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SCIP Doxygen Documentation: Expressions

an algebraic expression used for nonlinear constraints and NLPs

More details on the DFS mode: Many algorithms over expression trees need to traverse the tree in depth-first manner and a natural way of implementing these algorithms is by using recursion. In general, a function which traverses the tree in depth-first looks like

fun( expr )
   enterexpr()
   continue skip or abort
      for( child in expr->children )
         visitingchild()
         continue skip or abort
         fun(child, data, proceed)
         visitedchild()
         continue skip or abort
   leaveexpr()

Given that some expressions might be quite deep we provide this functionality in an iterative fashion.

Consider an expression (x*y) + z + log(x-y). The corresponding expression graph is

          [+]
      /    |   \
   [*]     |    [log]
   / \     |      |
  /   \    |     [-]
  |   |    |     / \
 [x] [y]  [z]  [x] [y]

(where [x] and [y] are actually the same expression).

If a pointer to the [+] expression is given as root to this expression, it will iterate the graph in a depth-first manner and stop at various stages.

• When entering an expression, it stops in the SCIP_EXPRITER_ENTEREXPR stage. The SCIPexpriterGetParentDFS() function indicates from where the expression has been entered (NULL for the root expression).
• Before visiting a child of an expression, it stops in the SCIP_EXPRITER_VISITINGCHILD stage. The SCIPexpriterGetChildIdxDFS() function returns which child will be visited (as an index in the current expr's children array). Use SCIPexpriterGetChildExprDFS() to obtain the corresponding expression.
• When returning from visiting a child of an expression, it stops in the SCIP_EXPRITER_VISITEDCHILD stage. Again the SCIPexpriterGetChildExprDFS() function returns which child has been visited.
• When leaving an expression, it stops in the SCIP_EXPRITER_LEAVEEXPR stage.

Thus, for the above expression, the expression are visited in the following order and stages:

• enterexpr([+])
• visitingchild([+]), currentchild = 0
• enterexpr([*])
• visitingchild([*]), currentchild = 0
• enterexpr([x])
• leaveexpr([x])
• visitedchild([*]), currentchild = 0
• visitingchild([*]), currentchild = 1
• enterexpr([y])
• leaveexpr([y])
• visitedchild([*]), currentchild = 1
• leaveexpr([*])
• visitedchild([+]), currentchild = 0
• visitingchild([+]), currentchild = 1
• enterexpr([z])
• leaveexpr([z])
• visitedchild([+]), currentchild = 1
• visitingchild([+]), currentchild = 2
• enterexpr([log])
• visitingchild([log]), currentchild = 0
• enterexpr([-])
• visitingchild([-]), currentchild = 0
• enterexpr([x])
• leaveexpr([x])
• visitedchild([-]), currentchild = 0
• visitingchild([-]), currentchild = 1
• enterexpr([y])
• leaveexpr([y])
• visitedchild([-]), currentchild = 1
• leaveexpr([-])
• visitedchild([log]), currentchild = 0
• leaveexpr([log])
• visitedchild([+]) currentchild = 2
• leaveexpr([+])

The caller can direct the iterator to skip parts of the tree:

• If calling SCIPexpriterSkipDFS() in SCIP_EXPRITER_ENTEREXPR stage, all children of that expression will be skipped. The SCIP_EXPRITER_LEAVEEXPR stage will still be next.
• If calling SCIPexpriterSkipDFS() in SCIP_EXPRITER_VISITINGCHILD stage, visiting the current child will be skipped.
• If calling SCIPexpriterSkipDFS() in SCIP_EXPRITER_VISITEDCHILD child, visiting the remaining children will be skipped.

Gradients (Automatic differentiation Backward mode)

Given a function, say, \(f(s(x,y),t(x,y))\) there is a common mnemonic technique to compute its partial derivatives, using a tree diagram. Suppose we want to compute the partial derivative of \(f\) w.r.t. \(x\). Write the function as a tree:

f
|-----|
s     t
|--|  |--|
x  y  x  y

The weight of an edge between two nodes represents the partial derivative of the parent w.r.t. the children, e.g.,

f
|
s

is \( \partial_sf \). The weight of a path is the product of the weight of the edges in the path. The partial derivative of \(f\) w.r.t. \(x\) is then the sum of the weights of all paths connecting \(f\) with \(x\):

\[ \frac{\partial f}{\partial x} = \partial_s f \cdot \partial_x s + \partial_t f \cdot \partial_x t. \]

We follow this method in order to compute the gradient of an expression (root) at a given point (point). Note that an expression is a DAG representation of a function, but there is a 1-1 correspondence between paths in the DAG and path in a tree diagram of a function. Initially, we set root->derivative to 1.0. Then, traversing the tree in Depth First (see SCIPexpriterInit), for every expr that has children, we store in its i-th child, child[i]->derivative, the derivative of expr w.r.t. child evaluated at point multiplied with expr->derivative.

For example:

1. f->derivative = 1.0
2. s->derivative = \(\partial_s f \,\cdot\) f->derivative = \(\partial_s f\)
3. x->derivative = \(\partial_x s \,\cdot\) s->derivative = \(\partial_x s \cdot \partial_s f\)

However, when the child is a variable expressions, we actually need to initialize child->derivative to 0.0 and afterwards add, instead of overwrite the computed value. The complete example would then be:

1. f->derivative = 1.0, x->derivative = 0.0, y->derivative = 0.0
2. s->derivative = \(\partial_s f \,\cdot\) f->derivative = \(\partial_s f\)
3. x->derivative += \(\partial_x s \,\cdot\) s->derivative = \(\partial_x s \cdot \partial_s f\)
4. y->derivative += \(\partial_y s \,\cdot\) s->derivative = \(\partial_y s \cdot \partial_s f\)
5. t->derivative = \(\partial_t f \,\cdot\) f->derivative = \(\partial_t f\)
6. x->derivative += \(\partial_x t \,\cdot\) t->derivative = \(\partial_x t \cdot \partial_t f\)
7. y->derivative += \(\partial_y t \,\cdot\) t->derivative = \(\partial_y t \cdot \partial_t f\)

Note that, to compute this, we only need to know, for each expression, its partial derivatives w.r.t a given child at a point. This is what the callback SCIP_DECL_EXPRBWDIFF should return. Indeed, from "derivative of expr w.r.t. child evaluated at point multiplied with expr->derivative", note that at the moment of processing a child, we already know expr->derivative, so the only missing piece of information is "the derivative of expr w.r.t. child evaluated at point".

An equivalent way of interpreting the procedure is that expr->derivative stores the derivative of the root w.r.t. expr. This way, x->derivative and y->derivative will contain the partial derivatives of root w.r.t. the variable, that is, the gradient. Note, however, that this analogy is only correct for leave expressions, since the derivative value of an intermediate expression gets overwritten.

Hessian (Automatic differentiation Backward on Forward mode)

Computing the Hessian is more complicated since it is the derivative of the gradient, which is a function with more than one output. We compute the Hessian by computing "directions" of the Hessian, that is \(H\cdot u\) for different \(u\). This is easy in general, since it is the gradient of the scalar function \(\nabla f u\), that is, the directional derivative of \(f\) in the direction \(u\): \(D_u f\).

This is easily computed via the so called forward mode. Just as expr->derivative stores the partial derivative of the root w.r.t. expr, expr->dot stores the directional derivative of expr in the direction \(u\). Then, by the chain rule, expr->dot = \(\sum_{c:\text{children}} \partial_c \text{expr} \,\cdot\) c->dot.

Starting with x[i]->dot = \(u_i\), we can compute expr->dot for every expression at the same time we evaluate expr. Computing expr->dot is the purpose of the callback SCIP_DECL_EXPRFWDIFF. Obviously, when this callback is called, the "dots" of all children are known (just like evaluation, where the value of all children are known).

Once we have this information, we compute the gradient of this function, following the same idea as before. We define expr->bardot to be the directional derivative in direction \(u\) of the partial derivative of the root w.r.t expr, that is \(D_u (\partial_{\text{expr}} f) = D_u\) (expr->derivative).

This way, x[i]->bardot = \(D_u (\partial_{x_i} f) = e_i^T H_f u\). Hence vars->bardot contain \(H_f u\). By the chain rule, product rule, and definition we have

\begin{eqnarray*} \texttt{expr->bardot} & = & D_u (\partial_{\text{expr}} f) \\ & = & D_u ( \partial_{\text{parent}} f \cdot \partial_{\text{expr}} \text{parent} ) \\ & = & D_u ( \texttt{parent->derivative} \cdot \partial_{\text{expr}} \text{parent} ) \\ & = & \partial_{\text{expr}} \text{parent} \cdot D_u (\texttt{parent->derivative}) + \texttt{parent->derivative} \cdot D_u (\partial_{\text{expr}} \text{parent}) \\ & = & \texttt{parent->bardot} \cdot \partial_{\text{expr}} \text{parent} + \texttt{parent->derivative} \cdot D_u (\partial_{\text{expr}} \text{parent}) \end{eqnarray*}

Note that we have computed parent->bardot and parent->derivative at this point, while \(\partial_{\text{expr}} \text{parent}\) is the return of SCIP_DECL_EXPRBWDIFF. Hence the only information we need to compute is \(D_u (\partial_{\text{expr}} \text{parent})\). This is the purpose of the callback SCIP_DECL_EXPRBWFWDIFF.

gives the number of children of an expression

Parameters

Definition at line 3860 of file expr.c.

References SCIP_Expr::nchildren, and NULL.

Referenced by addSymmetryInformation(), bilinboundGetX(), bilinboundGetY(), bilinearTermsInsertAll(), buildQuadExprMatrix(), checkAndCollectQuadratic(), collectLeafs(), computeEstimatorsTrig(), computeInitialCutsTrig(), constructExpr(), createNlhdlrExprData(), createNlRow(), DECL_CURVCHECK(), detectExpr(), detectMinors(), detectSocNorm(), detectSocQuadraticComplex(), detectSocQuadraticSimple(), doBfsNext(), doReverseTopologicalNext(), enforceSP11(), enforceSP12(), enforceSP12b(), eval(), evalExprInAux(), exprIsMultivarLinear(), exprIsSemicontinuous(), findUnlockedLinearVar(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), getBilinearBinaryTerms(), getBinaryProductExpr(), getBinaryProductExprDo(), getExprSize(), getFactorizedBinaryQuadraticExpr(), getFeasiblePointsBilinear(), hashExpr(), initBounds(), intevalBilinear(), isBinaryProduct(), isExprPolynomial(), isExprSignomial(), isPackingCons(), nlhdlrExprCreate(), nlhdlrExprGrowChildren(), presolveImplint(), presolveSingleLockedVars(), printRowNl(), printSignomial(), propagateLocks(), readConstraints(), readObjective(), replaceBinaryProducts(), reversePropBilinear(), reversePropQueue(), scaleConsSides(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRCOPYDATA(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRESTIMATE(), SCIP_DECL_EXPREVAL(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRHASH(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEGRALITY(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIP_DECL_NONLINCONSUPGD(), SCIPaddIneqBilinear(), SCIPappendExprSumExpr(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPexprCheckQuadratic(), SCIPexprGetMonomialData(), SCIPexprintCompile(), SCIPisExprVaridx(), SCIPmultiplyByConstantExprSum(), SCIPmultiplyBySumExprSum(), SCIPpowerExprSum(), SCIPregisterExprUsageNonlinear(), SCIPtightenExprIntervalNonlinear(), simplifyFactor(), simplifyTerm(), transformExpr(), tryAddGadgetBilinearProductSignedPerm(), tryAddGadgetEvenOperator(), tryAddGadgetEvenOperatorSum(), and tryAddGadgetSquaredDifference().

gives the children of an expression (can be NULL if no children)

Parameters

Definition at line 3870 of file expr.c.

