Class Expression

java.lang.Object

org.ojalgo.optimisation.ModelEntity<Expression>

org.ojalgo.optimisation.Expression

All Implemented Interfaces:

Comparable<Expression>, Optimisation, Optimisation.Constraint, Optimisation.Objective

public final class Expression
extends ModelEntity<Expression>

Expression represents a mathematical expression in the optimization model that can serve as either a constraint or a component of the objective function.

An Expression can be:

• Linear: Contains only linear terms (variable coefficients)
• Quadratic: Contains quadratic terms (products of variables)
• Compound: Contains both linear and quadratic terms

Basic usage:

• Set coefficients for variables with set(Variable, Comparable) or add(Variable, Comparable) methods
• Create quadratic terms with set(Variable, Variable, Comparable) methods
• Create constraints by setting lower/upper bounds using ModelEntity.lower(Comparable), ModelEntity.upper(Comparable), or ModelEntity.level(Comparable) for equality constraints
• Contribute to the objective function by setting a weight using ModelEntity.weight(Comparable)

Advanced features include:

• Integer expression handling with automatic detection and constraint tightening
• Support for binary variables with specialized methods for detecting binary constraints
• Expression evaluation at specific variable values using evaluate(Access1D)
• Compensation for fixed variables to simplify expressions during solving
• Numerical scaling for improved solver stability
• Convenient methods for creating common expression types (sums, distances, etc.)
• Conversion to various function types for integration with different solvers

The Expression class provides a fluent interface for building expressions with method chaining. It also supports automatic handling of numerical stability issues through scaling adjustments.

Note that while the Expression class supports quadratic terms in constraints, some solvers may only support linear constraints. Quadratic, linear, or compound expressions can typically be used in the objective function depending on the solver capabilities.

Nested Class Summary

Nested classes/interfaces inherited from interface Optimisation

Optimisation.Constraint, Optimisation.ConstraintType, Optimisation.Integration<M,S>, Optimisation.Model, Optimisation.Objective, Optimisation.Options, Optimisation.ProblemStructure, Optimisation.Result, Optimisation.Sense, Optimisation.Solver, Optimisation.State

Field Summary

Fields

Modifier and Type	Field	Description
private BigDecimal	myConstant
private boolean	myInfeasible
private Boolean	myInteger
private final Map<Structure1D.IntIndex, BigDecimal>	myLinear
private final ExpressionsBasedModel	myModel
private final Map<Structure2D.IntRowColumn, BigDecimal>	myQuadratic
private boolean	myRedundant
private final boolean	myShallowCopy	A shallow copy (typically created by presolver or integer solver) shares the Map:s holding the paramaters with other Expressions.

Fields inherited from class ModelEntity

PRINT, RANGE

Constructor Summary

Constructors

Modifier	Constructor	Description
(package private)	Expression(String name, ExpressionsBasedModel model)
protected	Expression(Expression expressionToCopy, ExpressionsBasedModel destinationModel, boolean deep)

