java.lang.Object
- org.apache.commons.math3.optim.linear.SimplexTableau

All Implemented Interfaces:: java.io.Serializable

class SimplexTableau
extends java.lang.Object
implements java.io.Serializable

A tableau for use in the Simplex method.

Example:

   W |  Z |  x1 |  x2 |  x- | s1 |  s2 |  a1 |  RHS
 ---------------------------------------------------
  -1    0    0     0     0     0     0     1     0   <= phase 1 objective
   0    1   -15   -10    0     0     0     0     0   <= phase 2 objective
   0    0    1     0     0     1     0     0     2   <= constraint 1
   0    0    0     1     0     0     1     0     3   <= constraint 2
   0    0    1     1     0     0     0     1     4   <= constraint 3

W: Phase 1 objective function
Z: Phase 2 objective function
x1 & x2: Decision variables
x-: Extra decision variable to allow for negative values
s1 & s2: Slack/Surplus variables
a1: Artificial variable
RHS: Right hand side

Since:: 2.0

Field Summary

Fields
Modifier and Type	Field	Description
`private int[]`	`basicRows`	Maps rows to their corresponding basic variables.
`private int[]`	`basicVariables`	Maps basic variables to row they are basic in.
`private java.util.List<java.lang.String>`	`columnLabels`	The variables each column represents
`private java.util.List<LinearConstraint>`	`constraints`	Linear constraints.
`private double`	`epsilon`	Amount of error to accept when checking for optimality.
`private LinearObjectiveFunction`	`f`	Linear objective function.
`private int`	`maxUlps`	Amount of error to accept in floating point comparisons.
`private static java.lang.String`	`NEGATIVE_VAR_COLUMN_LABEL`	Column label for negative vars.
`private int`	`numArtificialVariables`	Number of artificial variables.
`private int`	`numDecisionVariables`	Number of decision variables.
`private int`	`numSlackVariables`	Number of slack variables.
`private boolean`	`restrictToNonNegative`	Whether to restrict the variables to non-negative values.
`private static long`	`serialVersionUID`	Serializable version identifier.
`private Array2DRowRealMatrix`	`tableau`	Simple tableau.

Constructor Summary

Constructors
Constructor	Description
`SimplexTableau(LinearObjectiveFunction f, java.util.Collection<LinearConstraint> constraints, GoalType goalType, boolean restrictToNonNegative, double epsilon)`	Builds a tableau for a linear problem.
`SimplexTableau(LinearObjectiveFunction f, java.util.Collection<LinearConstraint> constraints, GoalType goalType, boolean restrictToNonNegative, double epsilon, int maxUlps)`	Build a tableau for a linear problem.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`private void`	`copyArray(double[] src, double[] dest)`
`protected Array2DRowRealMatrix`	`createTableau(boolean maximize)`	Create the tableau by itself.
`protected void`	`divideRow(int dividendRowIndex, double divisor)`	Divides one row by a given divisor.
`protected void`	`dropPhase1Objective()`	Removes the phase 1 objective function, positive cost non-artificial variables, and the non-basic artificial variables from this tableau.
`boolean`	`equals(java.lang.Object other)`
`private java.lang.Integer`	`findBasicRow(int col)`	Returns the row in which the given column is basic.
`protected int`	`getArtificialVariableOffset()`	Get the offset of the first artificial variable.
`protected java.lang.Integer`	`getBasicRow(int col)`	Checks whether the given column is basic.
`protected int`	`getBasicVariable(int row)`	Returns the variable that is basic in this row.
`private int`	`getConstraintTypeCounts(Relationship relationship)`	Get a count of constraints corresponding to a specified relationship.
`protected double[][]`	`getData()`	Get the tableau data.
`protected double`	`getEntry(int row, int column)`	Get an entry of the tableau.
`protected int`	`getHeight()`	Get the height of the tableau.
`protected static double`	`getInvertedCoefficientSum(RealVector coefficients)`	Get the -1 times the sum of all coefficients in the given array.
`protected int`	`getNumArtificialVariables()`	Get the number of artificial variables.
`protected int`	`getNumDecisionVariables()`	Get the number of decision variables.
`protected int`	`getNumObjectiveFunctions()`	Get the number of objective functions in this tableau.
`protected int`	`getNumSlackVariables()`	Get the number of slack variables.
`protected int`	`getOriginalNumDecisionVariables()`	Get the original number of decision variables.
`protected int`	`getRhsOffset()`	Get the offset of the right hand side.
`protected double[]`	`getRow(int row)`	Get the row from the tableau.
`protected int`	`getSlackVariableOffset()`	Get the offset of the first slack variable.
`protected PointValuePair`	`getSolution()`	Get the current solution.
`protected int`	`getWidth()`	Get the width of the tableau.
`int`	`hashCode()`
`private void`	`initializeBasicVariables(int startColumn)`	Initializes the basic variable / row mapping.
`protected void`	`initializeColumnLabels()`	Initialize the labels for the columns.
`(package private) boolean`	`isOptimal()`	Returns whether the problem is at an optimal state.
`private LinearConstraint`	`normalize(LinearConstraint constraint)`	Get a new equation equivalent to this one with a positive right hand side.
`java.util.List<LinearConstraint>`	`normalizeConstraints(java.util.Collection<LinearConstraint> originalConstraints)`	Get new versions of the constraints which have positive right hand sides.
`protected void`	`performRowOperations(int pivotCol, int pivotRow)`	Perform the row operations of the simplex algorithm with the selected pivot column and row.
`private void`	`readObject(java.io.ObjectInputStream ois)`	Deserialize the instance.
`protected void`	`setEntry(int row, int column, double value)`	Set an entry of the tableau.
`protected void`	`subtractRow(int minuendRowIndex, int subtrahendRowIndex, double multiplier)`	Subtracts a multiple of one row from another.
`private void`	`writeObject(java.io.ObjectOutputStream oos)`	Serialize the instance.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - NEGATIVE_VAR_COLUMN_LABEL
```
private static final java.lang.String NEGATIVE_VAR_COLUMN_LABEL
```
    Column label for negative vars.
    
