Interval Arithmetics

Detailed Description

methods for interval arithmetics

Data Structures
struct	SCIP_Interval

Typedefs
typedef struct SCIP_Interval	SCIP_INTERVAL
typedef int	SCIP_ROUNDMODE

Functions
SCIP_Bool	SCIPintervalHasRoundingControl (void)
void	SCIPintervalSetRoundingMode (SCIP_ROUNDMODE roundmode)
SCIP_ROUNDMODE	SCIPintervalGetRoundingMode (void)
void	SCIPintervalSetRoundingModeDownwards (void)
void	SCIPintervalSetRoundingModeUpwards (void)
void	SCIPintervalSetRoundingModeToNearest (void)
void	SCIPintervalSetRoundingModeTowardsZero (void)
SCIP_Real	SCIPintervalNegateReal (SCIP_Real x)
SCIP_Real	SCIPintervalGetInf (SCIP_INTERVAL interval)
SCIP_Real	SCIPintervalGetSup (SCIP_INTERVAL interval)
void	SCIPintervalSet (SCIP_INTERVAL *resultant, SCIP_Real value)
void	SCIPintervalSetBounds (SCIP_INTERVAL *resultant, SCIP_Real inf, SCIP_Real sup)
void	SCIPintervalSetEmpty (SCIP_INTERVAL *resultant)
SCIP_Bool	SCIPintervalIsEmpty (SCIP_Real infinity, SCIP_INTERVAL operand)
void	SCIPintervalSetEntire (SCIP_Real infinity, SCIP_INTERVAL *resultant)
SCIP_Bool	SCIPintervalIsEntire (SCIP_Real infinity, SCIP_INTERVAL operand)
SCIP_Bool	SCIPintervalIsPositiveInfinity (SCIP_Real infinity, SCIP_INTERVAL operand)
SCIP_Bool	SCIPintervalIsNegativeInfinity (SCIP_Real infinity, SCIP_INTERVAL operand)
SCIP_Bool	SCIPintervalIsSubsetEQ (SCIP_Real infinity, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
SCIP_Bool	SCIPintervalAreDisjoint (SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
SCIP_Bool	SCIPintervalAreDisjointEps (SCIP_Real eps, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalIntersect (SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalIntersectEps (SCIP_INTERVAL *resultant, SCIP_Real eps, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalUnify (SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalAddInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalAddSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalAdd (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalAddScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalAddVectors (SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_INTERVAL *operand2)
void	SCIPintervalSub (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalSubScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalMulInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalMulSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalMul (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalMulScalarInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalMulScalarSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalMulScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalDiv (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalDivScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalScalprod (SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_INTERVAL *operand2)
void	SCIPintervalScalprodScalarsInf (SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)
void	SCIPintervalScalprodScalarsSup (SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)
void	SCIPintervalScalprodScalars (SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)
void	SCIPintervalSquare (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalSquareRoot (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalPower (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalPowerScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalPowerScalarScalar (SCIP_INTERVAL *resultant, SCIP_Real operand1, SCIP_Real operand2)
SCIP_Real	SCIPintervalPowerScalarIntegerInf (SCIP_Real operand1, int operand2)
SCIP_Real	SCIPintervalPowerScalarIntegerSup (SCIP_Real operand1, int operand2)
void	SCIPintervalPowerScalarInteger (SCIP_INTERVAL *resultant, SCIP_Real operand1, int operand2)
void	SCIPintervalPowerScalarInverse (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL basedomain, SCIP_Real exponent, SCIP_INTERVAL image)
void	SCIPintervalSignPowerScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
void	SCIPintervalReciprocal (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalExp (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalLog (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalMin (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalMax (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)
void	SCIPintervalAbs (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalSin (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalCos (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalSign (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void	SCIPintervalEntropy (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
SCIP_Real	SCIPintervalQuadUpperBound (SCIP_Real infinity, SCIP_Real a, SCIP_INTERVAL b_, SCIP_INTERVAL x)
void	SCIPintervalQuad (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL xrng)
void	SCIPintervalSolveUnivariateQuadExpressionPositive (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
void	SCIPintervalSolveUnivariateQuadExpressionNegative (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
void	SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_Real lincoeff, SCIP_Real rhs, SCIP_INTERVAL xbnds)
void	SCIPintervalSolveUnivariateQuadExpression (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)
void	SCIPintervalQuadBivar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real ax, SCIP_Real ay, SCIP_Real axy, SCIP_Real bx, SCIP_Real by, SCIP_INTERVAL xbnds, SCIP_INTERVAL ybnds)
void	SCIPintervalSolveBivariateQuadExpressionAllScalar (SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real ax, SCIP_Real ay, SCIP_Real axy, SCIP_Real bx, SCIP_Real by, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds, SCIP_INTERVAL ybnds)
int	SCIPintervalPropagateWeightedSum (SCIP_Real infinity, int noperands, SCIP_INTERVAL *operands, SCIP_Real *weights, SCIP_Real constant, SCIP_INTERVAL rhs, SCIP_INTERVAL *resultants, SCIP_Bool *infeasible)

Typedef Documentation

SCIP_INTERVAL

typedef struct SCIP_Interval SCIP_INTERVAL

Definition at line 58 of file intervalarith.h.

SCIP_ROUNDMODE

typedef int SCIP_ROUNDMODE

rounding mode of floating point operations (upwards, downwards, nearest, ...)

exact values depend on machine and compiler

Definition at line 64 of file intervalarith.h.

Function Documentation

SCIPintervalHasRoundingControl()

SCIP_Bool SCIPintervalHasRoundingControl

(

void

)

returns whether rounding mode control is available

Definition at line 239 of file intervalarith.c.

References FALSE.

Referenced by SCIPfindSimpleRational().

SCIPintervalSetRoundingMode()

void SCIPintervalSetRoundingMode

(

SCIP_ROUNDMODE

roundmode

)

sets rounding mode of floating point operations

Parameters

roundmode

rounding mode to activate

Definition at line 268 of file intervalarith.c.

