either strict or non-strict).
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bool | is_nonstrict_inequality () const |
| Returns true if and only if *this is a non-strict inequality constraint.
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bool | is_strict_inequality () const |
| Returns true if and only if *this is a strict inequality constraint.
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Coefficient_traits::const_reference | coefficient (Variable v) const |
| Returns the coefficient of v in *this .
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Coefficient_traits::const_reference | inhomogeneous_term () const |
| Returns the inhomogeneous term of *this .
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memory_size_type | total_memory_in_bytes () const |
| Returns a lower bound to the total size in bytes of the memory occupied by *this .
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memory_size_type | external_memory_in_bytes () const |
| Returns the size in bytes of the memory managed by *this .
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bool | is_tautological () const |
| Returns true if and only if *this is a tautology (i.e., an always true constraint).
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bool | is_inconsistent () const |
| Returns true if and only if *this is inconsistent (i.e., an always false constraint).
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bool | is_equivalent_to (const Constraint &y) const |
| Returns true if and only if *this and y are equivalent constraints.
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void | ascii_dump () const |
| Writes to std::cerr an ASCII representation of *this .
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void | ascii_dump (std::ostream &s) const |
| Writes to s an ASCII representation of *this .
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void | print () const |
| Prints *this to std::cerr using operator<< .
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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.
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bool | OK () const |
| Checks if all the invariants are satisfied.
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void | m_swap (Constraint &y) |
| Swaps *this with y .
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Static Public Member Functions |
static dimension_type | max_space_dimension () |
| Returns the maximum space dimension a Constraint can handle.
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static void | initialize () |
| Initializes the class.
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static void | finalize () |
| Finalizes the class.
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static const Constraint & | zero_dim_false () |
| The unsatisfiable (zero-dimension space) constraint .
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static const Constraint & | zero_dim_positivity () |
| The true (zero-dimension space) constraint , also known as positivity constraint.
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Related Functions |
(Note that these are not member functions.)
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void | swap (Constraint &x, Constraint &y) |
| Swaps x with y .
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bool | operator== (const Constraint &x, const Constraint &y) |
| Returns true if and only if x is equivalent to y .
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bool | operator!= (const Constraint &x, const Constraint &y) |
| Returns true if and only if x is not equivalent to y .
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Constraint | operator== (const Linear_Expression &e1, const Linear_Expression &e2) |
| Returns the constraint e1 = e2 .
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Constraint | operator== (Variable v1, Variable v2) |
| Returns the constraint v1 = v2 .
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Constraint | operator== (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| Returns the constraint e = n .
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Constraint | operator== (Coefficient_traits::const_reference n, const Linear_Expression &e) |
| Returns the constraint n = e .
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Constraint | operator<= (const Linear_Expression &e1, const Linear_Expression &e2) |
| Returns the constraint e1 <= e2 .
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Constraint | operator<= (Variable v1, Variable v2) |
| Returns the constraint v1 <= v2 .
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Constraint | operator<= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| Returns the constraint e <= n .
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Constraint | operator<= (Coefficient_traits::const_reference n, const Linear_Expression &e) |
| Returns the constraint n <= e .
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Constraint | operator>= (const Linear_Expression &e1, const Linear_Expression &e2) |
| Returns the constraint e1 >= e2 .
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Constraint | operator>= (Variable v1, Variable v2) |
| Returns the constraint v1 >= v2 .
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Constraint | operator>= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| Returns the constraint e >= n .
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Constraint | operator>= (Coefficient_traits::const_reference n, const Linear_Expression &e) |
| Returns the constraint n >= e .
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Constraint | operator< (const Linear_Expression &e1, const Linear_Expression &e2) |
| Returns the constraint e1 < e2 .
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Constraint | operator< (Variable v1, Variable v2) |
| Returns the constraint v1 < v2 .
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Constraint | operator< (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| Returns the constraint e < n .
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Constraint | operator< (Coefficient_traits::const_reference n, const Linear_Expression &e) |
| Returns the constraint n < e .
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Constraint | operator> (const Linear_Expression &e1, const Linear_Expression &e2) |
| Returns the constraint e1 > e2 .
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Constraint | operator> (Variable v1, Variable v2) |
| Returns the constraint v1 > v2 .
