geometry-processing-js

Class: Solvers

Utils. Solvers

This class implements frequently used numerical algorithms such as the inverse power method.

new Solvers()

Methods

<static> residual(A, x)

Computes the residual of Ax - λx, where x has unit norm and λ = x.Ax.

Parameters:
Name Type Description
A module:LinearAlgebra.ComplexSparseMatrix

The complex sparse matrix whose eigen decomposition
is being computed.
x module:LinearAlgebra.ComplexDenseMatrix

The current guess for the smallest eigenvector
(corresponding to the smallest eigenvalue λ) of A.
Returns:
Type
number

<static> solveInversePowerMethod(A)

Solves Ax = λx, where λ is the smallest nonzero eigenvalue of A and x is the
corresponding eigenvector. x should be initialized to a random complex dense
vector (i.e., x.nCols() == 1).

Parameters:
Name Type Description
A module:LinearAlgebra.ComplexSparseMatrix

The complex positive definite sparse matrix
whose eigen decomposition needs to be computed.
Returns:

The smallest eigenvector (corresponding to the
smallest eigenvalue λ) of A.

Type
module:LinearAlgebra.ComplexDenseMatrix

<static> invert2x2(m)

Inverts a 2x2 matrix.

Parameters:
Name Type Description
m module:LinearAlgebra.DenseMatrix

The matrix to be inverted.
Returns:
Type
module:LinearAlgebra.DenseMatrix