Package elki.math.linearalgebra
Class QRDecomposition
- java.lang.Object
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- elki.math.linearalgebra.QRDecomposition
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- All Implemented Interfaces:
java.io.Serializable
public class QRDecomposition extends java.lang.Object implements java.io.Serializable
QR Decomposition. For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R. The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.- Since:
- 0.1
- Author:
- Arthur Zimek
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected static java.lang.String
ERR_MATRIX_RANK_DEFICIENT
When a matrix is rank deficient.private int
m
Row and column dimensions.private int
n
Row and column dimensions.private double[][]
QR
Array for internal storage of decomposition.private double[]
Rdiag
Array for internal storage of diagonal of R.private static long
serialVersionUID
Serial version
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Constructor Summary
Constructors Constructor Description QRDecomposition(double[][] A)
QR Decomposition, computed by Householder reflections.QRDecomposition(double[][] A, int m, int n)
QR Decomposition, computed by Householder reflections.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double[][]
getH()
Return the Householder vectorsdouble[][]
getQ()
Generate and return the (economy-sized, m by n) orthogonal factordouble[][]
getR()
Return the upper triangular factordouble[][]
inverse()
Find the inverse matrix.boolean
isFullRank()
Is the matrix full rank?int
rank(double t)
Get the matrix rank?double[]
solve(double[] b)
Least squares solution of A*X = bdouble[][]
solve(double[][] B)
Least squares solution of A*X = Bdouble[]
solveInplace(double[] b)
Least squares solution of A*X = bprivate double[][]
solveInplace(double[][] B)
Least squares solution of A*X = B
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Field Detail
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ERR_MATRIX_RANK_DEFICIENT
protected static final java.lang.String ERR_MATRIX_RANK_DEFICIENT
When a matrix is rank deficient.- See Also:
- Constant Field Values
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serialVersionUID
private static final long serialVersionUID
Serial version- See Also:
- Constant Field Values
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QR
private double[][] QR
Array for internal storage of decomposition.
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m
private int m
Row and column dimensions.
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n
private int n
Row and column dimensions.
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Rdiag
private double[] Rdiag
Array for internal storage of diagonal of R.
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Constructor Detail
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QRDecomposition
public QRDecomposition(double[][] A)
QR Decomposition, computed by Householder reflections.- Parameters:
A
- Rectangular matrix
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QRDecomposition
public QRDecomposition(double[][] A, int m, int n)
QR Decomposition, computed by Householder reflections.- Parameters:
A
- Rectangular matrixm
- row dimensionalityn
- column dimensionality
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Method Detail
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isFullRank
public boolean isFullRank()
Is the matrix full rank?- Returns:
- true if R, and hence A, has full rank.
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rank
public int rank(double t)
Get the matrix rank?- Parameters:
t
- Tolerance threshold- Returns:
- Rank of R
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getH
public double[][] getH()
Return the Householder vectors- Returns:
- Lower trapezoidal matrix whose columns define the reflections
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getR
public double[][] getR()
Return the upper triangular factor- Returns:
- R
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getQ
public double[][] getQ()
Generate and return the (economy-sized, m by n) orthogonal factor- Returns:
- Q
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solve
public double[][] solve(double[][] B)
Least squares solution of A*X = B- Parameters:
B
- The matrix B with as many rows as A and any number of columns.- Returns:
- X that minimizes the two norm of Q*R*X-B.
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is rank deficient.
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solveInplace
private double[][] solveInplace(double[][] B)
Least squares solution of A*X = B- Parameters:
B
- The matrix B with as many rows as A and any number of columns (will be overwritten).- Returns:
- X that minimizes the two norm of Q*R*X-B.
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is rank deficient.
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solve
public double[] solve(double[] b)
Least squares solution of A*X = b- Parameters:
b
- A column vector with as many rows as A.- Returns:
- X that minimizes the two norm of Q*R*X-b.
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is rank deficient.
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solveInplace
public double[] solveInplace(double[] b)
Least squares solution of A*X = b- Parameters:
b
- A column vector b with as many rows as A.- Returns:
- X that minimizes the two norm of Q*R*X-b.
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is rank deficient.
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inverse
public double[][] inverse()
Find the inverse matrix.- Returns:
- Inverse matrix
- Throws:
java.lang.ArithmeticException
- Matrix is rank deficient.
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