Function

class Function

General mathematical function of decision variables.

__abs__() → Function

Absolute value operator

__add__(rhs: ToFunction) → Function

Addition

__copy__() → Function

__deepcopy__(_memo: Any) → Function

__eq__(other: ToFunction) → Constraint

Create an equality constraint: self == other → Constraint with EqualToZero

Returns a Constraint where (self - other) == 0. Note: This does NOT return bool, it creates a Constraint object.

__ge__(other: ToFunction) → Constraint

Create a greater-than-or-equal constraint: self >= other → Constraint with LessThanOrEqualToZero

Returns a Constraint where (other - self) <= 0.

__iadd__(rhs: ToFunction) → Function

__le__(other: ToFunction) → Constraint

Create a less-than-or-equal constraint: self <= other → Constraint with LessThanOrEqualToZero

Returns a Constraint where (self - other) <= 0.

__mul__(rhs: ToFunction) → Function

Multiplication

__neg__() → Function

Negation operator

__new__(inner: ToFunction) → Function

Create a Function from various types.

Accepts:

• int or float: creates a constant function

• DecisionVariable: creates a linear function with single term

• AttachedDecisionVariable: creates a linear function with single term (only the id is used; no host borrow is taken)

• Parameter: creates a linear function with single term

• Linear: creates a linear function

• Quadratic: creates a quadratic function

• Polynomial: creates a polynomial function

• Function: returns a copy

__pow__(exponent: int, modulo: None = None) → Function

__radd__(lhs: ToFunction) → Function

Reverse addition (lhs + self)

__repr__() → str

__rmul__(lhs: ToFunction) → Function

Reverse multiplication (lhs * self)

__rsub__(lhs: ToFunction) → Function

Reverse subtraction (lhs - self)

__rtruediv__(lhs: ToFunction) → Function

Reverse division (lhs / self)

__sub__(rhs: ToFunction) → Function

Subtraction

__truediv__(rhs: ToFunction) → Function

Division

add_assign(rhs: ToFunction) → None

add_linear(linear: Linear) → Function

add_polynomial(polynomial: Polynomial) → Function

add_quadratic(quadratic: Quadratic) → Function

add_scalar(scalar: float) → Function

almost_equal(other: ToFunction, atol: float = 1e-06) → bool

as_linear() → Optional[Linear]

Try to convert this function to a linear function.

Returns Some(Linear) if the function can be represented as linear, None otherwise. This is useful for checking if a function is suitable for linear programming solvers.

as_quadratic() → Optional[Quadratic]

Try to convert this function to a quadratic function.

Returns Some(Quadratic) if the function can be represented as quadratic, None otherwise.

content_factor() → float

Return the minimal positive factor that makes all coefficients integers.

Raises TypeError for a composed, non-polynomial Function.

degree() → Optional[int]

Get the degree of this function.

Returns the highest degree of any term in a polynomial function. Zero function has degree 0, constant function has degree 0, linear function has degree 1, quadratic function has degree 2, etc. Returns None for non-polynomial expression functions.

evaluate(state: ToState, *, atol: Optional[float] = None) → float

evaluate_bound(bounds: Mapping[int, Bound], *, atol: Optional[float] = None) → Bound

Compute an interval bound of this function given variable bounds.

Missing IDs in bounds are treated as unbounded (Bound.unbounded()).

Args:

• bounds: Mapping from variable ID to its Bound.

• atol: Absolute tolerance used by operations whose semantics depend on whether a value is zero. If omitted, DEFAULT_ATOL is used. Use the same tolerance when point-evaluating this function.

Returns: A Bound that contains \([\inf f, \sup f]\) over the given variable bounds.

Tightness: Polynomial leaves are bounded term by term (monomial-wise), and composed expression operations combine their operand bounds with interval arithmetic. The result is a sound over-approximation of the true range \([\inf f, \sup f]\) but is not guaranteed to be tight, because it ignores dependencies between terms or operands that share variables. For example, \(f = x^2 - x\) with \(x \in [0, 1]\) has true range \([-1/4, 0]\) (minimum at \(x = 1/2\)), but term-wise evaluation yields \([0, 1] + (-[0, 1]) = [-1, 1]\).

Raises: RuntimeError when an interval contains a value treated as zero by atol in a denominator or as the base of a negative integer power. Raises ValueError if valid bound endpoints cannot be constructed after numeric overflow.

Examples

>>> from ommx import Function, Linear, Bound
>>> f = Function(Linear(terms={1: 2}, constant=3))  # 2*x1 + 3
>>> b = f.evaluate_bound({1: Bound(0.0, 2.0)})
>>> b.lower <= 3.0 and b.upper >= 7.0
True

from_linear(linear: Linear) → Function

from_polynomial(polynomial: Polynomial) → Function

from_quadratic(quadratic: Quadratic) → Function

from_scalar(scalar: float) → Function

maximum(rhs: ToFunction) → Function

Pointwise maximum

minimum(rhs: ToFunction) → Function

Pointwise minimum

mul_linear(linear: Linear) → Function

mul_polynomial(polynomial: Polynomial) → Function

mul_quadratic(quadratic: Quadratic) → Function

mul_scalar(scalar: float) → Function

num_terms() → Optional[int]

Get the number of terms in this function.

Zero function has 0 terms, constant function has 1 term, and polynomial functions have the number of non-zero coefficient terms. Returns None for non-polynomial expression functions.

partial_evaluate(state: ToState, *, atol: Optional[float] = None) → Function

powi(exponent: int) → Function

Raise this function to a signed 32-bit integer power.

random(rng: Rng, num_terms: int = 5, max_degree: int = 3, max_id: int = 10) → Function

reduce_binary_power(binary_ids: set[int]) → bool

Reduce binary powers in the function.

For binary variables, \(x^n = x\) for any \(n \geq 1\), so we can reduce higher powers to linear terms.

Args:

• binary_ids: Set of binary variable IDs to reduce powers for

Returns: True if any reduction was performed, False otherwise

required_ids() → set[int]

signum() → Function

Sign of the function value

property constant_term: float

Read-only property.

Get the constant term of the function.

Returns the constant term. Returns 0.0 if function has no constant term. Works for all polynomial functions by filtering the degree-0 term. Raises TypeError if this is a non-polynomial expression function.

property linear_terms: dict[int, float]

Read-only property.

Get linear terms as a dictionary mapping variable id to coefficient.

Returns dictionary mapping variable IDs to their linear coefficients. Returns empty dict if function has no linear terms. Works for all polynomial functions by filtering only degree-1 terms. Raises TypeError if this is a non-polynomial expression function.

property quadratic_terms: dict[tuple[int, int], float]

Read-only property.

Get quadratic terms as a dictionary mapping (row, col) to coefficient.

Returns dictionary mapping variable ID pairs to their quadratic coefficients. Returns empty dict if function has no quadratic terms. Works for all polynomial functions by filtering only degree-2 terms. Raises TypeError if this is a non-polynomial expression function.

property terms: dict

Read-only property.

Get all polynomial terms as a dictionary mapping monomial tuples to coefficients.

Raises TypeError if this is a non-polynomial expression function.

property type_name: str

Read-only property.