Method Summary

Modifier and Type	Method	Description
Expression	add(double scale, Expression values)
Expression	add(int index, double value)
Expression	add(int row, int column, double value)
Expression	add(int row, int column, long value)
Expression	add(int row, int column, Comparable<?> value)
Expression	add(int index, long value)
Expression	add(int index, Comparable<?> value)
Expression	add(long scale, Expression values)
Expression	add(Comparable<?> scale, Expression values)	Adds the scaled values from another Expression to this Expression.
Expression	add(Variable variable, double value)
Expression	add(Variable variable, long value)
Expression	add(Variable variable, Comparable<?> value)	Will add the value to this variable's factor.
Expression	add(Variable variable1, Variable variable2, double value)
Expression	add(Variable variable1, Variable variable2, long value)
Expression	add(Variable variable1, Variable variable2, Comparable<?> value)
(package private) void	addAll(Set<Structure1D.IntIndex> referenced)	Add all indices of referenced variables to the supplied Set.
(package private) void	addObjectiveConstant(BigDecimal value)
void	addTo(Expression target, BigDecimal scale)	Add this (Variable or Expression) to another Expression, scaled by a factor.
protected void	appendMiddlePart(StringBuilder builder, Access1D<BigDecimal> solution, NumberContext display)
(package private) void	appendToString(StringBuilder builder, Access1D<BigDecimal> solution, NumberContext display)
(package private) BigDecimal	calculateSetValue(Collection<Structure1D.IntIndex> subset)	Calculates this expression's value - the subset variables' part of this expression.
int	compareTo(Expression obj)
Expression	compensate(Set<Structure1D.IntIndex> fixedVariables)	Will return an Expression with factors corresponding to fixed variables removed, and lower/upper limits compensated for the fixed part of the expression.
private BigDecimal	convert(BigDecimal value, boolean adjusted)
(package private) Expression	copy(ExpressionsBasedModel destinationModel, boolean deep)
(package private) long	countIntegerFactors()
(package private) int	countLinearFactors()
(package private) int	countQuadraticFactors()
(package private) double	density()
(package private) int	deriveAdjustmentExponent()
protected void	destroy()
private Expression	doAdd(BigDecimal scale, Expression values)
private Expression	doAdd(Structure1D.IntIndex key, BigDecimal value)
private Expression	doAdd(Structure2D.IntRowColumn key, BigDecimal value)
(package private) void	doIntegerRounding()	Assumes at least 1 variable, and all variables integer!
(package private) void	doIntegerRounding(Set<Structure1D.IntIndex> remaining, BigDecimal lower, BigDecimal upper)
(package private) Expression	doMixedIntegerRounding()
(package private) Expression	doSet(Structure1D.IntIndex key, BigDecimal value)
(package private) Expression	doSet(Structure2D.IntRowColumn key, BigDecimal value)
double	doubleValue(Structure1D.IntIndex key, boolean adjusted)
double	doubleValue(Structure2D.IntRowColumn key, boolean adjusted)
void	enforce(NumberContext enforcer)
boolean	equals(Object obj)
BigDecimal	evaluate(Access1D<BigDecimal> point)
BigDecimal	get(Variable variable)
BigDecimal	get(Structure1D.IntIndex key)
BigDecimal	get(Structure1D.IntIndex key, boolean adjusted)
BigDecimal	get(Structure2D.IntRowColumn key)
BigDecimal	get(Structure2D.IntRowColumn key, boolean adjusted)
MatrixStore<Double>	getAdjustedGradient(Access1D<?> point)
MatrixStore<Double>	getAdjustedHessian()
(package private) Set<Variable>	getBinaryVariables(Set<Structure1D.IntIndex> subset)
private BigDecimal	getConstant()
(package private) Map<Structure1D.IntIndex, BigDecimal>	getLinear()
Set<Map.Entry<Structure1D.IntIndex, BigDecimal>>	getLinearEntrySet()
Set<Structure1D.IntIndex>	getLinearKeySet()
(package private) ExpressionsBasedModel	getModel()
(package private) Map<Structure2D.IntRowColumn, BigDecimal>	getQuadratic()
Set<Map.Entry<Structure2D.IntRowColumn, BigDecimal>>	getQuadraticEntrySet()
Set<Structure2D.IntRowColumn>	getQuadraticKeySet()
int	hashCode()
(package private) boolean	includes(Variable variable)
boolean	isAnyLinearFactorNonZero()
boolean	isAnyQuadraticFactorNonZero()
(package private) boolean	isConstantSet()
boolean	isFunctionConstant()
boolean	isFunctionLinear()
boolean	isFunctionPureQuadratic()
boolean	isFunctionQuadratic()
(package private) boolean	isInfeasible()
boolean	isInteger()	Is this entity (all involved variables) integer?
boolean	isLinearAndAllBinary()
boolean	isLinearAndAllInteger()
boolean	isLinearAndAnyBinary()
boolean	isLinearAndAnyInteger()
(package private) boolean	isNegativeOn(Set<Structure1D.IntIndex> subset)
(package private) boolean	isPositiveOn(Set<Structure1D.IntIndex> subset)
(package private) boolean	isRedundant()
private AffineFunction<Double>	makeAffineFunction()
private ConstantFunction<Double>	makeConstantFunction()
private PureQuadraticFunction<Double>	makePureQuadraticFunction()
private QuadraticFunction<Double>	makeQuadraticFunction()
(package private) Variable	resolve(Structure1D.IntIndex index)
Expression	set(int index, double value)
Expression	set(int row, int column, double value)
Expression	set(int row, int column, long value)
Expression	set(int row, int column, Comparable<?> value)
Expression	set(int index, long value)
Expression	set(int index, Comparable<?> value)
Expression	set(Variable variable, double value)
Expression	set(Variable variable, long value)
Expression	set(Variable variable, Comparable<?> value)	Will set (replace) the variable's factor to this value
Expression	set(Variable variable1, Variable variable2, double value)
Expression	set(Variable variable1, Variable variable2, long value)
Expression	set(Variable variable1, Variable variable2, Comparable<?> value)
void	setCompoundFactorsOffset(List<Variable> variables, Access1D<?> point)	Will set the quadratic and linear factors to an expression that measures (the square of) the distance from the given point.
(package private) void	setConstant(double value)
(package private) void	setConstant(long value)
(package private) void	setConstant(Comparable<?> value)
(package private) void	setInfeasible()
(package private) void	setInteger()
void	setLinearFactors(List<Variable> variables, Access1D<?> factors)
void	setLinearFactorsSimple(List<Variable> variables)	Will set the linear factors to a simple sum expression - all factors equal 1.0.
void	setQuadraticFactors(List<Variable> variables, Access2D<?> factors)
(package private) void	setRedundant()
void	tighten()	Will attempt to exploit integer property to tighten the lower and/or upper limits (integer rounding).
MultiaryFunction.TwiceDifferentiable<Double>	toFunction()
private Structure1D.IntIndex	toIntIndex(int index)
private Structure1D.IntIndex	toIntIndex(Variable variable)
private Structure2D.IntRowColumn	toIntRowColumn(int row, int column)
private Structure2D.IntRowColumn	toIntRowColumn(Variable variable1, Variable variable2)
private BigDecimal	toPositiveFraction(BigDecimal noninteger)

