Class HermitianEvD<N extends java.lang.Comparable<N>>
- java.lang.Object
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- org.ojalgo.matrix.decomposition.AbstractDecomposition<N>
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- org.ojalgo.matrix.decomposition.GenericDecomposition<N>
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- org.ojalgo.matrix.decomposition.EigenvalueDecomposition<N>
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- org.ojalgo.matrix.decomposition.HermitianEvD<N>
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- All Implemented Interfaces:
Eigenvalue<N>
,MatrixDecomposition<N>
,MatrixDecomposition.Determinant<N>
,MatrixDecomposition.Hermitian<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.Solver<N>
,MatrixDecomposition.Values<N>
,Provider2D
,Provider2D.Determinant<N>
,Provider2D.Eigenpairs
,Provider2D.Inverse<java.util.Optional<MatrixStore<N>>>
,Provider2D.Solution<java.util.Optional<MatrixStore<N>>>
,DeterminantTask<N>
,InverterTask<N>
,MatrixTask<N>
,SolverTask<N>
,InvertibleFactor<N>
,Structure1D
,Structure2D
- Direct Known Subclasses:
HermitianEvD.C128
,HermitianEvD.H256
,HermitianEvD.Q128
,HermitianEvD.R064
,HermitianEvD.R128
abstract class HermitianEvD<N extends java.lang.Comparable<N>> extends EigenvalueDecomposition<N> implements MatrixDecomposition.Solver<N>
Eigenvalues and eigenvectors of a real matrix.If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
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Nested Class Summary
Nested Classes Modifier and Type Class Description (package private) static class
HermitianEvD.C128
(package private) static class
HermitianEvD.H256
(package private) static class
HermitianEvD.Q128
(package private) static class
HermitianEvD.R064
(package private) static class
HermitianEvD.R128
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Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.Eigenvalue
Eigenvalue.Eigenpair, Eigenvalue.Factory<N extends java.lang.Comparable<N>>, Eigenvalue.Generalisation, Eigenvalue.Generalised<N extends java.lang.Comparable<N>>
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Nested classes/interfaces inherited from interface org.ojalgo.matrix.task.InverterTask
InverterTask.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.Factory<D extends MatrixDecomposition<?>>, 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.matrix.task.SolverTask
SolverTask.Factory<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 private double[]
d
private double[]
e
private MatrixStore<N>
myInverse
private TridiagonalDecomposition<N>
myTridiagonal
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Fields inherited from interface org.ojalgo.matrix.decomposition.Eigenvalue
C128, DESCENDING_NORM, H256, Q128, R064, R128
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Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Constructor Summary
Constructors Modifier Constructor Description private
HermitianEvD(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory)
protected
HermitianEvD(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory, TridiagonalDecomposition<N> tridiagonal)
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description void
btran(PhysicalStore<N> arg)
Backwards-transformationboolean
checkAndDecompose(MatrixStore<N> matrix)
Absolutely must check if the matrix is hermitian or not.protected boolean
checkSolvability()
protected boolean
doDecompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix, boolean valuesOnly)
N
getDeterminant()
A matrix' determinant is the product of its eigenvalues.void
getEigenvalues(double[] realParts, java.util.Optional<double[]> imaginaryParts)
MatrixStore<N>
getInverse()
The output must be a "right inverse" and a "generalised inverse".MatrixStore<N>
getInverse(PhysicalStore<N> preallocated)
Implementing this method is optional.MatrixStore<N>
getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs)
[A][X]=[B] or [this][return]=[rhs]MatrixStore<N>
getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)
Implementing this method is optional.ComplexNumber
getTrace()
A matrix' trace is the sum of the diagonal elements.MatrixStore<N>
invert(Access2D<?> original)
The output must be a "right inverse" and a "generalised inverse".MatrixStore<N>
invert(Access2D<?> original, PhysicalStore<N> preallocated)
Exactly how (if at all) a specific implementation makes use ofpreallocated
is not specified by this interface.boolean
isHermitian()
If [A] is hermitian then [V][D][V]-1 becomes [Q][D][Q]H...boolean
isOrdered()
The eigenvalues in D (and the eigenvectors in V) are not necessarily ordered.boolean
isSolvable()
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 MatrixStore<N>
makeD()
protected Array1D<ComplexNumber>
makeEigenvalues()
protected MatrixStore<N>
makeV()
PhysicalStore<N>
preallocate(Structure2D template)
Will create a PhysicalStore instance suitable for use withInverterTask.invert(Access2D, PhysicalStore)
.PhysicalStore<N>
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 valuesMatrixStore<N>
solve(Access2D<?> body, Access2D<?> rhs)
[A][X]=[B] or [body][return]=[rhs]MatrixStore<N>
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
tql2(double[] d, double[] e, RotateRight mtrxV)
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Methods inherited from class org.ojalgo.matrix.decomposition.EigenvalueDecomposition
calculateDeterminant, computeValuesOnly, decompose, getColDim, getD, getEigenvalues, getMaxDim, getMinDim, getRowDim, getV, setD, setEigenvalues, setV, sort
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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
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Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition
computed, countColumns, countRows, getDimensionalEpsilon, isAspectRatioNormal, isComputed
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.ojalgo.matrix.decomposition.Eigenvalue
getEigenpair, getEigenpairs, getEigenvectors, reconstruct
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Methods inherited from interface org.ojalgo.matrix.task.InverterTask
preallocate
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Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
btran
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
decompose, isComputed
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
toDeterminantProvider
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver
compute, ftran, ftran, invert, solve, toInverseProvider, toSolutionProvider
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Methods inherited from interface org.ojalgo.matrix.task.SolverTask
preallocate
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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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d
private double[] d
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e
private double[] e
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myInverse
private transient MatrixStore<N extends java.lang.Comparable<N>> myInverse
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myTridiagonal
private final TridiagonalDecomposition<N extends java.lang.Comparable<N>> myTridiagonal
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Constructor Detail
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HermitianEvD
private HermitianEvD(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory)
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HermitianEvD
protected HermitianEvD(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory, TridiagonalDecomposition<N> tridiagonal)
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Method Detail
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tql2
static void tql2(double[] d, double[] e, RotateRight mtrxV)
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btran
public final void btran(PhysicalStore<N> arg)
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 java.lang.Comparable<N>>
- Parameters:
arg
- [b] transformed into [x]
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checkAndDecompose
public boolean checkAndDecompose(MatrixStore<N> matrix)
Description copied from interface:MatrixDecomposition.Hermitian
Absolutely must check if the matrix is hermitian or not. Then, depending on the result different paths can be chosen - compute or not / choose different algorithms...- Specified by:
checkAndDecompose
in interfaceMatrixDecomposition.Hermitian<N extends java.lang.Comparable<N>>
- Parameters:
matrix
- A matrix to check and then (maybe) decompose- Returns:
- true if the hermitian check passed and decomposition succeeded; false if not
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getDeterminant
public N getDeterminant()
Description copied from interface:MatrixDecomposition.Determinant
A matrix' determinant is the product of its eigenvalues.
