# SCIP

Solving Constraint Integer Programs

## Detailed Description

methods to interpret (evaluate) an expression tree "fast" using CppAD

`#include "scip/def.h"`
`#include "blockmemshell/memory.h"`
`#include "nlpi/pub_expr.h"`
`#include "nlpi/exprinterpret.h"`
`#include <cmath>`
`#include <vector>`
`#include "nlpi/intervalarithext.h"`
`#include <cppad/cppad.hpp>`
`#include <cppad/error_handler.hpp>`
`#include <pthread.h>`

Go to the source code of this file.

## Macros

#define SIGN(x)   ((x) >= 0.0 ? 1.0 : -1.0)

## Functions

SCIPInterval CondExpOp (enum CppAD::CompareOp cop, const SCIPInterval &left, const SCIPInterval &right, const SCIPInterval &trueCase, const SCIPInterval &falseCase)

bool EqualOpSeq (const SCIPInterval &x, const SCIPInterval &y)

bool IdenticalPar (const SCIPInterval &x)

bool IdenticalZero (const SCIPInterval &x)

bool IdenticalOne (const SCIPInterval &x)

bool IdenticalEqualPar (const SCIPInterval &x, const SCIPInterval &y)

bool GreaterThanZero (const SCIPInterval &x)

bool GreaterThanOrZero (const SCIPInterval &x)

bool LessThanZero (const SCIPInterval &x)

bool LessThanOrZero (const SCIPInterval &x)

int Integer (const SCIPInterval &x)

std::ostream & operator<< (std::ostream &out, const SCIP_INTERVAL &x)

template<class Type >
SCIP_RETCODE exprEvalUser (SCIP_EXPR *expr, Type *x, Type &funcval, Type *gradient, Type *hessian)

template<>
SCIP_RETCODE exprEvalUser (SCIP_EXPR *expr, SCIPInterval *x, SCIPInterval &funcval, SCIPInterval *gradient, SCIPInterval *hessian)

template<>

template<>

template<>

const char * SCIPexprintGetName (void)

const char * SCIPexprintGetDesc (void)

SCIP_EXPRINTCAPABILITY SCIPexprintGetCapability (void)

SCIP_RETCODE SCIPexprintCreate (BMS_BLKMEM *blkmem, SCIP_EXPRINT **exprint)

SCIP_RETCODE SCIPexprintFree (SCIP_EXPRINT **exprint)

SCIP_RETCODE SCIPexprintCompile (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree)

SCIP_EXPRINTCAPABILITY SCIPexprintGetExprtreeCapability (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree)

SCIP_RETCODE SCIPexprintFreeData (SCIP_EXPRINTDATA **interpreterdata)

SCIP_RETCODE SCIPexprintNewParametrization (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree)

SCIP_RETCODE SCIPexprintEval (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree, SCIP_Real *varvals, SCIP_Real *val)

SCIP_RETCODE SCIPexprintEvalInt (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree, SCIP_Real infinity, SCIP_INTERVAL *varvals, SCIP_INTERVAL *val)

SCIP_RETCODE SCIPexprintGrad (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree, SCIP_Real *varvals, SCIP_Bool new_varvals, SCIP_Real *val, SCIP_Real *gradient)

SCIP_RETCODE SCIPexprintGradInt (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree, SCIP_Real infinity, SCIP_INTERVAL *varvals, SCIP_Bool new_varvals, SCIP_INTERVAL *val, SCIP_INTERVAL *gradient)

SCIP_RETCODE SCIPexprintHessianSparsityDense (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree, SCIP_Real *varvals, SCIP_Bool *sparsity)

SCIP_RETCODE SCIPexprintHessianDense (SCIP_EXPRINT *exprint, SCIP_EXPRTREE *tree, SCIP_Real *varvals, SCIP_Bool new_varvals, SCIP_Real *val, SCIP_Real *hessian)

## Macro Definition Documentation

 #define SIGN ( x ) ((x) >= 0.0 ? 1.0 : -1.0)

sign of a value (-1 or +1)

0.0 has sign +1

Definition at line 56 of file exprinterpret_cppad.cpp.

Definition at line 60 of file exprinterpret_cppad.cpp.

Definition at line 71 of file exprinterpret_cppad.cpp.