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Constraint | operator> (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| Returns the constraint e > n .
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Constraint | operator> (Coefficient_traits::const_reference n, const Linear_Expression &e) |
| Returns the constraint n > e .
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std::ostream & | operator<< (std::ostream &s, const Constraint &c) |
| Output operator.
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std::ostream & | operator<< (std::ostream &s, const Constraint::Type &t) |
| Output operator.
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bool | operator== (const Constraint &x, const Constraint &y) |
bool | operator!= (const Constraint &x, const Constraint &y) |
Constraint | operator== (const Linear_Expression &e1, const Linear_Expression &e2) |
Constraint | operator== (const Variable v1, const Variable v2) |
Constraint | operator>= (const Linear_Expression &e1, const Linear_Expression &e2) |
Constraint | operator>= (const Variable v1, const Variable v2) |
Constraint | operator> (const Linear_Expression &e1, const Linear_Expression &e2) |
Constraint | operator> (const Variable v1, const Variable v2) |
Constraint | operator== (Coefficient_traits::const_reference n, const Linear_Expression &e) |
Constraint | operator>= (Coefficient_traits::const_reference n, const Linear_Expression &e) |
Constraint | operator> (Coefficient_traits::const_reference n, const Linear_Expression &e) |
Constraint | operator== (const Linear_Expression &e, Coefficient_traits::const_reference n) |
Constraint | operator>= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
Constraint | operator> (const Linear_Expression &e, Coefficient_traits::const_reference n) |
Constraint | operator<= (const Linear_Expression &e1, const Linear_Expression &e2) |
Constraint | operator<= (const Variable v1, const Variable v2) |
Constraint | operator<= (Coefficient_traits::const_reference n, const Linear_Expression &e) |
Constraint | operator<= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
Constraint | operator< (const Linear_Expression &e1, const Linear_Expression &e2) |
Constraint | operator< (const Variable v1, const Variable v2) |
Constraint | operator< (Coefficient_traits::const_reference n, const Linear_Expression &e) |
Constraint | operator< (const Linear_Expression &e, Coefficient_traits::const_reference n) |
void | swap (Constraint &x, Constraint &y) |
A linear equality or inequality.
An object of the class Constraint is either:
- an equality:
;
- a non-strict inequality:
; or
- a strict inequality:
;
where
is the dimension of the space,
is the integer coefficient of variable
and
is the integer inhomogeneous term.
- How to build a constraint
- Constraints are typically built by applying a relation symbol to a pair of linear expressions. Available relation symbols are equality (
==
), non-strict inequalities (>=
and <=
) and strict inequalities (<
and >
). The space dimension of a constraint is defined as the maximum space dimension of the arguments of its constructor.
- In 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 the equality constraint
, having space dimension
: The following code builds the (non-strict) inequality constraint
, having space dimension
: The corresponding strict inequality constraint
is obtained as follows: An unsatisfiable constraint on the zero-dimension space
can be specified as follows: Equivalent, but more involved ways are the following: In contrast, the following code defines an unsatisfiable constraint having space dimension
:
- How to inspect a constraint
- Several methods are provided to examine a constraint and extract all the encoded information: its space dimension, its type (equality, non-strict inequality, strict inequality) and the value of its integer coefficients.
- Example 2
- The following code shows how it is possible to access each single coefficient of a constraint. Given an inequality constraint (in this case
), we construct a new constraint corresponding to its complement (thus, in this case we want to obtain the strict inequality constraint
). Constraint c1(x - 5*y + 3*z <= 4);
cout << "Constraint c1: " << c1 << endl;
if (c1.is_equality())
cout << "Constraint c1 is not an inequality." << endl;
else {
Linear_Expression e;
for (dimension_type i = c1.space_dimension(); i-- > 0; )
e += c1.coefficient(Variable(i)) * Variable(i);
e += c1.inhomogeneous_term();
Constraint c2 = c1.is_strict_inequality() ? (e <= 0) : (e < 0);
cout << "Complement c2: " << c2 << endl;
}
The actual output is the following: Constraint c1: -A + 5*B - 3*C >= -4
Complement c2: A - 5*B + 3*C > 4
Note that, in general, the particular output obtained can be syntactically different from the (semantically equivalent) constraint considered.