SimplexTableau.java
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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math4.legacy.optim.linear;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.TreeSet;
import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
import org.apache.commons.math4.legacy.linear.Array2DRowRealMatrix;
import org.apache.commons.math4.legacy.linear.RealVector;
import org.apache.commons.math4.legacy.optim.PointValuePair;
import org.apache.commons.math4.legacy.optim.nonlinear.scalar.GoalType;
import org.apache.commons.numbers.core.Precision;
/**
* A tableau for use in the Simplex method.
*
* <p>
* Example:
* <pre>
* 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
* </pre>
* W: Phase 1 objective function<br>
* Z: Phase 2 objective function<br>
* x1 & x2: Decision variables<br>
* x-: Extra decision variable to allow for negative values<br>
* s1 & s2: Slack/Surplus variables<br>
* a1: Artificial variable<br>
* RHS: Right hand side<br>
*
* Note on usage and safety:
* The class is package private. It is not meant for public usage.
* The core data structure, the tableau field, is mutated internally and
* even reallocated when necessary.
* Proper usage of this class is demonstrated in SimplexSolver,
* where the class is only ever constructed in a method (never a field
* of an object), and its lifetime, is therefore bound to a single thread (the
* thread that's invoking the method).
*
* @since 2.0
*/
class SimplexTableau {
/** Column label for negative vars. */
private static final String NEGATIVE_VAR_COLUMN_LABEL = "x-";
/** bit mask for IEEE double exponent. */
private static final long EXPN = 0x7ff0000000000000L;
/** bit mask for IEEE double mantissa and sign. */
private static final long FRAC = 0x800fffffffffffffL;
/** max IEEE exponent is 2047. */
private static final int MAX_IEEE_EXP = 2047;
/** min IEEE exponent is 0. */
private static final int MIN_IEEE_EXP = 0;
/** IEEE exponent is kept in an offset form, 1023 is zero. */
private static final int OFFSET_IEEE_EXP = 1023;
/** double exponent shift per IEEE standard. */
private static final int IEEE_EXPONENT_SHIFT = 52;
/** Linear objective function. */
private final LinearObjectiveFunction f;
/** Linear constraints. */
private final List<LinearConstraint> constraints;
/** Whether to restrict the variables to non-negative values. */
private final boolean restrictToNonNegative;
/** The variables each column represents. */
private final List<String> columnLabels = new ArrayList<>();
/** Simple tableau. */
private Array2DRowRealMatrix tableau;
/** Number of decision variables. */
private final int numDecisionVariables;
/** Number of slack variables. */
private final int numSlackVariables;
/** Number of artificial variables. */
private int numArtificialVariables;
/** Amount of error to accept when checking for optimality. */
private final double epsilon;
/** Amount of error to accept in floating point comparisons. */
private final int maxUlps;
/** Maps basic variables to row they are basic in. */
private int[] basicVariables;
/** Maps rows to their corresponding basic variables. */
private int[] basicRows;
/** changes in floating point exponent to scale the input. */
private int[] variableExpChange;
/**
* Builds a tableau for a linear problem.
*
* @param f Linear objective function.
* @param constraints Linear constraints.
* @param goalType Optimization goal: either {@link GoalType#MAXIMIZE}
* or {@link GoalType#MINIMIZE}.
* @param restrictToNonNegative Whether to restrict the variables to non-negative values.
* @param epsilon Amount of error to accept when checking for optimality.
* @throws DimensionMismatchException if the dimension of the constraints does not match the
* dimension of the objective function
*/
SimplexTableau(final LinearObjectiveFunction f,
final Collection<LinearConstraint> constraints,
final GoalType goalType,
final boolean restrictToNonNegative,
final double epsilon) {
this(f, constraints, goalType, restrictToNonNegative, epsilon, SimplexSolver.DEFAULT_ULPS);
}
/**
* Build a tableau for a linear problem.
