# LSOperator Enumeration¶

class localsolver.LSOperator

Mathematical operators available for modeling. These operators are used to type the expressions created in LocalSolver mathematical optimization model.

As other enumerations present in the localsolver module, LSOperator is enumerable and indexable:

print (LSOperator[0])        # Shows LSOperator.BOOL
print (LSOperator.BOOL.value)   # Shows 0

# Iterates over the members of LSOperator
for e in LSOperator:
print e

BOOL

Boolean decision. Decisional operator with no operand. Decision variable with domain {0,1}.

FLOAT

Float decision. Operator with two operands that represent the lower bound and the upper bound of the decision (domain [lb, ub]). The bounds must be constants (integers or doubles).

 Since: 4
CONST

Constant. Unary operator. Can be equal to any integer. Note that constants 0 or 1 are considered as boolean. Constants are implicitly created when passing integer arguments to LSModel.create_expression() or LSExpression.add_operand().

SUM

Sum. N-ary arithmetic operator. SUM(e1, e2, ..., eN) is equal to the sum of all operands e1, e2, ..., eN. This operator returns an integer if all the operands are booleans or integers and a double as soon as one operand is a double.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will sum all the values computed and returned by the function.

SUB

Substraction. Binary arithmetic operator. SUB(x, y) is equal to the value of x - y. This operator returns an integer or a double according to the type of its operands.

 Since: 4
PROD

Product. N-ary arithmetic operator. PROD(e1, e2, ..., eN) is equal to the product of all operands e1, e2, ..., eN. This operator returns an integer if all the operands are booleans or integers, and a double as soon as one operand is a double.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will compute the product of all the values returned by the function.

MAX

Maximum. N-ary arithmetic operator. MAX(e1, e2, ..., eN) is equal to the maximum value among all operands e1, e2, ..., eN. This operator returns an integer if all the operands are booleans or integers, and a double as soon as one operand is a double.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will find the maximum value among all the values returned by the function.

MIN

Minimum. N-ary arithmetic operator. MIN(e1, e2, ..., eN) is equal to the minimum value among all operands e1, e2, ..., eN. This operator returns an integer if all the operands are booleans or integers, and a double as soon as one operand is a double.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will find the minimum value among all the values returned by the function.

EQ

Equal. Binary relational operator. EQ(a, b) = 1 if a == b, and 0 otherwise. This operator returns a boolean.

NEQ

Not equal to. Binary relational operator. NEQ(a,b) = 1 if a != b, and 0 otherwise. This operator returns a boolean.

GEQ

Greater than or equal to. Binary relational operator. GEQ(a,b) = 1 if a >= b, and 0 otherwise. This operator returns a boolean.

LEQ

Lower than or equal to. Binary relational operator. LEQ(a,b) = 1 if a <= b, and 0 otherwise. This operator returns a boolean.

GT

Strictly greater than. Binary relational operator. GT(a,b) = 1 if a > b, and 0 otherwise. This operator returns a boolean.

LT

Strictly lower than. Binary relational operator. LQ(a, b) = 1 if a < b, and 0 otherwise. This operator returns a boolean.

IF

If-Then-Else. Ternary conditional operator. IF(a,b,c) is equal to b if a is true, and c otherwise. Note that the first operand must be a boolean (that is, equal to 0 or 1). This operator returns a boolean, an integer or a double according to the type of the second and third operands.

NOT

Not. Unary logical operator. NOT(a) = 1 - a. Note that the operand must be boolean (that is, equal to 0 or 1). This operator returns a boolean.

AND

And. N-ary logical operator. AND(e1, e2, ..., eN) is equal to 1 (true) if all the operands e1, e2, ..., eN are 1, and 0 otherwise. All the operands must be boolean (that is, equal to 0 or 1). This operator returns a boolean.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will return 1 if all the values returned by the function are 1 and 0 otherwise.

OR

Or. N-ary logical operator. OR(e1, e2, ..., eN) is equal to 0 (false) if all operands e1, e2, ..., eN are 0, and 1 otherwise. All the operands must be boolean (that is, equal to 0 or 1). This operator returns a boolean.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will return 0 if all the values returned by the function are 0 and otherwise.

XOR

Exclusive or (also called “xor”). N-ary logical operator. XOR(e1, e2, ..., eN) is equal to 0 if the number of operands with value 1 among e1, e2, ..., eN is even, and 1 otherwise. Remarkable case: XOR(a,b) = 1 if a == b, and 0 otherwise. All the operands must be boolean (that is, equal to 0 or 1). This operator returns a boolean.