## Function Documentation

 SCIPInterval CondExpOp ( enum CppAD::CompareOp cop, const SCIPInterval & left, const SCIPInterval & right, const SCIPInterval & trueCase, const SCIPInterval & falseCase )
inline

definition of CondExpOp for SCIPInterval (required by CppAD)

Definition at line 191 of file exprinterpret_cppad.cpp.

 bool EqualOpSeq ( const SCIPInterval & x, const SCIPInterval & y )
inline

another function that returns whether two intervals are the same (required by CppAD)

Parameters
 x first operand y second operand

Definition at line 208 of file exprinterpret_cppad.cpp.

 bool IdenticalPar ( const SCIPInterval & x )
inline

Parameters
 x operand

Definition at line 218 of file exprinterpret_cppad.cpp.

 bool IdenticalZero ( const SCIPInterval & x )
inline

returns whether the interval equals [0,0]

Parameters
 x operand

Definition at line 227 of file exprinterpret_cppad.cpp.

 bool IdenticalOne ( const SCIPInterval & x )
inline

returns whether the interval equals [1,1]

Parameters
 x operand

Definition at line 236 of file exprinterpret_cppad.cpp.

 bool IdenticalEqualPar ( const SCIPInterval & x, const SCIPInterval & y )
inline

yet another function that checks whether two intervals are equal

Parameters
 x first operand y second operand

Definition at line 245 of file exprinterpret_cppad.cpp.

 bool GreaterThanZero ( const SCIPInterval & x )
inline

greater than zero not defined for intervals

Parameters
 x operand

Definition at line 255 of file exprinterpret_cppad.cpp.

 bool GreaterThanOrZero ( const SCIPInterval & x )
inline

greater than or equal zero not defined for intervals

Parameters
 x operand

Definition at line 269 of file exprinterpret_cppad.cpp.

 bool LessThanZero ( const SCIPInterval & x )
inline

less than not defined for intervals

Parameters
 x operand

Definition at line 283 of file exprinterpret_cppad.cpp.

 bool LessThanOrZero ( const SCIPInterval & x )
inline

less than or equal not defined for intervals

Parameters
 x operand

Definition at line 297 of file exprinterpret_cppad.cpp.

 int Integer ( const SCIPInterval & x )
inline

conversion to integers not defined for intervals

Parameters
 x operand

Definition at line 311 of file exprinterpret_cppad.cpp.

 std::ostream& operator<< ( std::ostream & out, const SCIP_INTERVAL & x )
inline

printing of an interval (required by CppAD)

Definition at line 325 of file exprinterpret_cppad.cpp.

template<class Type >
 SCIP_RETCODE exprEvalUser ( SCIP_EXPR * expr, Type * x, Type & funcval, Type * gradient, Type * hessian )

Definition at line 1211 of file exprinterpret_cppad.cpp.

References SCIPexprEvalUser().

template<>
 SCIP_RETCODE exprEvalUser ( SCIP_EXPR * expr, SCIPInterval * x, SCIPInterval & funcval, SCIPInterval * gradient, SCIPInterval * hessian )

Definition at line 1223 of file exprinterpret_cppad.cpp.

References SCIPInterval::infinity, and SCIPexprEvalIntUser().

template<>

specialization of minimum evaluation for real numbers

Parameters
 resultant resultant arg1 first operand arg2 second operand

Definition at line 1656 of file exprinterpret_cppad.cpp.

template<>

specialization of maximum evaluation for real numbers

Parameters
 resultant resultant arg1 first operand arg2 second operand

Definition at line 1686 of file exprinterpret_cppad.cpp.

References MAX.

template<>

specialization of absolute value evaluation for intervals

Use sqrt(x^2) for now

Parameters
 resultant resultant arg operand

Definition at line 1725 of file exprinterpret_cppad.cpp.

References sqrt().

 const char* SCIPexprintGetName ( void )

gets name and version of expression interpreter

Definition at line 2157 of file exprinterpret_cppad.cpp.

 const char* SCIPexprintGetDesc ( void )

gets descriptive text of expression interpreter

Definition at line 2163 of file exprinterpret_cppad.cpp.

 SCIP_EXPRINTCAPABILITY SCIPexprintGetCapability ( void )

gets capabilities of expression interpreter (using bitflags)

Definition at line 2169 of file exprinterpret_cppad.cpp.

 SCIP_RETCODE SCIPexprintCreate ( BMS_BLKMEM * blkmem, SCIP_EXPRINT ** exprint )

creates an expression interpreter object

Parameters
 blkmem block memory data structure exprint buffer to store pointer to expression interpreter

Definition at line 2179 of file exprinterpret_cppad.cpp.

References NULL, SCIP_NOMEMORY, and SCIP_OKAY.

 SCIP_RETCODE SCIPexprintFree ( SCIP_EXPRINT ** exprint )

frees an expression interpreter object

Parameters
 exprint expression interpreter that should be freed

Definition at line 2196 of file exprinterpret_cppad.cpp.

References NULL, and SCIP_OKAY.

 SCIP_RETCODE SCIPexprintCompile ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree )

compiles an expression tree and stores compiled data in expression tree

Parameters
 exprint interpreter data structure tree expression tree

Definition at line 2209 of file exprinterpret_cppad.cpp.

