Package org.ojalgo.matrix.transformation
Interface InvertibleFactor<N extends Comparable<N>>
- All Superinterfaces:
Structure1D
,Structure2D
- All Known Subinterfaces:
Cholesky<N>
,LDL<N>
,LDU<N>
,LU<N>
,MatrixDecomposition.Solver<N>
,QR<N>
,SingularValue<N>
- All Known Implementing Classes:
CholeskyDecomposition
,CholeskyDecomposition.C128
,CholeskyDecomposition.H256
,CholeskyDecomposition.Q128
,CholeskyDecomposition.R064
,CholeskyDecomposition.R128
,HermitianEvD
,HermitianEvD.C128
,HermitianEvD.H256
,HermitianEvD.Q128
,HermitianEvD.R064
,HermitianEvD.R128
,InvertibleFactor.IdentityFactor
,LDLDecomposition
,LDLDecomposition.C128
,LDLDecomposition.H256
,LDLDecomposition.Q128
,LDLDecomposition.R064
,LDLDecomposition.R128
,LUDecomposition
,LUDecomposition.C128
,LUDecomposition.H256
,LUDecomposition.Q128
,LUDecomposition.R064
,LUDecomposition.R128
,ProductFormInverse
,ProductFormInverse.ElementaryFactor
,QRDecomposition
,QRDecomposition.C128
,QRDecomposition.H256
,QRDecomposition.Q128
,QRDecomposition.R064
,QRDecomposition.R128
,RawCholesky
,RawEigenvalue.Symmetric
,RawLU
,RawQR
,RawSingularValue
,SingularValueDecomposition
,SingularValueDecomposition.C128
,SingularValueDecomposition.H256
,SingularValueDecomposition.Q128
,SingularValueDecomposition.R064
,SingularValueDecomposition.R128
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:
- [L][y] = [b] or [y] = [L]-1[b]
- [U][x] = [y] or [x] = [U]-1[y]
If we instead want to solve [x]T[A] = [b]T or [A]T[x] = [b] the steps are:
- [U]T[y] = [b] or [y] = [U]-T[b]
- [L]T[x] = [y] or [x] = [L]-T[y]
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.
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Nested Class Summary
Nested ClassesModifier and TypeInterfaceDescriptionstatic final class
InvertibleFactor.IdentityFactor<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D
Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback
Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D
Structure2D.IntRowColumn, Structure2D.Logical<S extends Structure2D,
B extends Structure2D.Logical<S, B>>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.Reshapable, Structure2D.RowColumnKey<R, C>, Structure2D.RowColumnMapper<R, C> -
Method Summary
Modifier and TypeMethodDescriptionvoid
btran
(PhysicalStore<N> arg) Backwards-transformationdefault void
btran
(Access2D.Collectable<N, ? super PhysicalStore<N>> lhs, PhysicalStore<N> solution) void
ftran
(PhysicalStore<N> arg) Forward-transformationdefault void
ftran
(Access2D.Collectable<N, ? super PhysicalStore<N>> rhs, PhysicalStore<N> solution) static <N extends Comparable<N>>
InvertibleFactor<N> identity
(int dim) Methods inherited from interface org.ojalgo.structure.Structure2D
count, countColumns, countRows, firstInColumn, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size
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Method Details
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identity
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btran
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btran
Backwards-transformationSolve [x]T[A] = [b]T (equivalent to [A]T[x] = [b]) by transforming [b] into [x] in-place.
- Parameters:
arg
- [b] transformed into [x]
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ftran
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ftran
Forward-transformationSolve [A][x] = [b] by transforming [b] into [x] in-place.
- Parameters:
arg
- [b] transformed into [x]
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