    See Also:
    
    Constant Field Values
  - serialVersionUID
```
private static final long serialVersionUID
```
    Serializable version identifier.
    
    See Also:
    
    Constant Field Values
  - f
```
private final LinearObjectiveFunction f
```
    Linear objective function.
  - constraints
```
private final java.util.List<LinearConstraint> constraints
```
    Linear constraints.
  - restrictToNonNegative
```
private final boolean restrictToNonNegative
```
    Whether to restrict the variables to non-negative values.
  - columnLabels
```
private final java.util.List<java.lang.String> columnLabels
```
    The variables each column represents
  - tableau
```
private transient Array2DRowRealMatrix tableau
```
    Simple tableau.
  - numDecisionVariables
```
private final int numDecisionVariables
```
    Number of decision variables.
  - numSlackVariables
```
private final int numSlackVariables
```
    Number of slack variables.
  - numArtificialVariables
```
private int numArtificialVariables
```
    Number of artificial variables.
  - epsilon
```
private final double epsilon
```
    Amount of error to accept when checking for optimality.
  - maxUlps
```
private final int maxUlps
```
    Amount of error to accept in floating point comparisons.
  - basicVariables
```
private int[] basicVariables
```
    Maps basic variables to row they are basic in.
  - basicRows
```
private int[] basicRows
```
    Maps rows to their corresponding basic variables.
- Constructor Detail
  - SimplexTableau
```
SimplexTableau(LinearObjectiveFunction f,
               java.util.Collection<LinearConstraint> constraints,
               GoalType goalType,
               boolean restrictToNonNegative,
               double epsilon)
```
    Builds a tableau for a linear problem.
    
    Parameters:
    
    f - Linear objective function.
    
    constraints - Linear constraints.
    
    goalType - Optimization goal: either GoalType.MAXIMIZE or GoalType.MINIMIZE.
    
    restrictToNonNegative - Whether to restrict the variables to non-negative values.
    
    epsilon - Amount of error to accept when checking for optimality.
  - SimplexTableau
```
SimplexTableau(LinearObjectiveFunction f,
               java.util.Collection<LinearConstraint> constraints,
               GoalType goalType,
               boolean restrictToNonNegative,
               double epsilon,
               int maxUlps)
```
    Build a tableau for a linear problem.
    