References intervalSetRoundingMode().

Referenced by computeMaxBoundaryForBilinearProp(), computeMaxForBilinearProp(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPfindSimpleRational(), SCIPintervalCos(), and SCIPintervalPropagateWeightedSum().

SCIPintervalGetRoundingMode()

SCIP_ROUNDMODE SCIPintervalGetRoundingMode

(

void

)

gets current rounding mode of floating point operations

Definition at line 276 of file intervalarith.c.

References intervalGetRoundingMode(), negate(), and x.

Referenced by computeMaxBoundaryForBilinearProp(), computeMaxForBilinearProp(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPfindSimpleRational(), SCIPintervalCos(), SCIPintervalEntropy(), and SCIPintervalPropagateWeightedSum().

SCIPintervalSetRoundingModeDownwards()

void SCIPintervalSetRoundingModeDownwards

(

void

)

sets rounding mode of floating point operations to downwards rounding

Definition at line 344 of file intervalarith.c.

References intervalSetRoundingMode(), and SCIP_ROUND_DOWNWARDS.

Referenced by computeMaxForBilinearProp(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPfindSimpleRational(), SCIPintervalCos(), and SCIPintervalPropagateWeightedSum().

SCIPintervalSetRoundingModeUpwards()

void SCIPintervalSetRoundingModeUpwards

(

void

)

sets rounding mode of floating point operations to upwards rounding

Definition at line 352 of file intervalarith.c.

References intervalSetRoundingMode(), and SCIP_ROUND_UPWARDS.

Referenced by computeMaxBoundaryForBilinearProp(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), and SCIPintervalEntropy().

SCIPintervalSetRoundingModeToNearest()

void SCIPintervalSetRoundingModeToNearest

(

void

)

sets rounding mode of floating point operations to nearest rounding

Definition at line 360 of file intervalarith.c.

References intervalSetRoundingMode(), and SCIP_ROUND_NEAREST.

Referenced by SCIPintervalEntropy().

SCIPintervalSetRoundingModeTowardsZero()

void SCIPintervalSetRoundingModeTowardsZero

(

void

)

sets rounding mode of floating point operations to towards zero rounding

Definition at line 368 of file intervalarith.c.

References intervalSetRoundingMode(), and SCIP_ROUND_ZERO.

SCIPintervalNegateReal()

SCIP_Real SCIPintervalNegateReal

(

SCIP_Real

x

)

negates a number in a way that the compiler does not optimize it away

Parameters

x	number to negate

Definition at line 376 of file intervalarith.c.

References negate().

Referenced by computeMaxBoundaryForBilinearProp(), computeMaxForBilinearProp(), and SCIPintervalPropagateWeightedSum().

SCIPintervalGetInf()

SCIP_Real SCIPintervalGetInf

(

SCIP_INTERVAL

interval

)

returns infimum of interval

Parameters

interval

interval

Definition at line 405 of file intervalarith.c.

References SCIP_Interval::inf.

Referenced by computeRoot(), findMonoidalQuadRoot(), getFeasiblePointsBilinear(), intEvalQuotient(), lpUpdateVarColumnProved(), lpUpdateVarLooseProved(), lpUpdateVarProved(), nlrowCalcActivityBounds(), propagateBoundsQuadExpr(), provedBound(), reverseProp(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalSolveUnivariateQuadExpression(), SCIPlpGetModifiedProvedPseudoObjval(), and startProbing().

SCIPintervalGetSup()

SCIP_Real SCIPintervalGetSup

(

SCIP_INTERVAL

interval

)

returns supremum of interval

Parameters

interval

interval

Definition at line 413 of file intervalarith.c.

References SCIP_Interval::sup.

Referenced by getFeasiblePointsBilinear(), intEvalQuotient(), nlrowCalcActivityBounds(), propagateBoundsQuadExpr(), reverseProp(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalSolveUnivariateQuadExpression(), and startProbing().

SCIPintervalSet()

void SCIPintervalSet	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	value
	)

stores given value as interval

Parameters

resultant	interval to store value into
value	value to store

Definition at line 421 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by computeMaxForBilinearProp(), getFeasiblePointsBilinear(), intEvalQuotient(), lpUpdateVarColumnProved(), lpUpdateVarLooseProved(), lpUpdateVarProved(), nlrowCalcActivityBounds(), propagateBoundsQuadExpr(), provedBound(), reverseProp(), reversePropBilinear(), reversepropQuotient(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalDiv(), SCIPintervalEntropy(), SCIPintervalIntersectEps(), SCIPintervalPower(), SCIPintervalPowerScalarInteger(), SCIPintervalPowerScalarScalar(), SCIPintervalQuadBivar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPlpGetModifiedProvedPseudoObjval().

SCIPintervalSetBounds()

void SCIPintervalSetBounds	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	inf,
		SCIP_Real	sup
	)

stores given infimum and supremum as interval

Parameters

resultant	interval to store value into
inf	value to store as infimum
sup	value to store as supremum

Definition at line 433 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by computeRangeForBilinearProp(), computeRevPropIntervalSin(), computeRoot(), estimateBivariateQuotient(), estimateUnivariateQuotient(), findMonoidalQuadRoot(), getFeasiblePointsBilinear(), intevalBilinear(), nlrowCalcActivityBounds(), presolveRedundantConss(), propConss(), provedBound(), reverseProp(), SCIP_DECL_EXPR_INTEVALVAR(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIPexprcurvPower(), SCIPexprcurvPowerInv(), SCIPintervalCos(), SCIPintervalEntropy(), SCIPintervalPower(), SCIPintervalPowerScalarInverse(), SCIPintervalQuadBivar(), SCIPintervalSin(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIPintervalSetEmpty()

void SCIPintervalSetEmpty

(

SCIP_INTERVAL *

resultant

)

sets interval to empty interval, which will be [1.0, -1.0]

Parameters

resultant

resultant interval of operation

Definition at line 447 of file intervalarith.c.

