Document for lax

Author: termoshtt

ndarray-linalg/katex-header.html renamed to katex-header.html

@@ -1,4 +1,63 @@
 //! 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]               | -                                 |
+//!
+//! [lu]:    solve/trait.Solve_.html#tymethod.lu
+//! [solve]: solve/trait.Solve_.html#tymethod.solve
+//! [inv]:   solve/trait.Solve_.html#tymethod.inv
+//! [rcond]: solve/trait.Solve_.html#tymethod.rcond
+//!
+//! [bk]:     solveh/trait.Solveh_.html#tymethod.bk
+//! [solveh]: solveh/trait.Solveh_.html#tymethod.solveh
+//! [invh]:   solveh/trait.Solveh_.html#tymethod.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]                   |
+//!
+//! [eig]:              eig/trait.Eig_.html#tymethod.eig
+//! [eigh]:             eigh/trait.Eigh_.html#tymethod.eigh
+//! [eigh_generalized]: eigh/trait.Eigh_.html#tymethod.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]            |
+//!
+//! [svd]:   svd/trait.SVD_.html#tymethod.svd
+//! [svddc]: svddck/trait.SVDDC_.html#tymethod.svddc
+//! [least_squares]: least_squares/trait.LeastSquaresSvdDivideConquer_.html#tymethod.least_squares
 
 extern crate blas_src;
 extern crate lapack_src;