    Parameters:
    
    f - linear objective function
    
    constraints - linear constraints
    
    goalType - type of optimization goal: either GoalType.MAXIMIZE or GoalType.MINIMIZE
    
    restrictToNonNegative - whether to restrict the variables to non-negative values
    
    epsilon - amount of error to accept when checking for optimality
    
    maxUlps - amount of error to accept in floating point comparisons
- Method Detail
  - initializeColumnLabels
```
protected void initializeColumnLabels()
```
    Initialize the labels for the columns.
  - createTableau
```
protected Array2DRowRealMatrix createTableau(boolean maximize)
```
    Create the tableau by itself.
    
    Parameters:
    
    maximize - if true, goal is to maximize the objective function
    
    Returns:
    
    created tableau
  - normalizeConstraints
```
public java.util.List<LinearConstraint> normalizeConstraints(java.util.Collection<LinearConstraint> originalConstraints)
```
    Get new versions of the constraints which have positive right hand sides.
    
    Parameters:
    
    originalConstraints - original (not normalized) constraints
    
    Returns:
    
    new versions of the constraints
  - normalize
```
private LinearConstraint normalize(LinearConstraint constraint)
```
    Get a new equation equivalent to this one with a positive right hand side.
    
    Parameters:
    
    constraint - reference constraint
    
    Returns:
    
    new equation
  - getNumObjectiveFunctions
```
protected final int getNumObjectiveFunctions()
```
    Get the number of objective functions in this tableau.
    
    Returns:
    
    2 for Phase 1. 1 for Phase 2.
  - getConstraintTypeCounts
```
private int getConstraintTypeCounts(Relationship relationship)
```
    Get a count of constraints corresponding to a specified relationship.
    
    Parameters:
    
    relationship - relationship to count
    
    Returns:
    
    number of constraint with the specified relationship
  - getInvertedCoefficientSum
```
protected static double getInvertedCoefficientSum(RealVector coefficients)
```
    Get the -1 times the sum of all coefficients in the given array.
    
    Parameters:
    
    coefficients - coefficients to sum
    
    Returns:
    
    the -1 times the sum of all coefficients in the given array.
  - getBasicRow
```
protected java.lang.Integer getBasicRow(int col)
```
    Checks whether the given column is basic.
    
    Parameters:
    
    col - index of the column to check
    
    Returns:
    
    the row that the variable is basic in. null if the column is not basic
  - getBasicVariable
```
protected int getBasicVariable(int row)
```
    Returns the variable that is basic in this row.
    
    Parameters:
    
    row - the index of the row to check
    
    Returns:
    
    the variable that is basic for this row.
  - initializeBasicVariables
```
private void initializeBasicVariables(int startColumn)
```
    Initializes the basic variable / row mapping.
    
    Parameters:
    
    startColumn - the column to start
  - findBasicRow
```
private java.lang.Integer findBasicRow(int col)
```
    Returns the row in which the given column is basic.
    
    Parameters:
    
    col - index of the column
    
    Returns:
    
    the row that the variable is basic in, or null if the variable is not basic.
  - dropPhase1Objective
```
protected void dropPhase1Objective()
```
    Removes the phase 1 objective function, positive cost non-artificial variables, and the non-basic artificial variables from this tableau.
  - copyArray
```
private void copyArray(double[] src,
                       double[] dest)
```
    Parameters:
    
    src - the source array
    
    dest - the destination array
  - isOptimal
```
boolean isOptimal()
```
    Returns whether the problem is at an optimal state.
    
    Returns:
    
    whether the model has been solved
  - getSolution
```
protected PointValuePair getSolution()
```
    Get the current solution.
    
    Returns:
    
    current solution
  - performRowOperations
```
protected void performRowOperations(int pivotCol,
                                    int pivotRow)
```
    Perform the row operations of the simplex algorithm with the selected pivot column and row.
    
    Parameters:
    
    pivotCol - the pivot column
    
    pivotRow - the pivot row
  - divideRow
```
protected void divideRow(int dividendRowIndex,
                         double divisor)
```
    Divides one row by a given divisor.
    After application of this operation, the following will hold:
    dividendRow = dividendRow / divisor
    Parameters:
    
    dividendRowIndex - index of the row
    
    divisor - value of the divisor
  - subtractRow
```
protected void subtractRow(int minuendRowIndex,
                           int subtrahendRowIndex,
                           double multiplier)
```
    Subtracts a multiple of one row from another.
    After application of this operation, the following will hold:
    minuendRow = minuendRow - multiple * subtrahendRow
    Parameters:
    
    minuendRowIndex - row index
    
    subtrahendRowIndex - row index
    
    multiplier - multiplication factor
  - getWidth
```
protected final int getWidth()
```
    Get the width of the tableau.
    