References SCIP_Expr::children, and NULL.

Referenced by addSymmetryInformation(), bilinboundGetX(), bilinboundGetY(), bilinearTermsInsertAll(), buildQuadExprMatrix(), checkAndCollectQuadratic(), constructExpr(), createNlhdlrExprData(), createNlRow(), DECL_CURVCHECK(), detectExpr(), detectMinors(), detectSocNorm(), detectSocQuadraticSimple(), doBfsNext(), doReverseTopologicalNext(), enforceSP11(), enforceSP12(), enforceSP12b(), eval(), evalExprInAux(), exprIsMultivarLinear(), exprIsSemicontinuous(), findUnlockedLinearVar(), forbidNonlinearVariablesMultiaggration(), getBilinearBinaryTerms(), getBinaryProductExpr(), getBinaryProductExprDo(), getExprSize(), getFactorizedBinaryQuadraticExpr(), getFeasiblePointsBilinear(), hashExpr(), initBounds(), intevalBilinear(), isBinaryProduct(), isExprPolynomial(), isExprSignomial(), isPackingCons(), mergeProductExprlist(), nlhdlrExprGrowChildren(), presolveImplint(), presolveSingleLockedVars(), printRowNl(), printSignomial(), readConstraints(), readObjective(), reversePropBilinear(), reversePropQueue(), scaleConsSides(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRESTIMATE(), SCIP_DECL_EXPREVAL(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRGETSYMDATA(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEGRALITY(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIP_DECL_NONLINCONSUPGD(), SCIPaddIneqBilinear(), SCIPcomputeExprCurvature(), SCIPexprCheckQuadratic(), SCIPexprGetMonomialData(), SCIPexprintCompile(), SCIPmultiplyBySumExprSum(), SCIPpowerExprSum(), simplifyFactor(), simplifyTerm(), transformExpr(), tryAddGadgetBilinearProductSignedPerm(), tryAddGadgetEvenOperator(), tryAddGadgetEvenOperatorSum(), and tryAddGadgetSquaredDifference().

gets the expression handler of an expression

This identifies the type of the expression (sum, variable, ...).

Parameters

Definition at line 3883 of file expr.c.

References SCIP_Expr::exprhdlr, and NULL.

Referenced by addSymmetryInformation(), computeEstimatorsTrig(), computeInitialCutsTrig(), constructExpr(), createAuxVar(), DECL_CURVCHECK(), detectNlhdlr(), enforceExpr(), enforceSP11(), eval(), exprIsNonSmooth(), forwardPropExpr(), hashExpr(), printExpr(), propagateLocks(), reversePropQueue(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRESTIMATE(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRPRINT(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIPcallExprEval(), SCIPcallExprEvalFwdiff(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPexprGetSymData(), SCIPexprintCompile(), SCIPexprPrint(), SCIPgetCoefSymData(), SCIPgetIndexExprVaridx(), SCIPgetVarExprVar(), SCIPisExprAbs(), SCIPisExprCos(), SCIPisExprEntropy(), SCIPisExprErf(), SCIPisExprExp(), SCIPisExprLog(), SCIPisExprSignpower(), SCIPisExprSin(), SCIPisExprVaridx(), SCIPsetIndexExprVaridx(), SCIPtightenExprIntervalNonlinear(), tryAddGadgetBilinearProductSignedPerm(), tryAddGadgetEvenOperatorSum(), and tryAddGadgetEvenOperatorVariable().

gets the expression data of an expression

Parameters

Definition at line 3893 of file expr.c.

References SCIP_Expr::exprdata, and NULL.

Referenced by SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRCOPYDATA(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRESTIMATE(), SCIP_DECL_EXPREVAL(), SCIP_DECL_EXPRFREEDATA(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRGETSYMDATA(), SCIP_DECL_EXPRHASH(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEGRALITY(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRPRINT(), SCIP_DECL_EXPRREVERSEPROP(), SCIPappendExprSumExpr(), SCIPgetCoefExprProduct(), SCIPgetCoefsExprSum(), SCIPgetConstantExprSum(), SCIPgetExponentExprPow(), SCIPgetIndexExprVaridx(), SCIPgetValueExprValue(), SCIPgetVarExprVar(), SCIPmultiplyByConstantExprSum(), and SCIPsetConstantExprSum().

gets the data that the owner of an expression has stored in an expression

Parameters

Definition at line 3921 of file expr.c.

References NULL, and SCIP_Expr::ownerdata.

Referenced by addExprsViolScore(), analyzeViolation(), canonicalizeConstraints(), catchVarEvent(), collectBranchingCandidates(), createAuxVar(), detectNlhdlr(), detectNlhdlrs(), dropVarEvent(), enforceConstraint(), enforceExpr(), forwardPropExpr(), freeAuxVar(), freeEnfoData(), getExprAbsAuxViolation(), getExprAbsOrigViolation(), initSepa(), isSingleLockedCand(), notifyNlhdlrNewsol(), propagateLocks(), propConss(), propExprDomains(), registerBranchingCandidates(), reversePropQueue(), SCIP_DECL_CONSLOCK(), SCIP_DECL_EVENTEXEC(), SCIPaddExprsViolScoreNonlinear(), SCIPaddExprViolScoreNonlinear(), SCIPgetExprAuxVarNonlinear(), SCIPgetExprBoundsNonlinear(), SCIPgetExprEnfoDataNonlinear(), SCIPgetExprNAuxvarUsesNonlinear(), SCIPgetExprNEnfosNonlinear(), SCIPgetExprNLocksNegNonlinear(), SCIPgetExprNLocksPosNonlinear(), SCIPgetExprNPropUsesActivityNonlinear(), SCIPgetExprNSepaUsesActivityNonlinear(), SCIPgetExprPartialDiffGradientDirNonlinear(), SCIPgetExprPartialDiffNonlinear(), SCIPgetExprViolScoreNonlinear(), SCIPgetNlhdlrExprDataNonlinear(), SCIPmarkExprPropagateNonlinear(), SCIPregisterExprUsageNonlinear(), SCIPsetExprEnfoAuxValueNonlinear(), and SCIPtightenExprIntervalNonlinear().

gives the value from the last evaluation of an expression (or SCIP_INVALID if there was an eval error)

See also

SCIPevalExpr to evaluate the expression at a given solution.

Parameters

Definition at line 3934 of file expr.c.

References SCIP_Expr::evalvalue, and NULL.

Referenced by analyzeViolation(), computeOffValues(), computeViolation(), createAuxVar(), AMPLProblemHandler::EndInput(), enforceExpr(), estimateConvexSecant(), estimateGradientInner(), generateCut(), getConsRelViolation(), getExprAbsOrigViolation(), notifyNlhdlrNewsol(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPREVAL(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_VERTEXPOLYFUN(), SCIPexprEvalGradient(), SCIPexprintEval(), SCIPgetExprActivityNonlinear(), SCIPnlrowGetSolActivity(), SCIPnlrowRecalcNLPActivity(), and SCIPnlrowRecalcPseudoActivity().

returns the activity that is currently stored for an expression

See also

SCIPevalExprActivity

Parameters

Definition at line 4016 of file expr.c.

References SCIP_Expr::activity, and NULL.

Referenced by analyzeViolation(), createAuxVar(), DECL_CURVCHECK(), detectSocQuadraticComplex(), detectSocQuadraticSimple(), enforceExpr(), estimateBivariateQuotient(), estimateUnivariateQuotient(), forwardPropExpr(), getFeasiblePointsBilinear(), intevalBilinear(), nlrowCalcActivityBounds(), presolveRedundantConss(), propConss(), propExprDomains(), reversePropagateLinearExpr(), reversePropBilinear(), reversePropQueue(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRINTEVAL(), SCIPgetExprBoundsNonlinear(), SCIPtightenExprIntervalNonlinear(), and tryFillNlhdlrExprDataQuad().

gives the coefficients and expressions that define a quadratic expression

It can return the constant part, the number, arguments, and coefficients of the purely linear part and the number of quadratic terms and bilinear terms. Note that for arguments that appear in the quadratic part, a linear coefficient is stored with the quadratic term. Use SCIPexprGetQuadraticQuadTerm() and SCIPexprGetQuadraticBilinTerm() to access the data for a quadratic or bilinear term.

It can also return the eigenvalues and the eigenvectors of the matrix \(Q\) when the quadratic is written as \(x^T Q x + b^T x + c^T y + d\), where \(c^T y\) defines the purely linear part. Note, however, that to have access to them one needs to call SCIPcomputeExprQuadraticCurvature() with storeeigeninfo=TRUE. If the eigen information was not stored or it failed to be computed, eigenvalues and eigenvectors will be set to NULL.

This function returns pointers to internal data in linexprs and lincoefs. The user must not change this data.

Attention

SCIPcheckExprQuadratic() needs to be called first to check whether expression is quadratic and initialize the data of the quadratic representation.

Parameters

expr quadratic expression constant buffer to store constant term, or NULL nlinexprs buffer to store number of expressions that appear linearly, or NULL linexprs buffer to store pointer to array of expressions that appear linearly, or NULL lincoefs buffer to store pointer to array of coefficients of expressions that appear linearly, or NULL nquadexprs buffer to store number of expressions in quadratic terms, or NULL nbilinexprs buffer to store number of bilinear expressions terms, or NULL eigenvalues buffer to store pointer to array of eigenvalues of Q, or NULL eigenvectors buffer to store pointer to array of eigenvectors of Q, or NULL

Definition at line 4119 of file expr.c.

References SCIP_QuadExpr::constant, SCIP_QuadExpr::eigenvalues, SCIP_QuadExpr::eigenvectors, SCIP_QuadExpr::lincoefs, SCIP_QuadExpr::linexprs, SCIP_QuadExpr::nbilinexprterms, SCIP_QuadExpr::nlinexprs, SCIP_QuadExpr::nquadexprs, NULL, and SCIP_Expr::quaddata.

Referenced by checkConsQuadraticProblem(), computeApex(), computeIntercut(), computeMonoidalQuadCoefs(), computeMonoidalStrengthCoef(), computeRestrictionToLine(), computeRestrictionToRay(), computeVApexAndVRay(), computeWRayLinear(), constructLPPos2ConsPosMap(), countBasicVars(), createMIP(), createTcliqueGraph(), DECL_CURVCHECK(), doSeachEcAggr(), findAndStoreEcAggregations(), findVertexAndGetRays(), generateIntercut(), intercutsComputeCommonQuantities(), isCandidate(), isPropagable(), isQuadConsViolated(), isRayInStrip(), nlrowaggrCreate(), presolveAddKKTQuadBilinearTerms(), presolveAddKKTQuadLinearTerms(), presolveAddKKTQuadQuadraticTerms(), printRow(), processNlRow(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRENFO(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRFREEEXPRDATA(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NONLINCONSUPGD(), SCIPevalExprQuadratic(), SCIPevalExprQuadraticAuxNonlinear(), SCIPprintExprQuadratic(), SCIPwriteMps(), searchEcAggrWithCliques(), storeAggrFromMIP(), storeDenseTableauRowsByColumns(), and updateMIP().

gives the data of a quadratic expression term

For a term \(a \cdot \text{expr}^2 + b \cdot \text{expr} + \sum_i (c_i \cdot \text{expr} \cdot \text{otherexpr}_i)\), returns expr, \(a\), \(b\), the number of summands, and indices of bilinear terms in the quadratic expressions bilinexprterms.