Methods inherited from class ModelEntity

adjust, appendLeftPart, appendMiddlePart, appendRightPart, appendToString, deriveAdjustmentExponent, getAdjustmentExponent, getAdjustmentExponentValue, getAdjustmentFactor, getCompensatedLowerLimit, getCompensatedLowerLimit, getCompensatedUpperLimit, getCompensatedUpperLimit, getContributionWeight, getLowerLimit, getLowerLimit, getLowerLimit, getName, getUpperLimit, getUpperLimit, getUpperLimit, isClosedRange, isConstraint, isContributionWeightSet, isEqualityConstraint, isInfeasible, isLowerConstraint, isLowerLimitSet, isObjective, isUpperConstraint, isUpperLimitSet, level, level, level, lower, lower, lower, reverseAdjustment, shift, toAdjusted, toBigDecimal, toString, toUnadjusted, upper, upper, upper, validate, validate, weight, weight, weight

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

myConstant

private BigDecimal myConstant

myInfeasible

private transient boolean myInfeasible

myInteger

private transient Boolean myInteger

myLinear

private final Map<Structure1D.IntIndex, BigDecimal> myLinear

myModel

private final ExpressionsBasedModel myModel

myQuadratic

private final Map<Structure2D.IntRowColumn, BigDecimal> myQuadratic

myRedundant

private transient boolean myRedundant

myShallowCopy

private final boolean myShallowCopy

A shallow copy (typically created by presolver or integer solver) shares the Map:s holding the paramaters with other Expressions. They will only differ on the lower/upper limits and on meta data like flags indicating redundancy or infeasibility.

