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
See:LSExpression

O_Bool

Boolean decision.

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

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

O_Const

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.

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 ranges

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

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

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 ranges

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

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 ranges

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

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 ranges

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

O_Eq

Equal.

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

O_Neq

Not equal to.

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

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.

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.

O_Gt

Strictly greater than.

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

O_Lt

Strictly lower than.

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

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.

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.

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 ranges

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

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 ranges

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

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 ranges

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

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.

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.

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.

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 and |r| < b. The operands must be integers or booleans. This operator returns an integer.

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 or array (for multi-dimensional arrays). 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 as first operand and a function (O_Function or O_NativeFunction) 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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[0],y[0]), (x[1],y[1]), ..., (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

O_List

A list is a 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

O_Count

The number of elements in a collection.

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

Since:5.5

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

O_Partition

Partition.

N-ary logical operator. PARTITION(l1, l2, ..., lN) is true if all lists l1, l2, ..., lN form a partition of their common range. All the operands of this operator must be lists on the same range.

Since:5.5

O_Disjoint

Disjoint.

N-ary logical operator. DISJOINT(l1, l2, ..., lN) is true if all lists l1, l2, ..., lN are pairwise disjoint. All parameters of this operator must be lists on the same range.

Since:5.5

O_NativeFunction

Native function.

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

See:LSNativeFunction
Since:6.0

O_Call

Call a particular function.

The first operand must be a function (like O_NativeFunction or O_Function). The other operands are passed to the function as arguments. If the function is not a native function, the number of operands must match the number of arguments of the function.

Since:6.0

O_Function

Function.

Functions are created with the dedicated method LSModel#createFunction.

Since:7.0

O_Argument

Argument of a function.

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

Since:7.0

O_Range

Range expression.

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.

A range must have exacty two operands that represent the lower bound and the upper bound of the range. These operands must be integers.

Since:7.0

O_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