# LSOperator Enumeration¶

enum localsolver::LSOperator

Mathematical operators available for modeling.

These operators are used to type the expressions created in a LocalSolver mathematical optimization model.

See: LSModel LSExpression

Boolean decision.

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

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

Constant.

Operator with no argument. Constants can be booleans, integers or doubles. Note that constants 0 or 1 are considered as boolean. Constants are implicitly created when passing lsint or lsdouble arguments to LSModel#createExpression or LSExpression#addOperand. They can also be created with the dedicated function LSModel#createConstant.

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 O_Range, O_List or O_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 O_LambdaFunction 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.

Substraction.

Binary arithmetic operator. SUB(x, y) is equal to the value of x - y. This operator returns an integer if the two operands are booleans or integers, and a double as soon as one operand is a double.

 Since: 4

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 O_Range, O_List or O_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 O_LambdaFunction 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.

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 O_Range, O_List or O_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 O_LambdaFunction 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.

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 O_Range, O_List or O_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 O_LambdaFunction 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.

Equal.

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

Not equal to.

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

Greater than or equal to.

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

Lower than or equal to.

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

Strictly greater than.

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

Strictly lower than.

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

If-Then-Else.

Ternary conditional operator. IF(a, b, c) is equal to b if a = 1, and c otherwise. The first operand must be a boolean (that is, equal to 0 or 1). This operator returns a boolean if the three operands are booleans, an integer if the second and third operands are integers, and a double if the second or the third operand is a double.

Not.

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

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 O_Range, O_List or O_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 O_LambdaFunction 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.

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 O_Range, O_List or O_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 O_LambdaFunction 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 1 otherwise.

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 O_Range, O_List or O_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 O_LambdaFunction 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.

Absolute value.

Unary arithmetic operator. ABS(e) = e >= 0 ? e : -e. This operator returns an integer if the operand is a boolean or an integer, and a double otherwise.

Distance between two numbers.

Binary arithmetic operator. DIST(a,b) = ABS(a-b). This operator returns an integer if the two operands are booleans or integers, and a double as soon as one of the operand is a double.

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.

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|. The operands must be integers or booleans. This operator returns an integer.

Array.

An array is a collection of elements. Indexes begin at 0. It could be used with operators like O_At or O_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 collections (lists or sets). 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 O_Range to create an array with a dynamic number of elements. In that case, this operator becomes a binary operator that takes a range, a list or a set as first operand and a O_LambdaFunction as second operand. The operator will call the function on each value of the range, list or set and the returned values will be used to populate the array.

 Since: 2.1

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 product.

SCALAR(a, x) = sum(a[i]*x[i]) where a and x are two one-dimensional arrays. This operator returns an integer or a double according to the type of the operands in the arrays.

 Since: 2.1

Ceil.

Unary arithmetic operator. Returns a value rounded to the next highest integer. The operand can be a boolean, an integer or a double. This operator returns an integer.

 Since: 3

Floor.

Unary arithmetic operator. Returns a value rounded to the next lowest integer. The operand can be a boolean, an integer or a double. This operator returns an integer.

 Since: 3

Round.

Unary arithmetic operator. Returns a value rounded to the nearest integer. The operand can be a boolean, an integer or a double. This operator returns an integer.

 Since: 3

Square root.

Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

 Since: 3

Natural logarithm (base-e).

Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

 Since: 3

Base-e exponential.

Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

 Since: 3

Power operator.

POW(x, y) is equals to the value of x to the power of y. The operands can be booleans, integers or doubles. This operator returns a double.

 Since: 3

Cosine.

Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

 Since: 3

Sine.

Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

 Since: 3

Tangent.

Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

 Since: 3

Integer decision variable.

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

 Since: 5

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 sizes (necessarily larger or equal to 2). These arrays must contain constant numbers (integers or doubles). The first array must contain numbers in ascending order. The third operand must be an integer or a double expression. The evaluation of the piecewise will fail if the value of the third operand 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,y), (x,y), ..., (x[n-1],y[n-1]), For instance PIECEWISE(ARRAY(0, 50, 100), ARRAY(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(ARRAY(0, 50, 50, 100), ARRAY(0, 0.1, 0.9, 1), 50) returns 0.9;

 Since: 5

A list is an ordered collection of integers within a range [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 O_At.

 Since: 5.5

The number of elements in a list or a set.

This operator takes exactly one argument of type list or set and returns an integer.

 Since: 5.5

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.

N-ary logical operator. PARTITION(c1, c2, ..., cN) is true if all lists or sets c1, c2, ..., cN form a partition of their common range. All the operands of this operator 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.

N-ary logical operator. DISJOINT(c1, c2, ..., cN) is true if all lists or sets c1, c2, ..., cN are pairwise disjoint. All the operands of this operator 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

External function.

External functions are used to compute the value of expressions from external functions written with your favorite programming language. External functions are created with the dedicated method LSModel#createExternalFunction.

See: LSExternalFunction 9.5

Call a particular function.

The first operand must be a function (like O_ExternalFunction, O_BlackBoxFunction or O_LambdaFunction). The other operands are passed to the function as arguments. If the function is not a external function, the number of operands must match the number of arguments of the function.

 Since: 6

Lambda Function.

Lambda functions are created with the dedicated method LSModel#createLambdaFunction.

 Since: 9.5

Argument of a function.

Arguments are automatically and implicitely created when you create a function with method LSModel#createLambdaFunction.

 Since: 7

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 O_Sum, O_Prod, O_Min, O_Max, O_Or, O_And, O_Xor or O_Array to create expressions that have a dynamic number of operands.

 Since: 7

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

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 O_List operator, elements in a set are not ordered and cannot be indexed with O_At. Sets can only be manipulated with lambdas and n-ary operators like O_Sum, O_Min, O_And, …

 Since: 8

Black-box function.

Black-box functions can be used to optimize functions that are computationally expensive. For more information, please see the advanced features section on black-box optimization.

See: LSBlackBoxFunction 9.5

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 of this operator 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(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 O_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