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With the latest release (v0.13) nalgebra now supports Rust-native implementations of the following matrix factorizations:
In particular, this release includes pure-rust implementations of the following factorizations for real matrices ("general matrices" designates real-valued matrices that may be rectangular):
- Cholesky decomposition of symmetric definite-positive matrices (+ inverse, square linear system resolution).
- Hessenberg decomposition of square matrices.
- LU decompostion of general matrices with partial pivoting (+ inversion, determinant, square linear system resolution).
- LU decompostion of general matrices with full pivoting (+ inversion, determinant, square linear system resolution).
- QR decomposition of general matrices (+ inverse, square linear system resolution).
- Real Schur decomposition of general matrices (+ eigenvalues, complex eigenvalues).
- Eigendecomposition of symmetric matrices.
- Singular Value Decomposition (SVD) of general matrices (+ pseudo-inverse, linear system resolution, rank).
This made me wonder if instead of reinventing the wheel for rulinalg, maybe rulinalg and nalgebra should join or make use of the other side's efforts with these operations?
cc @sebcrozet
Related issues (varying degrees), but not limited to:
- Document that Cholesky only uses the lower triangular part
- Eigenvalues goes into infinite loop for certain matrices
- SVD goes in an infinite loop for certain matrices
- Rectangular matrix support for Full Pivot LU decomposition
- Moore–Penrose pseudo-inverse of Matrix
- LUP decomposition for singular matrices
- SVD bugs
- Custom types for decompositions
zolkko and c410-f3r
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