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[Type] Introduce function to compute the determinant of any square matrix #5877

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[Type] Introduce function to compute the determinant of any square matrix #5877

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21 changes: 21 additions & 0 deletions Sofa/framework/Type/src/sofa/type/Mat.h
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Original file line number Diff line number Diff line change
Expand Up @@ -914,6 +914,27 @@ class MatNoInit : public Mat<L,C,real>
}
};

template <sofa::Size N, typename real>
real determinant(const Mat<N, N, real>& mat)
{
real det = 0;
for (size_t p = 0; p < N; ++p)
{
Mat<N - 1, N - 1, real> submat;
for (size_t i = 1; i < N; ++i)
{
size_t colIndex = 0;
for (size_t j = 0; j < N; ++j)
{
if (j == p) continue;
submat(i - 1, colIndex++) = mat(i, j);
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@bakpaul bakpaul Jan 21, 2026

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Wouldn't it be more efficient to only create a vector of col and row indices that is reduced of one element for each determinant development ? So in the end your 'submatrix' is like a view on the original matrix, instead of copying the same values multiple times ?

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@alxbilger alxbilger Jan 21, 2026

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I did not try to reach high performances because I don't have the need. Currently, I use it only in init().

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@hugtalbot hugtalbot Jan 23, 2026

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would your changes be easily introduced @bakpaul ?
if yes, we can add it inside this PR
else, it could be done in a later one

}
}
det += ((p % 2 == 0) ? 1 : -1) * mat(0, p) * determinant(submat);
}
return det;
}

/// Determinant of a 3x3 matrix.
template<class real>
constexpr real determinant(const Mat<3,3,real>& m) noexcept
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9 changes: 9 additions & 0 deletions Sofa/framework/Type/test/MatTypes_test.cpp
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Expand Up @@ -443,3 +443,12 @@ TEST(MatTypesTest, determinant3x3)
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<3,3,SReal>{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}}), 1_sreal);
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<3,3,SReal>{{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}), -2_sreal);
}

TEST(MatTypesTest, determinant4x4)
{
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<4,4,SReal>{{1,0,0,0}, {0,1,0,0}, {0,0,1,0}, {0,0,0,1}}), 1_sreal);
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<4,4,SReal>{{2,0,0,0}, {0,3,0,0}, {0,0,4,0}, {0,0,0,5}}), 120_sreal);
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<4,4,SReal>{{0,1,0,0}, {1,0,0,0}, {0,0,1,0}, {0,0,0,1}}), -1_sreal);
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<4,4,SReal>{{1,0,0,0}, {0,2,0,0}, {0,0,3,0}, {0,0,0,4}}), 24_sreal);
EXPECT_DOUBLE_EQ(sofa::type::determinant(sofa::type::Mat<4,4,SReal>{{1,3,5,9}, {1,3,1,7}, {4,3,9,7}, {5,2,0,9}}), -376_sreal);
}
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