geometry-processing-js

Class: Cholesky

LinearAlgebra. Cholesky

new Cholesky()

This class represents a Choleksy LL^T factorization of a square positive definite
SparseMatrix. The factorization is computed on the first call to solvePositiveDefinite,
and is reused in subsequent calls to solvePositiveDefinite (e.g. when only the
right hand side b of the linear system Ax = b changes) unless the sparse matrix
itself is altered through operations such as *=, += and -=. Do not use the constructor
to initialize this class, instead access the Choleksy factorization of a sparse
matrix directly from the matrix itself.

Example
// solve the linear system Ax = b, where A is a square positive definite sparse matrix
let A = SparseMatrix.identity(5, 5);
let b = DenseMatrix.ones(5, 1);

let llt = A.chol();
let x = llt.solvePositiveDefinite(b);

b.scaleBy(5);
x = llt.solvePositiveDefinite(b); // factorization is reused

Methods

solvePositiveDefinite(b)

Solves the linear system Ax = b, where A is a square positive definite sparse matrix.

Parameters:
Name Type Description
b module:LinearAlgebra.DenseMatrix

The dense right hand side of the linear system Ax = b.
Returns:
Type
module:LinearAlgebra.DenseMatrix