Module linalg 

linear algebra module

contains low level routines and the implementation of their corresponding high level wrappers

memory allocation

since most faer crates aim to expose a low level api for optimal performance, most algorithms try to defer memory allocation to the user

however, since a lot of algorithms need some form of temporary space for intermediate computations, they may ask for a slice of memory for that purpose, by taking a stack: MemStack parameter. a MemStack is a thin wrapper over a slice of memory bytes. this memory may come from any valid source (heap allocation, fixed-size array on the stack, etc.). the functions taking a MemStack parameter have a corresponding function with a similar name ending in _scratch that returns the memory requirements of the algorithm. for example: householder::apply_block_householder_on_the_left_in_place_with_conj and householder::apply_block_householder_on_the_left_in_place_scratch

the memory stack may be reused in user-code to avoid repeated allocations, and it is also possible to compute the sum (dyn_stack::StackReq::all_of) or union (dyn_stack::StackReq::any_of) of multiple scratch requirements, in order to optimally combine them into a single allocation

after computing a dyn_stack::StackReq, one can query its size and alignment to allocate the required memory. the simplest way to do so is through dyn_stack::MemBuffer::new

Modules

cholesky

low level implementation of the various cholesky-like decompositions

evd

low level implementation of the eigenvalue decomposition of a square diagonalizable matrix.

householder

block householder transformations

jacobi

jacobi rotation matrix

kron

kronecker product

lu

low level implementation of the various $LU$ decompositions

matmul

matrix multiplication

qr

faer provides utilities for computing and manipulating the $QR$ factorization with and without pivoting. the $QR$ factorization decomposes a matrix into a product of a unitary matrix $Q$ (represented using block householder sequences), and an upper trapezoidal matrix $R$, such that their product is equal to the original matrix (or a column permutation of it in the case where column pivoting is used)

solvers

high level solvers

svd

low level implementation of the svd of a matrix

triangular_inverse

triangular matrix inverse

triangular_solve

triangular matrix solve Triangular solve module.

zip

matrix zipping implementation

Functions

temp_mat_scratch

returns the stack requirements for creating a temporary matrix with the given dimensions.

temp_mat_uninit^⚠

creates a temporary matrix of uninit values, from the given memory stack.

temp_mat_zeroed

creates a temporary matrix of zero values, from the given memory stack.