References SCIP_Interval::inf, NULL, and SCIP_Interval::sup.

Referenced by computeRevPropIntervalSin(), forwardPropExpr(), intevalBilinear(), intEvalQuotient(), reverseProp(), reversePropBilinear(), reversepropQuotient(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_NLHDLRINTEVAL(), SCIPexprEvalActivity(), SCIPintervalEntropy(), SCIPintervalLog(), SCIPintervalPowerScalar(), SCIPintervalPowerScalarInverse(), SCIPintervalQuad(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpression(), SCIPintervalSolveUnivariateQuadExpressionPositive(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), and SCIPintervalSquareRoot().

SCIPintervalIsEmpty()

SCIP_Bool SCIPintervalIsEmpty	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is empty, i.e., whether inf > sup

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 458 of file intervalarith.c.

References FALSE, SCIP_Interval::inf, and SCIP_Interval::sup.

Referenced by computeRoot(), createAuxVar(), estimateVertexPolyhedralProduct(), findMonoidalQuadRoot(), forwardPropExpr(), getFeasiblePointsBilinear(), intevalBilinear(), intEvalQuotient(), isIntervalBetter(), presolveRedundantConss(), propagateBoundsQuadExpr(), propConss(), reverseProp(), reversePropQueue(), reversepropQuotient(), SCIP_DECL_EXPRESTIMATE(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalAbs(), SCIPintervalAdd(), SCIPintervalAddScalar(), SCIPintervalCos(), SCIPintervalDiv(), SCIPintervalDivScalar(), SCIPintervalEntropy(), SCIPintervalExp(), SCIPintervalLog(), SCIPintervalMax(), SCIPintervalMin(), SCIPintervalMul(), SCIPintervalMulInf(), SCIPintervalMulScalar(), SCIPintervalMulScalarInf(), SCIPintervalMulScalarSup(), SCIPintervalMulSup(), SCIPintervalPower(), SCIPintervalPowerScalar(), SCIPintervalPropagateWeightedSum(), SCIPintervalQuad(), SCIPintervalQuadUpperBound(), SCIPintervalReciprocal(), SCIPintervalSign(), SCIPintervalSignPowerScalar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpression(), SCIPintervalSquare(), SCIPintervalSquareRoot(), SCIPintervalSub(), SCIPtightenExprIntervalNonlinear(), and tightenAuxVarBounds().

SCIPintervalSetEntire()

void SCIPintervalSetEntire	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant
	)

sets interval to entire [-infinity, +infinity]

Parameters

infinity	value for infinity
resultant	resultant interval of operation

Definition at line 470 of file intervalarith.c.

References SCIP_Interval::inf, infinity, NULL, and SCIP_Interval::sup.

Referenced by computeRangeForBilinearProp(), createAuxVar(), forwardPropExpr(), intevalBilinear(), intEvalQuotient(), reversepropQuotient(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPexprCreate(), SCIPexprEvalActivity(), SCIPgetExprBoundsNonlinear(), SCIPintervalPropagateWeightedSum(), SCIPintervalScalprod(), SCIPintervalScalprodScalarsInf(), and SCIPintervalScalprodScalarsSup().

SCIPintervalIsEntire()

SCIP_Bool SCIPintervalIsEntire	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is entire, i.e., whether inf ≤ -infinity and sup ≥ infinity

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 482 of file intervalarith.c.

References SCIP_Interval::inf, infinity, and SCIP_Interval::sup.

Referenced by nlrowCalcActivityBounds(), reversePropQueue(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalPropagateWeightedSum(), and SCIPtightenExprIntervalNonlinear().

SCIPintervalIsPositiveInfinity()

SCIP_Bool SCIPintervalIsPositiveInfinity	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is positive infinity, i.e., [infinity, infinity]

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 491 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

SCIPintervalIsNegativeInfinity()

SCIP_Bool SCIPintervalIsNegativeInfinity	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand
	)

indicates whether interval is negative infinity, i.e., [-infinity, -infinity]

Parameters

infinity	value for infinity
operand	operand of operation

Definition at line 500 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

SCIPintervalIsSubsetEQ()

SCIP_Bool SCIPintervalIsSubsetEQ	(	SCIP_Real	infinity,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

indicates whether operand1 is contained in operand2

Parameters

infinity	value for infinity
operand1	first operand of operation
operand2	second operand of operation

Definition at line 509 of file intervalarith.c.

References FALSE, SCIP_Interval::inf, MAX, MIN, SCIP_Interval::sup, and TRUE.

Referenced by isIntervalBetter(), presolveRedundantConss(), and reverseProp().

SCIPintervalAreDisjoint()

SCIP_Bool SCIPintervalAreDisjoint	(	SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

indicates whether operand1 and operand2 are disjoint

Parameters

operand1	first operand of operation
operand2	second operand of operation

Definition at line 528 of file intervalarith.c.

References SCIP_Interval::inf, and SCIP_Interval::sup.

SCIPintervalAreDisjointEps()

SCIP_Bool SCIPintervalAreDisjointEps	(	SCIP_Real	eps,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

indicates whether operand1 and operand2 are disjoint with epsilon tolerance

Returns whether minimal (relative) distance of intervals is larger than epsilon. Same as SCIPintervalIsEmpty(SCIPintervalIntersectEps(operand1, operand2)).

Parameters

eps	epsilon
operand1	first operand of operation
operand2	second operand of operation

Definition at line 541 of file intervalarith.c.

References eps, FALSE, SCIP_Interval::inf, SCIPrelDiff(), and SCIP_Interval::sup.

SCIPintervalIntersect()

void SCIPintervalIntersect	(	SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

intersection of two intervals

Parameters

resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 557 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, and SCIP_Interval::sup.

Referenced by reverseProp(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRINTEVAL(), SCIPintervalIntersectEps(), SCIPintervalPowerScalarInverse(), SCIPintervalPropagateWeightedSum(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpression(), SCIPintervalSolveUnivariateQuadExpressionPositive(), and SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar().