    Returns:
    
    width of the tableau
  - getHeight
```
protected final int getHeight()
```
    Get the height of the tableau.
    
    Returns:
    
    height of the tableau
  - getEntry
```
protected final double getEntry(int row,
                                int column)
```
    Get an entry of the tableau.
    
    Parameters:
    
    row - row index
    
    column - column index
    
    Returns:
    
    entry at (row, column)
  - setEntry
```
protected final void setEntry(int row,
                              int column,
                              double value)
```
    Set an entry of the tableau.
    
    Parameters:
    
    row - row index
    
    column - column index
    
    value - for the entry
  - getSlackVariableOffset
```
protected final int getSlackVariableOffset()
```
    Get the offset of the first slack variable.
    
    Returns:
    
    offset of the first slack variable
  - getArtificialVariableOffset
```
protected final int getArtificialVariableOffset()
```
    Get the offset of the first artificial variable.
    
    Returns:
    
    offset of the first artificial variable
  - getRhsOffset
```
protected final int getRhsOffset()
```
    Get the offset of the right hand side.
    
    Returns:
    
    offset of the right hand side
  - getNumDecisionVariables
```
protected final int getNumDecisionVariables()
```
    Get the number of decision variables.
    If variables are not restricted to positive values, this will include 1 extra decision variable to represent the absolute value of the most negative variable.
    
    Returns:
    
    number of decision variables
    
    See Also:
    
    getOriginalNumDecisionVariables()
  - getOriginalNumDecisionVariables
```
protected final int getOriginalNumDecisionVariables()
```
    Get the original number of decision variables.
    
    Returns:
    
    original number of decision variables
    
    See Also:
    
    getNumDecisionVariables()
  - getNumSlackVariables
```
protected final int getNumSlackVariables()
```
    Get the number of slack variables.
    
    Returns:
    
    number of slack variables
  - getNumArtificialVariables
```
protected final int getNumArtificialVariables()
```
    Get the number of artificial variables.
    
    Returns:
    
    number of artificial variables
  - getRow
```
protected final double[] getRow(int row)
```
    Get the row from the tableau.
    
    Parameters:
    
    row - the row index
    
    Returns:
    
    the reference to the underlying row data
  - getData
```
protected final double[][] getData()
```
    Get the tableau data.
    
    Returns:
    
    tableau data
  - equals
```
public boolean equals(java.lang.Object other)
```
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object
  - writeObject
```
private void writeObject(java.io.ObjectOutputStream oos)
                  throws java.io.IOException
```
    Serialize the instance.
    
    Parameters:
    
    oos - stream where object should be written
    
    Throws:
    
    java.io.IOException - if object cannot be written to stream
  - readObject
```
private void readObject(java.io.ObjectInputStream ois)
                 throws java.lang.ClassNotFoundException,
                        java.io.IOException
```
    Deserialize the instance.
    
    Parameters:
    
    ois - stream from which the object should be read
    
    Throws:
    
    java.lang.ClassNotFoundException - if a class in the stream cannot be found
    
    java.io.IOException - if object cannot be read from the stream

Class SimplexTableau

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

NEGATIVE_VAR_COLUMN_LABEL

serialVersionUID

f

constraints

restrictToNonNegative

columnLabels

tableau

numDecisionVariables

numSlackVariables

numArtificialVariables

epsilon

maxUlps

basicVariables

basicRows

Constructor Detail

SimplexTableau

SimplexTableau

Method Detail

initializeColumnLabels

createTableau

normalizeConstraints

normalize

getNumObjectiveFunctions

getConstraintTypeCounts

getInvertedCoefficientSum

getBasicRow

getBasicVariable

initializeBasicVariables

findBasicRow

dropPhase1Objective

copyArray

isOptimal

getSolution

performRowOperations

divideRow

subtractRow

getWidth

getHeight

getEntry

setEntry

getSlackVariableOffset

getArtificialVariableOffset

getRhsOffset

getNumDecisionVariables

getOriginalNumDecisionVariables

getNumSlackVariables

getNumArtificialVariables

getRow

getData

equals

hashCode

writeObject

readObject