* @param f linear objective function
* @param constraints linear constraints
* @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE} or {@link GoalType#MINIMIZE}
* @param restrictToNonNegative whether to restrict the variables to non-negative values
* @param epsilon amount of error to accept when checking for optimality
* @param maxUlps amount of error to accept in floating point comparisons
* @throws DimensionMismatchException if the dimension of the constraints does not match the
* dimension of the objective function
*/
SimplexTableau(final LinearObjectiveFunction f,
final Collection<LinearConstraint> constraints,
final GoalType goalType,
final boolean restrictToNonNegative,
final double epsilon,
final int maxUlps) throws DimensionMismatchException {
checkDimensions(f, constraints);
this.f = f;
this.constraints = normalizeConstraints(constraints);
this.restrictToNonNegative = restrictToNonNegative;
this.epsilon = epsilon;
this.maxUlps = maxUlps;
this.numDecisionVariables = f.getCoefficients().getDimension() + (restrictToNonNegative ? 0 : 1);
this.numSlackVariables = getConstraintTypeCounts(Relationship.LEQ) +
getConstraintTypeCounts(Relationship.GEQ);
this.numArtificialVariables = getConstraintTypeCounts(Relationship.EQ) +
getConstraintTypeCounts(Relationship.GEQ);
this.tableau = createTableau(goalType == GoalType.MAXIMIZE);
// initialize the basic variables for phase 1:
// we know that only slack or artificial variables can be basic
initializeBasicVariables(getSlackVariableOffset());
initializeColumnLabels();
}
/**
* Checks that the dimensions of the objective function and the constraints match.
* @param objectiveFunction the objective function
* @param c the set of constraints
* @throws DimensionMismatchException if the constraint dimensions do not match with the
* dimension of the objective function
*/
private void checkDimensions(final LinearObjectiveFunction objectiveFunction,
final Collection<LinearConstraint> c) {
final int dimension = objectiveFunction.getCoefficients().getDimension();
for (final LinearConstraint constraint : c) {
final int constraintDimension = constraint.getCoefficients().getDimension();
if (constraintDimension != dimension) {
throw new DimensionMismatchException(constraintDimension, dimension);
}
}
}
/**
* Initialize the labels for the columns.
*/
protected void initializeColumnLabels() {
if (getNumObjectiveFunctions() == 2) {
columnLabels.add("W");
}
columnLabels.add("Z");
for (int i = 0; i < getOriginalNumDecisionVariables(); i++) {
columnLabels.add("x" + i);
}
if (!restrictToNonNegative) {
columnLabels.add(NEGATIVE_VAR_COLUMN_LABEL);
}
for (int i = 0; i < getNumSlackVariables(); i++) {
columnLabels.add("s" + i);
}
for (int i = 0; i < getNumArtificialVariables(); i++) {
columnLabels.add("a" + i);
}
columnLabels.add("RHS");
}
/**
* Create the tableau by itself.
* @param maximize if true, goal is to maximize the objective function
* @return created tableau
*/
protected Array2DRowRealMatrix createTableau(final boolean maximize) {
// create a matrix of the correct size
int width = numDecisionVariables + numSlackVariables +
numArtificialVariables + getNumObjectiveFunctions() + 1; // + 1 is for RHS
int height = constraints.size() + getNumObjectiveFunctions();
Array2DRowRealMatrix matrix = new Array2DRowRealMatrix(height, width);
// initialize the objective function rows
if (getNumObjectiveFunctions() == 2) {
matrix.setEntry(0, 0, -1);
}
int zIndex = (getNumObjectiveFunctions() == 1) ? 0 : 1;
matrix.setEntry(zIndex, zIndex, maximize ? 1 : -1);
double[][] scaled = new double[constraints.size() + 1][];
RealVector objectiveCoefficients = maximize ? f.getCoefficients().mapMultiply(-1) : f.getCoefficients();
scaled[0] = objectiveCoefficients.toArray();
double[] scaledRhs = new double[constraints.size() + 1];
double value = maximize ? f.getConstantTerm() : -1 * f.getConstantTerm();
scaledRhs[0] = value;
for (int i = 0; i < constraints.size(); i++) {
LinearConstraint constraint = constraints.get(i);
scaled[i + 1] = constraint.getCoefficients().toArray();
scaledRhs[i + 1] = constraint.getValue();
}
variableExpChange = new int[scaled[0].length];
scale(scaled, scaledRhs);
copyArray(scaled[0], matrix.getDataRef()[zIndex]);
matrix.setEntry(zIndex, width - 1, scaledRhs[0]);
if (!restrictToNonNegative) {
matrix.setEntry(zIndex, getSlackVariableOffset() - 1,
getInvertedCoefficientSum(scaled[0]));
}
// initialize the constraint rows
int slackVar = 0;
int artificialVar = 0;
for (int i = 0; i < constraints.size(); i++) {
final LinearConstraint constraint = constraints.get(i);
final int row = getNumObjectiveFunctions() + i;
// decision variable coefficients
copyArray(scaled[i + 1], matrix.getDataRef()[row]);
// x-
if (!restrictToNonNegative) {
matrix.setEntry(row, getSlackVariableOffset() - 1,
getInvertedCoefficientSum(scaled[i + 1]));
}
// RHS
matrix.setEntry(row, width - 1, scaledRhs[i + 1]);
// slack variables
if (constraint.getRelationship() == Relationship.LEQ) {
matrix.setEntry(row, getSlackVariableOffset() + slackVar++, 1); // slack
} else if (constraint.getRelationship() == Relationship.GEQ) {
matrix.setEntry(row, getSlackVariableOffset() + slackVar++, -1); // excess
}
// artificial variables
if (constraint.getRelationship() == Relationship.EQ ||
constraint.getRelationship() == Relationship.GEQ) {
matrix.setEntry(0, getArtificialVariableOffset() + artificialVar, 1);
matrix.setEntry(row, getArtificialVariableOffset() + artificialVar++, 1);
matrix.setRowVector(0, matrix.getRowVector(0).subtract(matrix.getRowVector(row)));
}
}
return matrix;
}
/** We scale the constants in the equations and objective, which means we try
* to get the IEEE double exponent as close to zero (1023) as possible, which makes the
* constants closer to 1.
