Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from https://scip.zib.de/doc/html/group__PublicIntervalArithMethods.php below:

SCIP Doxygen Documentation: Interval Arithmetics

methods for interval arithmetics

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

exact values depend on machine and compiler

Definition at line 64 of file intervalarith.h.

returns infimum of interval

Parameters

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().

returns supremum of interval

Parameters

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().

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().

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().

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().

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, infinity, 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().

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().

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().

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.

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().

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

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

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 infinity, 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().

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().

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().

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 infinity, and SCIPintervalAddScalar().

Referenced by reversepropQuotient().

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().

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().

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 infinity, 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().

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, infinity, 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().

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().

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().

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.

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.

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().

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

Referenced by SCIPintervalPowerScalarInverse().

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().

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().

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

Referenced by SCIP_DECL_EXPRREVERSEPROP().

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().

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().

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().

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().

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, infinity, pi_d_l, pi_d_u, SCIP_Real, SCIPintervalAdd(), SCIPintervalCos(), SCIPintervalMulScalar(), SCIPintervalSetBounds(), SCIPintervalSub(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRINTEVAL().

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, infinity, MAX, MIN, NULL, pi_d_l, pi_d_u, 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().

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().

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 a, 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().

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().

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().

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, infinity, 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().

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.

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().

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, infinity, 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().

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4