Detailed Description

commonly used numerical methods

Modules
	Computations With Tolerances
	methods used by the majority of operations involving floating-point computations in SCIP

Macros
#define	SCIPisFinite(x) ((x) == (x))

Functions
SCIP_Real	SCIPcalcMachineEpsilon (void)

SCIP_Real	SCIPnextafter (SCIP_Real from, SCIP_Real to)

SCIP_Longint	SCIPcalcGreComDiv (SCIP_Longint val1, SCIP_Longint val2)

SCIP_Longint	SCIPcalcSmaComMul (SCIP_Longint val1, SCIP_Longint val2)

SCIP_Longint	SCIPcalcBinomCoef (int n, int m)

unsigned int	SCIPcalcFibHash (SCIP_Real v)

SCIP_Bool	SCIPrealToRational (SCIP_Real val, SCIP_Real mindelta, SCIP_Real maxdelta, SCIP_Longint maxdnom, SCIP_Longint nominator, SCIP_Longint denominator)

SCIP_RETCODE	SCIPcalcIntegralScalar (SCIP_Real vals, int nvals, SCIP_Real mindelta, SCIP_Real maxdelta, SCIP_Longint maxdnom, SCIP_Real maxscale, SCIP_Real intscalar, SCIP_Bool *success)

SCIP_Bool	SCIPfindSimpleRational (SCIP_Real lb, SCIP_Real ub, SCIP_Longint maxdnom, SCIP_Longint nominator, SCIP_Longint denominator)

SCIP_Real	SCIPselectSimpleValue (SCIP_Real lb, SCIP_Real ub, SCIP_Longint maxdnom)

SCIP_Real	SCIPcalcRootNewton (SCIP_DECL_NEWTONEVAL((function)), SCIP_DECL_NEWTONEVAL((derivative)), SCIP_Real *params, int nparams, SCIP_Real x, SCIP_Real eps, int k)

SCIP_Real	SCIPrelDiff (SCIP_Real val1, SCIP_Real val2)

SCIP_Real	SCIPcomputeGap (SCIP_Real eps, SCIP_Real inf, SCIP_Real primalbound, SCIP_Real dualbound)

Macro Definition Documentation

◆ SCIPisFinite

#define SCIPisFinite ( x ) ((x) == (x))

Function Documentation

◆ SCIPcalcMachineEpsilon()

SCIP_Real SCIPcalcMachineEpsilon ( void )

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

Definition at line 9009 of file misc.c.

References eps, and SCIP_Real.

Referenced by SCIPrealHashCode().

◆ SCIPnextafter()

SCIP_Real SCIPnextafter	(	SCIP_Real	from,
		SCIP_Real	to
	)

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 9275 of file misc.c.

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

◆ SCIPcalcGreComDiv()

SCIP_Longint SCIPcalcGreComDiv	(	SCIP_Longint	val1,
		SCIP_Longint	val2
	)

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 9032 of file misc.c.

References x, and y.

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

◆ SCIPcalcSmaComMul()

SCIP_Longint SCIPcalcSmaComMul	(	SCIP_Longint	val1,
		SCIP_Longint	val2
	)

calculates the smallest common multiple of the two given values

Parameters

val1	first value of smallest common multiple calculation
val2	second value of smallest common multiple calculation

Definition at line 9284 of file misc.c.

References SCIP_Longint, and SCIPcalcGreComDiv().

Referenced by SCIPrealHashCode(), and tryAggregateIntVars().

◆ SCIPcalcBinomCoef()

SCIP_Longint SCIPcalcBinomCoef	(	int	n,
		int	m
	)

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 10183 of file misc.c.

References SCIP_Longint, SCIP_LONGINT_MAX, and SCIP_Real.

Referenced by SCIPrealHashCode().

◆ SCIPcalcFibHash()

unsigned int SCIPcalcFibHash ( SCIP_Real v )

calculates hash for floating-point number by using Fibonacci hashing

Parameters

v	number to hash

Definition at line 10258 of file misc.c.

Referenced by SCIP_DECL_EXPRHASH(), SCIPexprhdlrHashExpr(), and SCIPrealHashCode().

◆ SCIPrealToRational()

SCIP_Bool SCIPrealToRational	(	SCIP_Real	val,
		SCIP_Real	mindelta,
		SCIP_Real	maxdelta,
		SCIP_Longint	maxdnom,
		SCIP_Longint *	nominator,
		SCIP_Longint *	denominator
	)

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
nominator	pointer to store the nominator n of the rational number
denominator	pointer to store the denominator d of the rational number

Definition at line 9305 of file misc.c.

