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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program. If not, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include <iostream>
#include "maths/matrix2.h"
namespace regina {
Matrix2 Matrix2::inverse() const {
long det = data_[0][0] * data_[1][1] - data_[0][1] * data_[1][0];
if (det == 1)
return Matrix2(data_[1][1], -data_[0][1], -data_[1][0], data_[0][0]);
else if (det == -1)
return Matrix2(-data_[1][1], data_[0][1], data_[1][0], -data_[0][0]);
else
return Matrix2();
}
Matrix2& Matrix2::operator *= (const Matrix2& other) {
long tmp00 = data_[0][0] * other.data_[0][0] +
data_[0][1] * other.data_[1][0];
long tmp01 = data_[0][0] * other.data_[0][1] +
data_[0][1] * other.data_[1][1];
long tmp10 = data_[1][0] * other.data_[0][0] +
data_[1][1] * other.data_[1][0];
long tmp11 = data_[1][0] * other.data_[0][1] +
data_[1][1] * other.data_[1][1];
data_[0][0] = tmp00;
data_[0][1] = tmp01;
data_[1][0] = tmp10;
data_[1][1] = tmp11;
return *this;
}
bool Matrix2::invert() {
long det = data_[0][0] * data_[1][1] - data_[0][1] * data_[1][0];
if (det == 1) {
long tmp = data_[0][0];
data_[0][0] = data_[1][1];
data_[1][1] = tmp;
data_[0][1] = -data_[0][1];
data_[1][0] = -data_[1][0];
return true;
} else if (det == -1) {
long tmp = data_[0][0];
data_[0][0] = -data_[1][1];
data_[1][1] = -tmp;
return true;
} else
return false;
}
std::strong_ordering simplerThreeWay(const Matrix2& m1, const Matrix2& m2) {
long maxAbs1 = 0, maxAbs2 = 0;
unsigned nZeroes1 = 0, nZeroes2 = 0;
unsigned nNeg1 = 0, nNeg2 = 0;
int i, j;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++) {
if (m1[i][j] > maxAbs1)
maxAbs1 = m1[i][j];
if (m1[i][j] < -maxAbs1)
maxAbs1 = -m1[i][j];
if (m2[i][j] > maxAbs2)
maxAbs2 = m2[i][j];
if (m2[i][j] < -maxAbs2)
maxAbs2 = -m2[i][j];
if (m1[i][j] == 0)
nZeroes1++;
else if (m1[i][j] < 0)
nNeg1++;
if (m2[i][j] == 0)
nZeroes2++;
else if (m2[i][j] < 0)
nNeg2++;
}
if (maxAbs1 < maxAbs2)
return std::strong_ordering::less;
if (maxAbs1 > maxAbs2)
return std::strong_ordering::greater;
if (nZeroes1 > nZeroes2)
return std::strong_ordering::less;
if (nZeroes1 < nZeroes2)
return std::strong_ordering::greater;
if (nNeg1 < nNeg2)
return std::strong_ordering::less;
if (nNeg1 > nNeg2)
return std::strong_ordering::greater;
// Go lexicograhpic.
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
if (m1[i][j] < m2[i][j])
return std::strong_ordering::less;
else if (m1[i][j] > m2[i][j])
return std::strong_ordering::greater;
// They're the same.
return std::strong_ordering::equal;
}
std::strong_ordering simplerThreeWay(
const Matrix2& pair1first, const Matrix2& pair1second,
const Matrix2& pair2first, const Matrix2& pair2second) {
long maxAbs0 = 0, maxAbs1 = 0;
unsigned nZeroes0 = 0, nZeroes1 = 0;
unsigned nNeg0 = 0, nNeg1 = 0;
int i, j;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++) {
if (pair1first[i][j] > maxAbs0)
maxAbs0 = pair1first[i][j];
if (pair1first[i][j] < -maxAbs0)
maxAbs0 = -pair1first[i][j];
if (pair1second[i][j] > maxAbs0)
maxAbs0 = pair1second[i][j];
if (pair1second[i][j] < -maxAbs0)
maxAbs0 = -pair1second[i][j];
if (pair2first[i][j] > maxAbs1)
maxAbs1 = pair2first[i][j];
if (pair2first[i][j] < -maxAbs1)
maxAbs1 = -pair2first[i][j];
if (pair2second[i][j] > maxAbs1)
maxAbs1 = pair2second[i][j];
if (pair2second[i][j] < -maxAbs1)
maxAbs1 = -pair2second[i][j];
if (pair1first[i][j] == 0)
nZeroes0++;
else if (pair1first[i][j] < 0)
nNeg0++;
if (pair1second[i][j] == 0)
nZeroes0++;
else if (pair1second[i][j] < 0)
nNeg0++;
if (pair2first[i][j] == 0)
nZeroes1++;
else if (pair2first[i][j] < 0)
nNeg1++;
if (pair2second[i][j] == 0)
nZeroes1++;
else if (pair2second[i][j] < 0)
nNeg1++;
}
if (maxAbs0 < maxAbs1)
return std::strong_ordering::less;
if (maxAbs0 > maxAbs1)
return std::strong_ordering::greater;
if (nZeroes0 > nZeroes1)
return std::strong_ordering::less;
if (nZeroes0 < nZeroes1)
return std::strong_ordering::greater;
if (nNeg0 < nNeg1)
return std::strong_ordering::less;
if (nNeg0 > nNeg1)
return std::strong_ordering::greater;
// Go lexicograhpic.
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
if (pair1first[i][j] < pair2first[i][j])
return std::strong_ordering::less;
else if (pair1first[i][j] > pair2first[i][j])
return std::strong_ordering::greater;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
if (pair1second[i][j] < pair2second[i][j])
return std::strong_ordering::less;
else if (pair1second[i][j] > pair2second[i][j])
return std::strong_ordering::greater;
// They're the same.
return std::strong_ordering::equal;
}
} // namespace regina
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