This function returns pointers to internal data in adjbilin. The user must not change this data.

Parameters

quadexpr quadratic expression termidx index of quadratic term expr buffer to store pointer to argument expression (the 'x') of this term, or NULL lincoef buffer to store linear coefficient of variable, or NULL sqrcoef buffer to store square coefficient of variable, or NULL nadjbilin buffer to store number of bilinear terms this variable is involved in, or NULL adjbilin buffer to store pointer to indices of associated bilinear terms, or NULL sqrexpr buffer to store pointer to square expression (the 'x^2') of this term or NULL if no square expression, or NULL

Definition at line 4164 of file expr.c.

References SCIP_QuadExpr_QuadTerm::adjbilin, SCIP_QuadExpr_QuadTerm::expr, SCIP_QuadExpr_QuadTerm::lincoef, SCIP_QuadExpr_QuadTerm::nadjbilin, NULL, SCIP_Expr::quaddata, SCIP_QuadExpr::quadexprterms, SCIP_QuadExpr_QuadTerm::sqrcoef, and SCIP_QuadExpr_QuadTerm::sqrexpr.

Referenced by constructLPPos2ConsPosMap(), countBasicVars(), createMIP(), createTcliqueGraph(), DECL_CURVCHECK(), doSeachEcAggr(), findVertexAndGetRays(), intercutsComputeCommonQuantities(), isCandidate(), isPropagable(), isPropagableTerm(), isQuadConsViolated(), nlrowaggrCreate(), presolveAddKKTQuadLinearTerms(), presolveAddKKTQuadQuadraticTerms(), printRow(), processNlRow(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NONLINCONSUPGD(), SCIPevalExprQuadratic(), SCIPevalExprQuadraticAuxNonlinear(), SCIPprintExprQuadratic(), SCIPwriteMps(), searchEcAggrWithCliques(), storeAggrFromMIP(), storeDenseTableauRowsByColumns(), and updateMIP().

gives the data of a bilinear expression term

For a term a*expr1*expr2, returns expr1, expr2, a, and the position of the quadratic expression term that uses expr2 in the quadratic expressions quadexprterms.

Parameters

expr quadratic expression termidx index of bilinear term expr1 buffer to store first factor, or NULL expr2 buffer to store second factor, or NULL coef buffer to coefficient, or NULL pos2 buffer to position of expr2 in quadexprterms array of quadratic expression, or NULL prodexpr buffer to store pointer to expression that is product if first and second factor, or NULL

Definition at line 4204 of file expr.c.

References SCIP_QuadExpr::bilinexprterms, SCIP_QuadExpr_BilinTerm::coef, SCIP_QuadExpr_BilinTerm::expr1, SCIP_QuadExpr_BilinTerm::expr2, NULL, SCIP_QuadExpr_BilinTerm::pos2, SCIP_QuadExpr_BilinTerm::prodexpr, and SCIP_Expr::quaddata.

Referenced by createMIP(), createTcliqueGraph(), isCandidate(), isQuadConsViolated(), nlrowaggrCreate(), presolveAddKKTQuadBilinearTerms(), printRow(), processNlRow(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_NONLINCONSUPGD(), SCIPevalExprQuadratic(), SCIPevalExprQuadraticAuxNonlinear(), SCIPprintExprQuadratic(), SCIPwriteMps(), searchEcAggrWithCliques(), storeAggrFromMIP(), and updateMIP().

gets the variable of a variable expression

Parameters

Definition at line 416 of file expr_var.c.

References EXPRHDLR_NAME, NULL, SCIPexprGetData(), SCIPexprGetHdlr(), and SCIPexprhdlrGetName().

Referenced by addSymmetryInformation(), analyzeViolation(), buildQuadExprMatrix(), catchVarEvent(), catchVarEvents(), checkAndCollectQuadratic(), collectBranchingCandidates(), collectLeafs(), computeGradient(), computeOffValues(), createMIP(), createNlRow(), createTcliqueGraph(), detectSocNorm(), detectSocQuadraticSimple(), doSeachEcAggr(), dropVarEvent(), enforceConstraints(), estimateConvexSecant(), estimateGradient(), estimateGradientInner(), estimateVertexPolyhedral(), exprIsSemicontinuous(), findUnlockedLinearVar(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), generateCut(), getBilinearBinaryTerms(), getBinaryProductExpr(), getBinaryProductExprDo(), isBinaryProduct(), isCandidate(), isPackingCons(), isSingleLockedCand(), nlpAddNlRows(), nlpDelVarPos(), nlrowaggrCreate(), notifyNlhdlrNewsol(), presolveAddKKTQuadBilinearTerms(), presolveAddKKTQuadLinearTerms(), presolveAddKKTQuadQuadraticTerms(), presolveImplint(), presolveRedundantConss(), presolveSingleLockedVars(), printExpr(), printRow(), printSignomial(), processNlRow(), propagateLocks(), readConstraints(), readObjective(), registerBranchingCandidates(), registerBranchingCandidatesAllUnfixed(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_CONSGETVARS(), SCIP_DECL_EXPR_MAPEXPR(), SCIP_DECL_EXPR_OWNERCREATE(), SCIP_DECL_EXPR_OWNERFREE(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRCOPYDATA(), SCIP_DECL_EXPREVAL(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRHASH(), SCIP_DECL_EXPRINTEGRALITY(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRPRINT(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NONLINCONSUPGD(), SCIP_DECL_VERTEXPOLYFUN(), SCIPaddNlRowGradientBenderscutOpt(), SCIPevalExprQuadratic(), SCIPexprComputeQuadraticCurvature(), SCIPexprDismantle(), SCIPgetExprAuxVarNonlinear(), SCIPisSOCNonlinear(), SCIPnlpGetVarsNonlinearity(), SCIPnlpHasContinuousNonlinearity(), SCIPwriteMps(), storeVarExprs(), tryAddGadgetBilinearProductSignedPerm(), tryAddGadgetEvenOperatorSum(), tryAddGadgetEvenOperatorVariable(), and tryAddGadgetSquaredDifference().

gets the value of a constant value expression

Parameters

Definition at line 294 of file expr_value.c.

References NULL, and SCIPexprGetData().

Referenced by addSymmetryInformation(), canonicalizeConstraints(), eval(), nlrowSimplifyExpr(), AMPLProblemHandler::OnBinary(), AMPLProblemHandler::OnObj(), parseExpr(), presolveRedundantConss(), printSignomial(), readExpression(), SCIP_DECL_EXPRSIMPLIFY(), SCIPexprDismantle(), simplifyFactor(), and simplifyTerm().

gets the coefficients of a summation expression

Parameters

Definition at line 1552 of file expr_sum.c.

References NULL, and SCIPexprGetData().

Referenced by addSymmetryInformation(), buildQuadExprMatrix(), createNlRow(), DECL_CURVCHECK(), detectExpr(), detectSocNorm(), detectSocQuadraticSimple(), enforceSP12(), enforceSP12b(), eval(), findUnlockedLinearVar(), getFactorizedBinaryQuadraticExpr(), presolveImplint(), presolveSingleLockedVars(), printRowNl(), readConstraints(), readObjective(), scaleConsSides(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NONLINCONSUPGD(), SCIPexprCheckQuadratic(), SCIPexprCompare(), SCIPexprDismantle(), SCIPmultiplyBySumExprSum(), SCIPpowerExprSum(), simplifyFactor(), simplifyTerm(), transformExpr(), tryAddGadgetEvenOperatorSum(), and tryAddGadgetSquaredDifference().

gets the constant of a summation expression

Parameters

Definition at line 1567 of file expr_sum.c.

References NULL, and SCIPexprGetData().

Referenced by addSymmetryInformation(), createNlRow(), DECL_CURVCHECK(), detectExpr(), detectSocNorm(), detectSocQuadraticComplex(), detectSocQuadraticSimple(), enforceSP12(), enforceSP12b(), eval(), getFactorizedBinaryQuadraticExpr(), presolveImplint(), printRowNl(), readConstraints(), readObjective(), scaleConsSides(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NONLINCONSUPGD(), SCIPexprCheckQuadratic(), SCIPexprDismantle(), SCIPmultiplyBySumExprSum(), SCIPpowerExprSum(), simplifyFactor(), simplifyTerm(), transformExpr(), and tryAddGadgetEvenOperatorSum().

gets the constant coefficient of a product expression

Parameters

Definition at line 2301 of file expr_product.c.

References exprnode::expr, NULL, and SCIPexprGetData().

Referenced by DECL_CURVCHECK(), detectExpr(), eval(), getFeasiblePointsBilinear(), intevalBilinear(), isBinaryProduct(), printSignomial(), reversePropBilinear(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRGETSYMDATA(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLREVALAUX(), SCIPexprCheckQuadratic(), SCIPexprDismantle(), SCIPexprGetMonomialData(), and simplifyFactor().

gets the exponent of a power or signed power expression

Parameters

Definition at line 3456 of file expr_pow.c.

References NULL, and SCIPexprGetData().

Referenced by bilinearTermsInsertAll(), buildQuadExprMatrix(), checkAndCollectQuadratic(), DECL_CURVCHECK(), detectExpr(), detectMinors(), detectSocNorm(), detectSocQuadraticSimple(), eval(), evalSignPower(), isPackingCons(), mergeProductExprlist(), presolveSingleLockedVars(), printExpr(), printSignomial(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRESTIMATE(), SCIP_DECL_EXPREVAL(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRINTEGRALITY(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_EXPRPRINT(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLREVALAUX(), SCIPexprCheckQuadratic(), SCIPexprCompare(), SCIPexprDismantle(), SCIPexprGetMonomialData(), and SCIPexprintCompile().

initializes an expression iterator

Note

If expr is NULL, then iterator will be set into ended-state (SCIPexpriterIsEnd() is TRUE). Useful if following with SCIPexpriterRestartDFS().

If type is DFS, then stopstages will be set to SCIP_EXPRITER_ENTEREXPR. Use SCIPexpriterSetStagesDFS to change this.

Parameters

iterator expression iterator expr expression of the iterator, can be NULL type type of expression iterator allowrevisit whether expression are allowed to be visited more than once

Definition at line 501 of file expriter.c.

References SCIP_ExprIter::curr, deinit(), SCIP_ExprIter::dfsstage, ensureStackSize(), SCIP_Stat::exprlastvisitedtag, SCIP_ExprIter::initialized, SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, MINBFSSIZE, MINDFSSIZE, SCIP_Stat::nactiveexpriter, NULL, printBacktraces(), SCIP_ExprIter::queue, reverseTopologicalInsert(), SCIP_CALL, SCIP_EXPRITER_BFS, SCIP_EXPRITER_DFS, SCIP_EXPRITER_ENTEREXPR, SCIP_EXPRITER_MAXNACTIVE, SCIP_EXPRITER_RTOPOLOGIC, SCIP_MAXDEPTHLEVEL, SCIP_OKAY, SCIPerrorMessage, SCIPexpriterGetNext(), SCIPqueueClear(), SCIPqueueCreate(), SCIPqueueInsert(), SCIP_ExprIter::stat, SCIP_ExprIter::stopstages, storeBacktrace, SCIP_Stat::subscipdepth, TRUE, and SCIP_ExprIter::visitedtag.

