Class SingularValueDecomposition<N extends Comparable<N>>
- All Implemented Interfaces:
MatrixDecomposition<N>
,MatrixDecomposition.EconomySize<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.RankRevealing<N>
,MatrixDecomposition.Solver<N>
,MatrixDecomposition.Values<N>
,SingularValue<N>
,Provider2D
,Provider2D.Condition
,Provider2D.Inverse<Optional<MatrixStore<N>>>
,Provider2D.Rank
,Provider2D.Solution<Optional<MatrixStore<N>>>
,InverterTask<N>
,MatrixTask<N>
,SolverTask<N>
,InvertibleFactor<N>
,Structure1D
,Structure2D
- Direct Known Subclasses:
SingularValueDecomposition.C128
,SingularValueDecomposition.H256
,SingularValueDecomposition.Q128
,SingularValueDecomposition.R064
,SingularValueDecomposition.R128
-
Nested Class Summary
Nested ClassesModifier and TypeClassDescription(package private) static final class
(package private) static final class
(package private) static final class
(package private) static final class
(package private) static final class
Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
InvertibleFactor.IdentityFactor<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
MatrixDecomposition.Determinant<N extends Comparable<N>>, MatrixDecomposition.EconomySize<N extends Comparable<N>>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, MatrixDecomposition.Hermitian<N extends Comparable<N>>, MatrixDecomposition.Ordered<N extends Comparable<N>>, MatrixDecomposition.Pivoting<N extends Comparable<N>>, MatrixDecomposition.RankRevealing<N extends Comparable<N>>, MatrixDecomposition.Solver<N extends Comparable<N>>, MatrixDecomposition.Values<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D
Provider2D.Condition, Provider2D.Determinant<N extends Comparable<N>>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.SingularValue
SingularValue.Factory<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> -
Field Summary
FieldsModifier and TypeFieldDescriptionprivate double[]
private final BidiagonalDecomposition
<N> private MatrixStore
<N> private final boolean
private final Structure2D
private MatrixStore
<N> private boolean
private MatrixStore
<N> private MatrixStore
<N> private boolean
private double[]
private static final double
≈ 1.6E-291Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
-
Constructor Summary
ConstructorsModifierConstructorDescriptionprivate
SingularValueDecomposition
(PhysicalStore.Factory<N, ? extends DecompositionStore<N>> factory) protected
SingularValueDecomposition
(PhysicalStore.Factory<N, ? extends DecompositionStore<N>> factory, BidiagonalDecomposition<N> bidiagonal, boolean fullSize) -
Method Summary
Modifier and TypeMethodDescriptionfinal void
btran
(PhysicalStore<N> arg) Backwards-transformationprotected boolean
protected boolean
compute
(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix, boolean valuesOnly, boolean fullSize) protected boolean
computeBidiagonal
(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix, boolean fullSize) boolean
computeValuesOnly
(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix) int
countSignificant
(double threshold) boolean
decompose
(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix) private static void
doCase1
(double[] s, double[] e, int p, int k, RotateRight q2RotR) private static void
doCase2
(double[] s, double[] e, int p, int k, RotateRight mtrxQ1) private static void
doCase3
(double[] s, double[] e, int p, int k, RotateRight q1RotR, RotateRight q2RotR) private static void
doCase4
(double[] s, int k, NegateColumn q2NegCol, ExchangeColumns q1XchgCols, ExchangeColumns q2XchgCols) protected boolean
doCompute
(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix, boolean valuesOnly, boolean fullSize) int
double
The condition number.getD()
double
Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.The output must be a "right inverse" and a "generalised inverse".getInverse
(PhysicalStore<N> preallocated) Implementing this method is optional.private MatrixStore
<N> getInverseOldVersion
(DecompositionStore<N> preallocated) double
getKyFanNorm
(int k) Ky Fan k-norm.double
double
int
getSolution
(Access2D.Collectable<N, ? super PhysicalStore<N>> rhs) [A][X]=[B] or [this][return]=[rhs]getSolution
(Access2D.Collectable<N, ? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated) Implementing this method is optional.double
