Class QRDecomposition.Solver
- java.lang.Object
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- org.apache.commons.math3.linear.QRDecomposition.Solver
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- All Implemented Interfaces:
DecompositionSolver
- Enclosing class:
- QRDecomposition
private static class QRDecomposition.Solver extends java.lang.Object implements DecompositionSolver
Specialized solver.
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Constructor Summary
Constructors Modifier Constructor Description private
Solver(double[][] qrt, double[] rDiag, double threshold)
Build a solver from decomposed matrix.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description RealMatrix
getInverse()
Get the pseudo-inverse of the decomposed matrix.boolean
isNonSingular()
Check if the decomposed matrix is non-singular.RealMatrix
solve(RealMatrix b)
Solve the linear equation A × X = B for matrices A.RealVector
solve(RealVector b)
Solve the linear equation A × X = B for matrices A.
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Field Detail
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qrt
private final double[][] qrt
A packed TRANSPOSED representation of the QR decomposition.The elements BELOW the diagonal are the elements of the UPPER triangular matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors from which an explicit form of Q can be recomputed if desired.
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rDiag
private final double[] rDiag
The diagonal elements of R.
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threshold
private final double threshold
Singularity threshold.
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Method Detail
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isNonSingular
public boolean isNonSingular()
Check if the decomposed matrix is non-singular.- Specified by:
isNonSingular
in interfaceDecompositionSolver
- Returns:
- true if the decomposed matrix is non-singular.
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solve
public RealVector solve(RealVector b)
Solve the linear equation A × X = B for matrices A.The A matrix is implicit, it is provided by the underlying decomposition algorithm.
- Specified by:
solve
in interfaceDecompositionSolver
- Parameters:
b
- right-hand side of the equation A × X = B- Returns:
- a vector X that minimizes the two norm of A × X - B
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solve
public RealMatrix solve(RealMatrix b)
Solve the linear equation A × X = B for matrices A.The A matrix is implicit, it is provided by the underlying decomposition algorithm.
- Specified by:
solve
in interfaceDecompositionSolver
- Parameters:
b
- right-hand side of the equation A × X = B- Returns:
- a matrix X that minimizes the two norm of A × X - B
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getInverse
public RealMatrix getInverse()
Get the pseudo-inverse of the decomposed matrix.This is equal to the inverse of the decomposed matrix, if such an inverse exists.
If no such inverse exists, then the result has properties that resemble that of an inverse.
In particular, in this case, if the decomposed matrix is A, then the system of equations \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right \|_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, meaning \( \left \| z \right \|_2 \) is minimized.
Note however that some decompositions cannot compute a pseudo-inverse for all matrices. For example, the
LUDecomposition
is not defined for non-square matrices to begin with. TheQRDecomposition
can operate on non-square matrices, but will throwSingularMatrixException
if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details.- Specified by:
getInverse
in interfaceDecompositionSolver
- Returns:
- pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can pseudo-invert the decomposed matrix
- Throws:
SingularMatrixException
- if the decomposed matrix is singular.
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