Referenced by addExprViolScoresAuxVars(), addSymmetryInformation(), analyzeViolation(), bilinearTermsInsertAll(), canonicalizeConstraints(), collectBranchingCandidates(), collectLeafs(), computeGradient(), computeOffValues(), constructExpr(), createNlhdlrExprData(), deinitSolve(), detectMinors(), detectNlhdlrs(), enforceConstraints(), evalAndDiff(), exprIsNonSmooth(), exprIsSemicontinuous(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), generateCut(), initSepa(), nlpAddNlRows(), nlpDelVarPos(), notifyNlhdlrNewsol(), presolveBinaryProducts(), presolveSingleLockedVars(), printExpr(), processNlRow(), propagateLocks(), propConss(), propExprDomains(), registerBranchingCandidates(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_TABLEOUTPUT(), SCIPaddExprsViolScoreNonlinear(), SCIPaddNlRowGradientBenderscutOpt(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPcreateNlpiProblemFromNlRows(), SCIPexprCopy(), SCIPexprDismantle(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprintCompile(), SCIPexprPrint(), SCIPexprPrintDot(), SCIPexprRelease(), SCIPexprSimplify(), SCIPgetExprNVars(), SCIPgetExprVarExprs(), SCIPhashExpr(), SCIPmarkExprPropagateNonlinear(), SCIPnlpGetVarsNonlinearity(), SCIPnlpHasContinuousNonlinearity(), SCIPnlpiOracleDelVarSet(), SCIPnlpiOracleGetJacobianSparsity(), SCIPregisterExprUsageNonlinear(), SCIPreplaceCommonSubexpressions(), and updateVariableCounts().

restarts an already initialized expression iterator in DFS mode

The expression iterator will continue from the given expression, not revisiting expressions that this iterator has already been visited (if initialized with allowrevisit=FALSE) and giving access to the same iterator specified expression data that may have been set already. Also the stop-stages are not reset.

If revisiting is forbidden and given expr has already been visited, then the iterator will behave as on the end of iteration (SCIPexpriterIsEnd() is TRUE). If the enterexpr stage is not one of the stop stages, then the iterator will be moved forward (SCIPexpriterGetNext() is called).

Returns

The current expression.

Parameters

iterator expression iterator expr expression of the iterator

Definition at line 630 of file expriter.c.

References SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, SCIP_ExprIter::initialized, SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, NULL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_ENTEREXPR, SCIPexpriterGetNext(), SCIP_ExprIter::stopstages, and SCIP_ExprIter::visitedtag.

Referenced by analyzeViolation(), bilinearTermsInsertAll(), collectBranchingCandidates(), deinitSolve(), detectMinors(), detectNlhdlrs(), enforceConstraint(), forbidNonlinearVariablesMultiaggration(), hashExpr(), initSepa(), notifyNlhdlrNewsol(), propExprDomains(), registerBranchingCandidates(), removeSingleLockedVars(), replaceBinaryProducts(), SCIPaddExprsViolScoreNonlinear(), SCIPnlpHasContinuousNonlinearity(), and SCIPnlpiOracleGetJacobianSparsity().

specifies in which stages to stop a DFS iterator

Parameter stopstages should be a bitwise OR of different SCIP_EXPRITER_STAGE values

If the current stage is not one of the stopstages, then the iterator will be moved on.

Parameters

iterator expression iterator stopstages the stages in which to stop when iterating via DFS

Definition at line 664 of file expriter.c.

References SCIP_ExprIter::dfsstage, NULL, SCIPexpriterGetNext(), and SCIP_ExprIter::stopstages.

Referenced by addSymmetryInformation(), bilinearTermsInsertAll(), collectLeafs(), constructExpr(), createNlhdlrExprData(), deinitSolve(), detectMinors(), evalAndDiff(), forwardPropExpr(), notifyNlhdlrNewsol(), presolveBinaryProducts(), presolveSingleLockedVars(), printExpr(), propagateLocks(), SCIP_DECL_CONSACTIVE(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPexprCopy(), SCIPexprDismantle(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprPrint(), SCIPexprRelease(), SCIPexprSimplify(), SCIPhashExpr(), and SCIPreplaceCommonSubexpressions().

gets the current expression that the expression iterator points to

Parameters

iterator expression iterator

Definition at line 683 of file expriter.c.

References SCIP_ExprIter::curr, and NULL.

Referenced by addSymmetryInformation(), collectLeafs(), computeOffValues(), evalAndDiff(), exprIsSemicontinuous(), forwardPropExpr(), propagateLocks(), propConss(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_TABLEOUTPUT(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPexprEvalActivity(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprintCompile(), SCIPexprRelease(), SCIPexprSimplify(), and SCIPreplaceCommonSubexpressions().

gets the current stage that the expression iterator is in when using DFS

If the iterator has finished (SCIPexpriterIsEnd() is TRUE), then the stage is undefined.

Parameters

iterator expression iterator

Definition at line 696 of file expriter.c.

References SCIP_ExprIter::dfsstage, SCIP_ExprIter::itertype, NULL, and SCIP_EXPRITER_DFS.

Referenced by addSymmetryInformation(), forwardPropExpr(), hashExpr(), printExpr(), propagateLocks(), SCIPexprCopy(), SCIPexprDismantle(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprPrint(), SCIPexprRelease(), and SCIPexprSimplify().

gets the index of the child that the expression iterator considers when in DFS mode and stage SCIP_EXPRITER_VISITINGCHILD or SCIP_EXPRITER_VISITEDCHILD

Parameters

iterator expression iterator

Definition at line 707 of file expriter.c.

References SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, NULL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_VISITEDCHILD, and SCIP_EXPRITER_VISITINGCHILD.

Referenced by collectLeafs(), printExpr(), propagateLocks(), replaceBinaryProducts(), SCIP_DECL_CONSACTIVE(), SCIPexprDismantle(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprPrint(), SCIPexprRelease(), SCIPexprSimplify(), and SCIPreplaceCommonSubexpressions().

gets the child expression that the expression iterator considers when in DFS mode and stage SCIP_EXPRITER_VISITINGCHILD or SCIP_EXPRITER_VISITEDCHILD

Parameters

iterator expression iterator

Definition at line 721 of file expriter.c.

References SCIP_Expr::children, SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, SCIP_Expr::nchildren, NULL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_VISITEDCHILD, and SCIP_EXPRITER_VISITINGCHILD.

Referenced by collectLeafs(), constructExpr(), createNlhdlrExprData(), forwardPropExpr(), replaceBinaryProducts(), SCIP_DECL_CONSACTIVE(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprRelease(), SCIPexprSimplify(), and SCIPreplaceCommonSubexpressions().

gives the iterator specific user data of the current expressions current child

Note

The expression iterator mode must be in DFS mode and stage SCIP_EXPRITER_VISITINGCHILD or SCIP_EXPRITER_VISITEDCHILD

Parameters

iterator expression iterator

Definition at line 771 of file expriter.c.

References SCIP_Expr::children, SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, SCIP_Expr::nchildren, NULL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_VISITEDCHILD, and SCIP_EXPRITER_VISITINGCHILD.

Referenced by SCIPexprCopy(), and SCIPexprSimplify().

sets the iterator specific user data of a given expression

Note

The expression iterator mode must be DFS or another mode with allowrevisit=FALSE

Parameters

iterator expression iterator expr expression where to set iterator data userdata data to be stored in current child

Definition at line 822 of file expriter.c.

References SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, and NULL.

sets the iterator specific user data of the current expressions current child

Note

The expression iterator mode must be in DFS mode and stage SCIP_EXPRITER_VISITINGCHILD or SCIP_EXPRITER_VISITEDCHILD

Parameters

iterator expression iterator userdata data to be stored in current child

Definition at line 838 of file expriter.c.

References SCIP_Expr::children, SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, SCIP_Expr::nchildren, NULL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_VISITEDCHILD, and SCIP_EXPRITER_VISITINGCHILD.

Referenced by propagateLocks().

moves the iterator to the next expression according to the mode of the expression iterator

Returns

the next expression, if any, and NULL otherwise

Parameters

iterator expression iterator

Definition at line 858 of file expriter.c.

References SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, doBfsNext(), doDfsNext(), doReverseTopologicalNext(), SCIP_Expr::iterdata, SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, NULL, SCIP_EXPRITER_BFS, SCIP_EXPRITER_DFS, SCIP_EXPRITER_MAXNACTIVE, SCIP_EXPRITER_RTOPOLOGIC, SCIP_ExprIter::stopstages, and SCIP_ExprIter::visitedtag.

Referenced by addExprViolScoresAuxVars(), addSymmetryInformation(), analyzeViolation(), bilinearTermsInsertAll(), canonicalizeConstraints(), collectBranchingCandidates(), collectLeafs(), computeGradient(), computeOffValues(), constructExpr(), createNlhdlrExprData(), deinitSolve(), detectMinors(), detectNlhdlrs(), enforceConstraint(), evalAndDiff(), exprIsNonSmooth(), exprIsSemicontinuous(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), generateCut(), hashExpr(), initSepa(), nlpAddNlRows(), nlpDelVarPos(), notifyNlhdlrNewsol(), printExpr(), processNlRow(), propagateLocks(), propConss(), propExprDomains(), registerBranchingCandidates(), removeSingleLockedVars(), replaceBinaryProducts(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_TABLEOUTPUT(), SCIPaddExprsViolScoreNonlinear(), SCIPaddNlRowGradientBenderscutOpt(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPcreateNlpiProblemFromNlRows(), SCIPexprCopy(), SCIPexprDismantle(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprintCompile(), SCIPexpriterInit(), SCIPexpriterRestartDFS(), SCIPexpriterSetStagesDFS(), SCIPexpriterSkipDFS(), SCIPexprPrint(), SCIPexprPrintDot(), SCIPexprRelease(), SCIPexprSimplify(), SCIPgetExprNVars(), SCIPgetExprVarExprs(), SCIPmarkExprPropagateNonlinear(), SCIPnlpGetVarsNonlinearity(), SCIPnlpHasContinuousNonlinearity(), SCIPnlpiOracleDelVarSet(), SCIPnlpiOracleGetJacobianSparsity(), SCIPregisterExprUsageNonlinear(), SCIPreplaceCommonSubexpressions(), and updateVariableCounts().

moves a DFS iterator to one of the next expressions

• If in SCIP_EXPRITER_ENTEREXPR stage, then all children of that expression will be skipped. If SCIP_EXPRITER_LEAVEEXPR is one of the stopstages, then it will be the next stage. Otherwise, the iterator will move further on (go to the parent, etc).
• If in SCIP_EXPRITER_VISITINGCHILD stage, then the child that was going to be visited next will be skipped and the iterator will be moved on to the next child (if any).
• If in SCIP_EXPRITER_VISITEDCHILD stage, then all remaining children will be skipped and we move on to the SCIP_EXPRITER_LEAVEEXPR stage (if a stop stage, otherwise further on).
• It is not allowed to call this function when in SCIP_EXPRITER_LEAVEEXPR stage.

Returns

the next expression, if any, and NULL otherwise

Parameters

iterator expression iterator

Definition at line 930 of file expriter.c.

References SCIP_ExprIter::curr, SCIP_ExprIter::dfsstage, doDfsNext(), SCIP_ExprIter::iterindex, SCIP_ExprIter::itertype, NULL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_ENTEREXPR, SCIP_EXPRITER_LEAVEEXPR, SCIP_EXPRITER_VISITEDCHILD, SCIP_EXPRITER_VISITINGCHILD, SCIPABORT, SCIPerrorMessage, SCIPexpriterGetNext(), and SCIP_ExprIter::stopstages.

Referenced by constructExpr(), forwardPropExpr(), SCIPexprCopy(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprRelease(), and SCIPreplaceCommonSubexpressions().

returns whether the iterator visited all expressions already

Parameters

iterator expression iterator

Definition at line 969 of file expriter.c.

