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SCIP Doxygen Documentation: Numerical Methods

commonly used numerical methods

returns the machine epsilon: the smallest number eps > 0, for which 1.0 + eps > 1.0

Definition at line 9101 of file misc.c.

References eps, and SCIP_Real.

returns the next representable value of from in the direction of to

Parameters

from value from which the next representable value should be returned to direction in which the next representable value should be returned

Definition at line 9367 of file misc.c.

Referenced by computeMaxForBilinearProp(), initSolve(), SCIPintervalCos(), SCIPintervalEntropy(), SCIPintervalExp(), SCIPintervalLog(), SCIPintervalPowerScalar(), SCIPintervalPowerScalarScalar(), SCIPintervalSignPowerScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), and SCIPintervalSquareRoot().

calculates the greatest common divisor of the two given values

Parameters

val1 first value of greatest common devisor calculation val2 second value of greatest common devisor calculation

Definition at line 9124 of file misc.c.

Referenced by deleteRedundantVars(), normalizeCons(), normalizeCumulativeCondition(), normalizeWeights(), rangedRowPropagation(), SCIPcalcIntegralScalar(), SCIPcalcSmaComMul(), SCIPprobScaleObj(), SCIProwCalcIntegralScalar(), SCIPsolveKnapsackExactly(), simplifyInequalities(), and tryAggregateIntVars().

calculates a binomial coefficient n over m, choose m elements out of n, maximal value will be 33 over 16 (because the n=33 is the last line in the Pascal's triangle where each entry fits in a 4 byte value), an error occurs due to big numbers or an negative value m (and m < n) and -1 will be returned

Parameters

n number of different elements m number to choose out of the above

Definition at line 10275 of file misc.c.

References SCIP_Longint, SCIP_LONGINT_MAX, and SCIP_Real.

converts a real number into a (approximate) rational representation, and returns TRUE iff the conversion was successful

Parameters

val real value r to convert into rational number mindelta minimal allowed difference r - q of real r and rational q = n/d maxdelta maximal allowed difference r - q of real r and rational q = n/d maxdnom maximal denominator allowed numerator pointer to store the numerator n of the rational number denominator pointer to store the denominator d of the rational number

Definition at line 9397 of file misc.c.

References a, b, EPSFLOOR, EPSGT, FALSE, MIN, NULL, REALABS, SCIP_Longint, SCIP_LONGINT_MAX, SCIP_Real, simplednoms, and TRUE.

Referenced by normalizeCons(), prettifyConss(), SCIPcalcIntegralScalar(), SCIPfindSimpleRational(), SCIProwCalcIntegralScalar(), and tryAggregateIntVars().

tries to find a value, such that all given values, if scaled with this value become integral in relative allowed difference in between mindelta and maxdelta

Parameters

vals values to scale nvals number of values to scale mindelta minimal relative allowed difference of scaled coefficient s*c and integral i maxdelta maximal relative allowed difference of scaled coefficient s*c and integral i maxdnom maximal denominator allowed in rational numbers maxscale maximal allowed scalar intscalar pointer to store scalar that would make the coefficients integral, or NULL success stores whether returned value is valid

Definition at line 9560 of file misc.c.

References ABS, EPSEQ, FALSE, isIntegralScalar(), MIN, nscalars, NULL, REALABS, scalars, SCIP_Bool, SCIP_DEFAULT_EPSILON, SCIP_INVALID, SCIP_Longint, SCIP_LONGINT_FORMAT, SCIP_OKAY, SCIP_Real, SCIP_REAL_MAX, SCIPcalcGreComDiv(), SCIPdebugMessage, SCIPrealToRational(), and TRUE.

Referenced by calculateScalingValue(), cutTightenCoefs(), cutTightenCoefsQuad(), SCIPcutGenerationHeuristicCMIR(), SCIPprobScaleObj(), SCIPseparateRelaxedKnapsack(), and transformNonIntegralRow().

given a (usually very small) interval, selects a value inside this interval; it is tried to select a rational number with simple denominator (i.e. a small number, probably multiplied with powers of 10); if no valid rational number inside the interval was found, selects the central value of the interval

Parameters

lb lower bound of the interval ub upper bound of the interval maxdnom maximal denominator allowed for resulting rational number

Definition at line 9827 of file misc.c.

References MAX, SCIP_Bool, SCIP_Longint, SCIP_LONGINT_FORMAT, SCIP_Real, SCIPdebugMessage, SCIPdebugPrintf, and SCIPfindSimpleRational().

Referenced by convertUnaryEquality(), fixVariables(), SCIP_DECL_PRESOLEXEC(), and SCIPanalyzeDeductionsProbing().

returns the relative difference: (val1-val2)/max(|val1|,|val2|,1.0)

Parameters

val1 first value to be compared val2 second value to be compared

Definition at line 11215 of file misc.c.

References MAX3, REALABS, and SCIP_Real.

Referenced by checkCons(), checkCumulativeCondition(), checkOrigPbCons(), createGenVBound(), getIntegralScalar(), getScaledDualWeight(), isConsViolated(), isIntegralScalar(), priceAndCutLoop(), SCIP_DECL_CONSCHECK(), SCIPbendersSubproblemIsOptimal(), SCIPbranchExecExtern(), SCIPbranchGetBranchingPoint(), SCIPconcsolverSync(), SCIPcutGenerationHeuristicCMIR(), SCIPintervalAreDisjointEps(), SCIPintervalIntersectEps(), SCIPsolCheckOrig(), SCIPtreeBranchVar(), SCIPtreeBranchVarNary(), SCIPvalidateSolve(), solveBendersSubproblems(), and updateBestCandidate().

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