Package org.ojalgo.matrix.decomposition
Interface SingularValue<N extends java.lang.Comparable<N>>
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- All Superinterfaces:
InverterTask<N>
,InvertibleFactor<N>
,MatrixDecomposition<N>
,MatrixDecomposition.EconomySize<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.RankRevealing<N>
,MatrixDecomposition.Solver<N>
,MatrixDecomposition.Values<N>
,MatrixTask<N>
,Provider2D
,Provider2D.Condition
,Provider2D.Inverse<java.util.Optional<MatrixStore<N>>>
,Provider2D.Rank
,Provider2D.Solution<java.util.Optional<MatrixStore<N>>>
,SolverTask<N>
,Structure1D
,Structure2D
- All Known Implementing Classes:
RawSingularValue
,SingularValueDecomposition
,SingularValueDecomposition.C128
,SingularValueDecomposition.H256
,SingularValueDecomposition.Q128
,SingularValueDecomposition.R064
,SingularValueDecomposition.R128
public interface SingularValue<N extends java.lang.Comparable<N>> extends MatrixDecomposition<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Values<N>, Provider2D.Condition
Singular Value: [A] = [U][D][V]T Decomposes [this] into [U], [D] and [V] where:- [U] is an orthogonal matrix. The columns are the left, orthonormal, singular vectors of [this]. Its columns are the eigenvectors of [A][A]T, and therefore has the same number of rows as [this].
- [D] is a diagonal matrix. The elements on the diagonal are the singular values of [this]. It is either square or has the same dimensions as [this]. The singular values of [this] are the square roots of the nonzero eigenvalues of [A][A]T and [A]T[A] (they are the same)
- [V] is an orthogonal matrix. The columns are the right, orthonormal, singular vectors of [this]. Its columns are the eigenvectors of [A][A]T, and therefore has the same number of rows as [this] has columns.
- [this] = [U][D][V]T
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Nested Class Summary
Nested Classes Modifier and Type Interface Description static interface
SingularValue.Factory<N extends java.lang.Comparable<N>>
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Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
InvertibleFactor.IdentityFactor<N extends java.lang.Comparable<N>>
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Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>, MatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>, MatrixDecomposition.Hermitian<N extends java.lang.Comparable<N>>, MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>, MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>, MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>, MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>, MatrixDecomposition.Values<N extends java.lang.Comparable<N>>
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Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D
Provider2D.Condition, Provider2D.Determinant<N extends java.lang.Comparable<N>>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N extends java.lang.Comparable<N>>
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Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D
Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback
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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>
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Field Summary
Fields Modifier and Type Field Description static SingularValue.Factory<ComplexNumber>
C128
static SingularValue.Factory<Quaternion>
H256
static SingularValue.Factory<RationalNumber>
Q128
static SingularValue.Factory<java.lang.Double>
R064
static SingularValue.Factory<Quadruple>
R128
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Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Method Summary
All Methods Static Methods Instance Methods Abstract Methods Default Methods Modifier and Type Method Description static <N extends java.lang.Comparable<N>>
booleanequals(MatrixStore<N> matrix, SingularValue<N> decomposition, NumberContext context)
double
getCondition()
The condition number.MatrixStore<N>
getCovariance()
MatrixStore<N>
getD()
double
getFrobeniusNorm()
Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.double
getKyFanNorm(int k)
Ky Fan k-norm.double
getOperatorNorm()
Array1D<java.lang.Double>
getSingularValues()
default void
getSingularValues(double[] values)
double
getTraceNorm()
MatrixStore<N>
getU()
If [A] is m-by-n and its rank is r, then: The first r columns of [U] span the column space, range or image of [A]. The last m-r columns of [U] span the left nullspace or cokernel of [A]. Calculating the QR decomposition of [A] is a faster alternative.MatrixStore<N>
getV()
If [A] is m-by-n and its rank is r, then: The first r columns of [V] span the row space or coimage of [A]. The last n-r columns of [V] span the nullspace or kernel of [A]. Calculating the QR decomposition of [A]T is a faster alternative.default MatrixStore<N>
reconstruct()
default MatrixStore<N>
reconstruct(int k)
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Methods inherited from interface org.ojalgo.matrix.task.InverterTask
invert, invert, preallocate, preallocate
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Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
btran, btran
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
decompose, isComputed, reset
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.EconomySize
isFullSize
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Ordered
isOrdered
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing
countSignificant, getRank, getRankThreshold, isFullRank
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver
compute, ftran, ftran, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, solve, toInverseProvider, toSolutionProvider
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Values
computeValuesOnly
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Methods inherited from interface org.ojalgo.matrix.task.SolverTask
preallocate, preallocate, solve, solve
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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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Field Detail
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C128
static final SingularValue.Factory<ComplexNumber> C128
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H256
static final SingularValue.Factory<Quaternion> H256
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R064
static final SingularValue.Factory<java.lang.Double> R064
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Q128
static final SingularValue.Factory<RationalNumber> Q128
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R128
static final SingularValue.Factory<Quadruple> R128
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Method Detail
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equals
static <N extends java.lang.Comparable<N>> boolean equals(MatrixStore<N> matrix, SingularValue<N> decomposition, NumberContext context)
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getCondition
double getCondition()
The condition number.- Specified by:
getCondition
in interfaceProvider2D.Condition
- Returns:
- The largest singular value divided by the smallest singular value.
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getCovariance
MatrixStore<N> getCovariance()
- Returns:
- [[A]T[A]]-1 Where [A] is the original matrix.
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getD
MatrixStore<N> getD()
- Returns:
- The diagonal matrix of singular values.
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getFrobeniusNorm
double getFrobeniusNorm()
Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.- Returns:
- The square root of the sum of squares of the singular values.
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getKyFanNorm
double getKyFanNorm(int k)
Ky Fan k-norm.
The first Ky Fan k-norm is the operator norm (the largest singular value), and the last is called the trace norm (the sum of all singular values).
- Parameters:
k
- The number of singular values to add up.- Returns:
- The sum of the k largest singular values.
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getOperatorNorm
double getOperatorNorm()
- Returns:
- 2-norm
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getSingularValues
Array1D<java.lang.Double> getSingularValues()
- Returns:
- The singular values ordered in descending order.
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getSingularValues
default void getSingularValues(double[] values)
- Parameters:
values
- An array that will receive the singular values
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getTraceNorm
double getTraceNorm()
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getU
MatrixStore<N> getU()
If [A] is m-by-n and its rank is r, then:- The first r columns of [U] span the column space, range or image of [A].
- The last m-r columns of [U] span the left nullspace or cokernel of [A].
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getV
MatrixStore<N> getV()
If [A] is m-by-n and its rank is r, then:- The first r columns of [V] span the row space or coimage of [A].
- The last n-r columns of [V] span the nullspace or kernel of [A].
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reconstruct
default MatrixStore<N> reconstruct()
- Specified by:
reconstruct
in interfaceMatrixDecomposition<N extends java.lang.Comparable<N>>
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reconstruct
default MatrixStore<N> reconstruct(int k)
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