Interface InvertibleFactor<N extends Comparable<N>>

All Superinterfaces:

Structure1D, Structure2D

All Known Subinterfaces:

Cholesky<N>, Eigenvalue.Spectral<N>, LDL<N>, LDU<N>, LU<N>, MatrixDecomposition.Factor<N>, MatrixDecomposition.Solver<N>, QR<N>, SingularValue<N>

All Known Implementing Classes:

InvertibleFactor.IdentityFactor, SparseLU, 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.

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface	Description
static final class	InvertibleFactor.IdentityFactor<N extends Comparable<N>>

Nested classes/interfaces inherited from interface Structure1D

Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback, Structure1D.Sparse

Nested classes/interfaces inherited from interface Structure2D

Structure2D.IntRowColumn, Structure2D.Logical<S,B>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R>, Structure2D.Reshapable, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Method Summary

Modifier and Type	Method	Description
void	btran(double[] arg)
static <N extends Comparable<N>> void	btran(List<InvertibleFactor<N>> factors, double[] arg)
static <N extends Comparable<N>> void	btran(List<InvertibleFactor<N>> factors, PhysicalStore<N> arg)
void	btran(PhysicalStore<N> arg)	Backwards-transformation
static void	doPrimitive(PhysicalStore<Double> arg, InvertibleFactor<Double> factor)	Do primitive btran(double[])
static void	doPrimitive(InvertibleFactor<Double> factor, PhysicalStore<Double> arg)	Do primitive ftran(double[])
void	ftran(double[] arg)
static <N extends Comparable<N>> void	ftran(List<InvertibleFactor<N>> factors, double[] arg)
static <N extends Comparable<N>> void	ftran(List<InvertibleFactor<N>> factors, PhysicalStore<N> arg)
void	ftran(PhysicalStore<N> arg)	Forward-transformation
static <N extends Comparable<N>> InvertibleFactor<N>	identity(int dim)

Methods inherited from interface Structure2D

count, countColumns, countRows, firstInColumn, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

Method Details

btran

static <N extends Comparable<N>> void btran(List<InvertibleFactor<N>> factors,
 double[] arg)

btran

static <N extends Comparable<N>> void btran(List<InvertibleFactor<N>> factors,
 PhysicalStore<N> arg)

doPrimitive

static void doPrimitive(InvertibleFactor<Double> factor,
 PhysicalStore<Double> arg)

Do primitive ftran(double[])

doPrimitive

static void doPrimitive(PhysicalStore<Double> arg,
 InvertibleFactor<Double> factor)

Do primitive btran(double[])

ftran

static <N extends Comparable<N>> void ftran(List<InvertibleFactor<N>> factors,
 double[] arg)

ftran

static <N extends Comparable<N>> void ftran(List<InvertibleFactor<N>> factors,
 PhysicalStore<N> arg)

identity

static <N extends Comparable<N>>
InvertibleFactor<N> identity(int dim)

btran

void btran(double[] arg)

See Also:

• InvertibleFactor.IdentityFactor.btran(PhysicalStore)

btran

void btran(PhysicalStore<N> arg)

Backwards-transformation

Solve [x]^T[A] = [b]^T (equivalent to [A]^T[x] = [b]) by transforming [b] into [x] in-place.

Parameters:

arg - [b] transformed into [x]

ftran

void ftran(double[] arg)

See Also:

• InvertibleFactor.IdentityFactor.ftran(PhysicalStore)

ftran

void ftran(PhysicalStore<N> arg)

Forward-transformation

Solve [A][x] = [b] by transforming [b] into [x] in-place.

Parameters:

arg - [b] transformed into [x]