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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Test Suite *
* *
* 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 "maths/matrixops.h"
#include "maths/matrix.h"
#include "testhelper.h"
using regina::MatrixInt;
class MatrixOpsTest : public testing::Test {
protected:
MatrixInt zero34 { 3, 4 };
MatrixInt zero43 { 4, 3 };
MatrixInt identity3 { MatrixInt::identity(3) };
// SNF diagonal: (2, 6, 12)
MatrixInt square3 {{ 2, 4, 4 },
{ -6, 6, 12 },
{ 10, -4, -16 }};
// SNF diagonal: (1, 1, 6)
MatrixInt rect34 {{ 4, -17, 0, 6 },
{ -2, 4, 9, 0 },
{ 6, -3, -2, 10 }};
// SNF diagonal: (1, 1, 12)
MatrixInt rect43 {{ 4, -17, 0 },
{ 6, -2, 4 },
{ 9, 0, 6 },
{ -3, -2, 10 }};
// SNF diagonal: (1, 4, 0)
MatrixInt redundant34 {{ 3, 8, 11, -5 },
{ 1, 4, 5, -3 },
{ 2, 8, 10, -6 }};
MatrixInt redundant43 { redundant34.transpose() };
// SNF diagonal: (1, 1, 1); has a duplicate column
MatrixInt duplicate34 {{ 1, 1, 1, 1 },
{ 0, 0, 2, 3 },
{ 0, 0, 3, 5 }};
MatrixInt duplicate43 { duplicate34.transpose() };
};
static void verifySNF(const MatrixInt& m, std::initializer_list<long> diag) {
SCOPED_TRACE_REGINA(m);
MatrixInt ans(m);
regina::smithNormalForm(ans);
ASSERT_EQ(ans.rows(), m.rows());
ASSERT_EQ(ans.columns(), m.columns());
for (size_t r = 0; r < ans.rows(); ++r)
for (size_t c = 0; c < ans.columns(); ++c) {
if (r != c || r >= diag.size())
EXPECT_EQ(ans.entry(r, c), 0);
}
size_t i = 0;
for (auto d : diag) {
EXPECT_EQ(ans.entry(i, i), d);
++i;
}
}
TEST_F(MatrixOpsTest, smithNormalForm) {
verifySNF(zero34, { });
verifySNF(zero43, { });
verifySNF(identity3, { 1, 1, 1 });
verifySNF(square3, { 2, 6, 12 });
verifySNF(rect34, { 1, 1, 6 });
verifySNF(rect43, { 1, 1, 12 });
verifySNF(redundant34, { 1, 4 });
verifySNF(redundant43, { 1, 4 });
verifySNF(duplicate34, { 1, 1, 1 });
verifySNF(duplicate43, { 1, 1, 1 });
}
static void verifySNFBasis(const MatrixInt& m, bool metrical) {
SCOPED_TRACE_REGINA(m);
// We assume here that the one-argument smithNormalForm() is known to
// be working. We compare its results with the change-of-basis variant
// of smithNormalForm(), and verify that the change-of-basis matrices
// behave as advertised.
// Get the SNF result from the one-argument routine.
MatrixInt snf(m);
regina::smithNormalForm(snf);
// Do it now with the five-argument routine, to collect
// change of basis matrices.
MatrixInt snfBasis(m);
MatrixInt R, C, invR, invC;
if (metrical)
regina::metricalSmithNormalForm(snfBasis, R, invR, C, invC);
else
regina::smithNormalForm(snfBasis, R, invR, C, invC);
EXPECT_EQ(snf, snfBasis);
ASSERT_EQ(R.rows(), m.columns());
ASSERT_EQ(R.columns(), m.columns());
ASSERT_EQ(invR.rows(), m.columns());
ASSERT_EQ(invR.columns(), m.columns());
ASSERT_EQ(C.rows(), m.rows());
ASSERT_EQ(C.columns(), m.rows());
ASSERT_EQ(invC.rows(), m.rows());
ASSERT_EQ(invC.columns(), m.rows());
EXPECT_TRUE((R * invR).isIdentity());
EXPECT_TRUE((C * invC).isIdentity());
EXPECT_EQ((C * m * R), snfBasis);
EXPECT_EQ((invC * snfBasis * invR), m);
}
TEST_F(MatrixOpsTest, smithNormalFormBasis) {
verifySNFBasis(zero34, false);
verifySNFBasis(zero43, false);
verifySNFBasis(identity3, false);
verifySNFBasis(square3, false);
verifySNFBasis(rect34, false);
verifySNFBasis(rect43, false);
verifySNFBasis(redundant34, false);
verifySNFBasis(redundant43, false);
verifySNFBasis(duplicate34, false);
verifySNFBasis(duplicate43, false);
}
TEST_F(MatrixOpsTest, metricalSmithNormalForm) {
verifySNFBasis(zero34, true);
verifySNFBasis(zero43, true);
verifySNFBasis(identity3, true);
verifySNFBasis(square3, true);
verifySNFBasis(rect34, true);
verifySNFBasis(rect43, true);
verifySNFBasis(redundant34, true);
verifySNFBasis(redundant43, true);
verifySNFBasis(duplicate34, true);
verifySNFBasis(duplicate43, true);
}
static void verifyEchelonForm(const MatrixInt& m) {
SCOPED_TRACE_REGINA(m);
MatrixInt m1 = m;
MatrixInt m2 = m.transpose();
size_t rankCol = m1.columnEchelonForm();
size_t rankRow = m2.rowEchelonForm();
EXPECT_EQ(rankCol, rankRow);
EXPECT_EQ(m2.transpose(), m1);
// Verify that m2 is actually in row echelon form.
{
size_t fromCol = 0;
for (size_t r = 0; r < m2.rows(); ++r) {
// The initial non-zero entry in this row must appear in
// column ≥ fromCol.
do {
// Whether or not m2[r, fromCol] is zero, the entire
// column beneath this position must be zero.
for (size_t i = r + 1; i < m2.rows(); ++i)
EXPECT_EQ(m2.entry(i, fromCol), 0);
if (m2.entry(r, fromCol) != 0)
break;
++fromCol;
} while (fromCol < m2.columns());
if (fromCol == m2.columns())
break;
// The first non-zero entry in this row is m2[r, fromCol].
auto corner = m2.entry(r, fromCol);
EXPECT_GT(corner, 0);
for (size_t i = 0; i < r; ++i) {
EXPECT_GE(m2.entry(i, fromCol), 0);
EXPECT_LT(m2.entry(i, fromCol), corner);
}
++fromCol;
if (fromCol == m2.columns())
break;
}
}
// Compare results with the more complex global columnEchelonForm().
MatrixInt copy(m);
auto r = MatrixInt::identity(copy.columns());
auto ri = MatrixInt::identity(copy.columns());
std::vector<size_t> rowList;
for (size_t i = 0; i < copy.rows(); ++i)
rowList.push_back(i);
regina::columnEchelonForm(copy, r, ri, rowList);
EXPECT_EQ(copy, m1);
}
TEST_F(MatrixOpsTest, echelonForm) {
verifyEchelonForm(zero34);
verifyEchelonForm(zero43);
verifyEchelonForm(identity3);
verifyEchelonForm(square3);
verifyEchelonForm(rect34);
verifyEchelonForm(rect43);
verifyEchelonForm(redundant34);
verifyEchelonForm(redundant43);
verifyEchelonForm(duplicate34);
verifyEchelonForm(duplicate43);
}
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