Interface InvertibleFactor<N extends Comparable<N>>

All Superinterfaces:
Structure1D, Structure2D
All Known Subinterfaces:
BasisRepresentation, Cholesky<N>, Eigenvalue.Spectral<N>, LDL<N>, LDU<N>, LU<N>, MatrixDecomposition.Solver<N>, QR<N>, SingularValue<N>
All Known Implementing Classes:
DecomposedInverse, DenseCholesky, DenseCholesky.C128, DenseCholesky.H256, DenseCholesky.Q128, DenseCholesky.R064, DenseCholesky.R128, DenseLDL, DenseLDL.C128, DenseLDL.H256, DenseLDL.Q128, DenseLDL.R064, DenseLDL.R128, DenseLU, DenseLU.C128, DenseLU.H256, DenseLU.Q128, DenseLU.R064, DenseLU.R128, DenseQR, DenseQR.C128, DenseQR.H256, DenseQR.Q128, DenseQR.R064, DenseQR.R128, DenseSingularValue, DenseSingularValue.C128, DenseSingularValue.H256, DenseSingularValue.Q128, DenseSingularValue.R064, DenseSingularValue.R128, HermitianEvD, HermitianEvD.C128, HermitianEvD.H256, HermitianEvD.Q128, HermitianEvD.R064, HermitianEvD.R128, InvertibleFactor.IdentityFactor, ProductFormInverse, ProductFormInverse.ElementaryFactor, RawCholesky, RawEigenvalue.Symmetric, RawLU, RawQR, RawSingularValue, SparseLU, SparseLU.PermutationEta, SparseQDLDL
public interface InvertibleFactor<N extends Comparable<N>> extends Structure2D
A chainable and reversible in-place (equation system) solver.

Matrix decompositions produce factorisations like [A] = [L][U], [A] = [Q][R] or [A] = [U][D][V]T. When solving equation systems the factors are used in sequence:

[A][x] = [b] and [A] = [L][U] gives [L][U][x] = [b], which is solved in these steps:

  1. [L][y] = [b] or [y] = [L]-1[b]
  2. [U][x] = [y] or [x] = [U]-1[y]
That's forward transformation (ftran) using the [L] and [U] (invertible) factors of [A].

If we instead want to solve [x]T[A] = [b]T or [A]T[x] = [b] the steps are:

  1. [U]T[y] = [b] or [y] = [U]-T[b]
  2. [L]T[x] = [y] or [x] = [L]-T[y]
That's backwards transformation (btran).

Implementing this interface can be useful whenever a matrix (or its inverse) can be constructed using a sequence of factors.

An invertible factor needs to be square.