const bool Test_Matrix_Submatrix()
{
const TMatrix4d kA4d{ 1.00, 2.00, 3.00, 4.00,
5.00, 6.00, 7.00, 8.00,
9.00, 10.0, 11.0, 12.0,
13.0, 14.0, 15.0, 16.0};
const TMatrix3d kB4d{ 1.00, 3.00, 4.00,
9.00, 11.0, 12.0,
13.0, 15.0, 16.0};
const TMatrix4f kA4f{ 1.00f, 2.00f, 3.00f, 4.00f,
5.00f, 6.00f, 7.00f, 8.00f,
9.00f, 10.0f, 11.0f, 12.0f,
13.0f, 14.0f, 15.0f, 16.0f};
const TMatrix3f kB4f{ 1.00f, 3.00f, 4.00f,
9.00f, 11.0f, 12.0f,
13.0f, 15.0f, 16.0f};
const bool kbPass4d = Equal(Submatrix(TMatrix3d(), kA4d, 2, 2), kB4d, s_kdEpsilon);
const bool kbPass4f = Equal(Submatrix(TMatrix3f(), kA4f, 2, 2), kB4f, s_kfEpsilon);
const TMatrix3d kA3d{ 1.0, 2.0, 3.0,
4.0, 5.0, 6.0,
7.0, 8.0, 9.0};
const TMatrix2d kB3d{ 1.0, 3.0,
7.0, 9.0};
const TMatrix3f kA3f{ 1.0f, 2.0f, 3.0f,
4.0f, 5.0f, 6.0f,
7.0f, 8.0f, 9.0f};
const TMatrix2f kB3f{ 1.0f, 3.0f,
7.0f, 9.0f};
const bool kbPass3d = Equal(Submatrix(TMatrix2d(), kA3d, 2, 2), kB3d, s_kdEpsilon);
const bool kbPass3f = Equal(Submatrix(TMatrix2f(), kA3f, 2, 2), kB3f, s_kfEpsilon);
return( kbPass4d
&& kbPass4f
&& kbPass3d
&& kbPass3f);
}
const bool Test_Matrix_FirstMinor()
{
const TMatrix4d kA4d{ 1.00, 2.00, 3.00, 4.00,
5.00, 6.00, 7.00, 8.00,
9.00, 10.0, 11.0, 12.0,
13.0, 14.0, 15.0, 16.0};
const double kB4d = Determinant(Submatrix(TMatrix3d(), kA4d, 3, 4));
const TMatrix4f kA4f{ 1.00f, 2.00f, 3.00f, 4.00f,
5.00f, 6.00f, 7.00f, 8.00f,
9.00f, 10.0f, 11.0f, 12.0f,
13.0f, 14.0f, 15.0f, 16.0f};
const float kB4f = Determinant(Submatrix(TMatrix3f(), kA4f, 1, 2));
const bool kbPass4d = Equal(FirstMinor(kA4d, 3, 4), kB4d, s_kdEpsilon);
const bool kbPass4f = Equal(FirstMinor(kA4f, 1, 2), kB4f, s_kfEpsilon);
const TMatrix3d kA3d{ 1.0, 2.0, 3.0,
4.0, 5.0, 6.0,
7.0, 8.0, 9.0};
const double kB3d = Determinant(Submatrix(TMatrix2d(), kA3d, 2, 2));
const TMatrix3f kA3f{ 1.0f, 2.0f, 3.0f,
4.0f, 5.0f, 6.0f,
7.0f, 8.0f, 9.0f};
const float kB3f = Determinant(Submatrix(TMatrix2f(), kA3f, 3, 1));
const bool kbPass3d = Equal(FirstMinor(kA3d, 2, 2), kB3d, s_kdEpsilon);
const bool kbPass3f = Equal(FirstMinor(kA3f, 3, 1), kB3f, s_kfEpsilon);
return( kbPass4d
&& kbPass4f
&& kbPass3d
&& kbPass3f);
}
Submatrix computeLargestSumSubmatrix(int **matrix, int n) {
if ((matrix == nullptr) || (n == 0)) {
return Submatrix(-1, -1, -1, -1);
}
Submatrix largestSumSubmatrix(-1, -1, -1, -1);
std::unordered_map<Submatrix, int> submatrixSums;
int largestSum = std::numeric_limits<int>::min();
computeLargestSumSubmatrix(matrix, 0, 0, n - 1, n - 1, largestSumSubmatrix, largestSum, submatrixSums);
return largestSumSubmatrix;
}
