Crate ndarray_linalg

The ndarray-linalg crate provides linear algebra functionalities for ArrayBase, the n-dimensional array data structure provided by ndarray.

ndarray-linalg leverages LAPACK’s routines using the bindings provided by blas-lapack-rs/lapack.

Linear algebra methods

• Decomposition methods:
  • QR decomposition
  • Cholesky/LU decomposition
  • Eigenvalue decomposition
  • Eigenvalue decomposition for Hermite matrices
  • Singular Value Decomposition
• Solution of linear systems:
  • General matrices
  • Triangular matrices
  • Hermitian/real symmetric matrices
  • Tridiagonal matrices
• Inverse matrix computation

Naming Convention

Each routine is usually exposed as a trait, implemented by the relevant types.

For each routine there might be multiple “variants”: different traits corresponding to the different ownership possibilities of the array you intend to work on.

For example, if you are interested in the QR decomposition of a square matrix, you can use:

• QRSquare, if you hold an immutable reference (i.e. &self) to the matrix you want to decompose;
• QRSquareInplace, if you hold a mutable reference (i.e. &mut self) to the matrix you want to decompose;
• QRSquareInto, if you can pass the matrix you want to decompose by value (e.g. self).

Depending on the algorithm, each variant might require more or less copy operations of the underlying data.

Details are provided in the description of each routine.

Utilities

• Assertions for array
• Random matrix generators
• Scalar trait

Re-exports

• pub use crate::lobpcg::TruncatedEig;
• pub use crate::lobpcg::TruncatedOrder;
• pub use crate::lobpcg::TruncatedSvd;
• pub use crate::assert::*;
• pub use crate::cholesky::*;
• pub use crate::convert::*;
• pub use crate::diagonal::*;
• pub use crate::eig::*;
• pub use crate::eigh::*;
• pub use crate::generate::*;
• pub use crate::inner::*;
• pub use crate::layout::*;
• pub use crate::least_squares::*;
• pub use crate::norm::*;
• pub use crate::operator::*;
• pub use crate::opnorm::*;
• pub use crate::qr::*;
• pub use crate::solve::*;
• pub use crate::solveh::*;
• pub use crate::svd::*;
• pub use crate::svddc::*;
• pub use crate::trace::*;
• pub use crate::triangular::*;
• pub use crate::tridiagonal::*;
• pub use crate::types::*;

Modules

• assert
  Assertions for array
• cholesky
  Cholesky decomposition of Hermitian (or real symmetric) positive definite matrices
• convert
  utilities for convert array
• diagonal
  Vector as a Diagonal matrix
• eig
  Eigenvalue decomposition for non-symmetric square matrices
• eigh
  Eigendecomposition for Hermitian matrices.
• error
  Define Errors
• generate
  Generator functions for matrices
• inner
• krylov
  Krylov subspace methods
• layout
  Convert ndarray into LAPACK-compatible matrix format
• least_squares
  Least Squares
• lobpcg
• norm
  Norm of vectors
• operator
  Linear operator algebra
• opnorm
  Operator norm
• qr
  QR decomposition
• solve
  Solve systems of linear equations and invert matrices
• solveh
  Solve Hermitian (or real symmetric) linear problems and invert Hermitian (or real symmetric) matrices
• svd
  Singular-value decomposition (SVD)
• svddc
  Singular-value decomposition (SVD) by divide-and-conquer (?gesdd)
• trace
  Trace calculation
• triangular
  Methods for triangular matrices
• tridiagonal
  Vectors as a Tridiagonal matrix & Methods for tridiagonal matrices
• types
  Basic types and their methods for linear algebra

Macros

• assert_aclose
• assert_close_l1
• assert_close_l2
• assert_close_max
• assert_rclose