Documentation API of the 'jhplot.math.LUDecomposition' Java class
LUDecomposition
jhplot.math

## Class LUDecomposition

• `public class LUDecompositionextends 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.

• ### Constructor Summary

Constructors
Constructor and Description
`LUDecomposition(double[][] A)`
LU Decomposition
• ### Method Summary

All Methods
Modifier and TypeMethod and Description
`double``det()`
Determinant
`double[][]``getL()`
Return lower triangular factor
`double[][]``getP()`
Return pivot permutation vector
`double[][]``getU()`
Return upper triangular factor
`boolean``isNonsingular()`
Is the matrix nonsingular?
`double[][]``solve(double[][] B)`
Solve A*X = B
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### LUDecomposition

`public LUDecomposition(double[][] A)`
LU Decomposition
Parameters:
`A` - Rectangular matrix
• ### Method Detail

• #### isNonsingular

`public boolean isNonsingular()`
Is the matrix nonsingular?
Returns:
true if U, and hence A, is nonsingular.
• #### getL

`public double[][] getL()`
Return lower triangular factor
Returns:
L
• #### getU

`public double[][] getU()`
Return upper triangular factor
Returns:
U
• #### getP

`public double[][] getP()`
Return pivot permutation vector
Returns:
piv
• #### det

`public double det()`
Determinant
Returns:
det(A)
Throws:
`IllegalArgumentException` - Matrix must be square
• #### 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:
`IllegalArgumentException` - Matrix row dimensions must agree.
`RuntimeException` - Matrix is singular.

DMelt 1.2 © DataMelt by jWork.ORG

LUDecomposition
jhplot.math

## Class LUDecomposition

• `public class LUDecompositionextends 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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