Constructor Details

Expression

protected Expression(Expression expressionToCopy,
 ExpressionsBasedModel destinationModel,
 boolean deep)

Expression

Expression(String name,
 ExpressionsBasedModel model)

Method Details

add

public Expression add(Comparable<?> scale,
 Expression values)

Adds the scaled values from another Expression to this Expression. The lower and upper limits/bounds, of either involved Expression, are not affected. Nor is the objective weight. Only the factors (linear and quadratic) are scaled and added.

This allows for constructs like:

Expression expr1 = model.newExpression("Expr1");
Expression expr2 = model.newExpression("Expr2");
...
model.newExpression("Expr3").add(2.0, expr1).add(-3.0, expr2).lower(0.0);

add

public Expression add(double scale,
 Expression values)

See Also:

• add(Comparable, Expression)

add

public Expression add(int index,
 Comparable<?> value)

See Also:

• add(Variable, Comparable)

add

public Expression add(int index,
 double value)

See Also:

• add(Variable, Comparable)

add

public Expression add(int row,
 int column,
 Comparable<?> value)

See Also:

• add(Variable, Comparable)

add

public Expression add(int row,
 int column,
 double value)

See Also:

• add(Variable, Comparable)

add

public Expression add(int row,
 int column,
 long value)

See Also:

• add(Variable, Comparable)

add

public Expression add(int index,
 long value)

See Also:

• add(Variable, Comparable)

add

public Expression add(long scale,
 Expression values)

See Also:

• add(Comparable, Expression)

add

public Expression add(Variable variable,
 Comparable<?> value)

Will add the value to this variable's factor.

add

public Expression add(Variable variable,
 double value)

See Also:

• add(Variable, Comparable)

add

public Expression add(Variable variable,
 long value)

See Also:

• add(Variable, Comparable)

add

public Expression add(Variable variable1,
 Variable variable2,
 Comparable<?> value)

See Also:

• add(Variable, Comparable)

add

public Expression add(Variable variable1,
 Variable variable2,
 double value)

See Also:

• add(Variable, Comparable)

add

public Expression add(Variable variable1,
 Variable variable2,
 long value)

See Also:

• add(Variable, Comparable)

addTo

public void addTo(Expression target,
 BigDecimal scale)

Description copied from class: ModelEntity

Add this (Variable or Expression) to another Expression, scaled by a factor.

Specified by:

addTo in class ModelEntity<Expression>

Parameters:

target - The target Expression

scale - The scaling factor

compareTo

public int compareTo(Expression obj)

compensate

public Expression compensate(Set<Structure1D.IntIndex> fixedVariables)

Will return an Expression with factors corresponding to fixed variables removed, and lower/upper limits compensated for the fixed part of the expression. Factors corresponding to bilinear variables, where one is fixed and the other is not, are linearized.

Parameters:

fixedVariables - A set of (by the presolver) fixed variable indices

Returns:

The reduced/modified expression

doubleValue

public double doubleValue(Structure1D.IntIndex key,
 boolean adjusted)

doubleValue

public double doubleValue(Structure2D.IntRowColumn key,
 boolean adjusted)

enforce

public void enforce(NumberContext enforcer)

equals

public boolean equals(Object obj)

Overrides:

equals in class ModelEntity<Expression>

evaluate

public BigDecimal evaluate(Access1D<BigDecimal> point)

get

public BigDecimal get(Structure1D.IntIndex key)

get

public BigDecimal get(Structure1D.IntIndex key,
 boolean adjusted)

get

public BigDecimal get(Structure2D.IntRowColumn key)

get

public BigDecimal get(Structure2D.IntRowColumn key,
 boolean adjusted)

get

public BigDecimal get(Variable variable)

getAdjustedGradient

public MatrixStore<Double> getAdjustedGradient(Access1D<?> point)

getAdjustedHessian

public MatrixStore<Double> getAdjustedHessian()

getLinearEntrySet

public Set<Map.Entry<Structure1D.IntIndex, BigDecimal>> getLinearEntrySet()

getLinearKeySet

public Set<Structure1D.IntIndex> getLinearKeySet()

getQuadraticEntrySet

public Set<Map.Entry<Structure2D.IntRowColumn, BigDecimal>> getQuadraticEntrySet()

getQuadraticKeySet

public Set<Structure2D.IntRowColumn> getQuadraticKeySet()

hashCode

public int hashCode()