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.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.The output must be a "right inverse" and a "generalised inverse".invert
(Access2D<?> original, PhysicalStore<N> preallocated) Exactly how (if at all) a specific implementation makes use ofpreallocated
is not specified by this interface.boolean
boolean
boolean
This is a property of the algorithm/implementation, not the data.boolean
Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever.protected boolean
protected MatrixStore
<N> makeD()
preallocate
(Structure2D template) Will create a PhysicalStore instance suitable for use withInverterTask.invert(Access2D, PhysicalStore)
.preallocate
(Structure2D templateBody, Structure2D templateRHS) Will create a PhysicalStore instance suitable for use withSolverTask.solve(Access2D, Access2D, PhysicalStore)
.void
reset()
Delete computed results, and resets attributes to default values(package private) void
setD
(MatrixStore<N> someD) (package private) void
setSingularValues
(Array1D<Double> singularValues) [A][X]=[B] or [body][return]=[rhs]solve
(Access2D<?> body, Access2D<?> rhs, PhysicalStore<N> preallocated) Exactly how (if at all) a specific implementation makes use ofpreallocated
is not specified by this interface.(package private) static void
toDiagonal
(double[] s, double[] e, RotateRight q1RotR, RotateRight q2RotR, ExchangeColumns q1XchgCols, ExchangeColumns q2XchgCols, NegateColumn q2NegCol) Methods inherited from class org.ojalgo.matrix.decomposition.GenericDecomposition
aggregator, allocate, collect, copy, function, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, scalar, wrap
Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition
computed, countColumns, countRows, getDimensionalEpsilon, isAspectRatioNormal, isComputed
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.ojalgo.matrix.task.InverterTask
preallocate
Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
btran
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
isComputed
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing
getRank
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver
compute, ftran, ftran, invert, solve, toInverseProvider, toSolutionProvider
Methods inherited from interface org.ojalgo.matrix.decomposition.SingularValue
getSingularValues, reconstruct, reconstruct
Methods inherited from interface org.ojalgo.matrix.task.SolverTask
preallocate
Methods inherited from interface org.ojalgo.structure.Structure2D
count, countColumns, countRows, firstInColumn, firstInRow, getMaxDim, getMinDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size
-
Field Details
-
TINY
private static final double TINY≈ 1.6E-291 -
e
private double[] e -
myBidiagonal
-
myD
-
myFullSize
private final boolean myFullSize -
myInputStructure
-
myInverse
-
mySingularValues
-
myTransposed
private boolean myTransposed -
myU
-
myV
-
myValuesOnly
private boolean myValuesOnly -
s
private double[] s
-
-
Constructor Details
-
SingularValueDecomposition
private SingularValueDecomposition(PhysicalStore.Factory<N, ? extends DecompositionStore<N>> factory) -
SingularValueDecomposition
protected SingularValueDecomposition(PhysicalStore.Factory<N, ? extends DecompositionStore<N>> factory, BidiagonalDecomposition<N> bidiagonal, boolean fullSize)
-
-
Method Details
-
doCase1
-
doCase2
-
doCase3
private static void doCase3(double[] s, double[] e, int p, int k, RotateRight q1RotR, RotateRight q2RotR) -
doCase4
private static void doCase4(double[] s, int k, NegateColumn q2NegCol, ExchangeColumns q1XchgCols, ExchangeColumns q2XchgCols) -
toDiagonal
static void toDiagonal(double[] s, double[] e, RotateRight q1RotR, RotateRight q2RotR, ExchangeColumns q1XchgCols, ExchangeColumns q2XchgCols, NegateColumn q2NegCol) -
btran
Description copied from interface:InvertibleFactor
Backwards-transformationSolve [x]T[A] = [b]T (equivalent to [A]T[x] = [b]) by transforming [b] into [x] in-place.
- Specified by:
btran
in interfaceInvertibleFactor<N extends Comparable<N>>
- Parameters:
arg
- [b] transformed into [x]
-
computeValuesOnly
- Specified by:
computeValuesOnly
in interfaceMatrixDecomposition.Values<N extends Comparable<N>>
- Parameters:
matrix
- The matrix to decompose- Returns:
- The same as
MatrixDecomposition.Solver.compute(Collectable)
orMatrixDecomposition.decompose(Collectable)
if the instance does not implementMatrixDecomposition.Solver
.
