如何在 Eigen 库中获取矩阵的秩？
How to get rank of a matrix in Eigen library?
您需要将矩阵转换为显示秩的分解。例如FullPivLU。如果你有 matrix3f 它看起来像这样：
FullPivLU<Matrix3f> lu_decomp(your_matrix);
auto rank = lu_decomp.rank();
编辑
分解矩阵是最常用的求秩方式。虽然，如 rank article on wikipedia
中所述，LU 并不是实现浮动值的最可靠方法
When applied to floating point computations on computers, basic
Gaussian elimination (LU decomposition) can be unreliable, and a
rank-revealing decomposition should be used instead. An effective
alternative is the singular value decomposition (SVD), but there are
other less expensive choices, such as QR decomposition with pivoting
(so-called rank-revealing QR factorization), which are still more
numerically robust than Gaussian elimination. Numerical determination
of rank requires a criterion for deciding when a value, such as a
singular value from the SVD, should be treated as zero, a practical
choice which depends on both the matrix and the application.
因此您可能会通过 Eigen::ColPivHouseholderQR< MatrixType >
获得更准确的结果
使用 QR 或 SVD 分解并检查结果矩阵是否也有效。 SVD 可能更可靠。
您需要将矩阵转换为显示秩的分解。例如FullPivLU。如果你有 matrix3f 它看起来像这样：
FullPivLU<Matrix3f> lu_decomp(your_matrix);
auto rank = lu_decomp.rank();
编辑
分解矩阵是最常用的求秩方式。虽然，如 rank article on wikipedia
中所述，LU 并不是实现浮动值的最可靠方法When applied to floating point computations on computers, basic Gaussian elimination (LU decomposition) can be unreliable, and a rank-revealing decomposition should be used instead. An effective alternative is the singular value decomposition (SVD), but there are other less expensive choices, such as QR decomposition with pivoting (so-called rank-revealing QR factorization), which are still more numerically robust than Gaussian elimination. Numerical determination of rank requires a criterion for deciding when a value, such as a singular value from the SVD, should be treated as zero, a practical choice which depends on both the matrix and the application.
因此您可能会通过 Eigen::ColPivHouseholderQR< MatrixType >
使用 QR 或 SVD 分解并检查结果矩阵是否也有效。 SVD 可能更可靠。