* We use exponent shifts instead of division because that introduces no bit errors.
*
* @param scaled coefficients before scaling
* @param scaledRhs right hand side before scaling
*/
private void scale(double[][] scaled, double[] scaledRhs) {
/*
first transform across:
c0 x0 + c1 x1 + ... + cn xn = vn ==> (2^expChange) * (c0 x0 + c1 x1 + ... + cn xn = vn)
expChange will be negative if the constants are larger than 1,
it'll be positive if the constants are less than 1.
*/
for (int i = 0; i < scaled.length; i++) {
int minExp = MAX_IEEE_EXP + 1;
int maxExp = MIN_IEEE_EXP - 1;
for (double d: scaled[i]) {
if (d != 0) {
int e = exponent(d);
if (e < minExp) {
minExp = e;
}
if (e > maxExp) {
maxExp = e;
}
}
}
if (scaledRhs[i] != 0) {
final int e = exponent(scaledRhs[i]);
if (e < minExp) {
minExp = e;
}
if (e > maxExp) {
maxExp = e;
}
}
final int expChange = computeExpChange(minExp, maxExp);
if (expChange != 0) {
scaledRhs[i] = updateExponent(scaledRhs[i], expChange);
updateExponent(scaled[i], expChange);
}
}
/*
second, transform down the columns. this is like defining a new variable for that column
that is yi = xi * (2^expChange)
After solving for yi, we compute xi by shifting again. See getSolution()
*/
for (int i = 0; i < variableExpChange.length; i++) {
int minExp = MAX_IEEE_EXP + 1;
int maxExp = MIN_IEEE_EXP - 1;
for (double[] coefficients : scaled) {
final double d = coefficients[i];
if (d != 0) {
int e = exponent(d);
if (e < minExp) {
minExp = e;
}
if (e > maxExp) {
maxExp = e;
}
}
}
final int expChange = computeExpChange(minExp, maxExp);
variableExpChange[i] = expChange;
if (expChange != 0) {
for (double[] coefficients : scaled) {
coefficients[i] = updateExponent(coefficients[i], expChange);
}
}
}
}
/**
* Given the minimum and maximum value of the exponent of two {@code double}
* values, pick a change in exponent to bring those values closer to 1.
*
* @param minExp Smallest exponent.
* @param maxExp Largest exponent.
* @return the new exponent.
*/
private int computeExpChange(int minExp, int maxExp) {
int expChange = 0;
if (minExp <= MAX_IEEE_EXP &&
minExp > OFFSET_IEEE_EXP) {
expChange = OFFSET_IEEE_EXP - minExp;
} else if (maxExp >= MIN_IEEE_EXP &&
maxExp < OFFSET_IEEE_EXP) {
expChange = OFFSET_IEEE_EXP - maxExp;
}
return expChange;
}
/**
* Changes the exponent of every member of the array by the given amount.
*
* @param dar array of doubles to change
* @param exp exponent value to change
*/
private static void updateExponent(double[] dar, int exp) {
for (int i = 0; i < dar.length; i++) {
dar[i] = updateExponent(dar[i], exp);
}
}
/**
* Extract the exponent of a {@code double}.