SCIPintervalIntersectEps()

void SCIPintervalIntersectEps	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	eps,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

intersection of two intervals with epsilon tolerance

If intersection of operand1 and operand2 is empty, but minimal (relative) distance of intervals is at most epsilon, then set resultant to singleton containing the point in operand1 that is closest to operand2, i.e.,

• resultant = { operand1.sup }, if operand1.sup < operand2.inf and reldiff(operand2.inf,operand1.sup) ≤ eps
• resultant = { operand1.inf }, if operand1.inf > operand2.sup and reldiff(operand1.inf,operand2.sup) ≤ eps
• resultant = intersection of operand1 and operand2, otherwise

Parameters

resultant	resultant interval of operation
eps	epsilon
operand1	first operand of operation
operand2	second operand of operation

Definition at line 578 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIPintervalIntersect(), SCIPintervalSet(), SCIPrelDiff(), and SCIP_Interval::sup.

Referenced by estimateBivariateQuotient(), estimateUnivariateQuotient(), forwardPropExpr(), SCIP_DECL_NLHDLRESTIMATE(), SCIPgetExprBoundsNonlinear(), and SCIPtightenExprIntervalNonlinear().

SCIPintervalUnify()

void SCIPintervalUnify	(	SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

interval enclosure of the union of two intervals

Parameters

resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 609 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, and SCIP_Interval::sup.

Referenced by intEvalQuotient(), reversepropQuotient(), SCIP_DECL_EXPRREVERSEPROP(), SCIPintervalPowerScalarInverse(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSolveUnivariateQuadExpression().

SCIPintervalAddInf()

void SCIPintervalAddInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

adds operand1 and operand2 and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 636 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), NULL, and SCIP_ROUND_DOWNWARDS.

Referenced by SCIPintervalAdd(), SCIPintervalAddVectors(), SCIPintervalScalprod(), and SCIPintervalScalprodScalarsInf().

SCIPintervalAddSup()

void SCIPintervalAddSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

adds operand1 and operand2 and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 663 of file intervalarith.c.

References infinity, intervalGetRoundingMode(), NULL, SCIP_ROUND_UPWARDS, and SCIP_Interval::sup.

Referenced by SCIPintervalAdd(), SCIPintervalAddVectors(), SCIPintervalScalprod(), and SCIPintervalScalprodScalarsSup().

SCIPintervalAdd()

void SCIPintervalAdd	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

adds operand1 and operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 690 of file intervalarith.c.

References intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalAddInf(), SCIPintervalAddSup(), and SCIPintervalIsEmpty().

Referenced by lpUpdateVarLooseProved(), lpUpdateVarProved(), nlrowCalcActivityBounds(), provedBound(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalQuadBivar(), SCIPintervalSin(), and SCIPlpGetModifiedProvedPseudoObjval().

SCIPintervalAddScalar()

void SCIPintervalAddScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

adds operand1 and scalar operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 717 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by intEvalQuotient(), reversepropQuotient(), SCIP_DECL_EXPRREVERSEPROP(), SCIPintervalQuadBivar(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSubScalar().

SCIPintervalAddVectors()

void SCIPintervalAddVectors	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_INTERVAL *	operand2
	)

adds vector operand1 and vector operand2 and stores result in vector resultant

Parameters

infinity	value for infinity
resultant	array of resultant intervals of operation
length	length of arrays
operand1	array of first operands of operation
operand2	array of second operands of operation

Definition at line 767 of file intervalarith.c.

References intervalGetRoundingMode(), intervalSetRoundingMode(), SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalAddInf(), and SCIPintervalAddSup().

SCIPintervalSub()

void SCIPintervalSub	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

subtracts operand2 from operand1 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 797 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by lpUpdateVarColumnProved(), lpUpdateVarProved(), provedBound(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalCos(), SCIPintervalSin(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPlpGetModifiedProvedPseudoObjval().

SCIPintervalSubScalar()

void SCIPintervalSubScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

subtracts scalar operand2 from operand1 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 845 of file intervalarith.c.

References SCIPintervalAddScalar().

Referenced by reversepropQuotient().

SCIPintervalMulInf()

void SCIPintervalMulInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

multiplies operand1 with operand2 and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation; can be +/-inf
operand2	second operand of operation; can be +/-inf

Definition at line 856 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), MIN, NULL, SCIP_Real, SCIP_ROUND_DOWNWARDS, SCIPintervalIsEmpty(), SCIPintervalMulScalarInf(), and SCIP_Interval::sup.

Referenced by SCIPintervalMul(), and SCIPintervalScalprod().

SCIPintervalMulSup()

void SCIPintervalMulSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

multiplies operand1 with operand2 and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation; can be +/-inf
operand2	second operand of operation; can be +/-inf

Definition at line 916 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), MAX, NULL, SCIP_Real, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIPintervalMulScalarSup(), and SCIP_Interval::sup.

Referenced by SCIPintervalMul(), and SCIPintervalScalprod().

SCIPintervalMul()

void SCIPintervalMul	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

multiplies operand1 with operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation; can be +/-inf
operand2	second operand of operation; can be +/-inf

Definition at line 976 of file intervalarith.c.

References intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIPintervalMulInf(), and SCIPintervalMulSup().

Referenced by lpUpdateVarColumnProved(), lpUpdateVarLooseProved(), lpUpdateVarProved(), provedBound(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), SCIPintervalDiv(), SCIPintervalPower(), SCIPintervalQuad(), and SCIPlpGetModifiedProvedPseudoObjval().

SCIPintervalMulScalarInf()

void SCIPintervalMulScalarInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

multiplies operand1 with scalar operand2 and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation; can be +/- inf

Definition at line 1003 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIPintervalMulInf(), SCIPintervalMulScalar(), and SCIPintervalScalprodScalarsInf().