- Specified by:
getDeterminant
in interfaceMatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>
- Specified by:
getDeterminant
in interfaceProvider2D.Determinant<N extends java.lang.Comparable<N>>
- Returns:
- The matrix' determinant
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getEigenvalues
public void getEigenvalues(double[] realParts, java.util.Optional<double[]> imaginaryParts)
- Specified by:
getEigenvalues
in interfaceEigenvalue<N extends java.lang.Comparable<N>>
- Parameters:
realParts
- An array that will receive the real parts of the eigenvaluesimaginaryParts
- An optional array that, if present, will receive the imaginary parts of the eigenvalues
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getInverse
public MatrixStore<N> 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 java.lang.Comparable<N>>
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getInverse
public MatrixStore<N> getInverse(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.getInverse()
.- Specified by:
getInverse
in interfaceMatrixDecomposition.Solver<N extends java.lang.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
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getSolution
public MatrixStore<N> getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs)
Description copied from interface:MatrixDecomposition.Solver
[A][X]=[B] or [this][return]=[rhs]- Specified by:
getSolution
in interfaceMatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
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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 java.lang.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
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getTrace
public ComplexNumber getTrace()
Description copied from interface:Eigenvalue
A matrix' trace is the sum of the diagonal elements. It is also the sum of the eigenvalues. This method should return the sum of the eigenvalues.- Specified by:
getTrace
in interfaceEigenvalue<N extends java.lang.Comparable<N>>
- Returns:
- The matrix' trace
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invert
public MatrixStore<N> invert(Access2D<?> original) throws RecoverableCondition
Description copied from interface:InverterTask
The output must be a "right inverse" and a "generalised inverse".- Specified by:
invert
in interfaceInverterTask<N extends java.lang.Comparable<N>>
- Throws:
RecoverableCondition
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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 java.lang.Comparable<N>>
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
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isHermitian
public boolean isHermitian()
Description copied from interface:Eigenvalue
If [A] is hermitian then [V][D][V]-1 becomes [Q][D][Q]H...- Specified by:
isHermitian
in interfaceEigenvalue<N extends java.lang.Comparable<N>>
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isOrdered
public boolean isOrdered()
Description copied from interface:Eigenvalue
The eigenvalues in D (and the eigenvectors in V) are not necessarily ordered. This is a property of the algorithm/implementation, not the data.- Specified by:
isOrdered
in interfaceEigenvalue<N extends java.lang.Comparable<N>>
- Specified by:
isOrdered
in interfaceMatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>
- Returns:
- true if they are ordered
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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 java.lang.Comparable<N>>
- Overrides:
isSolvable
in classAbstractDecomposition<N extends java.lang.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).
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preallocate
public PhysicalStore<N> preallocate(Structure2D template)
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 java.lang.Comparable<N>>
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preallocate
public PhysicalStore<N> preallocate(Structure2D templateBody, Structure2D templateRHS)
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 java.lang.Comparable<N>>
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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 java.lang.Comparable<N>>
- Overrides:
reset
in classEigenvalueDecomposition<N extends java.lang.Comparable<N>>
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solve
public MatrixStore<N> solve(Access2D<?> body, Access2D<?> rhs) throws RecoverableCondition
Description copied from interface:SolverTask
[A][X]=[B] or [body][return]=[rhs]- Specified by:
solve
in interfaceSolverTask<N extends java.lang.Comparable<N>>
- Throws:
RecoverableCondition
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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 java.lang.Comparable<N>>
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
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checkSolvability
protected boolean checkSolvability()
- Overrides:
checkSolvability
in classAbstractDecomposition<N extends java.lang.Comparable<N>>
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doDecompose
protected boolean doDecompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix, boolean valuesOnly)
- Specified by:
doDecompose
in classEigenvalueDecomposition<N extends java.lang.Comparable<N>>
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makeD
protected MatrixStore<N> makeD()
- Specified by:
makeD
in classEigenvalueDecomposition<N extends java.lang.Comparable<N>>
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makeEigenvalues
protected Array1D<ComplexNumber> makeEigenvalues()
- Specified by:
makeEigenvalues
in classEigenvalueDecomposition<N extends java.lang.Comparable<N>>
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makeV
protected MatrixStore<N> makeV()
- Specified by:
makeV
in classEigenvalueDecomposition<N extends java.lang.Comparable<N>>
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