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remove Minor

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adapt 3x3 and 4x4 (non-SSE) inverse paths
This commit is contained in:
Benoit Jacob
2010-04-22 20:40:31 -04:00
parent abbe260905
commit 2362eadcdd
7 changed files with 67 additions and 194 deletions
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93
Eigen/src/LU/Inverse.h
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@@ -122,6 +122,19 @@ struct ei_compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
*** Size 3 implementation ***
****************************/
template<typename MatrixType, int i, int j>
inline typename MatrixType::Scalar ei_3x3_cofactor(const MatrixType& m)
{
enum {
i1 = (i+1) % 3,
i2 = (i+2) % 3,
j1 = (j+1) % 3,
j2 = (j+2) % 3
};
return m.coeff(i1, j1) * m.coeff(i2, j2)
- m.coeff(i1, j2) * m.coeff(i2, j1);
}
template<typename MatrixType, typename ResultType>
inline void ei_compute_inverse_size3_helper(
const MatrixType& matrix,
@@ -130,12 +143,12 @@ inline void ei_compute_inverse_size3_helper(
ResultType& result)
{
result.row(0) = cofactors_col0 * invdet;
result.coeffRef(1,0) = -matrix.minor(0,1).determinant() * invdet;
result.coeffRef(1,1) = matrix.minor(1,1).determinant() * invdet;
result.coeffRef(1,2) = -matrix.minor(2,1).determinant() * invdet;
result.coeffRef(2,0) = matrix.minor(0,2).determinant() * invdet;
result.coeffRef(2,1) = -matrix.minor(1,2).determinant() * invdet;
result.coeffRef(2,2) = matrix.minor(2,2).determinant() * invdet;
result.coeffRef(1,0) = ei_3x3_cofactor<MatrixType,0,1>(matrix) * invdet;
result.coeffRef(1,1) = ei_3x3_cofactor<MatrixType,1,1>(matrix) * invdet;
result.coeffRef(1,2) = ei_3x3_cofactor<MatrixType,2,1>(matrix) * invdet;
result.coeffRef(2,0) = ei_3x3_cofactor<MatrixType,0,2>(matrix) * invdet;
result.coeffRef(2,1) = ei_3x3_cofactor<MatrixType,1,2>(matrix) * invdet;
result.coeffRef(2,2) = ei_3x3_cofactor<MatrixType,2,2>(matrix) * invdet;
}
template<typename MatrixType, typename ResultType>
@@ -145,9 +158,9 @@ struct ei_compute_inverse<MatrixType, ResultType, 3>
{
typedef typename ResultType::Scalar Scalar;
Matrix<Scalar,3,1> cofactors_col0;
cofactors_col0.coeffRef(0) = matrix.minor(0,0).determinant();
cofactors_col0.coeffRef(1) = -matrix.minor(1,0).determinant();
cofactors_col0.coeffRef(2) = matrix.minor(2,0).determinant();
cofactors_col0.coeffRef(0) = ei_3x3_cofactor<MatrixType,0,0>(matrix);
cofactors_col0.coeffRef(1) = ei_3x3_cofactor<MatrixType,1,0>(matrix);
cofactors_col0.coeffRef(2) = ei_3x3_cofactor<MatrixType,2,0>(matrix);
const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
const Scalar invdet = Scalar(1) / det;
ei_compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
@@ -167,9 +180,9 @@ struct ei_compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
{
typedef typename ResultType::Scalar Scalar;
Matrix<Scalar,3,1> cofactors_col0;
cofactors_col0.coeffRef(0) = matrix.minor(0,0).determinant();
cofactors_col0.coeffRef(1) = -matrix.minor(1,0).determinant();
cofactors_col0.coeffRef(2) = matrix.minor(2,0).determinant();
cofactors_col0.coeffRef(0) = ei_3x3_cofactor<MatrixType,0,0>(matrix);
cofactors_col0.coeffRef(1) = ei_3x3_cofactor<MatrixType,1,0>(matrix);
