ILOG OPL Development Studio Language Reference Manual

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Numeric functionsNote: For C/C++ programmers: Most of the numeric functions are wrap-ups for standardmath library functions.Numeric functionsSyntaxMath.abs(x)Math.max(x, y)Math.min(x, y)Math.random()Math.ceil(x)Math.floor(x)Math.round(x)Math.sqrt(x)Math.sin(x)Math.cos(x)Math.tan(x)Math.asin(x)Math.acos(x)Math.atan(x)Math.atan2(y, x)Math.exp(x)Math.log(x)Math.pow(x, y)EffectReturns the absolute value of x.Math.max(x, y) returns the larger of x and y, and Math.min(x, y) returns the smaller ofthe two.Returns a pseudo-random number between 0, inclusive, and 1, exclusive.Math.ceil(x) returns the smallest integer value greater than or equal to x. Math.floor(x)returns the greatest integer value less than or equal to x. Math.round(x) returns thenearest integer value to x.Returns the square root of x.Math.sin(x), Math.cos(x) and Math.tan(x) return the trigonometric functions sine, cosineand tangent respectively of a radian argument.Math.asin(x) returns the arcsine of x in the range -pi/2 to pi/2.Math.acos(x) returns the arc cosine of x in the range 0 to pi.Math.atan(x) returns the arc tangent of x in the range -pi/2 to pi/2.Math.atan2(y, x) converts rectangular coordinates (x, y) to polar coordinates (r,a) by computing a as an arc tangent of y/x in the range -pi to pi.Math.exp(x) computes the exponential function. Math.log(x) computes the naturallogarithm of x. Math.pow(x, y) computes x raised to the power y.216I L O G O P L D E V E L O P M E N T S T U D I O L A N G U A G ER E F E R E N C E M A N U A L
Numeric constantsThe following numeric constants are defined.Numeric constantsSyntaxValueNaNContains the NaN value.InfinityContains the Infinity value.Number.NaNSame as NaN.Number.MAX_VALUE The maximum representable number, approximately 1.79E+308.Number.MIN_VALUE The smallest representable positive number, approximately 2.22E-308.Math.ENapier’s constant, e, and the base of natural logarithms, approximately 2.718.Math.LN10Math.LN2Math.LOG2EMath.LOG10EMath.PIMath.SQRT1_2Math.SQRT2The natural logarithm of 10, approximately 2.302.The natural logarithm of 2, approximately 0.693.The base 2 logarithm of e, approximately 1.442.The base 10 logarithm of e, approximately 0.434.The ratio of the circumference of a circle to its diameter, approximately 3.142.The square root of one-half, approximately 0.707.The square root of 2, approximately 1.414.I L O G O P L D E V E L O P M E N T S T U D I O L A N G U A G ER E F E R E N C E M A N U A L217
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CopyrightCOPYRIGHT NOTICECopyright
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C O N T E N T STable of contentsLan
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Language Reference ManualThis manua
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OPL, the modeling languagePresents
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ModelsDescribes the overall structu
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}ctMaxTotal:Gas + Chloride
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Data typesDescribes basic data type
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Basic data typesDescribes integers,
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FloatsShows how to declare floats i
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Data structuresDescribes how the ba
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The range float declarationA range
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{Edge} Edges = {, , };int a[Edges]
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TuplesData structures in OPL can al
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In Declaring a tuple using a set of
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SetsDefinitionSets are non-indexed
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Sorted and ordered setsBy default,
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The data shows that the team includ
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Data sourcesDescribes data and data
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Data initializationDefines internal
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{Ship} shipData = ...;and assume th
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* .dat file */a = #[“Monday”: 1
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}}the same can be expressed with th
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Initializing tuplesYou initialize t
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Initializing setsYou can initialize
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As generic setsOPL supports generic
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Initialization and memory allocatio
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Database initializationDescribes ho
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Supported databasesSupported databa
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Reading from a databaseIn OPL, data
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DBconnection db("oracle9", connecti
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Note: OPL supports the same element
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Spreadsheet Input/OutputDescribes h
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Connection to a spreadsheetThe spre
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♦Sets of tuples: The data has to
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Data consistencyDefines the purpose
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Data membership consistencyThe keyw
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AssertionsOPL provides assertions t
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execute{writeln(s2);s1.add(3);write
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Decision typesVariables in an OPL a
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tuple Route {City orig;City dest;}{
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Dynamic collection of elements into
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The all syntaxThen, the all syntax
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Appending arraysYou can also concat
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ExpressionsDescribes data and decis