Overrides:

hashCode in class ModelEntity<Expression>

isAnyLinearFactorNonZero

public boolean isAnyLinearFactorNonZero()

isAnyQuadraticFactorNonZero

public boolean isAnyQuadraticFactorNonZero()

isFunctionConstant

public boolean isFunctionConstant()

isFunctionLinear

public boolean isFunctionLinear()

isFunctionPureQuadratic

public boolean isFunctionPureQuadratic()

isFunctionQuadratic

public boolean isFunctionQuadratic()

isInteger

public boolean isInteger()

Description copied from class: ModelEntity

Is this entity (all involved variables) integer?

Specified by:

isInteger in class ModelEntity<Expression>

isLinearAndAllBinary

public boolean isLinearAndAllBinary()

Returns:

Are all the (linear) variables binary

isLinearAndAllInteger

public boolean isLinearAndAllInteger()

Returns:

Are all the (linear) variables integer

isLinearAndAnyBinary

public boolean isLinearAndAnyBinary()

Returns:

Are any of the (linear) variables binary

isLinearAndAnyInteger

public boolean isLinearAndAnyInteger()

Returns:

Are any of the (linear) variables integer

set

public Expression set(int index,
 Comparable<?> value)

See Also:

• set(Variable, Comparable)

set

public Expression set(int index,
 double value)

See Also:

• set(Variable, Comparable)

set

public Expression set(int row,
 int column,
 Comparable<?> value)

See Also:

• set(Variable, Comparable)

set

public Expression set(int row,
 int column,
 double value)

See Also:

• set(Variable, Comparable)

set

public Expression set(int row,
 int column,
 long value)

See Also:

• set(Variable, Comparable)

set

public Expression set(int index,
 long value)

See Also:

• set(Variable, Comparable)

set

public Expression set(Variable variable,
 Comparable<?> value)

Will set (replace) the variable's factor to this value

set

public Expression set(Variable variable,
 double value)

See Also:

• set(Variable, Comparable)

set

public Expression set(Variable variable,
 long value)

See Also:

• set(Variable, Comparable)

set

public Expression set(Variable variable1,
 Variable variable2,
 Comparable<?> value)

See Also:

• set(Variable, Comparable)

set

public Expression set(Variable variable1,
 Variable variable2,
 double value)

See Also:

• set(Variable, Comparable)

set

public Expression set(Variable variable1,
 Variable variable2,
 long value)

See Also:

• set(Variable, Comparable)

setCompoundFactorsOffset

public void setCompoundFactorsOffset(List<Variable> variables,
 Access1D<?> point)

Will set the quadratic and linear factors to an expression that measures (the square of) the distance from the given point.

Parameters:

variables - The relevant variables

point - The point to measure from

setLinearFactors

public void setLinearFactors(List<Variable> variables,
 Access1D<?> factors)

setLinearFactorsSimple

public void setLinearFactorsSimple(List<Variable> variables)

Will set the linear factors to a simple sum expression - all factors equal 1.0.

Parameters:

variables - The relevant variables

setQuadraticFactors

public void setQuadraticFactors(List<Variable> variables,
 Access2D<?> factors)

tighten

public void tighten()

Will attempt to exploit integer property to tighten the lower and/or upper limits (integer rounding).