With collections (lists, sets) or ranges

This operator can also be used with RANGE, LIST or SET to create expressions with a dynamic number of operands. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range, list or set and will return 0 if the number of value 1 returned by the function is even, and 1 otherwise.

ABS

Absolute value. Unary arithmetic operator. ABS(e) = e >= 0 ? e : -e. This operator returns an integer or a double according to the type of its operand.

DIST

Distance between two numbers. Binary arithmetic operator. DIST(a,b) = ABS(a-b). This operator returns an integer or a double according to the type of its operands.

DIV

Division. Binary arithmetic operator. This operator always returns a double. Note that until version 4.0, the division was an integer division if both operands were integers.

MOD

Modulo (remainder of the integer division). Binary arithmetic operator. MOD(a, b) = r such that a = q * b + r with q, r integers, where r, a have the same sign and |r| < |b|. Note that the operands must be integers. This operator returns an integer. Be careful: when a > 0 and b < 0, the value computed by MOD(a, b) differs from the evaluation of a%b in python.

ARRAY

Array. An array is a collection of elements. Indexes begin at 0. It could be used with operators like AT or SCALAR. An array doesn’t have a value by itself, but can contain operands of type boolean, integer, double, array (for multi-dimensional arrays) or collection (list or set). In the latter case, the collections must share the same domain and same type (either list or set). All the elements of an array must be of the same type.

With ranges

This operator can also be used with RANGE to create an array with a dynamic number of elements. In that case, this operator becomes a binary operator that takes a range as first operand and a LAMBDA_FUNCTION as second operand. The operator will call the function on each value of the range and the returned values will be used to populate the array.

 Since: 2.1
AT

Returns the element at specific coordinates of an array or a list.

For arrays

The first operand must be the array and the other operands must be the coordinates of the element to get. The number of coordinates depends on the dimension of the array. Thus AT(myArray, i) returns the i element of the one-dimensional array myArray. This operator returns a boolean, an integer or a double according to the type of the operands in the array. If one of the specified coordinate is out of range, the evaluation of the expression will fail.

For lists

The first operand must be the list and the second operand must be the index of the element to get. If the index is out of range (index < 0 or index > count(list)), the evaluation of the expression will not fail but will return -1.

 Since: 2.1
SCALAR

Scalar product. SCALAR(a, x) = sum(a[i]*x[i]) with a and x two arrays. This operator returns an integer or a double according to the type of the operands in the arrays.

 Since: 2.1
CEIL

Ceil. Unary arithmetic operator. Returns a value rounded to the next highest integer. This operator returns an integer.

 Since: 3
FLOOR

Floor. Unary arithmetic operator. Returns a value rounded to the next lowest integer. This operator returns an integer.

 Since: 3
ROUND

Round. Unary arithmetic operator. Returns a value rounded to the nearest integer. This operator returns an integer.

 Since: 3
SQRT

Square root. Unary arithmetic operator. This operator returns a double.

 Since: 3
LOG

Natural logarithm (base-e). Unary arithmetic operator. This operator returns a double.

 Since: 3
EXP

Base-e exponential. Unary arithmetic operator. This operator returns a double.

 Since: 3
POW

Power operator. POW(x, y) is equals to the value of x to the power of y. This operator returns a double.

 Since: 3
COS

Cosine. Unary arithmetic operator. This operator returns a double.

 Since: 3
SIN

Sine. Unary arithmetic operator. This operator returns a double.

 Since: 3
TAN

Tangent. Unary arithmetic operator. This operator returns a double.

 Since: 3
INT

Integer decision variable. Decisional operator with two operands min and max. Decision variable with domain [min,max].

 Since: 5
PIECEWISE

Piecewise-linear function operator. The piecewise linear function is defined by two arrays of numbers giving the breakpoints of the function. This operator has exactly 3 operands: The first two operands must be two arrays of equal lengths (necessarily larger or equal to 2). These arrays must contain constant numbers (int or double). The first array must contain numbers in ascending order. The third operand must be an integer or double expression. An exception will be thrown if its value is strictly smaller that the first element of the first array, or strictly larger than the last element of the first array. This operator returns a double.

