# LSOperator Enumeration¶

enum LSOperator

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

See

`LSModel`

See

`LSExpression`

enumerator O_Bool

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

enumerator O_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

4.0

enumerator O_Const

Constant. Operator with no argument. Constants can be booleans, long or doubles. Note that constants 0 or 1 are considered as boolean. Constants are implicitly created when passing long or double arguments to `LSModel::createExpression()` or `LSExpression::addOperand()`. They can also be created with the dedicated function `LSModel::createConstant()`.

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will sum all the values computed and returned by the function.

enumerator O_Sub

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

4.0

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will compute the product of all the values returned by the function.

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will find the maximum value among all the values returned by the function.

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will find the minimum value among all the values returned by the function.

enumerator O_Eq

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

enumerator O_Neq

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

enumerator O_Geq

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

enumerator O_Leq

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

enumerator O_Gt

Strictly greater than. Binary relational operator. `GT(a,b) = 1` if `a > b`, and `0` otherwise. Can be used to compare two intervals, in that case `GT(a, b) = 1` if `start(a) >= end(b)`, and `0` otherwise. Undefined if `a` or `b` is void. This operator returns a boolean.

enumerator O_Lt

Strictly lower than. Binary relational operator. `LT(a, b) = 1` if `a < b`, and `0` otherwise. Can be used to compare two intervals, in that case `LT(a, b) = 1` if `end(a) <= start(b)`, and `0` otherwise. Undefined if `a` or `b` is void. This operator returns a boolean.

enumerator O_If

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.

enumerator O_Not

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.

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will return 1 if all the values returned by the function are 1 and 0 otherwise.

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will return 0 if all the values returned by the function are 0 and 1 otherwise.

enumerator O_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 intervals

This operator can also be used with intervals, `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 an interval, 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 interval, list or set and will return 0 if the number of value 1 returned by the function is even, and 1 otherwise.

enumerator O_Abs

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.

enumerator O_Dist

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.

enumerator O_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.

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

enumerator O_Array

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 collection (list, 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 intervals

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

Since

2.1

enumerator O_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

enumerator O_Scalar

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

enumerator O_Ceil

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

3.0

enumerator O_Floor

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

3.0

enumerator O_Round

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

3.0

enumerator O_Sqrt

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

Since

3.0

enumerator O_Log

Natural logarithm (base-e). Unary arithmetic operator. The operand can be a boolean, an integer or a double. This operator returns a double.

Since

3.0

enumerator O_Exp

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

Since

3.0

enumerator O_Pow

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

3.0

enumerator O_Cos

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

Since

3.0

enumerator O_Sin

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

Since

3.0

enumerator O_Tan

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

Since

3.0

enumerator O_Int

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

5.0

enumerator O_Interval

Interval decision variable. Operator with two integer constant operands that represent the min start and the max end of the decision. The interval is included in `[minStart, maxEnd)`. Its start is inclusive and its end is exclusive.

Since

12.0

enumerator O_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 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

5.0

enumerator O_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 `O_At`.

Since

5.5

enumerator O_Count

The number of elements in an array, a collection or an interval. This operator takes exactly one argument of type array, collection or interval and returns an integer.

Since

5.5

enumerator O_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

enumerator O_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

enumerator O_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

enumerator O_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

enumerator O_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 `O_Array` of collections, the second one is the value searched. All the collections of the array must be of the same type and on the same range.

Since

10.5

enumerator O_ExternalFunction

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 methods `LSModel::createIntExternalFunction()` or `LSModel::createDoubleExternalFunction()`.

See

LSIntExternalFunction

See

LSDoubleExternalFunction

Since

9.5

enumerator O_Call

Call a particular function. The first operand must be a function (like `O_ExternalFunction` 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

6.0

enumerator O_LambdaFunction

Lambda function. Lambda functions are created with the dedicated method `LSModel::createLambdaFunction()`.

Since

9.5

enumerator O_Argument

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

Since

7.0

enumerator O_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 has an interval value and 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

7.0

enumerator O_Contains

Contains. `contains(expr, v)` is true if and only if the expression `expr` contains the value `v`. This operator takes exactly two arguments: the first one is a collection (`O_List` or `O_Set`), an interval or an `O_Array` of collections, the second one is the integer expression searched. If `expr` is an array, all its collections must be of the same type and on the same range.

Since

7.5

enumerator O_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 `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

8.0

enumerator O_Sort

Sort operator takes a one-dimensional array of integers or doubles as input and returns an array sorted by ascending values. This operator returns an array of integers if the input array is solely composed of booleans or integers, and an array of doubles as soon as the input array contains a double.

Since

11.0

enumerator O_Start

The start of a non-void interval. This operator takes exactly one argument of type interval and returns an integer.

Since

12.0

enumerator O_End

The end of a non-void interval. This operator takes exactly one argument of type interval and returns an integer.

Since

12.0

enumerator O_Length

The length of a non-void interval. This operator takes exactly one argument of type interval and returns an integer. The length of an interval is equivalent to `end(interval) - start(interval).` It differs from the count on void intervals since the length of a void interval is undefined whereas the count of a void interval is 0.

Since

12.0