toFunction

public MultiaryFunction.TwiceDifferentiable<Double> toFunction()

convert

private BigDecimal convert(BigDecimal value,
 boolean adjusted)

doAdd

private Expression doAdd(BigDecimal scale,
 Expression values)

doAdd

private Expression doAdd(Structure1D.IntIndex key,
 BigDecimal value)

doAdd

private Expression doAdd(Structure2D.IntRowColumn key,
 BigDecimal value)

getConstant

private BigDecimal getConstant()

makeAffineFunction

private AffineFunction<Double> makeAffineFunction()

makeConstantFunction

private ConstantFunction<Double> makeConstantFunction()

makePureQuadraticFunction

private PureQuadraticFunction<Double> makePureQuadraticFunction()

makeQuadraticFunction

private QuadraticFunction<Double> makeQuadraticFunction()

toIntIndex

private Structure1D.IntIndex toIntIndex(int index)

toIntIndex

private Structure1D.IntIndex toIntIndex(Variable variable)

toIntRowColumn

private Structure2D.IntRowColumn toIntRowColumn(int row,
 int column)

toIntRowColumn

private Structure2D.IntRowColumn toIntRowColumn(Variable variable1,
 Variable variable2)

toPositiveFraction

private BigDecimal toPositiveFraction(BigDecimal noninteger)

appendMiddlePart

protected void appendMiddlePart(StringBuilder builder,
 Access1D<BigDecimal> solution,
 NumberContext display)

destroy

protected void destroy()

Overrides:

destroy in class ModelEntity<Expression>

addAll

void addAll(Set<Structure1D.IntIndex> referenced)

Add all indices of referenced variables to the supplied Set.

addObjectiveConstant

void addObjectiveConstant(BigDecimal value)

appendToString

void appendToString(StringBuilder builder,
 Access1D<BigDecimal> solution,
 NumberContext display)

calculateSetValue

BigDecimal calculateSetValue(Collection<Structure1D.IntIndex> subset)

Calculates this expression's value - the subset variables' part of this expression. Will never return null.

copy

Expression copy(ExpressionsBasedModel destinationModel,
 boolean deep)

countIntegerFactors

long countIntegerFactors()

countLinearFactors

int countLinearFactors()

countQuadraticFactors

int countQuadraticFactors()

density

double density()

deriveAdjustmentExponent

int deriveAdjustmentExponent()

Specified by:

deriveAdjustmentExponent in class ModelEntity<Expression>

doIntegerRounding

void doIntegerRounding()

Assumes at least 1 variable, and all variables integer!

Specified by:

doIntegerRounding in class ModelEntity<Expression>

See Also:

• ModelEntity.doIntegerRounding()

doIntegerRounding

void doIntegerRounding(Set<Structure1D.IntIndex> remaining,
 BigDecimal lower,
 BigDecimal upper)

doMixedIntegerRounding

Expression doMixedIntegerRounding()

doSet

Expression doSet(Structure1D.IntIndex key,
 BigDecimal value)

doSet

Expression doSet(Structure2D.IntRowColumn key,
 BigDecimal value)

getBinaryVariables

Set<Variable> getBinaryVariables(Set<Structure1D.IntIndex> subset)

getLinear

Map<Structure1D.IntIndex, BigDecimal> getLinear()

getModel

ExpressionsBasedModel getModel()

getQuadratic

Map<Structure2D.IntRowColumn, BigDecimal> getQuadratic()

includes

boolean includes(Variable variable)

isConstantSet

boolean isConstantSet()

isInfeasible

boolean isInfeasible()

Overrides:

isInfeasible in class ModelEntity<Expression>

isNegativeOn

boolean isNegativeOn(Set<Structure1D.IntIndex> subset)

Parameters:

subset - The indices of a variable subset

Returns:

true if none of the variables in the subset can make a positve contribution to the expression value

isPositiveOn

boolean isPositiveOn(Set<Structure1D.IntIndex> subset)

Parameters:

subset - The indices of a variable subset

Returns:

true if none of the variables in the subset can make a negative contribution to the expression value

isRedundant

boolean isRedundant()

resolve

Variable resolve(Structure1D.IntIndex index)

setConstant

void setConstant(Comparable<?> value)

setConstant

void setConstant(double value)

setConstant

void setConstant(long value)

setInfeasible

void setInfeasible()

setInteger

void setInteger()

setRedundant

void setRedundant()