SCIPintervalMulScalarSup()

void SCIPintervalMulScalarSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

multiplies operand1 with scalar operand2 and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation; can be +/- inf

Definition at line 1059 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), NULL, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIPintervalMulScalar(), SCIPintervalMulSup(), and SCIPintervalScalprodScalarsSup().

SCIPintervalMulScalar()

void SCIPintervalMulScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

multiplies operand1 with scalar operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1115 of file intervalarith.c.

References SCIP_Interval::inf, intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIPintervalMulScalarInf(), SCIPintervalMulScalarSup(), and SCIP_Interval::sup.

Referenced by computeRangeForBilinearProp(), intevalBilinear(), intEvalQuotient(), nlrowCalcActivityBounds(), reversepropQuotient(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIPintervalCos(), SCIPintervalPropagateWeightedSum(), SCIPintervalSin(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIPintervalDiv()

void SCIPintervalDiv	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

divides operand1 by operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1154 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIPintervalMul(), SCIPintervalSet(), and SCIP_Interval::sup.

Referenced by intEvalQuotient(), reversepropQuotient(), and SCIPintervalSolveUnivariateQuadExpression().

SCIPintervalDivScalar()

void SCIPintervalDivScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

divides operand1 by scalar operand2 and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1208 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by computeMaxForBilinearProp(), intEvalQuotient(), propagateBoundsLinExpr(), and SCIPintervalPropagateWeightedSum().

SCIPintervalScalprod()

void SCIPintervalScalprod	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_INTERVAL *	operand2
	)

computes the scalar product of two vectors of intervals and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals; can have +/-inf entries
operand2	second vector as array of intervals; can have +/-inf entries

Definition at line 1311 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalAddInf(), SCIPintervalAddSup(), SCIPintervalMulInf(), SCIPintervalMulSup(), SCIPintervalSetEntire(), and SCIP_Interval::sup.

SCIPintervalScalprodScalarsInf()

void SCIPintervalScalprodScalarsInf	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_Real *	operand2
	)

computes the scalar product of a vector of intervals and a vector of scalars and stores infimum of result in infimum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals
operand2	second vector as array of scalars; can have +/-inf entries

Definition at line 1351 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), SCIP_ROUND_DOWNWARDS, SCIPintervalAddInf(), SCIPintervalMulScalarInf(), SCIPintervalSetEntire(), and SCIP_Interval::sup.

Referenced by SCIPintervalScalprodScalars().

SCIPintervalScalprodScalarsSup()

void SCIPintervalScalprodScalarsSup	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_Real *	operand2
	)

computes the scalar product of a vector of intervals and a vector of scalars and stores supremum of result in supremum of resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals
operand2	second vector as array of scalars; can have +/-inf entries

Definition at line 1377 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), SCIP_ROUND_UPWARDS, SCIPintervalAddSup(), SCIPintervalMulScalarSup(), SCIPintervalSetEntire(), and SCIP_Interval::sup.

Referenced by SCIPintervalScalprodScalars().

SCIPintervalScalprodScalars()

void SCIPintervalScalprodScalars	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		int	length,
		SCIP_INTERVAL *	operand1,
		SCIP_Real *	operand2
	)

computes the scalar product of a vector of intervals and a vector of scalars and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
length	length of vectors
operand1	first vector as array of intervals
operand2	second vector as array of scalars; can have +/-inf entries

Definition at line 1403 of file intervalarith.c.

References SCIP_Interval::inf, intervalGetRoundingMode(), intervalSetRoundingMode(), SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalScalprodScalarsInf(), SCIPintervalScalprodScalarsSup(), and SCIP_Interval::sup.

SCIPintervalSquare()

void SCIPintervalSquare	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

squares operand and stores result in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 1431 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), MAX, NULL, SCIP_Real, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIP_Interval::sup, x, and y.

SCIPintervalSquareRoot()

void SCIPintervalSquareRoot	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores (positive part of) square root of operand in resultant

Attention

we assume a correctly rounded sqrt(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 1503 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalIsEmpty(), SCIPintervalSetEmpty(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by computeMaxForBilinearProp().

SCIPintervalPower()

void SCIPintervalPower	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

stores operand1 to the power of operand2 in resultant

uses SCIPintervalPowerScalar if operand2 is a scalar, otherwise computes exp(op2*log(op1))

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1564 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIPintervalExp(), SCIPintervalIsEmpty(), SCIPintervalLog(), SCIPintervalMul(), SCIPintervalPowerScalar(), SCIPintervalSet(), SCIPintervalSetBounds(), and SCIP_Interval::sup.

Referenced by SCIPintervalPowerScalarInverse().

SCIPintervalPowerScalar()

void SCIPintervalPowerScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

stores operand1 to the power of the scalar operand2 in resultant

Attention

we assume a correctly rounded pow(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1903 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), MAX, NULL, SCIP_Bool, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalIsEmpty(), SCIPintervalPowerScalarIntegerInf(), SCIPintervalPowerScalarIntegerSup(), SCIPintervalSetEmpty(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL(), and SCIPintervalPower().

SCIPintervalPowerScalarScalar()

void SCIPintervalPowerScalarScalar	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	operand1,
		SCIP_Real	operand2
	)

stores bounds on the power of a scalar operand1 to a scalar operand2 in resultant

Both operands need to be finite numbers. Needs to have operand1 ≥ 0 or operand2 integer and needs to have operand2 ≥ 0 if operand1 = 0.

Attention

we assume a correctly rounded pow(double) function when rounding is to nearest

Parameters

resultant	resultant of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1860 of file intervalarith.c.

References SCIP_Interval::inf, intervalGetRoundingMode(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalSet(), SCIPnextafter(), and SCIP_Interval::sup.

SCIPintervalPowerScalarIntegerInf()

SCIP_Real SCIPintervalPowerScalarIntegerInf	(	SCIP_Real	operand1,
		int	operand2
	)

computes lower bound on power of a scalar operand1 to an integer operand2

Both operands need to be finite numbers. Needs to have operand1 ≥ 0 and need to have operand2 ≥ 0 if operand1 = 0.