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Data and decision variable identifi
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(condition)?thenExpr : elseExprwher
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Piecewise-linear functionsPiecewise
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eakpoint[k-1] < ship[o][d] 0; 0}(1,
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Figure The discontinuous piecewise
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x == y;signx == piecewise{0->0; 2->
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Functions over setsFunction Descrip
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ConstraintsSpecifies the constraint
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Using constraintsExplains how to ap
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Conditional constraintsIf-then-else
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Constraint labelsExplains why label
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Labeling constraintsTo label a cons
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subject to {forall( p in Products ,
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Limitations to constraint labelingN
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Compatibility between constraint na
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Types of constraintsDescribes const
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Discrete constraintsDiscrete constr
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Implicit constraintsImplicit constr
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Symbol=>!===MeaningImplyDifferent f
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Constraints available in constraint
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♦Interval grouping constraint: al
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Formal parametersDescribes basic fo
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{forall(i in 1..8)forall(j in 1..8:
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Tuples of parametersOPL allows tupl
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int array[i in set1] = ((sum(j in s
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SchedulingDescribes how to model sc
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IntroductionILOG OPL Development St
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Piecewise linear and stepwise funct
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I L O G O P L D E V E L O P M E N T
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e equal to 1. For a fixed interval
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ExamplesFor examples of using inter
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Precedence constraints between inte
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A logical constraint between interv
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Important:The piecewise linear func
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♦prev(p, a, b) states that if bot
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Cumulative functionsIn scheduling p
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Constraints on cumul function expre
Page 165 and 166: Syntax and examplesFor the syntax a
Page 167 and 168: ♦That everywhere over a given fix
Page 169 and 170: in state s. If algn e is true, it m
Page 171 and 172: NotationsThe main notations used th
Page 173 and 174: ILOG Script for OPLDescribes the st
Page 175 and 176: Language structurePresents the stru
Page 177 and 178: SyntaxWhat composes a scripting sta
Page 179 and 180: Compound statementsA compound state
Page 181 and 182: IdentifiersIdentifiers are used to
Page 183 and 184: Expressions in ILOG ScriptExpressio
Page 185 and 186: LiteralsLiterals can represent the
Page 187 and 188: Syntax of different types of expres
Page 189 and 190: Property accessThere are two ways o
Page 191 and 192: Function callsSyntactic shorthandSy
Page 193 and 194: Special operatorsSpecial operator s
Page 195 and 196: Other operatorsOther operators are
Page 197 and 198: StatementsA statement can be a cond
Page 199 and 200: SyntaxEffectfor (var i=0; i < a.len
Page 201 and 202: Outside a function definitionAt the
Page 203 and 204: Default valuesDefault value syntaxS
Page 205 and 206: Built-in values and functionsPresen
Page 207 and 208: NumbersNumber representations and f
Page 209 and 210: IntroductionNumbers can be expresse
Page 211 and 212: Hexadecimal numbersA hexadecimal nu
Page 213 and 214: Special numbersThere are three spec
Page 215: Number methodsThere is only one num
Page 219 and 220: Syntax~ xx > yx >>> yEffectBitwise
Page 221 and 222: ILOG Script stringsString represent
Page 223 and 224: Examples of string literals using e
Page 225 and 226: String propertiesThere is a single,
Page 227 and 228: Syntaxstring.toUpperCase()EffectExa
Page 229 and 230: String operatorsString operatorsSyn
Page 231 and 232: ILOG Script BooleansBoolean represe
Page 233 and 234: Automatic conversion to BooleanWhen
Page 235 and 236: Logical operatorsThe following Bool
Page 237 and 238: ILOG Script arraysArray representat
Page 239 and 240: Array constructorThe array construc
Page 241 and 242: Array methodsArray methodsSyntaxarr
Page 243 and 244: ObjectsObject representation and fu
Page 245 and 246: Defining methodsSince a method is r
Page 247 and 248: Object constructorObject constructo
Page 249 and 250: Built-in methodsThere is only one o
Page 251 and 252: DatesDate representation and functi
Page 253 and 254: Date constructorThe date constructo
Page 255 and 256: Date methodsDate methodsSyntaxdate.
Page 257 and 258: Date functionsDate functionsSyntaxD
Page 259 and 260: The null valueThe null value is a s
Page 261 and 262: ILOG Script functionsIn ILOG Script
Page 263 and 264: I N D E XIndexABabs, OPL function 9
Page 265 and 266: limitations in tuples 29ranges 22se
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GHIgeneric sets 51, 137groundbreakp
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NOfor the null value 259for the und
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sparsityand multidimensional arrays
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ILOG OPL Development Studio Language Reference Manual

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