References SCIP_ExprIter::curr, and NULL.

Referenced by addExprViolScoresAuxVars(), addSymmetryInformation(), analyzeViolation(), bilinearTermsInsertAll(), canonicalizeConstraints(), collectBranchingCandidates(), collectLeafs(), computeGradient(), computeOffValues(), constructExpr(), createNlhdlrExprData(), deinitSolve(), detectMinors(), detectNlhdlrs(), enforceConstraint(), evalAndDiff(), exprIsNonSmooth(), exprIsSemicontinuous(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), generateCut(), hashExpr(), initSepa(), nlpAddNlRows(), nlpDelVarPos(), notifyNlhdlrNewsol(), printExpr(), processNlRow(), propagateLocks(), propConss(), propExprDomains(), registerBranchingCandidates(), removeSingleLockedVars(), replaceBinaryProducts(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_TABLEOUTPUT(), SCIPaddExprsViolScoreNonlinear(), SCIPaddNlRowGradientBenderscutOpt(), SCIPcomputeExprCurvature(), SCIPcomputeExprIntegrality(), SCIPcreateNlpiProblemFromNlRows(), SCIPexprCopy(), SCIPexprDismantle(), SCIPexprEval(), SCIPexprEvalActivity(), SCIPexprEvalGradient(), SCIPexprEvalHessianDir(), SCIPexprintCompile(), SCIPexprPrint(), SCIPexprPrintDot(), SCIPexprRelease(), SCIPexprSimplify(), SCIPgetExprNVars(), SCIPgetExprVarExprs(), SCIPmarkExprPropagateNonlinear(), SCIPnlpGetVarsNonlinearity(), SCIPnlpHasContinuousNonlinearity(), SCIPnlpiOracleDelVarSet(), SCIPnlpiOracleGetJacobianSparsity(), SCIPregisterExprUsageNonlinear(), SCIPreplaceCommonSubexpressions(), and updateVariableCounts().

gives curvature for a sum of two functions with given curvature

Parameters

curv1 curvature of first summand curv2 curvature of second summand

Definition at line 53 of file exprcurv.c.

gives curvature for base^exponent for given bounds and curvature of base-function and constant exponent

Parameters

basebounds bounds on base function basecurv curvature of base function exponent exponent

Definition at line 101 of file exprcurv.c.

References EPSISINT, SCIP_Interval::inf, SCIP_Bool, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_EXPRCURV_LINEAR, SCIP_EXPRCURV_UNKNOWN, SCIP_Real, SCIPexprcurvPower(), SCIPintervalSetBounds(), and SCIP_Interval::sup.

Referenced by SCIPexprcurvMonomial(), and SCIPexprcurvPower().

gives required curvature for base so that base^exponent has given curvature under given bounds on base and constant exponent

returns curvature unknown if expected curvature cannot be obtained

Parameters

basebounds bounds on base function exponent exponent, must not be 0 powercurv expected curvature for power

Definition at line 209 of file exprcurv.c.

References EPSISINT, SCIP_Interval::inf, SCIP_Bool, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_EXPRCURV_LINEAR, SCIP_EXPRCURV_UNKNOWN, SCIP_Real, SCIPexprcurvPowerInv(), SCIPintervalSetBounds(), and SCIP_Interval::sup.

Referenced by SCIP_DECL_EXPRCURVATURE(), SCIPexprcurvMonomialInv(), and SCIPexprcurvPowerInv().

gives curvature for a monomial with given curvatures and bounds for each factor

See Maranas and Floudas, Finding All Solutions of Nonlinearly Constrained Systems of Equations, JOGO 7, 1995 for the categorization in the case that all factors are linear.

Exponents can also be negative or rational.

Parameters

nfactors number of factors in monomial exponents exponents in monomial, or NULL if all 1.0 factoridxs indices of factors (but not exponents), or NULL if identity mapping factorcurv curvature of each factor factorbounds bounds of each factor

Definition at line 331 of file exprcurv.c.

References EPSGE, EPSISINT, EPSLE, FALSE, SCIP_Interval::inf, NULL, SCIP_Bool, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_EXPRCURV_LINEAR, SCIP_EXPRCURV_UNKNOWN, SCIP_Real, SCIPexprcurvMultiply(), SCIPexprcurvNegate(), SCIPexprcurvPower(), SCIP_Interval::sup, and TRUE.

for a monomial with given bounds for each factor, gives condition on the curvature of each factor, so that monomial has a requested curvature, if possible

Returns

whether monomialcurv can be achieved

Parameters

monomialcurv desired curvature nfactors number of factors in monomial exponents exponents in monomial, or NULL if all 1.0 factorbounds bounds of each factor factorcurv buffer to store required curvature of each factor

Definition at line 457 of file exprcurv.c.

References EPSGE, EPSISINT, EPSLE, FALSE, SCIP_Interval::inf, NULL, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_EXPRCURV_LINEAR, SCIP_EXPRCURV_UNKNOWN, SCIP_Real, SCIPexprcurvNegate(), SCIPexprcurvPowerInv(), SCIP_Interval::sup, and TRUE.

Referenced by DECL_CURVCHECK().

creates and captures an expression with given expression data and children

Parameters

scip SCIP data structure expr pointer where to store expression exprhdlr expression handler exprdata expression data (expression assumes ownership) nchildren number of children children children (can be NULL if nchildren is 0) ownercreatedata data to pass to ownercreate

Definition at line 981 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprCreate().

Referenced by SCIPcreateExpr2(), SCIPcreateExprAbs(), SCIPcreateExprCos(), SCIPcreateExprEntropy(), SCIPcreateExprErf(), SCIPcreateExprExp(), SCIPcreateExprLog(), SCIPcreateExprPow(), SCIPcreateExprProduct(), SCIPcreateExprSignpower(), SCIPcreateExprSin(), SCIPcreateExprSum(), SCIPcreateExprValue(), SCIPcreateExprVar(), and SCIPcreateExprVaridx().

creates and captures an expression with given expression data and up to two children

Parameters

scip SCIP data structure expr pointer where to store expression exprhdlr expression handler exprdata expression data child1 first child (can be NULL) child2 second child (can be NULL) ownercreatedata data to pass to ownercreate

Definition at line 1002 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPcreateExpr().

creates and captures an expression representing a quadratic function

Parameters

scip SCIP data structure expr pointer where to store expression nlinvars number of linear terms linvars array with variables in linear part lincoefs array with coefficients of variables in linear part nquadterms number of quadratic terms quadvars1 array with first variables in quadratic terms quadvars2 array with second variables in quadratic terms quadcoefs array with coefficients of quadratic terms ownercreatedata data to pass to ownercreate

Definition at line 1040 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPallocBufferArray, SCIPcreateExprPow(), SCIPcreateExprProduct(), SCIPcreateExprSum(), SCIPcreateExprVar(), SCIPfreeBufferArray, and SCIPreleaseExpr().

Referenced by createConstraint(), readExpression(), and SCIPcreateConsQuadraticNonlinear().

creates and captures an expression representing a monomial

Note

In deviation from the actual definition of monomials, we also allow for negative and rational exponents. So this function actually creates an expression for a signomial that has exactly one term.

Parameters

scip SCIP data structure expr pointer where to store expression nfactors number of factors in monomial vars variables in the monomial exponents exponent in each factor, or NULL if all 1.0 ownercreatedata data to pass to ownercreate

Definition at line 1148 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPallocBufferArray, SCIPcreateExprPow(), SCIPcreateExprProduct(), SCIPcreateExprValue(), SCIPcreateExprVar(), SCIPfreeBufferArray, and SCIPreleaseExpr().

Referenced by readPolynomial().

duplicates the given expression and its children

Parameters

scip SCIP data structure expr original expression copyexpr buffer to store duplicate of expr mapexprdata data of expression mapping function ownercreatedata data to pass to ownercreate

Definition at line 1288 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprCopy().

Referenced by createCons(), SCIP_DECL_CONSTRANS(), SCIP_DECL_EXPRSIMPLIFY(), SCIPaddExprNonlinear(), SCIPaddNlpiProblemNlRows(), SCIPchgExprNonlinear(), SCIPcreateNlpiProblemFromNlRows(), and SCIPwritePip().

copies an expression including children to use in a (possibly different) SCIP instance

Parameters

sourcescip source SCIP data structure targetscip target SCIP data structure expr original expression copyexpr buffer to store duplicate of expr ownercreatedata data to pass to ownercreate varmap a SCIP_HASHMAP mapping variables of the source SCIP to the corresponding variables of the target SCIP, or NULL consmap a hashmap to store the mapping of source constraints to the corresponding target constraints, or NULL global create a global or a local copy? valid pointer to store whether all checked or enforced constraints were validly copied

Definition at line 1325 of file scip_expr.c.

References COPY_MAPEXPR_DATA::consmap, COPY_MAPEXPR_DATA::global, Scip::mem, NULL, SCIP_Mem::probmem, SCIP_CALL, SCIP_OKAY, SCIPexprCopy(), Scip::set, Scip::stat, TRUE, COPY_MAPEXPR_DATA::valid, and COPY_MAPEXPR_DATA::varmap.

Referenced by SCIP_DECL_CONSCOPY().

creates an expression from a string

We specify the grammar that defines the syntax of an expression. Loosely speaking, a Base will be any "block", a Factor is a Base to a power, a Term is a product of Factors and an Expression is a sum of Terms.

The actual definition:

Expression -> ["+" | "-"] Term { [ ("+" | "-" | "number *") Term | ("number" <varname>) ] }

Term -> Factor { ("*" | "/" ) Factor }

Factor -> Base [ "^" "number" | "^(" "number" ")" ]

Base -> "number" | "<varname>" | "(" Expression ")" | Op "(" OpExpression ")

where [a|b] means a or b or none, (a|b) means a or b, {a} means 0 or more a.

Note that Op and OpExpression are undefined. Op corresponds to the name of an expression handler and OpExpression to whatever string the expression handler accepts (through its parse method).

Parameters

scip SCIP data structure expr pointer to store the expr parsed exprstr string with the expr to parse finalpos buffer to store the position of exprstr where we finished reading, or NULL if not of interest ownercreatedata data to pass to ownercreate

Definition at line 1387 of file scip_expr.c.

References NULL, parseExpr(), SCIP_CALL, SCIPblkmem(), SCIPgetNVars(), SCIPhashmapCreate(), and SCIPhashmapFree().

Referenced by SCIP_DECL_CONSPARSE(), and SCIP_DECL_EXPRPARSE().

captures an expression (increments usage count)

Parameters

expr expression to be captured

Definition at line 1416 of file scip_expr.c.

References SCIPexprCapture().

Referenced by createCons(), createConstraint(), createExprNode(), createExprVar(), enforceSP10(), exprdataCreate(), getBinaryProductExpr(), initBounds(), nlhdlrExprCreate(), readExpression(), scaleConsSides(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIPgetExprVarExprs(), and SCIPnlpiOracleChgExpr().

releases an expression (decrements usage count and possibly frees expression)

Parameters

scip SCIP data structure expr pointer to expression to be released

Definition at line 1424 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprRelease().

