Module sum

Classes

SumOperator

class SumOperator(
    self,
    sum_index: Element,
    operand: Expression,
    condition: Optional[Condition] = None,
    uuid: Optional[str] = None,)

Class that represents the sum.

Example: Create $`\sum_{i=0}^n d_i x_i`$

>>> from jijmodeling import Placeholder, Binary, SumOperator
>>> from jijmodeling import Element
>>> d = Placeholder('d', dim=1)
>>> n = d.shape[0]
>>> x = Binary('x', shape=n)
>>> i = Element("i", n)
>>> SumOperator(sum_index=i, \
    operand=d[i]*x[i], condition=None)
Σ_{i}(d[i]x[i])

Initialize self. See help(type(self)) for accurate signature.

---

Base classes

• jijmodeling.Expression

---

Instance attributes

• condition summation condition

• operand summation operand

• sum_index summation index

• uuid

---

Methods

children

def children(self) -> list

[sum_index, operand, condition]

---

is_operatable

def is_operatable(self) -> bool

specify whether the operators (+, -, *, /,...) can be applied to the expression. For example, "a[3]" is true, whereas "a" is not.

Returns: bool: defaults False.

Functions

Sum

def Sum(
    indices: Union[INDEXWITHCOND, List[INDEXWITHCOND]],
    term: Expression,
    condition: Optional[Union[Condition, List[Optional[Condition]]]] = None
    ) -> SumOperator

Sum function

Args: indices: summation index dict or list of index. term (Expression): operand of summation condition: [deprecated] summation conditions. Defaults to None.

Returns: SumOperator: SumOperator object.

Example: Create $`\sum_{i=0}^n d_i x_i`$

>>> import jijmodeling as jm
>>> d = jm.Placeholder('d', dim=1)
>>> n = d.shape[0]
>>> x = jm.Binary('x', shape=n)
>>> i = jm.Element('i', n)
>>> jm.Sum(i, d[i]*x[i])
Σ_{i}(d[i]x[i])

Create $`\sum_{i}\sum_j d_{ij}x_i x_j`$

>>> import jijmodeling as jm
>>> d = jm.Placeholder('d', dim = 2)
>>> n = d.shape[0]
>>> x = jm.Binary('x', shape=n)
>>> i = jm.Element('i', n)
>>> j = jm.Element('j', n)
>>> jm.Sum([i, j], d[i, j]*x[i]*x[j])

Conditional sum
>>> import jijmodeling as jm
>>> d = jm.Placeholder('d', dim = 2)
>>> n = d.shape[0]
>>> i, j = jm.Element("i", n), jm.Element("j", n)
>>> x = jm.Binary('x', shape=n)
>>> jm.Sum([i, (j, i < j)], d[i, j]*x[i]*x[j])