PIECEWISE(x,y,z) returns the image of z by the function defined by geometric points (x[0], y[0]), (x[1], y[1]), ..... (x[n-1], y[n-1]), For instance PIECEWISE({0, 50, 100}, {0, 10, 100}, 75) returns 55.

Discontinuities are allowed in the definition of the function, that is to say that two geometric points can share the same x-coordinate. By convention the value taken by the function at such a discontinuous point is the one associated to the last occurrence of this x-coordinate in array x. For instance PIECEWISE({0, 50, 50, 100},{0, 0.1, 0.9, 1}, 50) returns 0.9;

 Since: 5
LIST

A list is an ordered collection of integers within a domain [0, n-1] where n is the unique argument of this operator. Mathematically a list is a permutation of a subset of [0, n-1]. This operator takes exactly one operand: a strictly positive integer constant. All values in the list will be pairwise different, non negative and strictly smaller that this number.

The elements of the list can be accessed individually with the operator AT.

COUNT

The number of elements in a collection. This operator takes exactly one argument of type list.

 Since: 5.5
INDEXOF

The index of a value in a list (-1 if the value is not in the list). This operator takes exactly two arguments: the first one is a list, the second one is an integer expression.

 Since: 5.5
PARTITION

Partition. N-ary logical operator. PARTITION(c1, c2, ..., cN) is true if all lists or sets c1, c2, ..., cN form a partition of their common domain. All the operands must be collections of the same type (either list or set) and on the same range. These collections can be stored in a LSArray that will be passed as argument of the partition: PARTITION(array(c1, c2, ..., cN)).

 Since: 5.5
DISJOINT

Disjoint. N-ary logical operator. DISJOINT(c1, c2, ..., cN) is true if all lists or sets c1, c2, ..., cN are pairwise disjoint. All the operands must be collections of the same type (either list or set) and on the same range. These collections can be stored in a LSArray that will be passed as argument of the disjoint: DISJOINT(array(c1, c2, ..., cN)).

 Since: 5.5
COVER

Cover. N-ary logical operator. COVER(c1, c2, ..., cN) is true if all values in the domain are at least in one list or set c1, c2, ..., cN. All the operands must be collections of the same type (either list or set) and on the same range. These collections can be stored in a LSArray that will be passed as argument of the cover: COVER(array(c1, c2, ..., cN)).

 Since: 10.5
FIND

Find. find(a, v) returns the position of the collection in the array a that contains the value v. If the value is not in any collections of the array, it returns -1. This operator takes exactly two arguments: the first one is an ARRAY of collections, the second one is the value searched. All the collections of the array must be of same type and on the same range.

 Since: 10.5
EXTERNAL_FUNCTION

External function.

External functions are used to retrieve the value of expressions from external functions written with your favorite language. External functions are created with the dedicated methods LSModel.create_int_external_function() or LSModel.create_double_external_function().

 Since: 9.5
CALL

Call a particular function.

The first operand must be a function (like EXTERNAL_FUNCTION, BLACKBOX_FUNCTION or : attr:LAMBDA_FUNCTION.). The other operands are passed to the function as arguments.

 Since: 6
LAMBDA_FUNCTION

Lambda function. Lambda functions are created with the dedicated method LSModel.create_lambda_function().

 Since: 9.5
ARGUMENT

Argument of a function. Arguments are automatically and implicitely created when you create a function with method LSModel.create_function().

 Since: 7
RANGE

Range expression. This operator takes exactly two integer operands. The first one is the lower bound (inclusive), the second one is the upper bound (exclusive).

A range doesn’t have a value by itself but can be used with N-ary operators like SUM, PROD, MIN, MAX, OR, AND, XOR or ARRAY to create expressions that have a dynamic number of operands.

 Since: 7
CONTAINS

Contains. contains(l, v) is true if and only if the list l contains the value v. This operator takes exactly two arguments: the first one is a list, the second one is an integer expression.

 Since: 7.5
SET

A set is an unordered collection of integers within a range [0, n-1] where n is the unique argument of this operator. This operator takes exactly one operand: a strictly positive integer constant. All values in the set will be pairwise different, non negative and strictly smaller that this number. Contrary to the LIST operator, elements in a set are not ordered and cannot be indexed with AT. Sets can only be manipulated with lambdas and n-ary operators like SUM, MIN, AND, …

 Since: 8
BLACKBOX_FUNCTION

Black-box function. Black-box functions can be used to optimize functions that are computationally expensive. For more information, please see the modeling features.

 Since: 9.5