Referenced by addNlrow(), addRegularScholtes(), AMPLProblemHandler::LinearExprHandler::AddTerm(), buildSimplifiedProduct(), canonicalizeConstraints(), AMPLProblemHandler::cleanup(), collectLeafs(), computeOffValues(), constructExpr(), createConstraint(), createNlRow(), createSOCExpression(), enforceSP10(), enforceSP11(), enforceSP12(), enforceSP12b(), exprdataFree(), freeConstraint(), freeExprNode(), freeVarExprs(), getBinaryProductExpr(), getFactorizedBinaryQuadraticExpr(), mergeProductExprlist(), nlhdlrExprGrowChildren(), AMPLProblemHandler::OnBinary(), AMPLProblemHandler::OnHeader(), AMPLProblemHandler::OnUnary(), parseBase(), parseExpr(), parseFactor(), parseTerm(), presolveBinaryProducts(), readConstraints(), readExpression(), readObjective(), readPolynomial(), replaceBinaryProducts(), scaleConsSides(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_CONSCOPY(), SCIP_DECL_CONSDELETE(), SCIP_DECL_CONSINITSOL(), SCIP_DECL_CONSPARSE(), SCIP_DECL_CONSTRANS(), SCIP_DECL_EXPRPARSE(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRFREEEXPRDATA(), SCIP_DECL_PROPEXITSOL(), SCIP_DECL_READERREAD(), SCIPaddBilinTermQuadratic(), SCIPaddExprNonlinear(), SCIPaddLinearVarNonlinear(), SCIPaddNlpiProblemNlRows(), SCIPaddQuadVarQuadratic(), SCIPaddSquareCoefQuadratic(), SCIPchgExprNonlinear(), SCIPcreateConsBasicSignpowerNonlinear(), SCIPcreateConsBasicSOC(), SCIPcreateConsBasicSOCNonlinear(), SCIPcreateConsQuadraticNonlinear(), SCIPcreateConsSOC(), SCIPcreateExprMonomial(), SCIPcreateExprQuadratic(), SCIPcreateNlpiProblemFromNlRows(), SCIPhasExprCurvature(), SCIPmultiplyBySumExprSum(), SCIPnlpiOracleChgExpr(), SCIPnlpiOracleDelVarSet(), SCIPpowerExprSum(), SCIPreplaceCommonSubexpressions(), SCIPwritePip(), setQuadraticObj(), setupProblem(), and simplifyTerm().

returns whether an expression is a variable expression

Parameters

scip SCIP data structure expr expression

Definition at line 1438 of file scip_expr.c.

References NULL, and SCIPexprIsVar().

Referenced by addSymmetryInformation(), analyzeViolation(), buildQuadExprMatrix(), catchVarEvent(), catchVarEvents(), checkAndCollectQuadratic(), collectLeafs(), computeGradient(), computeOffValues(), constructExpr(), createAuxVar(), createNlRow(), detectSocNorm(), detectSocQuadraticSimple(), doSeachEcAggr(), dropVarEvent(), exprIsSemicontinuous(), findUnlockedLinearVar(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), generateCut(), getNLPVarsNonConvexity(), isBinaryProduct(), isCandidate(), isExprSignomial(), isPackingCons(), isSingleLockedCand(), nlrowaggrCreate(), presolveAddKKTQuadBilinearTerms(), presolveAddKKTQuadLinearTerms(), presolveAddKKTQuadQuadraticTerms(), presolveImplint(), presolveRedundantConss(), presolveSingleLockedVars(), printExpr(), printRow(), printSignomial(), processNlRow(), propagateLocks(), readConstraints(), readObjective(), removeSingleLockedVars(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_EVENTEXEC(), SCIP_DECL_EXPR_MAPEXPR(), SCIP_DECL_EXPR_OWNERCREATE(), SCIP_DECL_EXPR_OWNERFREE(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NONLINCONSUPGD(), SCIPaddExprsViolScoreNonlinear(), SCIPaddExprViolScoreNonlinear(), SCIPaddNlRowGradientBenderscutOpt(), SCIPexprintCompile(), SCIPgetExprPartialDiffGradientDirNonlinear(), SCIPgetExprPartialDiffNonlinear(), SCIPisSOCNonlinear(), SCIPmarkExprPropagateNonlinear(), SCIPregisterExprUsageNonlinear(), SCIPwriteMps(), tryAddGadgetBilinearProductSignedPerm(), tryAddGadgetEvenOperator(), tryAddGadgetEvenOperatorSum(), tryAddGadgetEvenOperatorVariable(), and tryAddGadgetSquaredDifference().

returns whether an expression is a value expression

Parameters

scip SCIP data structure expr expression

Definition at line 1449 of file scip_expr.c.

References NULL, and SCIPexprIsValue().

Referenced by addSymmetryInformation(), canonicalizeConstraints(), constructExpr(), createAuxVar(), eval(), isExprSignomial(), mergeProductExprlist(), AMPLProblemHandler::OnBinary(), AMPLProblemHandler::OnObj(), presolveRedundantConss(), printExpr(), printSignomial(), readExpression(), SCIP_DECL_EXPRBWDIFF(), SCIP_DECL_EXPRBWFWDIFF(), SCIP_DECL_EXPRFWDIFF(), SCIP_DECL_EXPRSIMPLIFY(), SCIPexprintCompile(), SCIPgetExprPartialDiffGradientDirNonlinear(), SCIPgetExprPartialDiffNonlinear(), simplifyFactor(), simplifyTerm(), and tryAddGadgetEvenOperator().

returns whether an expression is a sum expression

Parameters

scip SCIP data structure expr expression

Definition at line 1460 of file scip_expr.c.

References NULL, and SCIPexprIsSum().

Referenced by addSymmetryInformation(), computeOffValues(), constructExpr(), createConstraint(), createNlRow(), DECL_CURVCHECK(), detectExpr(), detectSocNorm(), detectSocQuadraticComplex(), detectSocQuadraticSimple(), enforceSP12(), enforceSP12b(), eval(), exprIsMultivarLinear(), exprIsSemicontinuous(), findUnlockedLinearVar(), forbidNonlinearVariablesMultiaggration(), getBilinearBinaryTerms(), getFactorizedBinaryQuadraticExpr(), isExprPolynomial(), isPackingCons(), presolveImplint(), presolveSingleLockedVars(), printExpr(), printRowNl(), scaleConsSides(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIP_DECL_NONLINCONSUPGD(), SCIPaddExprNonlinear(), SCIPaddLinearVarNonlinear(), SCIPappendExprSumExpr(), SCIPexprintCompile(), SCIPmultiplyBySumExprSum(), SCIPpowerExprSum(), simplifyFactor(), simplifyTerm(), transformExpr(), tryAddGadgetEvenOperator(), tryAddGadgetEvenOperatorSum(), and tryAddGadgetSquaredDifference().

returns whether an expression is a product expression

Parameters

scip SCIP data structure expr expression

Definition at line 1471 of file scip_expr.c.

References NULL, and SCIPexprIsProduct().

Referenced by addSymmetryInformation(), bilinearTermsInsertAll(), buildQuadExprMatrix(), checkAndCollectQuadratic(), DECL_CURVCHECK(), detectExpr(), detectMinors(), detectSocQuadraticSimple(), eval(), getBinaryProductExprDo(), isBinaryProduct(), isExprSignomial(), isPackingCons(), presolveSingleLockedVars(), printExpr(), printSignomial(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLREVALAUX(), SCIPexprintCompile(), simplifyFactor(), simplifyTerm(), tryAddGadgetBilinearProductSignedPerm(), and tryAddGadgetSquaredDifference().

returns whether an expression is a power expression

Parameters

scip SCIP data structure expr expression

Definition at line 1482 of file scip_expr.c.

References NULL, and SCIPexprIsPower().

Referenced by bilinearTermsInsertAll(), buildQuadExprMatrix(), checkAndCollectQuadratic(), DECL_CURVCHECK(), detectExpr(), detectMinors(), detectSocNorm(), detectSocQuadraticSimple(), eval(), isEvenOperator(), isExprSignomial(), isPackingCons(), mergeProductExprlist(), presolveSingleLockedVars(), printExpr(), printSignomial(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLREVALAUX(), SCIPexprintCompile(), and tryAddGadgetSquaredDifference().

print an expression as info-message

Parameters

scip SCIP data structure expr expression to be printed file file to print to, or NULL for stdout

Definition at line 1493 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprPrint().

Referenced by analyzeViolation(), constructExpr(), createNlhdlrExprData(), DECL_CURVCHECK(), detectExpr(), detectSocNorm(), detectSocQuadraticComplex(), detectSocQuadraticSimple(), enforceConstraint(), enforceExpr(), enforceSP12(), estimateConvexSecant(), estimateGradient(), estimateVertexPolyhedral(), forwardPropExpr(), generateIntercut(), printFunction(), propagateBoundsLinExpr(), propagateBoundsQuadExpr(), readPolynomial(), reversePropQueue(), SCIP_DECL_CONSPRINT(), SCIP_DECL_EXPRINITESTIMATES(), SCIP_DECL_EXPRINTEVAL(), SCIP_DECL_EXPRREVERSEPROP(), SCIP_DECL_EXPRSIMPLIFY(), SCIP_DECL_NLHDLRDETECT(), SCIP_DECL_NLHDLRENFO(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRINITSEPA(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIPexprEvalActivity(), SCIPexprintGrad(), SCIPexprintHessian(), SCIPexprintHessianSparsity(), SCIPpowerExprSum(), SCIPprintExprQuadratic(), SCIPtightenExprIntervalNonlinear(), and simplifyMultiplyChildren().

initializes printing of expressions in dot format to a give FILE* pointer

Parameters

scip SCIP data structure printdata buffer to store dot printing data file file to print to, or NULL for stdout whattoprint info on what to print for each expression

Definition at line 1508 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprPrintDotInit().

Referenced by SCIPshowExpr().

initializes printing of expressions in dot format to a file with given filename

Parameters

scip SCIP data structure printdata buffer to store dot printing data filename name of file to print to whattoprint info on what to print for each expression

Definition at line 1524 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprPrintDotInit2().

shows a single expression by use of dot and gv

This function is meant for debugging purposes. It's signature is kept as simple as possible to make it easily callable from gdb, for example.

It prints the expression into a temporary file in dot format, then calls dot to create a postscript file, then calls ghostview (gv) to show the file. SCIP will hold until ghostscript is closed.

Parameters

scip SCIP data structure expr expression to be printed

Definition at line 1576 of file scip_expr.c.

References NULL, SCIP_CALL_TERMINATE, SCIP_ERROR, SCIP_EXPRPRINT_ALL, SCIP_FILECREATEERROR, SCIP_OKAY, SCIPerrorMessage, SCIPprintExprDot(), SCIPprintExprDotFinal(), and SCIPprintExprDotInit().

evaluate an expression in a point

Iterates over expressions to also evaluate children, if necessary. Value can be received via SCIPexprGetEvalValue(). If an evaluation error (division by zero, ...) occurs, this value will be set to SCIP_INVALID.

If a nonzero soltag is passed, then only (sub)expressions are reevaluated that have a different solution tag. If a soltag of 0 is passed, then subexpressions are always reevaluated. The tag is stored together with the value and can be received via SCIPexprGetEvalTag().

Parameters

scip SCIP data structure expr expression to be evaluated sol solution to be evaluated soltag tag that uniquely identifies the solution (with its values), or 0.

Definition at line 1642 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprEval().

Referenced by computeOffValues(), computeViolation(), AMPLProblemHandler::EndInput(), enforceExpr(), estimateConvexSecant(), initSepa(), notifyNlhdlrNewsol(), SCIP_DECL_NLHDLREVALAUX(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIP_DECL_VERTEXPOLYFUN(), SCIPexprintEval(), SCIPgetExprAbsOrigViolationNonlinear(), and SCIPgetExprActivityNonlinear().

evaluates gradient of an expression for a given point

Initiates an expression walk to also evaluate children, if necessary. Value can be received via SCIPgetExprPartialDiffNonlinear(). If an error (division by zero, ...) occurs, this value will be set to SCIP_INVALID.