*
* @param d value to extract the exponent from
* @return the IEEE exponent in the EXPN bits, as an integer
*/
private static int exponent(double d) {
final long bits = Double.doubleToLongBits(d);
return (int) ((bits & EXPN) >>> IEEE_EXPONENT_SHIFT);
}
/**
* Changes the exponent of a number by the given amount.
*
* @param d value to change
* @param exp exponent to add to the existing exponent (may be negative)
* @return a double with the same sign/mantissa bits as d, but exponent changed by exp
*/
private static double updateExponent(double d, int exp) {
if (d == 0 ||
exp == 0) {
return d;
}
final long bits = Double.doubleToLongBits(d);
return Double.longBitsToDouble((bits & FRAC) | ((((bits & EXPN) >>> IEEE_EXPONENT_SHIFT) + exp) << IEEE_EXPONENT_SHIFT));
}
/**
* Get new versions of the constraints which have positive right hand sides.
* @param originalConstraints original (not normalized) constraints
* @return new versions of the constraints
*/
public List<LinearConstraint> normalizeConstraints(Collection<LinearConstraint> originalConstraints) {
final List<LinearConstraint> normalized = new ArrayList<>(originalConstraints.size());
for (LinearConstraint constraint : originalConstraints) {
normalized.add(normalize(constraint));
}
return normalized;
}
/**
* Get a new equation equivalent to this one with a positive right hand side.
* @param constraint reference constraint
* @return new equation
*/
private LinearConstraint normalize(final LinearConstraint constraint) {
if (constraint.getValue() < 0) {
return new LinearConstraint(constraint.getCoefficients().mapMultiply(-1),
constraint.getRelationship().oppositeRelationship(),
-1 * constraint.getValue());
}
return new LinearConstraint(constraint.getCoefficients(),
constraint.getRelationship(), constraint.getValue());
}
/**
* Get the number of objective functions in this tableau.
* @return 2 for Phase 1. 1 for Phase 2.
*/
protected final int getNumObjectiveFunctions() {
return this.numArtificialVariables > 0 ? 2 : 1;
}
/**
* Get a count of constraints corresponding to a specified relationship.
* @param relationship relationship to count
* @return number of constraint with the specified relationship
*/
private int getConstraintTypeCounts(final Relationship relationship) {
int count = 0;
for (final LinearConstraint constraint : constraints) {
if (constraint.getRelationship() == relationship) {
++count;
}
}
return count;
}
/**
* Get the -1 times the sum of all coefficients in the given array.
* @param coefficients coefficients to sum
* @return the -1 times the sum of all coefficients in the given array.
*/
private static double getInvertedCoefficientSum(final double[] coefficients) {
double sum = 0;
for (double coefficient : coefficients) {
sum -= coefficient;
}
return sum;
}
/**
* Checks whether the given column is basic.
* @param col index of the column to check
* @return the row that the variable is basic in. null if the column is not basic
*/
protected Integer getBasicRow(final int col) {
final int row = basicVariables[col];
return row == -1 ? null : row;
}
/**
* Returns the variable that is basic in this row.
* @param row the index of the row to check
* @return the variable that is basic for this row.
*/
protected int getBasicVariable(final int row) {
return basicRows[row];
}
/**
* Initializes the basic variable / row mapping.
* @param startColumn the column to start
*/
private void initializeBasicVariables(final int startColumn) {
basicVariables = new int[getWidth() - 1];
basicRows = new int[getHeight()];
Arrays.fill(basicVariables, -1);
for (int i = startColumn; i < getWidth() - 1; i++) {
Integer row = findBasicRow(i);
if (row != null) {
basicVariables[i] = row;
basicRows[row] = i;
}
}
}
/**
* Returns the row in which the given column is basic.
* @param col index of the column
* @return the row that the variable is basic in, or {@code null} if the variable is not basic.
*/
private Integer findBasicRow(final int col) {
Integer row = null;
for (int i = 0; i < getHeight(); i++) {
final double entry = getEntry(i, col);
if (Precision.equals(entry, 1d, maxUlps) && row == null) {
row = i;
} else if (!Precision.equals(entry, 0d, maxUlps)) {
return null;
}
}
return row;
}
/**
* Removes the phase 1 objective function, positive cost non-artificial variables,
* and the non-basic artificial variables from this tableau.