-
countSignificant
public int countSignificant(double threshold) - Specified by:
countSignificant
in interfaceMatrixDecomposition.RankRevealing<N extends Comparable<N>>
- Parameters:
threshold
- Significance limit- Returns:
- The number of elements in the diagonal matrix that are greater than the threshold
-
decompose
- Specified by:
decompose
in interfaceMatrixDecomposition<N extends Comparable<N>>
- Parameters:
matrix
- A matrix to decompose- Returns:
- true if decomposition suceeded; false if not
-
getColDim
public int getColDim()- Specified by:
getColDim
in interfaceStructure2D
- Returns:
- The number of columns
-
getCondition
public double getCondition()Description copied from interface:SingularValue
The condition number.- Specified by:
getCondition
in interfaceProvider2D.Condition
- Specified by:
getCondition
in interfaceSingularValue<N extends Comparable<N>>
- Returns:
- The largest singular value divided by the smallest singular value.
-
getCovariance
- Specified by:
getCovariance
in interfaceSingularValue<N extends Comparable<N>>
- Returns:
- [[A]T[A]]-1 Where [A] is the original matrix.
-
getD
- Specified by:
getD
in interfaceSingularValue<N extends Comparable<N>>
- Returns:
- The diagonal matrix of singular values.
-
getFrobeniusNorm
public double getFrobeniusNorm()Description copied from interface:SingularValue
Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.- Specified by:
getFrobeniusNorm
in interfaceSingularValue<N extends Comparable<N>>
- Returns:
- The square root of the sum of squares of the singular values.
-
getInverse
Description copied from interface:MatrixDecomposition.Solver
The output must be a "right inverse" and a "generalised inverse".- Specified by:
getInverse
in interfaceMatrixDecomposition.Solver<N extends Comparable<N>>
-
getInverse
Description copied from interface:MatrixDecomposition.Solver
Implementing this method is optional.
Exactly how a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
MatrixDecomposition.Solver.getInverse()
.- Specified by:
getInverse
in interfaceMatrixDecomposition.Solver<N extends Comparable<N>>
- Parameters:
preallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. UseInverterTask.preallocate(int, int)
orInverterTask.preallocate(Structure2D)
to get a suitable instance.- Returns:
- The inverse, this is where you get the solution
-
getKyFanNorm
public double getKyFanNorm(int k) Description copied from interface:SingularValue
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).
- Specified by:
getKyFanNorm
in interfaceSingularValue<N extends Comparable<N>>
- Parameters:
k
- The number of singular values to add up.- Returns:
- The sum of the k largest singular values.
-
getOperatorNorm
public double getOperatorNorm()- Specified by:
getOperatorNorm
in interfaceSingularValue<N extends Comparable<N>>
- Returns:
- 2-norm
-
getRankThreshold
public double getRankThreshold()- Specified by:
getRankThreshold
in interfaceMatrixDecomposition.RankRevealing<N extends Comparable<N>>
-
getRowDim
public int getRowDim()- Specified by:
getRowDim
in interfaceStructure2D
- Returns:
- The number of rows
-
getSingularValues
- Specified by:
getSingularValues
in interfaceSingularValue<N extends Comparable<N>>
- Returns:
- The singular values ordered in descending order.
-
getSolution
Description copied from interface:MatrixDecomposition.Solver
[A][X]=[B] or [this][return]=[rhs]- Specified by:
getSolution
in interfaceMatrixDecomposition.Solver<N extends Comparable<N>>
-
getSolution
public MatrixStore<N> getSolution(Access2D.Collectable<N, ? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated) Description copied from interface:MatrixDecomposition.Solver
Implementing this method is optional.
Exactly how a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
MatrixDecomposition.Solver.getSolution(Collectable)
.- Specified by:
getSolution
in interfaceMatrixDecomposition.Solver<N extends Comparable<N>>
- Parameters:
rhs
- The Right Hand Side, wont be modfiedpreallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. UseSolverTask.preallocate(int, int, int)
orSolverTask.preallocate(Structure2D, Structure2D)
to get a suitable instance.- Returns:
- The solution
-
getTraceNorm
public double getTraceNorm()- Specified by:
getTraceNorm
in interfaceSingularValue<N extends Comparable<N>>
-
getU
Description copied from interface:SingularValue
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].
- Specified by:
getU
in interfaceSingularValue<N extends Comparable<N>>
-
getV
Description copied from interface:SingularValue
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].
