Package elki.math.linearalgebra
Class LUDecomposition
- java.lang.Object
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- elki.math.linearalgebra.LUDecomposition
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- All Implemented Interfaces:
java.io.Serializable
public class LUDecomposition extends java.lang.Object implements java.io.Serializable
LU Decomposition.For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.
The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.
- Since:
- 0.1
- Author:
- Arthur Zimek
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description private double[][]
LU
Array for internal storage of decomposition.private int
m
Row and column dimensions, and pivot sign.private int
n
Row and column dimensions, and pivot sign.private int[]
piv
Internal storage of pivot vector.private int
pivsign
Row and column dimensions, and pivot sign.private static long
serialVersionUID
Serial version
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Constructor Summary
Constructors Constructor Description LUDecomposition(double[][] LU)
LU DecompositionLUDecomposition(double[][] LU, int m, int n)
LU Decomposition
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
det()
Determinantdouble[][]
getL()
Return lower triangular factorint[]
getPivot()
Return pivot permutation vectordouble[][]
getU()
Return upper triangular factordouble[][]
inverse()
Find the inverse matrix.boolean
isNonsingular()
Is the matrix nonsingular?double[]
solve(double[] b)
Solve A*X = bdouble[][]
solve(double[][] B)
Solve A*X = Bdouble[]
solveInplace(double[] b)
Solve A*X = bprivate double[][]
solveInplace(double[][] B)
Solve A*X = B
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Field Detail
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serialVersionUID
private static final long serialVersionUID
Serial version- See Also:
- Constant Field Values
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LU
private double[][] LU
Array for internal storage of decomposition.
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m
private int m
Row and column dimensions, and pivot sign.
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n
private int n
Row and column dimensions, and pivot sign.
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pivsign
private int pivsign
Row and column dimensions, and pivot sign.
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piv
private int[] piv
Internal storage of pivot vector.
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Method Detail
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isNonsingular
public boolean isNonsingular()
Is the matrix nonsingular?- Returns:
- true if U, and hence A, is nonsingular.
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getL
public double[][] getL()
Return lower triangular factor- Returns:
- L
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getU
public double[][] getU()
Return upper triangular factor- Returns:
- U
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getPivot
public int[] getPivot()
Return pivot permutation vector- Returns:
- piv
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det
public double det()
Determinant- Returns:
- det(A)
- Throws:
java.lang.IllegalArgumentException
- Matrix must be square
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solve
public double[][] solve(double[][] B)
Solve A*X = B- Parameters:
B
- A Matrix with as many rows as A and any number of columns.- Returns:
- X so that L*U*X = B(piv,:)
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is singular.
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solveInplace
private double[][] solveInplace(double[][] B)
Solve A*X = B- Parameters:
B
- A Matrix with as many rows as A and any number of columns.- Returns:
- B
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is singular.
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solve
public double[] solve(double[] b)
Solve A*X = b- Parameters:
b
- A column vector with as many rows as A- Returns:
- X so that L*U*X = b(piv)
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is singular.
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solveInplace
public double[] solveInplace(double[] b)
Solve A*X = b- Parameters:
b
- A vector- Returns:
- b
- Throws:
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.java.lang.ArithmeticException
- Matrix is singular.
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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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