Parameters

operand1	first operand of operation
operand2	second operand of operation

Definition at line 1610 of file intervalarith.c.

References intervalGetRoundingMode(), intervalSetRoundingMode(), SCIP_Real, SCIP_ROUND_DOWNWARDS, SCIPintervalPowerScalarIntegerSup(), and TRUE.

Referenced by SCIPintervalPowerScalar(), and SCIPintervalPowerScalarIntegerSup().

SCIPintervalPowerScalarIntegerSup()

SCIP_Real SCIPintervalPowerScalarIntegerSup	(	SCIP_Real	operand1,
		int	operand2
	)

computes upper bound on power of a scalar operand1 to an integer operand2

Both operands need to be finite numbers. Needs to have operand1 ≥ 0 and needs to have operand2 ≥ 0 if operand1 = 0.

Parameters

operand1	first operand of operation
operand2	second operand of operation

Definition at line 1693 of file intervalarith.c.

References intervalGetRoundingMode(), intervalSetRoundingMode(), SCIP_Real, SCIP_ROUND_UPWARDS, SCIPintervalPowerScalarIntegerInf(), and TRUE.

Referenced by SCIPintervalPowerScalar(), and SCIPintervalPowerScalarIntegerInf().

SCIPintervalPowerScalarInteger()

void SCIPintervalPowerScalarInteger	(	SCIP_INTERVAL *	resultant,
		SCIP_Real	operand1,
		int	operand2
	)

computes bounds on power of a scalar operand1 to an integer operand2

Both operands need to be finite numbers. Needs to have operand1 ≥ 0 and needs to have operand2 ≥ 0 if operand1 = 0.

Parameters

resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 1768 of file intervalarith.c.

References SCIP_Interval::inf, intervalGetRoundingMode(), intervalSetRoundingMode(), negate(), SCIP_Real, SCIP_REAL_MAX, SCIP_ROUND_UPWARDS, SCIPintervalPowerScalarInteger(), SCIPintervalReciprocal(), SCIPintervalSet(), SCIP_Interval::sup, and TRUE.

Referenced by SCIPintervalPowerScalarInteger().

SCIPintervalPowerScalarInverse()

void SCIPintervalPowerScalarInverse	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	basedomain,
		SCIP_Real	exponent,
		SCIP_INTERVAL	image
	)

given an interval for the image of a power operation, computes an interval for the origin

That is, for \(y = x^p\) with the exponent \(p\) a given scalar and \(y\) = image a given interval, computes \(x \subseteq \text{basedomain}\) such that \(y \in x^p\) and such that for all \(z \in \text{basedomain} \setminus x: z^p \not \in y\).

Parameters

infinity	value for infinity
resultant	resultant interval of operation
basedomain	domain of base
exponent	exponent
image	interval image of power

Definition at line 2152 of file intervalarith.c.

References EPSISINT, SCIP_Interval::inf, MAX, MIN, NULL, SCIPintervalIntersect(), SCIPintervalPower(), SCIPintervalReciprocal(), SCIPintervalSetBounds(), SCIPintervalSetEmpty(), SCIPintervalUnify(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRREVERSEPROP().

SCIPintervalSignPowerScalar()

void SCIPintervalSignPowerScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_Real	operand2
	)

stores operand1 to the signed power of the scalar positive operand2 in resultant

The signed power of x w.r.t. an exponent n ≥ 0 is given as \(\mathrm{sign}(x) |x|^n\).

Attention

we assume correctly rounded sqrt(double) and pow(double) functions when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 2233 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), negate(), NULL, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_NEAREST, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL(), and SCIP_DECL_EXPRREVERSEPROP().

SCIPintervalReciprocal()

void SCIPintervalReciprocal	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

computes the reciprocal of an interval

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2405 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), NULL, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRREVERSEPROP(), SCIPintervalPowerScalarInteger(), and SCIPintervalPowerScalarInverse().

SCIPintervalExp()

void SCIPintervalExp	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores exponential of operand in resultant

Attention

we assume a correctly rounded exp(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2478 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalIsEmpty(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), and SCIPintervalPower().

SCIPintervalLog()

void SCIPintervalLog	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores natural logarithm of operand in resultant

Attention

we assume a correctly rounded log(double) function when rounding is to nearest

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2562 of file intervalarith.c.

References SCIP_Interval::inf, infinity, intervalGetRoundingMode(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalIsEmpty(), SCIPintervalSetEmpty(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), and SCIPintervalPower().

SCIPintervalMin()

void SCIPintervalMin	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

stores minimum of operands in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 2630 of file intervalarith.c.

References SCIP_Interval::inf, MIN, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

SCIPintervalMax()

void SCIPintervalMax	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand1,
		SCIP_INTERVAL	operand2
	)

stores maximum of operands in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand1	first operand of operation
operand2	second operand of operation

Definition at line 2646 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

SCIPintervalAbs()

void SCIPintervalAbs	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores absolute value of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2662 of file intervalarith.c.

References SCIP_Interval::inf, MAX, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

SCIPintervalSin()

void SCIPintervalSin	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores sine value of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2700 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_Real, SCIPintervalAdd(), SCIPintervalCos(), SCIPintervalMulScalar(), SCIPintervalSetBounds(), SCIPintervalSub(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

SCIPintervalCos()

void SCIPintervalCos	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores cosine value of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2742 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPdebugMessage, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalMulScalar(), SCIPintervalSetBounds(), SCIPintervalSetRoundingMode(), SCIPintervalSetRoundingModeDownwards(), SCIPintervalSub(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL(), and SCIPintervalSin().

SCIPintervalSign()

void SCIPintervalSign	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores sign of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2869 of file intervalarith.c.

References SCIP_Interval::inf, NULL, SCIPintervalIsEmpty(), and SCIP_Interval::sup.

