qsimplex_p.h

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// Copyright (C) 2016 The Qt Company Ltd.
// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
 
#ifndef QSIMPLEX_P_H
#define QSIMPLEX_P_H
 
//
//  W A R N I N G
//  -------------
//
// This file is not part of the Qt API.  It exists purely as an
// implementation detail.  This header file may change from version to
// version without notice, or even be removed.
//
// We mean it.
//
 
#include <QtWidgets/private/qtwidgetsglobal_p.h>
#include <QtCore/qhash.h>
#include <QtCore/qpair.h>
#include <QtCore/qstring.h>
 
QT_REQUIRE_CONFIG(graphicsview);
 
QT_BEGIN_NAMESPACE
 
struct QSimplexVariable
{
    QSimplexVariable() : result(0), index(0) {}
 
    qreal result;
    int index;
};
 
 
/*!
  \internal
 
  Representation of a LP constraint like:
 
    (c1 * X1) + (c2 * X2) + ...  =  K
                             or <=  K
                             or >=  K
 
    Where (ci, Xi) are the pairs in "variables" and K the real "constant".
*/
struct QSimplexConstraint
{
    QSimplexConstraint() : constant(0), ratio(Equal), artificial(nullptr) {}
 
    enum Ratio {
        LessOrEqual = 0,
        Equal,
        MoreOrEqual
    };
 
    QHash<QSimplexVariable *, qreal> variables;
    qreal constant;
    Ratio ratio;
 
    QPair<QSimplexVariable *, qreal> helper;
    QSimplexVariable * artificial;
 
    void invert();
 
    bool isSatisfied() {
        qreal leftHandSide(0);
 
        QHash<QSimplexVariable *, qreal>::const_iterator iter;
        for (iter = variables.constBegin(); iter != variables.constEnd(); ++iter) {
            leftHandSide += iter.value() * iter.key()->result;
        }
 
        Q_ASSERT(constant > 0 || qFuzzyCompare(1, 1 + constant));
 
        if ((leftHandSide == constant) || qAbs(leftHandSide - constant) < 0.0000001)
            return true;
 
        switch (ratio) {
        case LessOrEqual:
            return leftHandSide < constant;
        case MoreOrEqual:
            return leftHandSide > constant;
        default:
            return false;
        }
    }
 
#ifdef QT_DEBUG
    QString toString() {
        QString result;
        result += QString::fromLatin1("-- QSimplexConstraint %1 --").arg(quintptr(this), 0, 16);
 
        QHash<QSimplexVariable *, qreal>::const_iterator iter;
        for (iter = variables.constBegin(); iter != variables.constEnd(); ++iter) {
            result += QString::fromLatin1("  %1 x %2").arg(iter.value()).arg(quintptr(iter.key()), 0, 16);
        }
 
        switch (ratio) {
        case LessOrEqual:
            result += QString::fromLatin1("  (less) <= %1").arg(constant);
            break;
        case MoreOrEqual:
            result += QString::fromLatin1("  (more) >= %1").arg(constant);
            break;
        default:
            result += QString::fromLatin1("  (eqal) == %1").arg(constant);
        }
 
        return result;
    }
#endif
};
 
class QSimplex
{
    Q_DISABLE_COPY_MOVE(QSimplex)
public:
    QSimplex();
    ~QSimplex();
 
    qreal solveMin();
    qreal solveMax();
 
    bool setConstraints(const QList<QSimplexConstraint *> &constraints);
    void setObjective(QSimplexConstraint *objective);
 
    void dumpMatrix();
 
private:
    // Matrix handling
    inline qreal valueAt(int row, int column);
    inline void setValueAt(int row, int column, qreal value);
    void clearRow(int rowIndex);
    void clearColumns(int first, int last);
    void combineRows(int toIndex, int fromIndex, qreal factor);
 
    // Simplex
    bool simplifyConstraints(QList<QSimplexConstraint *> *constraints);
    int findPivotColumn();
    int pivotRowForColumn(int column);
    void reducedRowEchelon();
    bool iterate();
 
    // Helpers
    void clearDataStructures();
    void solveMaxHelper();
    enum SolverFactor { Minimum = -1, Maximum = 1 };
    qreal solver(SolverFactor factor);
    void collectResults();
 
    QList<QSimplexConstraint *> constraints;
    QList<QSimplexVariable *> variables;
    QSimplexConstraint *objective;
 
    int rows;
    int columns;
    int firstArtificial;
 
    qreal *matrix;
};
 
inline qreal QSimplex::valueAt(int rowIndex, int columnIndex)
{
    return matrix[rowIndex * columns + columnIndex];
}
 
inline void QSimplex::setValueAt(int rowIndex, int columnIndex, qreal value)
{
    matrix[rowIndex * columns + columnIndex] = value;
}
 
QT_END_NAMESPACE
 
#endif // QSIMPLEX_P_H