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

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

◆ SCIPcalcIntegralScalar()

SCIP_RETCODE SCIPcalcIntegralScalar	(	SCIP_Real *	vals,
		int	nvals,
		SCIP_Real	mindelta,
		SCIP_Real	maxdelta,
		SCIP_Longint	maxdnom,
		SCIP_Real	maxscale,
		SCIP_Real *	intscalar,
		SCIP_Bool *	success
	)

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 9468 of file misc.c.

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

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

◆ SCIPfindSimpleRational()

SCIP_Bool SCIPfindSimpleRational	(	SCIP_Real	lb,
		SCIP_Real	ub,
		SCIP_Longint	maxdnom,
		SCIP_Longint *	nominator,
		SCIP_Longint *	denominator
	)

given a (usually very small) interval, tries to find a rational number with simple denominator (i.e. a small number, probably multiplied with powers of 10) out of this interval; returns TRUE iff a valid rational number inside the interval was found

Parameters

lb	lower bound of the interval
ub	upper bound of the interval
maxdnom	maximal denominator allowed for resulting rational number
nominator	pointer to store the nominator n of the rational number
denominator	pointer to store the denominator d of the rational number

Definition at line 9688 of file misc.c.

References SCIP_Real, SCIPintervalGetRoundingMode(), SCIPintervalHasRoundingControl(), SCIPintervalSetRoundingMode(), SCIPintervalSetRoundingModeDownwards(), and SCIPrealToRational().

Referenced by SCIPrealHashCode(), and SCIPselectSimpleValue().

◆ SCIPselectSimpleValue()

SCIP_Real SCIPselectSimpleValue	(	SCIP_Real	lb,
		SCIP_Real	ub,
		SCIP_Longint	maxdnom
	)

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 9735 of file misc.c.

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

Referenced by SCIP_DECL_PRESOLEXEC(), SCIPanalyzeDeductionsProbing(), and SCIPrealHashCode().

◆ SCIPcalcRootNewton()

SCIP_Real SCIPcalcRootNewton	(	SCIP_DECL_NEWTONEVAL((*function))	,
		SCIP_DECL_NEWTONEVAL((*derivative))	,
		SCIP_Real *	params,
		int	nparams,
		SCIP_Real	x,
		SCIP_Real	eps,
		int	k
	)

Performs the Newton Procedure from a given starting point to compute a root of the given function with specified precision and maximum number of iterations. If the procedure fails, SCIP_INVALID is returned.

Parameters

params	parameters needed for function (can be NULL)
nparams	number of parameters (can be 0)
x	starting point
eps	tolerance
k	iteration limit

Definition at line 9776 of file misc.c.

References eps, getRand(), NULL, REALABS, SCIP_INVALID, SCIP_Longint, SCIP_RAND_MAX, SCIP_Real, and x.

Referenced by computeLeftSecantSin(), computeRightSecantSin(), computeSolTangentSin(), and SCIPrealHashCode().

◆ SCIPrelDiff()

SCIP_Real SCIPrelDiff	(	SCIP_Real	val1,
		SCIP_Real	val2
	)

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 11096 of file misc.c.

References REALABS, and SCIP_Real.

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

◆ SCIPcomputeGap()

SCIP_Real SCIPcomputeGap	(	SCIP_Real	eps,
		SCIP_Real	inf,
		SCIP_Real	primalbound,
		SCIP_Real	dualbound
	)

computes the gap from the primal and the dual bound

Parameters

eps	the value treated as zero
inf	the value treated as infinity
primalbound	the primal bound
dualbound	the dual bound

Definition at line 11114 of file misc.c.

References EPSEQ, EPSZ, SCIP_Interval::inf, REALABS, and SCIP_Real.

Referenced by SCIPgetConcurrentGap(), SCIPgetGap(), SCIPgetTransGap(), and SCIPstoreSolutionGap().

SCIP

Detailed Description

Modules

Macros

Functions

Macro Definition Documentation

◆ SCIPisFinite

Function Documentation

◆ SCIPcalcMachineEpsilon()

◆ SCIPnextafter()

◆ SCIPcalcGreComDiv()

◆ SCIPcalcSmaComMul()

◆ SCIPcalcBinomCoef()

◆ SCIPcalcFibHash()

◆ SCIPrealToRational()

◆ SCIPcalcIntegralScalar()

◆ SCIPfindSimpleRational()

◆ SCIPselectSimpleValue()

◆ SCIPcalcRootNewton()

◆ SCIPrelDiff()

◆ SCIPcomputeGap()