*/
protected void dropPhase1Objective() {
if (getNumObjectiveFunctions() == 1) {
return;
}
final Set<Integer> columnsToDrop = new TreeSet<>();
columnsToDrop.add(0);
// positive cost non-artificial variables
for (int i = getNumObjectiveFunctions(); i < getArtificialVariableOffset(); i++) {
final double entry = getEntry(0, i);
if (Precision.compareTo(entry, 0d, epsilon) > 0) {
columnsToDrop.add(i);
}
}
// non-basic artificial variables
for (int i = 0; i < getNumArtificialVariables(); i++) {
int col = i + getArtificialVariableOffset();
if (getBasicRow(col) == null) {
columnsToDrop.add(col);
}
}
final double[][] matrix = new double[getHeight() - 1][getWidth() - columnsToDrop.size()];
for (int i = 1; i < getHeight(); i++) {
int col = 0;
for (int j = 0; j < getWidth(); j++) {
if (!columnsToDrop.contains(j)) {
matrix[i - 1][col++] = getEntry(i, j);
}
}
}
// remove the columns in reverse order so the indices are correct
Integer[] drop = columnsToDrop.toArray(new Integer[0]);
for (int i = drop.length - 1; i >= 0; i--) {
columnLabels.remove((int) drop[i]);
}
this.tableau = new Array2DRowRealMatrix(matrix);
this.numArtificialVariables = 0;
// need to update the basic variable mappings as row/columns have been dropped
initializeBasicVariables(getNumObjectiveFunctions());
}
/**
* @param src the source array
* @param dest the destination array
*/
private void copyArray(final double[] src, final double[] dest) {
System.arraycopy(src, 0, dest, getNumObjectiveFunctions(), src.length);
}
/**
* Returns whether the problem is at an optimal state.
* @return whether the model has been solved
*/
boolean isOptimal() {
final double[] objectiveFunctionRow = getRow(0);
final int end = getRhsOffset();
for (int i = getNumObjectiveFunctions(); i < end; i++) {
final double entry = objectiveFunctionRow[i];
if (Precision.compareTo(entry, 0d, epsilon) < 0) {
return false;
}
}
return true;
}
/**
* Get the current solution.
* @return current solution
*/
protected PointValuePair getSolution() {
int negativeVarColumn = columnLabels.indexOf(NEGATIVE_VAR_COLUMN_LABEL);
Integer negativeVarBasicRow = negativeVarColumn > 0 ? getBasicRow(negativeVarColumn) : null;
double mostNegative = negativeVarBasicRow == null ? 0 : getEntry(negativeVarBasicRow, getRhsOffset());
final Set<Integer> usedBasicRows = new HashSet<>();
final double[] coefficients = new double[getOriginalNumDecisionVariables()];
for (int i = 0; i < coefficients.length; i++) {
int colIndex = columnLabels.indexOf("x" + i);
if (colIndex < 0) {
coefficients[i] = 0;
continue;
}
Integer basicRow = getBasicRow(colIndex);
if (basicRow != null && basicRow == 0) {
// if the basic row is found to be the objective function row
// set the coefficient to 0 -> this case handles unconstrained
// variables that are still part of the objective function
coefficients[i] = 0;
} else if (usedBasicRows.contains(basicRow)) {
// if multiple variables can take a given value
// then we choose the first and set the rest equal to 0
coefficients[i] = 0 - (restrictToNonNegative ? 0 : mostNegative);
} else {
usedBasicRows.add(basicRow);
coefficients[i] =
(basicRow == null ? 0 : getEntry(basicRow, getRhsOffset())) -
(restrictToNonNegative ? 0 : mostNegative);
}
coefficients[i] = updateExponent(coefficients[i], variableExpChange[i]);
}
return new PointValuePair(coefficients, f.value(coefficients));
}
/**
* Perform the row operations of the simplex algorithm with the selected
* pivot column and row.
* @param pivotCol the pivot column
* @param pivotRow the pivot row
*/
protected void performRowOperations(int pivotCol, int pivotRow) {
// set the pivot element to 1
final double pivotVal = getEntry(pivotRow, pivotCol);
divideRow(pivotRow, pivotVal);
// set the rest of the pivot column to 0
for (int i = 0; i < getHeight(); i++) {
if (i != pivotRow) {
final double multiplier = getEntry(i, pivotCol);
if (multiplier != 0.0) {
subtractRow(i, pivotRow, multiplier);
}
}
}
// update the basic variable mappings
final int previousBasicVariable = getBasicVariable(pivotRow);
basicVariables[previousBasicVariable] = -1;
basicVariables[pivotCol] = pivotRow;
basicRows[pivotRow] = pivotCol;
}
/**
* Divides one row by a given divisor.