- Specified by:
getV
in interfaceSingularValue<N extends Comparable<N>>
-
invert
Description copied from interface:InverterTask
The output must be a "right inverse" and a "generalised inverse".- Specified by:
invert
in interfaceInverterTask<N extends Comparable<N>>
- Throws:
RecoverableCondition
-
invert
public MatrixStore<N> invert(Access2D<?> original, PhysicalStore<N> preallocated) throws RecoverableCondition Description copied from interface:InverterTask
Exactly how (if at all) a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
InverterTask.invert(Access2D)
.Use
InverterTask.preallocate(Structure2D)
to obtain a suitbalepreallocated
.- Specified by:
invert
in interfaceInverterTask<N extends Comparable<N>>
- Parameters:
preallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.- Returns:
- The inverse
- Throws:
RecoverableCondition
- TODO
-
isFullRank
public boolean isFullRank()- Specified by:
isFullRank
in interfaceMatrixDecomposition.RankRevealing<N extends Comparable<N>>
- Returns:
- true if the rank is equal to the minimum of the row and column dimensions; false if not
-
isFullSize
public boolean isFullSize()- Specified by:
isFullSize
in interfaceMatrixDecomposition.EconomySize<N extends Comparable<N>>
- Returns:
- True if it will generate a full sized decomposition.
-
isOrdered
public boolean isOrdered()Description copied from interface:MatrixDecomposition.Ordered
This is a property of the algorithm/implementation, not the data. Typically relevant forSingularValue
,Eigenvalue
or anyMatrixDecomposition.RankRevealing
decomposition.- Specified by:
isOrdered
in interfaceMatrixDecomposition.Ordered<N extends Comparable<N>>
- Returns:
- true if the rows/columns of the returned matrix factors are guaranteed some specific order; false if there is no such guarantee.
-
isSolvable
public boolean isSolvable()Description copied from interface:MatrixDecomposition.Solver
Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever. It's that in combination with the specific decomposition algorithm's capabilities.- Specified by:
isSolvable
in interfaceMatrixDecomposition.Solver<N extends Comparable<N>>
- Overrides:
isSolvable
in classAbstractDecomposition<N extends Comparable<N>>
- Returns:
- true if this matrix decomposition is in a state to be able to deliver an inverse or an equation system solution (with some degree of numerical stability).
-
preallocate
Description copied from interface:InverterTask
Will create a PhysicalStore instance suitable for use with
InverterTask.invert(Access2D, PhysicalStore)
.When inverting a matrix (mxn) the preallocated memory/matrix will typically be nxm (and of course most of the time A is square).
- Specified by:
preallocate
in interfaceInverterTask<N extends Comparable<N>>
-
preallocate
Description copied from interface:SolverTask
Will create a PhysicalStore instance suitable for use with
SolverTask.solve(Access2D, Access2D, PhysicalStore)
. The dimensions of the returned instance is not specified by this interface - it is specified by the behaviour/requirements of each implementation.When solving an equation system [A][X]=[B] ([mxn][nxb]=[mxb]) the preallocated memory/matrix will typically be either mxb or nxb.
- Specified by:
preallocate
in interfaceSolverTask<N extends Comparable<N>>
-
reset
public void reset()Description copied from interface:MatrixDecomposition
Delete computed results, and resets attributes to default values- Specified by:
reset
in interfaceMatrixDecomposition<N extends Comparable<N>>
- Overrides:
reset
in classAbstractDecomposition<N extends Comparable<N>>
-
solve
Description copied from interface:SolverTask
[A][X]=[B] or [body][return]=[rhs]- Specified by:
solve
in interfaceSolverTask<N extends Comparable<N>>
- Throws:
RecoverableCondition
-
solve
public MatrixStore<N> solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<N> preallocated) throws RecoverableCondition Description copied from interface:SolverTask
Exactly how (if at all) a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
SolverTask.solve(Access2D, Access2D)
.Use
SolverTask.preallocate(Structure2D, Structure2D)
to obtain a suitbalepreallocated
.- Specified by:
solve
in interfaceSolverTask<N extends Comparable<N>>
- Parameters:
rhs
- The Right Hand Side, wont be modfiedpreallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.- Returns:
- The solution
- Throws:
RecoverableCondition
-
getInverseOldVersion
-
checkSolvability
protected boolean checkSolvability()- Overrides:
checkSolvability
in classAbstractDecomposition<N extends Comparable<N>>
-
compute
protected boolean compute(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix, boolean valuesOnly, boolean fullSize) -
computeBidiagonal
protected boolean computeBidiagonal(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix, boolean fullSize) -
doCompute
protected boolean doCompute(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix, boolean valuesOnly, boolean fullSize) -
isTransposed
protected boolean isTransposed() -
makeD
-
makeSingularValues
-
setD
-
setSingularValues
-