 SCIP_EXPRINTCAPABILITY SCIPexprintGetExprtreeCapability ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree )

gives the capability to evaluate an expression by the expression interpreter

In cases of user-given expressions, higher order derivatives may not be available for the user-expression, even if the expression interpreter could handle these. This method allows to recognize that, e.g., the Hessian for an expression is not available because it contains a user expression that does not provide Hessians.

Parameters
 exprint interpreter data structure tree expression tree

Definition at line 2264 of file exprinterpret_cppad.cpp.

References NULL, and SCIPexprtreeGetInterpreterData().

 SCIP_RETCODE SCIPexprintFreeData ( SCIP_EXPRINTDATA ** interpreterdata )

frees interpreter data

Parameters
 interpreterdata interpreter data that should freed

Definition at line 2278 of file exprinterpret_cppad.cpp.

References NULL, SCIP_OKAY, and SCIPexprFreeDeep().

 SCIP_RETCODE SCIPexprintNewParametrization ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree )

notify expression interpreter that a new parameterization is used

This probably causes retaping by AD algorithms.

Parameters
 exprint interpreter data structure tree expression tree

Definition at line 2298 of file exprinterpret_cppad.cpp.

References NULL, SCIP_OKAY, and SCIPexprtreeGetInterpreterData().

 SCIP_RETCODE SCIPexprintEval ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree, SCIP_Real * varvals, SCIP_Real * val )

evaluates an expression tree

Parameters
 exprint interpreter data structure tree expression tree varvals values of variables val buffer to store value

Definition at line 2317 of file exprinterpret_cppad.cpp.

Referenced by SCIPexprintGrad(), SCIPexprintHessianDense(), and SCIPexprintHessianSparsityDense().

 SCIP_RETCODE SCIPexprintEvalInt ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree, SCIP_Real infinity, SCIP_INTERVAL * varvals, SCIP_INTERVAL * val )

evaluates an expression tree on intervals

Parameters
 exprint interpreter data structure tree expression tree infinity value for infinity varvals interval values of variables val buffer to store interval value of expression

Definition at line 2385 of file exprinterpret_cppad.cpp.

 SCIP_RETCODE SCIPexprintGrad ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree, SCIP_Real * varvals, SCIP_Bool new_varvals, SCIP_Real * val, SCIP_Real * gradient )

computes value and gradient of an expression tree

Parameters
 exprint interpreter data structure tree expression tree varvals values of variables, can be NULL if new_varvals is FALSE new_varvals have variable values changed since last call to a point evaluation routine? val buffer to store expression value gradient buffer to store expression gradient, need to have length at least SCIPexprtreeGetNVars(tree)

Definition at line 2451 of file exprinterpret_cppad.cpp.

 SCIP_RETCODE SCIPexprintGradInt ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree, SCIP_Real infinity, SCIP_INTERVAL * varvals, SCIP_Bool new_varvals, SCIP_INTERVAL * val, SCIP_INTERVAL * gradient )

computes interval value and interval gradient of an expression tree

Parameters
 exprint interpreter data structure tree expression tree infinity value for infinity varvals interval values of variables, can be NULL if new_varvals is FALSE new_varvals have variable interval values changed since last call to an interval evaluation routine? val buffer to store expression interval value gradient buffer to store expression interval gradient, need to have length at least SCIPexprtreeGetNVars(tree)

Definition at line 2498 of file exprinterpret_cppad.cpp.

 SCIP_RETCODE SCIPexprintHessianSparsityDense ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree, SCIP_Real * varvals, SCIP_Bool * sparsity )

gives sparsity pattern of hessian

NOTE: this function might be replaced later by something nicer. Since the AD code might need to do a forward sweep, you should pass variable values in here.

Parameters
 exprint interpreter data structure tree expression tree varvals values of variables sparsity buffer to store sparsity pattern of Hessian, sparsity[i+n*j] indicates whether entry (i,j) is nonzero in the hessian

Definition at line 2548 of file exprinterpret_cppad.cpp.

 SCIP_RETCODE SCIPexprintHessianDense ( SCIP_EXPRINT * exprint, SCIP_EXPRTREE * tree, SCIP_Real * varvals, SCIP_Bool new_varvals, SCIP_Real * val, SCIP_Real * hessian )

computes value and dense hessian of an expression tree

The full hessian is computed (lower left and upper right triangle).

Parameters
 exprint interpreter data structure tree expression tree varvals values of variables, can be NULL if new_varvals is FALSE new_varvals have variable values changed since last call to an evaluation routine? val buffer to store function value hessian buffer to store hessian values, need to have size at least n*n

Definition at line 2621 of file exprinterpret_cppad.cpp.