geometry-processing-js

Class: ComplexCholesky

LinearAlgebra. ComplexCholesky

new ComplexCholesky()

This class represents a complex Choleksy LL^T factorization of a square and
positive definite ComplexSparseMatrix. 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 complex sparse matrix itself is altered through
operations such as *=, += and -=. Do not use the constructor to initialize
this class, instead access the complex Choleksy factorization of a complex
sparse matrix directly from the matrix itself.

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

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

b.scaleBy(new Complex(5, 0));
x = llt.solvePositiveDefinite(b); // factorization is reused

Methods

solvePositiveDefinite(b)

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

Parameters:
Name Type Description
b module:LinearAlgebra.ComplexDenseMatrix

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