SCIPintervalEntropy()

void SCIPintervalEntropy	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	operand
	)

stores entropy of operand in resultant

Parameters

infinity	value for infinity
resultant	resultant interval of operation
operand	operand of operation

Definition at line 2896 of file intervalarith.c.

References SCIP_Interval::inf, infinity, MAX, MAX3, MIN, NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_NEAREST, SCIPintervalGetRoundingMode(), SCIPintervalIsEmpty(), SCIPintervalSet(), SCIPintervalSetBounds(), SCIPintervalSetEmpty(), SCIPintervalSetRoundingModeToNearest(), SCIPintervalSetRoundingModeUpwards(), SCIPnegateReal(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by reverseProp(), and SCIP_DECL_EXPRINTEVAL().

SCIPintervalQuadUpperBound()

SCIP_Real SCIPintervalQuadUpperBound	(	SCIP_Real	infinity,
		SCIP_Real	a,
		SCIP_INTERVAL	b_,
		SCIP_INTERVAL	x
	)

computes exact upper bound on \( a x^2 + b x \) for x in [xlb, xub], b an interval, and a scalar

Uses Algorithm 2.2 from Domes and Neumaier: Constraint propagation on quadratic constraints (2008).

Parameters

infinity	value for infinity
a	coefficient of x^2
b_	coefficient of x
x	range of x

Definition at line 2995 of file intervalarith.c.

References b, SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), MAX, negate(), SCIP_Real, SCIP_ROUND_UPWARDS, SCIPintervalIsEmpty(), SCIPintervalQuadUpperBound(), SCIP_Interval::sup, and x.

Referenced by SCIP_DECL_NLHDLRINTEVAL(), SCIPintervalQuad(), SCIPintervalQuadUpperBound(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIPintervalQuad()

void SCIPintervalQuad	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	xrng
	)

stores range of quadratic term in resultant

given scalar a and intervals b and x, computes interval for \( a x^2 + b x \)

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
xrng	range of x

Definition at line 3090 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_Real, SCIPintervalIsEmpty(), SCIPintervalMul(), SCIPintervalQuadUpperBound(), SCIPintervalSetEmpty(), and SCIP_Interval::sup.

Referenced by SCIPintervalQuadBivar(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIPintervalSolveUnivariateQuadExpressionPositive()

void SCIPintervalSolveUnivariateQuadExpressionPositive	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	rhs,
		SCIP_INTERVAL	xbnds
	)

computes interval with positive solutions of a quadratic equation with interval coefficients

Given intervals a, b, and c, this function computes an interval that contains all positive solutions of \( a x^2 + b x \in c\) within xbnds.

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation
xbnds	bounds on x

Definition at line 3125 of file intervalarith.c.

References SCIP_Interval::inf, infinity, NULL, SCIPdebugMessage, SCIPdebugPrintf, SCIPintervalIntersect(), SCIPintervalSetEmpty(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), and SCIP_Interval::sup.

Referenced by SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpression(), and SCIPintervalSolveUnivariateQuadExpressionNegative().

SCIPintervalSolveUnivariateQuadExpressionNegative()

void SCIPintervalSolveUnivariateQuadExpressionNegative	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	rhs,
		SCIP_INTERVAL	xbnds
	)

computes interval with negative solutions of a quadratic equation with interval coefficients

Given intervals a, b, and c, this function computes an interval that contains all negative solutions of \( a x^2 + b x \in c\) within xbnds.

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation
xbnds	bounds on x

Definition at line 3172 of file intervalarith.c.

References SCIP_Interval::inf, SCIP_Real, SCIPintervalSolveUnivariateQuadExpressionPositive(), and SCIP_Interval::sup.

Referenced by SCIPintervalSolveBivariateQuadExpressionAllScalar(), and SCIPintervalSolveUnivariateQuadExpression().

SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar()

void SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	sqrcoeff,
		SCIP_Real	lincoeff,
		SCIP_Real	rhs,
		SCIP_INTERVAL	xbnds
	)

computes positive solutions of a quadratic equation with scalar coefficients

Givens scalar a, b, and c, this function computes an interval that contains all positive solutions of \( a x^2 + b x \geq c\) within xbnds. Implements Algorithm 3.2 from Domes and Neumaier: Constraint propagation on quadratic constraints (2008).

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation
xbnds	bounds on x

Definition at line 3208 of file intervalarith.c.

References b, SCIP_Interval::inf, infinity, intervalGetRoundingMode(), intervalSetRoundingMode(), MAX, negate(), NULL, SCIP_Real, SCIP_REAL_MAX, SCIP_REAL_MIN, SCIP_ROUND_DOWNWARDS, SCIP_ROUND_NEAREST, SCIP_ROUND_UPWARDS, SCIPintervalIntersect(), SCIPintervalSetEmpty(), SCIPnextafter(), and SCIP_Interval::sup.

Referenced by computeRoot(), findMonoidalQuadRoot(), and SCIPintervalSolveUnivariateQuadExpressionPositive().

SCIPintervalSolveUnivariateQuadExpression()

void SCIPintervalSolveUnivariateQuadExpression	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_INTERVAL	sqrcoeff,
		SCIP_INTERVAL	lincoeff,
		SCIP_INTERVAL	rhs,
		SCIP_INTERVAL	xbnds
	)

solves a quadratic equation with interval coefficients

Given intervals a, b and c, this function computes an interval that contains all solutions of \( a x^2 + b x \in c\) within xbnds.

Parameters

infinity	value for infinity
resultant	resultant interval of operation
sqrcoeff	coefficient of x^2
lincoeff	coefficient of x
rhs	right hand side of equation
xbnds	bounds on x

Definition at line 3412 of file intervalarith.c.