* <p>
* After application of this operation, the following will hold:
* <pre>dividendRow = dividendRow / divisor</pre>
*
* @param dividendRowIndex index of the row
* @param divisor value of the divisor
*/
protected void divideRow(final int dividendRowIndex, final double divisor) {
final double[] dividendRow = getRow(dividendRowIndex);
for (int j = 0; j < getWidth(); j++) {
dividendRow[j] /= divisor;
}
}
/**
* Subtracts a multiple of one row from another.
* <p>
* After application of this operation, the following will hold:
* <pre>minuendRow = minuendRow - multiple * subtrahendRow</pre>
*
* @param minuendRowIndex row index
* @param subtrahendRowIndex row index
* @param multiplier multiplication factor
*/
protected void subtractRow(final int minuendRowIndex, final int subtrahendRowIndex, final double multiplier) {
final double[] minuendRow = getRow(minuendRowIndex);
final double[] subtrahendRow = getRow(subtrahendRowIndex);
for (int i = 0; i < getWidth(); i++) {
minuendRow[i] -= subtrahendRow[i] * multiplier;
}
}
/**
* Get the width of the tableau.
* @return width of the tableau
*/
protected final int getWidth() {
return tableau.getColumnDimension();
}
/**
* Get the height of the tableau.
* @return height of the tableau
*/
protected final int getHeight() {
return tableau.getRowDimension();
}
/**
* Get an entry of the tableau.
* @param row row index
* @param column column index
* @return entry at (row, column)
*/
protected final double getEntry(final int row, final int column) {
return tableau.getEntry(row, column);
}
/**
* Set an entry of the tableau.
* @param row row index
* @param column column index
* @param value for the entry
*/
protected final void setEntry(final int row, final int column, final double value) {
tableau.setEntry(row, column, value);
}
/**
* Get the offset of the first slack variable.
* @return offset of the first slack variable
*/
protected final int getSlackVariableOffset() {
return getNumObjectiveFunctions() + numDecisionVariables;
}
/**
* Get the offset of the first artificial variable.
* @return offset of the first artificial variable
*/
protected final int getArtificialVariableOffset() {
return getNumObjectiveFunctions() + numDecisionVariables + numSlackVariables;
}
/**
* Get the offset of the right hand side.
* @return offset of the right hand side
*/
protected final int getRhsOffset() {
return getWidth() - 1;
}
/**
* Get the number of decision variables.
* <p>
* 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.
*
* @return number of decision variables
* @see #getOriginalNumDecisionVariables()
*/
protected final int getNumDecisionVariables() {
return numDecisionVariables;
}
/**
* Get the original number of decision variables.
* @return original number of decision variables
* @see #getNumDecisionVariables()
*/
protected final int getOriginalNumDecisionVariables() {
return f.getCoefficients().getDimension();
}
/**
* Get the number of slack variables.
* @return number of slack variables
*/
protected final int getNumSlackVariables() {
return numSlackVariables;
}
/**
* Get the number of artificial variables.
* @return number of artificial variables
*/
protected final int getNumArtificialVariables() {
return numArtificialVariables;
}
/**
* Get the row from the tableau.
* @param row the row index
* @return the reference to the underlying row data
*/
protected final double[] getRow(int row) {
return tableau.getDataRef()[row];
}
/**
* Get the tableau data.
* @return tableau data
*/
protected final double[][] getData() {
return tableau.getData();
}
/** {@inheritDoc} */
@Override
public boolean equals(Object other) {
if (this == other) {
return true;
}
if (other instanceof SimplexTableau) {
SimplexTableau rhs = (SimplexTableau) other;
return restrictToNonNegative == rhs.restrictToNonNegative &&
numDecisionVariables == rhs.numDecisionVariables &&
numSlackVariables == rhs.numSlackVariables &&
numArtificialVariables == rhs.numArtificialVariables &&
epsilon == rhs.epsilon &&
maxUlps == rhs.maxUlps &&
f.equals(rhs.f) &&
constraints.equals(rhs.constraints) &&
tableau.equals(rhs.tableau);
}
return false;
}
/** {@inheritDoc} */
@Override
public int hashCode() {
return Boolean.valueOf(restrictToNonNegative).hashCode() ^
numDecisionVariables ^
numSlackVariables ^
numArtificialVariables ^
Double.valueOf(epsilon).hashCode() ^
maxUlps ^
f.hashCode() ^
constraints.hashCode() ^
tableau.hashCode();
}
}