Package cern.colt.matrix.linalg
Class QRDecomposition
- java.lang.Object
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- cern.colt.matrix.linalg.QRDecomposition
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- All Implemented Interfaces:
java.io.Serializable
public class QRDecomposition extends java.lang.Object implements java.io.Serializable
For an m x n matrix A with m >= n, the QR decomposition is an m x n orthogonal matrix Q and an n x 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.
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- Serialized Form
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Field Summary
Fields Modifier and Type Field Description private int
m
Row and column dimensions.private int
n
Row and column dimensions.private DoubleMatrix2D
QR
Array for internal storage of decomposition.private DoubleMatrix1D
Rdiag
Array for internal storage of diagonal of R.(package private) static long
serialVersionUID
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Constructor Summary
Constructors Constructor Description QRDecomposition(DoubleMatrix2D A)
Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description DoubleMatrix2D
getH()
Returns the Householder vectors H.DoubleMatrix2D
getQ()
Generates and returns the (economy-sized) orthogonal factor Q.DoubleMatrix2D
getR()
Returns the upper triangular factor, R.boolean
hasFullRank()
Returns whether the matrix A has full rank.DoubleMatrix2D
solve(DoubleMatrix2D B)
Least squares solution of A*X = B; returns X.java.lang.String
toString()
Returns a String with (propertyName, propertyValue) pairs.
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Field Detail
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serialVersionUID
static final long serialVersionUID
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- Constant Field Values
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QR
private DoubleMatrix2D 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 DoubleMatrix1D Rdiag
Array for internal storage of diagonal of R.
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Constructor Detail
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QRDecomposition
public QRDecomposition(DoubleMatrix2D A)
Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.- Parameters:
A
- A rectangular matrix.- Throws:
java.lang.IllegalArgumentException
- if A.rows() < A.columns().
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Method Detail
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getH
public DoubleMatrix2D getH()
Returns the Householder vectors H.- Returns:
- A lower trapezoidal matrix whose columns define the householder reflections.
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getQ
public DoubleMatrix2D getQ()
Generates and returns the (economy-sized) orthogonal factor Q.- Returns:
- Q
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getR
public DoubleMatrix2D getR()
Returns the upper triangular factor, R.- Returns:
- R
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hasFullRank
public boolean hasFullRank()
Returns whether the matrix A has full rank.- Returns:
- true if R, and hence A, has full rank.
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solve
public DoubleMatrix2D solve(DoubleMatrix2D B)
Least squares solution of A*X = B; returns X.- Parameters:
B
- A matrix 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
- if B.rows() != A.rows().java.lang.IllegalArgumentException
- if !this.hasFullRank() (A is rank deficient).
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toString
public java.lang.String toString()
Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,rank : 3 trace : 0
- Overrides:
toString
in classjava.lang.Object
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