1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
|
/****************************************************************************
**
** Copyright (C) 2013 Digia Plc and/or its subsidiary(-ies).
** Contact: http://www.qt-project.org/legal
**
** This file is part of the QtGui module of the Qt Toolkit.
**
** $QT_BEGIN_LICENSE:LGPL$
** Commercial License Usage
** Licensees holding valid commercial Qt licenses may use this file in
** accordance with the commercial license agreement provided with the
** Software or, alternatively, in accordance with the terms contained in
** a written agreement between you and Digia. For licensing terms and
** conditions see http://qt.digia.com/licensing. For further information
** use the contact form at http://qt.digia.com/contact-us.
**
** GNU Lesser General Public License Usage
** Alternatively, this file may be used under the terms of the GNU Lesser
** General Public License version 2.1 as published by the Free Software
** Foundation and appearing in the file LICENSE.LGPL included in the
** packaging of this file. Please review the following information to
** ensure the GNU Lesser General Public License version 2.1 requirements
** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
**
** In addition, as a special exception, Digia gives you certain additional
** rights. These rights are described in the Digia Qt LGPL Exception
** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
**
** GNU General Public License Usage
** Alternatively, this file may be used under the terms of the GNU
** General Public License version 3.0 as published by the Free Software
** Foundation and appearing in the file LICENSE.GPL included in the
** packaging of this file. Please review the following information to
** ensure the GNU General Public License version 3.0 requirements will be
** met: http://www.gnu.org/copyleft/gpl.html.
**
**
** $QT_END_LICENSE$
**
****************************************************************************/
#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 <QtCore/qhash.h>
#include <QtCore/qpair.h>
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(0) {}
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::fromAscii("-- QSimplexConstraint %1 --").arg(quintptr(this), 0, 16);
QHash<QSimplexVariable *, qreal>::const_iterator iter;
for (iter = variables.constBegin(); iter != variables.constEnd(); ++iter) {
result += QString::fromAscii(" %1 x %2").arg(iter.value()).arg(quintptr(iter.key()), 0, 16);
}
switch (ratio) {
case LessOrEqual:
result += QString::fromAscii(" (less) <= %1").arg(constant);
break;
case MoreOrEqual:
result += QString::fromAscii(" (more) >= %1").arg(constant);
break;
default:
result += QString::fromAscii(" (eqal) == %1").arg(constant);
}
return result;
}
#endif
};
class QSimplex
{
public:
QSimplex();
virtual ~QSimplex();
qreal solveMin();
qreal solveMax();
bool setConstraints(const QList<QSimplexConstraint *> constraints);
void setObjective(QSimplexConstraint *objective);
void dumpMatrix();
private:
// Matrix handling
qreal valueAt(int row, int column);
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
|
