jhplot.math
Class LUDecomposition
- java.lang.Object
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- jhplot.math.LUDecomposition
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public class LUDecomposition extends java.lang.Object
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. In other words, assuming P the permutation Matrix, P*A = 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.
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Constructor Summary
Constructors Constructor and Description LUDecomposition(double[][] A)
LU Decomposition
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method and Description double
det()
Determinantdouble[][]
getL()
Return lower triangular factordouble[][]
getP()
Return pivot permutation vectordouble[][]
getU()
Return upper triangular factorboolean
isNonsingular()
Is the matrix nonsingular?double[][]
solve(double[][] B)
Solve A*X = B
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Constructor Detail
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LUDecomposition
public LUDecomposition(double[][] A)
LU Decomposition- Parameters:
A
- Rectangular matrix
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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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getP
public double[][] getP()
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.RuntimeException
- Matrix is singular.
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