Parameters

scip SCIP data structure expr expression to be differentiated sol solution to be evaluated (NULL for the current LP solution) soltag tag that uniquely identifies the solution (with its values), or 0.

Definition at line 1674 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprEvalGradient().

Referenced by computeGradient(), estimateGradientInner(), generateCut(), getConsRelViolation(), and SCIPaddNlRowGradientBenderscutOpt().

evaluates Hessian-vector product of an expression for a given point and direction

Evaluates children, if necessary. Value can be received via SCIPgetExprPartialDiffGradientDirNonlinear(). If an error (division by zero, ...) occurs, this value will be set to SCIP_INVALID.

Parameters

scip SCIP data structure expr expression to be differentiated sol solution to be evaluated (NULL for the current LP solution) soltag tag that uniquely identifies the solution (with its values), or 0. direction direction

Definition at line 1696 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprEvalHessianDir().

possibly reevaluates and then returns the activity of the expression

Reevaluate activity if currently stored is no longer uptodate (some bound was changed since last evaluation).

The owner of the expression may overwrite the methods used to evaluate the activity, including whether the local or global domain of variables is used. By default (no owner, or owner doesn't overwrite activity evaluation), the local domain of variables is used.

Note

If expression is set to be integral, then activities are tightened to integral values. Thus, ensure that the integrality information is valid (if set to TRUE; the default (FALSE) is always ok).

Parameters

scip SCIP data structure expr expression

Definition at line 1724 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprEvalActivity().

Referenced by checkSubproblemConvexity(), DECL_CURVCHECK(), deinitSolve(), detectSocQuadraticComplex(), detectSocQuadraticSimple(), estimateBivariateQuotient(), estimateUnivariateQuotient(), initSepa(), SCIP_DECL_EXPRCURVATURE(), SCIP_DECL_EXPRMONOTONICITY(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRINITSEPA(), SCIPregisterExprUsageNonlinear(), and tryFillNlhdlrExprDataQuad().

compare expressions

Returns

-1, 0 or 1 if expr1 <, =, > expr2, respectively

Note

The given expressions are assumed to be simplified.

Parameters

scip SCIP data structure expr1 first expression expr2 second expression

Definition at line 1741 of file scip_expr.c.

References NULL, and SCIPexprCompare().

Referenced by DECL_CURVCHECK(), enforceSP11(), mergeProductExprlist(), SCIP_DECL_EXPRCOMPARE(), SCIP_DECL_EXPRSIMPLIFY(), and SCIP_DECL_SORTINDCOMP().

compute the hash value of an expression

Parameters

scip SCIP data structure expr expression hashval pointer to store the hash value

Definition at line 1753 of file scip_expr.c.

References FALSE, hashExpr(), NULL, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_LEAVEEXPR, SCIP_OKAY, SCIPexpriterCreate(), SCIPexpriterFree(), SCIPexpriterGetExprUserData(), SCIPexpriterInit(), SCIPexpriterSetStagesDFS(), and SCIP_EXPRITER_USERDATA::uintval.

simplifies an expression

This is largely inspired by Joel Cohen's Computer algebra and symbolic computation: Mathematical methods, in particular Chapter 3. The other fountain of inspiration are the simplifying methods of expr.c in SCIP 7.

Note: The things to keep in mind when adding simplification rules are the following. I will be using the product expressions (see expr_product.c) as an example. There are mainly 3 parts of the simplification process. You need to decide at which stage the simplification rule makes sense.

1. Simplify each factor (simplifyFactor()): At this stage we got the children of the product expression. At this point, each child is simplified when viewed as a stand-alone expression, but not necessarily when viewed as child of a product expression. Rules like SP2, SP7, etc are enforced at this point.
2. Multiply the factors (mergeProductExprlist()): At this point rules like SP4, SP5 and SP14 are enforced.
3. Build the actual simplified product expression (buildSimplifiedProduct()): At this point rules like SP10, SP11, etc are enforced.

During steps 1 and 2 do not forget to set the flag changed to TRUE when something actually changes.

Definition of simplified expressions

An expression is simplified if it

• is a value expression
• is a var expression
• is a product expression such that
  • SP1: every child is simplified
  • SP2: no child is a product
  • SP4: no two children are the same expression (those should be multiplied)
  • SP5: the children are sorted [commutative rule]
  • SP7: no child is a value
  • SP8: its coefficient is 1.0 (otherwise should be written as sum)
  • SP10: it has at least two children
  • TODO?: at most one child is an abs
  • SP11: no two children are expr*log(expr) (TODO: we could handle more complicated stuff like \(xy\log(x) \to - y * \mathrm{entropy}(x)\), but I am not sure this should happen at the simplification level; similar for \((xy) \log(xy)\), which currently simplifies to \(xy \log(xy)\))
  • SP12: if it has two children, then neither of them is a sum (expand sums)
  • SP12b: if it has at least two children and expandalways is set, then no child is a sum (expand sums always)
  • SP13: no child is a sum with a single term
  • SP14: at most one child is an exp
• is a power expression such that
  • POW1: exponent is not 0
  • POW2: exponent is not 1
  • POW3: its child is not a value
  • POW4: its child is simplified
  • POW5: if exponent is integer, its child is not a product
  • POW5a: if exponent is fractional and distribfracexponent param is enabled, its child is not a product
  • POW6: if exponent is integer, its child is not a sum with a single term ( \((2x)^2 \to 4x^2\))
  • POW7: if exponent is integer and at most expandmaxeponent param, its child is not a sum (expand sums)
  • POW8: its child is not a power unless \((x^n)^m\) with \(nm\) being integer and \(n\) or \(m\) fractional and \(n\) not being even integer
  • POW9: its child is not a sum with a single term with a positive coefficient: \((25x)^{0.5} \to 5 x^{0.5}\)
  • POW10: its child is not a binary variable: \(b^e, e > 0 \to b\); \(b^e, e < 0 \to b := 1\)
  • POW11: its child is not an exponential: \(\exp(\text{expr})^e \to \exp(e\cdot\text{expr})\)
  • POW12: its child is not an absolute value if the exponent is an even integer: \(\abs(\text{expr})^e, e \text{ even} \to \text{expr}^e\)

• is a signedpower expression such that

  • SPOW1: exponent is not 0
  • SPOW2: exponent is not 1
  • SPOW3: its child is not a value
  • SPOW4: its child is simplified
  • SPOW5: (TODO) do we want to distribute signpowers over products like we do for powers?
  • SPOW6: exponent is not an odd integer: (signpow odd expr) -> (pow odd expr)
  • SPOW8: if exponent is integer, its child is not a power
  • SPOW9: its child is not a sum with a single term: \(\mathrm{signpow}(25x,0.5) \to 5\mathrm{signpow}(x,0.5)\)
  • SPOW10: its child is not a binary variable: \(\mathrm{signpow}(b,e), e > 0 \to b\); \(\mathrm{signpow}(b,e), e < 0 \to b := 1\)
  • SPOW11: its child is not an exponential: \(\mathrm{signpow}(\exp(\text{expr}),e) \to \exp(e\cdot\text{expr})\)
  • TODO: what happens when child is another signed power?
  • TODO: if child ≥ 0 -> transform to normal power; if child < 0 -> transform to - normal power

  TODO: Some of these criteria are too restrictive for signed powers; for example, the exponent does not need to be an integer for signedpower to distribute over a product (SPOW5, SPOW6, SPOW8). Others can also be improved.

• is a sum expression such that
  • SS1: every child is simplified
  • SS2: no child is a sum
  • SS3: no child is a value (values should go in the constant of the sum)
  • SS4: no two children are the same expression (those should be summed up)
  • SS5: the children are sorted [commutative rule]
  • SS6: it has at least one child
  • SS7: if it consists of a single child, then either constant is != 0.0 or coef != 1
  • SS8: no child has coefficient 0
  • SS9: if a child c is a product that has an exponential expression as one of its factors, then the coefficient of c is +/-1.0
  • SS10: if a child c is an exponential, then the coefficient of c is +/-1.0
• it is a function with simplified arguments, but not all of them can be values
• TODO? a logarithm doesn't have a product as a child
• TODO? the exponent of an exponential is always 1

Ordering Rules (see SCIPexprCompare())

These rules define a total order on simplified expressions. There are two groups of rules, when comparing equal type expressions and different type expressions.

Equal type expressions:

• OR1: u,v value expressions: u < v ⇔ val(u) < val(v)
• OR2: u,v var expressions: u < v ⇔ SCIPvarGetIndex(var(u)) < SCIPvarGetIndex(var(v))
• OR3: u,v are both sum or product expression: < is a lexicographical order on the terms
• OR4: u,v are both pow: u < v ⇔ base(u) < base(v) or, base(u) = base(v) and expo(u) < expo(v)
• OR5: u,v are \(u = f(u_1, ..., u_n), v = f(v_1, ..., v_m)\): u < v ⇔ For the first k such that \(u_k \neq v_k\), \(u_k < v_k\), or if such a \(k\) doesn't exist, then \(n < m\).

Different type expressions:

• OR6: u value, v other: u < v always
• OR7: u sum, v var or func: u < v ⇔ u < 0+v; In other words, if \(u = \sum_{i=1}^n \alpha_i u_i\), then u < v ⇔ \(u_n\) < v or if \(u_n\) = v and \(\alpha_n\) < 1.
• OR8: u product, v pow, sum, var or func: u < v ⇔ u < 1*v; In other words, if \(u = \prod_{i=1}^n u_i\), then u < v ⇔ \(u_n\) < v. Note: since this applies only to simplified expressions, the form of the product is correct. Simplified products do not have constant coefficients.
• OR9: u pow, v sum, var or func: u < v ⇔ u < v^1
• OR10: u var, v func: u < v always
• OR11: u func, v other type of func: u < v ⇔ name(type(u)) < name(type(v))
• OR12: none of the rules apply: u < v ⇔ ! v < u

Examples:

• x < x^2 ?: x is var and x^2 power, so none applies (OR12). Hence, we try to answer x^2 < x ?: x^2 < x ⇔ x < x or if x = x and 2 < 1 ⇔ 2 < 1 ⇔ False. So x < x^2 is True.
• x < x^-1 –OR12→ ~(x^-1 < x) –OR9→ ~(x^-1 < x^1) –OR4→ ~(x < x or -1 < 1) → ~True → False
• x*y < x –OR8→ x*y < 1*x –OR3→ y < x –OR2→ False
• x*y < y –OR8→ x*y < 1*y –OR3→ y < x –OR2→ False

Algorithm

The recursive version of the algorithm is

EXPR simplify(expr)
   for c in 1..expr->nchildren
      expr->children[c] = simplify(expr->children[c])
   end
   return expr->exprhdlr->simplify(expr)
end

Important: Whatever is returned by a simplify callback has to be simplified. Also, all children of the given expression are already simplified.

simplifies an expression (duplication of long doxygen comment omitted here)

Parameters

scip SCIP data structure rootexpr expression to be simplified simplified buffer to store simplified expression changed buffer to store if rootexpr actually changed infeasible buffer to store whether infeasibility has been detected ownercreatedata data to pass to ownercreate

Definition at line 1780 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprSimplify().

Referenced by canonicalizeConstraints(), SCIP_DECL_CONSACTIVE(), SCIPmultiplyBySumExprSum(), SCIPpowerExprSum(), and SCIPwritePip().

replaces common sub-expressions in a given expression graph by using a hash key for each expression

The algorithm consists of two steps:

1. traverse through all given expressions and compute for each of them a (not necessarily unique) hash
2. initialize an empty hash table and traverse through all expression; check for each of them if we can find a structural equivalent expression in the hash table; if yes we replace the expression by the expression inside the hash table, otherwise we add it to the hash table

Note

the hash keys of the expressions are used for the hashing inside the hash table; to compute if two expressions (with the same hash) are structurally the same we use the function SCIPexprCompare().