cofactors_col0.coeffRef(2) = ei_3x3_cofactor<MatrixType,2,0>(matrix);
determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
invertible = ei_abs(determinant) > absDeterminantThreshold;
if(!invertible) return;
@@ -182,27 +195,51 @@ struct ei_compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
*** Size 4 implementation ***
****************************/
template<typename Derived>
inline const typename Derived::Scalar ei_general_det3_helper
(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)
{
return matrix.coeff(i1,j1)
* (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));
}
template<typename MatrixType, int i, int j>
inline typename MatrixType::Scalar ei_4x4_cofactor(const MatrixType& matrix)
{
enum {
i1 = (i+1) % 4,
i2 = (i+2) % 4,
i3 = (i+3) % 4,
j1 = (j+1) % 4,
j2 = (j+2) % 4,
j3 = (j+3) % 4
};
return ei_general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)
+ ei_general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)
+ ei_general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
}
template<int Arch, typename Scalar, typename MatrixType, typename ResultType>
struct ei_compute_inverse_size4
{
static void run(const MatrixType& matrix, ResultType& result)
{
result.coeffRef(0,0) = matrix.minor(0,0).determinant();
result.coeffRef(1,0) = -matrix.minor(0,1).determinant();
result.coeffRef(2,0) = matrix.minor(0,2).determinant();
result.coeffRef(3,0) = -matrix.minor(0,3).determinant();
result.coeffRef(0,2) = matrix.minor(2,0).determinant();
result.coeffRef(1,2) = -matrix.minor(2,1).determinant();
result.coeffRef(2,2) = matrix.minor(2,2).determinant();
result.coeffRef(3,2) = -matrix.minor(2,3).determinant();
result.coeffRef(0,1) = -matrix.minor(1,0).determinant();
result.coeffRef(1,1) = matrix.minor(1,1).determinant();
result.coeffRef(2,1) = -matrix.minor(1,2).determinant();
result.coeffRef(3,1) = matrix.minor(1,3).determinant();
result.coeffRef(0,3) = -matrix.minor(3,0).determinant();
result.coeffRef(1,3) = matrix.minor(3,1).determinant();
result.coeffRef(2,3) = -matrix.minor(3,2).determinant();
result.coeffRef(3,3) = matrix.minor(3,3).determinant();
result.coeffRef(0,0) = ei_4x4_cofactor<MatrixType,0,0>(matrix);
result.coeffRef(1,0) = -ei_4x4_cofactor<MatrixType,0,1>(matrix);
result.coeffRef(2,0) = ei_4x4_cofactor<MatrixType,0,2>(matrix);
result.coeffRef(3,0) = -ei_4x4_cofactor<MatrixType,0,3>(matrix);
result.coeffRef(0,2) = ei_4x4_cofactor<MatrixType,2,0>(matrix);
result.coeffRef(1,2) = -ei_4x4_cofactor<MatrixType,2,1>(matrix);
result.coeffRef(2,2) = ei_4x4_cofactor<MatrixType,2,2>(matrix);
result.coeffRef(3,2) = -ei_4x4_cofactor<MatrixType,2,3>(matrix);
result.coeffRef(0,1) = -ei_4x4_cofactor<MatrixType,1,0>(matrix);
result.coeffRef(1,1) = ei_4x4_cofactor<MatrixType,1,1>(matrix);
result.coeffRef(2,1) = -ei_4x4_cofactor<MatrixType,1,2>(matrix);
result.coeffRef(3,1) = ei_4x4_cofactor<MatrixType,1,3>(matrix);
result.coeffRef(0,3) = -ei_4x4_cofactor<MatrixType,3,0>(matrix);
result.coeffRef(1,3) = ei_4x4_cofactor<MatrixType,3,1>(matrix);
result.coeffRef(2,3) = -ei_4x4_cofactor<MatrixType,3,2>(matrix);
result.coeffRef(3,3) = ei_4x4_cofactor<MatrixType,3,3>(matrix);
result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
}
};