References SCIP_Interval::inf, MAX, MIN, NULL, SCIPdebugMessage, SCIPintervalDiv(), SCIPintervalGetInf(), SCIPintervalGetSup(), SCIPintervalIntersect(), SCIPintervalIsEmpty(), SCIPintervalSetEmpty(), SCIPintervalSolveUnivariateQuadExpressionNegative(), SCIPintervalSolveUnivariateQuadExpressionPositive(), SCIPintervalUnify(), and SCIP_Interval::sup.

Referenced by getFeasiblePointsBilinear(), propagateBoundsQuadExpr(), SCIP_DECL_EXPRREVERSEPROP(), and SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIPintervalQuadBivar()

void SCIPintervalQuadBivar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	ax,
		SCIP_Real	ay,
		SCIP_Real	axy,
		SCIP_Real	bx,
		SCIP_Real	by,
		SCIP_INTERVAL	xbnds,
		SCIP_INTERVAL	ybnds
	)

stores range of bivariate quadratic term in resultant

Given scalars \(a_x\), \(a_y\), \(a_{xy}\), \(b_x\), and \(b_y\) and intervals for \(x\) and \(y\), computes interval for \( a_x x^2 + a_y y^2 + a_{xy} x y + b_x x + b_y y \).

Attention

The operations are not applied rounding-safe here!

Parameters

infinity	value for infinity in interval arithmetics
resultant	buffer where to store result of operation
ax	square coefficient of x
ay	square coefficient of y
axy	bilinear coefficients
bx	linear coefficient of x
by	linear coefficient of y
xbnds	bounds on x
ybnds	bounds on y

Definition at line 3478 of file intervalarith.c.

References SCIP_Interval::inf, infinity, MAX, MIN, NULL, REALABS, SCIP_Real, SCIPdebugMessage, SCIPintervalAdd(), SCIPintervalAddScalar(), SCIPintervalQuad(), SCIPintervalSet(), SCIPintervalSetBounds(), SCIP_Interval::sup, x, and y.

SCIPintervalSolveBivariateQuadExpressionAllScalar()

void SCIPintervalSolveBivariateQuadExpressionAllScalar	(	SCIP_Real	infinity,
		SCIP_INTERVAL *	resultant,
		SCIP_Real	ax,
		SCIP_Real	ay,
		SCIP_Real	axy,
		SCIP_Real	bx,
		SCIP_Real	by,
		SCIP_INTERVAL	rhs,
		SCIP_INTERVAL	xbnds,
		SCIP_INTERVAL	ybnds
	)

solves a bivariate quadratic equation for the first variable

Given scalars \(a_x\), \(a_y\), \(a_{xy}\), \(b_x\) and \(b_y\), and intervals for \(x\), \(y\), and rhs, computes \( \{ x \in \mathbf{x} : \exists y \in \mathbf{y} : a_x x^2 + a_y y^2 + a_{xy} x y + b_x x + b_y y \in \mathbf{\mbox{rhs}} \} \).

Attention

the operations are not applied rounding-safe here

Parameters

infinity	value for infinity in interval arithmetics
resultant	buffer where to store result of operation
ax	square coefficient of x
ay	square coefficient of y
axy	bilinear coefficients
bx	linear coefficient of x
by	linear coefficient of y
rhs	right-hand-side of equation
xbnds	bounds on x
ybnds	bounds on y

Definition at line 3739 of file intervalarith.c.

References b, CALCB, CALCR, EPSGE, EPSGT, EPSLE, EPSLT, EPSN, EPSZ, SCIP_Interval::inf, infinity, MAX, MIN, NULL, REALABS, SCIP_Real, SCIPintervalAddScalar(), SCIPintervalIntersect(), SCIPintervalIsEmpty(), SCIPintervalMulScalar(), SCIPintervalQuad(), SCIPintervalQuadUpperBound(), SCIPintervalSet(), SCIPintervalSetBounds(), SCIPintervalSetEmpty(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpression(), SCIPintervalSolveUnivariateQuadExpressionNegative(), SCIPintervalSolveUnivariateQuadExpressionPositive(), SCIPintervalSub(), SCIPintervalUnify(), and SCIP_Interval::sup.

Referenced by SCIPintervalSolveBivariateQuadExpressionAllScalar().

SCIPintervalPropagateWeightedSum()

int SCIPintervalPropagateWeightedSum	(	SCIP_Real	infinity,
		int	noperands,
		SCIP_INTERVAL *	operands,
		SCIP_Real *	weights,
		SCIP_Real	constant,
		SCIP_INTERVAL	rhs,
		SCIP_INTERVAL *	resultants,
		SCIP_Bool *	infeasible
	)

propagates a weighted sum of intervals in a given interval

Given \(\text{constant} + \sum_i \text{weights}_i \text{operands}_i \in \text{rhs}\), computes possibly tighter interval for each term.

Attention

Valid values are returned in resultants only if any tightening has been found and no empty interval, that is, function returns with non-zero and *infeasible = FALSE.

Returns

Number of terms for which resulting interval is smaller than operand interval.

Parameters

infinity	value for infinity in interval arithmetics
noperands	number of operands (intervals) to propagate
operands	intervals to propagate
weights	weights of intervals in sum
constant	constant in sum
rhs	right-hand-side interval
resultants	array to store propagated intervals, if any reduction is found at all (check return code and *infeasible)
infeasible	buffer to store if propagation produced empty interval

Definition at line 4625 of file intervalarith.c.

References BMScopyMemoryArray, FALSE, SCIP_Interval::inf, NULL, SCIP_Real, SCIPdebugMessage, SCIPdebugPrintf, SCIPintervalDivScalar(), SCIPintervalGetRoundingMode(), SCIPintervalIntersect(), SCIPintervalIsEmpty(), SCIPintervalIsEntire(), SCIPintervalMulScalar(), SCIPintervalNegateReal(), SCIPintervalSetEntire(), SCIPintervalSetRoundingMode(), SCIPintervalSetRoundingModeDownwards(), SCIP_Interval::sup, and TRUE.

Referenced by reversePropagateLinearExpr(), and SCIP_DECL_EXPRREVERSEPROP().