Expand description
§Linear Algebra eXtension (LAX)
ndarray-free safe Rust wrapper for LAPACK FFI
§Linear equation, Inverse matrix, Condition number
As the property of $A$, several types of triangular factorization are used:
- LU-decomposition for general matrix
- $PA = LU$, where $L$ is lower matrix, $U$ is upper matrix, and $P$ is permutation matrix
- Bunch-Kaufman diagonal pivoting method for nonpositive-definite Hermitian matrix
- $A = U D U^\dagger$, where $U$ is upper matrix, $D$ is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
| matrix type | Triangler factorization (TRF) | Solve (TRS) | Inverse matrix (TRI) | Reciprocal condition number (CON) |
|---|---|---|---|---|
| General (GE) | lu | solve | inv | rcond |
| Symmetric (SY) / Hermitian (HE) | bk | solveh | invh | - |
§Eigenvalue Problem
Solve eigenvalue problem for a matrix $A$
$$ Av_i = \lambda_i v_i $$
or generalized eigenvalue problem
$$ Av_i = \lambda_i B v_i $$
| matrix type | Eigenvalue (EV) | Generalized Eigenvalue Problem (EG) |
|---|---|---|
| General (GE) | eig | - |
| Symmetric (SY) / Hermitian (HE) | eigh | eigh_generalized |
§Singular Value Decomposition (SVD), Least square problem
| matrix type | Singular Value Decomposition (SVD) | SVD with divided-and-conquer (SDD) | Least square problem (LSD) |
|---|---|---|---|
| General (GE) | svd | svddc | least_squares |
Modules§
- Memory layout of matrices
Structs§
- Represents the LU factorization of a tridiagonal matrix
AasA = P*L*U. - Result of LeastSquares
- Result of SVD
- Represents a tridiagonal matrix as 3 one-dimensional vectors.
Enums§
- Upper/Lower specification for seveal usages
- Specifies how many of the columns of U and rows of Vᵀ are computed and returned.
Traits§
- Wraps
*geevfor general matrices - Trait for primitive types which implements LAPACK subroutines
- Wraps
*gelsd - Wraps
*gesvd - Wraps
*trtriand*trtrs - Wraps
*gttrf,*gtconand*gttrs