Parameters

scip SCIP data structure exprs expressions (possibly replaced by equivalent on output) nexprs total number of expressions replacedroot buffer to store whether any root expression (expression in exprs) was replaced

Definition at line 1827 of file scip_expr.c.

References FALSE, findEqualExpr(), hashExpr(), COMMONSUBEXPR_HASH_DATA::hashiterator, NULL, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_LEAVEEXPR, SCIP_EXPRITER_VISITINGCHILD, SCIP_OKAY, SCIPcreateExpriter(), SCIPdebugMsg, SCIPexprCapture(), SCIPexprCompare(), SCIPexpriterFree(), SCIPexpriterGetChildExprDFS(), SCIPexpriterGetChildIdxDFS(), SCIPexpriterGetCurrent(), SCIPexpriterGetNext(), SCIPexpriterInit(), SCIPexpriterIsEnd(), SCIPexpriterSetStagesDFS(), SCIPexpriterSkipDFS(), SCIPmultihashCreate(), SCIPmultihashFree(), SCIPreleaseExpr(), SCIPreplaceExprChild(), COMMONSUBEXPR_HASH_DATA::set, and TRUE.

Referenced by canonicalizeConstraints(), and SCIP_DECL_CONSACTIVE().

computes the curvature of a given expression and all its subexpressions

Note

this function also evaluates all subexpressions w.r.t. current variable bounds

this function relies on information from the curvature callback of expression handlers only, consider using function SCIPhasExprCurvature() of the convex-nlhdlr instead, as that uses more information to deduce convexity

Parameters

scip SCIP data structure expr expression

Definition at line 1942 of file scip_expr.c.

References FALSE, NULL, SCIP_Bool, SCIP_CALL, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_EXPRCURV_LINEAR, SCIP_EXPRCURV_UNKNOWN, SCIP_EXPRITER_DFS, SCIP_EXPRITER_LEAVEEXPR, SCIP_OKAY, SCIPallocBufferArray, SCIPcalcMemGrowSize(), SCIPexprGetChildren(), SCIPexprGetCurvature(), SCIPexprGetHdlr(), SCIPexprGetNChildren(), SCIPexprhdlrCurvatureExpr(), SCIPexprhdlrHasCurvature(), SCIPexpriterCreate(), SCIPexpriterFree(), SCIPexpriterGetCurrent(), SCIPexpriterGetNext(), SCIPexpriterInit(), SCIPexpriterIsEnd(), SCIPexpriterSetStagesDFS(), SCIPexprSetCurvature(), SCIPfreeBufferArray, and SCIPreallocBufferArray.

computes integrality information of a given expression and all its subexpressions

The integrality information can be accessed via SCIPexprIsIntegral().

Parameters

scip SCIP data structure expr expression

Definition at line 2022 of file scip_expr.c.

References FALSE, NULL, SCIP_Bool, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_EXPRITER_LEAVEEXPR, SCIP_OKAY, SCIPexprGetHdlr(), SCIPexprGetNChildren(), SCIPexprhdlrIntegralityExpr(), SCIPexpriterCreate(), SCIPexpriterFree(), SCIPexpriterGetCurrent(), SCIPexpriterGetNext(), SCIPexpriterInit(), SCIPexpriterIsEnd(), SCIPexpriterSetStagesDFS(), and SCIPexprSetIntegrality().

Referenced by collectLeafs(), and detectNlhdlrs().

returns the total number of variable expressions in an expression

The function counts variable expressions in common sub-expressions only once, but counts variables appearing in several variable expressions multiple times.

Parameters

scip SCIP data structure expr expression nvars buffer to store the total number of variables

Definition at line 2065 of file scip_expr.c.

References FALSE, NULL, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_OKAY, SCIPexprIsVar(), SCIPexpriterCreate(), SCIPexpriterFree(), SCIPexpriterGetNext(), SCIPexpriterInit(), and SCIPexpriterIsEnd().

Referenced by SCIP_DECL_NLHDLRDETECT(), and storeVarExprs().

returns all variable expressions contained in a given expression

The array to store all variable expressions needs to be at least of size the number of unique variable expressions in the expression which is given by SCIPgetExprNVars().

If every variable is represented by only one variable expression (common subexpression have been removed) then SCIPgetExprNVars() can be bounded by SCIPgetNTotalVars(). If, in addition, non-active variables have been removed from the expression, e.g., by simplifying, then SCIPgetExprNVars() can be bounded by SCIPgetNVars().

Note

function captures variable expressions

Parameters

scip SCIP data structure expr expression varexprs array to store all variable expressions nvarexprs buffer to store the total number of variable expressions

Definition at line 2103 of file scip_expr.c.

References FALSE, NULL, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_OKAY, SCIPcaptureExpr(), SCIPexprIsVar(), SCIPexpriterCreate(), SCIPexpriterFree(), SCIPexpriterGetNext(), SCIPexpriterInit(), and SCIPexpriterIsEnd().

Referenced by computeOffValues(), SCIP_DECL_NLHDLRDETECT(), and storeVarExprs().

calls the eval callback for an expression with given values for children

Does not iterates over expressions, but requires values for children to be given. Value is not stored in expression, but returned in val. If an evaluation error (division by zero, ...) occurs, this value will be set to SCIP_INVALID.

Parameters

scip SCIP data structure expr expression to be evaluated childrenvalues values for children val buffer to store evaluated value

Definition at line 2192 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPexprGetHdlr(), and SCIPexprhdlrEvalExpr().

Referenced by evalExprInAux().

calls the eval and fwdiff callback of an expression with given values for children

Does not iterates over expressions, but requires values for children and direction to be given.

Value is not stored in expression, but returned in val. If an evaluation error (division by zero, ...) occurs, this value will be set to SCIP_INVALID.

Direction is not stored in expression, but returned in dot. If an differentiation error (division by zero, ...) occurs, this value will be set to SCIP_INVALID.

Parameters

scip SCIP data structure expr expression to be evaluated childrenvalues values for children direction direction in which to differentiate val buffer to store evaluated value dot buffer to store derivative value

Definition at line 2219 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPexprGetHdlr(), and SCIPexprhdlrEvalFwDiffExpr().

calls the symmetry information callback for an expression

Returns NULL pointer if not implemented.

calls the symmetry data callback for an expression

Returns no information if not implemented.

Definition at line 2322 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprGetSymData().

creates an expression iterator

Parameters

scip SCIP data structure iterator buffer to store expression iterator

Definition at line 2344 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexpriterCreate().

Referenced by addExprViolScoresAuxVars(), addSymmetryInformation(), analyzeViolation(), bilinearTermsInsertAll(), canonicalizeConstraints(), collectBranchingCandidates(), collectLeafs(), computeOffValues(), constructExpr(), createNlhdlrExprData(), deinitSolve(), detectMinors(), detectNlhdlrs(), enforceConstraints(), exprIsNonSmooth(), exprIsSemicontinuous(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), improvePoint(), initSepa(), notifyNlhdlrNewsol(), presolveBinaryProducts(), presolveSingleLockedVars(), printExpr(), processNlRow(), propagateLocks(), propConss(), propExprDomains(), registerBranchingCandidates(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_TABLEOUTPUT(), SCIPaddExprsViolScoreNonlinear(), SCIPaddNlRowGradientBenderscutOpt(), SCIPcreateNlpiProblemFromNlRows(), SCIPexprintCompile(), SCIPmarkExprPropagateNonlinear(), SCIPnlpiOracleDelVarSet(), SCIPnlpiOracleGetJacobianSparsity(), SCIPregisterExprUsageNonlinear(), SCIPreplaceCommonSubexpressions(), separateCuts(), and updateVariableCounts().

frees an expression iterator

Parameters

iterator pointer to the expression iterator

Definition at line 2358 of file scip_expr.c.

References SCIPexpriterFree().

Referenced by addExprViolScoresAuxVars(), addSymmetryInformation(), analyzeViolation(), bilinearTermsInsertAll(), canonicalizeConstraints(), collectBranchingCandidates(), collectLeafs(), computeOffValues(), constructExpr(), createNlhdlrExprData(), deinitSolve(), detectMinors(), detectNlhdlrs(), enforceConstraints(), exprIsNonSmooth(), exprIsSemicontinuous(), forbidNonlinearVariablesMultiaggration(), forwardPropExpr(), improvePoint(), initSepa(), notifyNlhdlrNewsol(), presolveBinaryProducts(), presolveSingleLockedVars(), printExpr(), processNlRow(), propagateLocks(), propConss(), propExprDomains(), registerBranchingCandidates(), SCIP_DECL_CONSACTIVE(), SCIP_DECL_TABLEOUTPUT(), SCIPaddExprsViolScoreNonlinear(), SCIPaddNlRowGradientBenderscutOpt(), SCIPcreateNlpiProblemFromNlRows(), SCIPexprintCompile(), SCIPmarkExprPropagateNonlinear(), SCIPnlpiOracleDelVarSet(), SCIPnlpiOracleGetJacobianSparsity(), SCIPregisterExprUsageNonlinear(), separateCuts(), and updateVariableCounts().

checks whether an expression is quadratic

An expression is quadratic if it is either a square (of some expression), a product (of two expressions), or a sum of terms where at least one is a square or a product.

Use SCIPexprGetQuadraticData() to get data about the representation as quadratic.

Parameters

scip SCIP data structure expr expression isquadratic buffer to store result

Definition at line 2384 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprCheckQuadratic().

Referenced by DECL_CURVCHECK(), isCandidate(), printNonlinearCons(), processNlRow(), SCIP_DECL_NLHDLRDETECT(), SCIPcheckQuadraticNonlinear(), and SCIPwritePip().

checks the curvature of the quadratic expression

For this, it builds the matrix Q of quadratic coefficients and computes its eigenvalues using LAPACK. If Q is

• semidefinite positive -> curv is set to convex,
• semidefinite negative -> curv is set to concave,
• otherwise -> curv is set to unknown.

If assumevarfixed is given and some expressions in quadratic terms correspond to variables present in this hashmap, then the corresponding rows and columns are ignored in the matrix Q.

Parameters

scip SCIP data structure expr quadratic expression curv pointer to store the curvature of quadratics assumevarfixed hashmap containing variables that should be assumed to be fixed, or NULL storeeigeninfo whether the eigenvalues and eigenvectors should be stored

Definition at line 2593 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprComputeQuadraticCurvature().

Referenced by DECL_CURVCHECK(), SCIP_DECL_NLHDLRDETECT(), and SCIP_DECL_PRESOLEXEC().

returns a monomial representation of a product expression

The array to store all factor expressions needs to be of size the number of children in the expression which is given by SCIPexprGetNChildren().

Given a non-trivial monomial expression, the function finds its representation as \(cx^\alpha\), where \(c\) is a real coefficient, \(x\) is a vector of auxiliary or original variables (where some entries can be NULL is the auxiliary variable has not been created yet), and \(\alpha\) is a real vector of exponents.

A non-trivial monomial is a product of a least two expressions.

Parameters

scip SCIP data structure expr expression coef coefficient \(c\) exponents exponents \(\alpha\) factors factor expressions \(x\)

Definition at line 2630 of file scip_expr.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPexprGetMonomialData().

Referenced by SCIP_DECL_NLHDLRDETECT().

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