LUDecomposition
Jama

## Class LUDecomposition

• All Implemented Interfaces:
Serializable

```public class LUDecomposition
extends Object
implements 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.

Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
`LUDecomposition(Matrix A)`
LU Decomposition
• ### Method Summary

Methods
Modifier and Type Method and Description
`double` `det()`
Determinant
`double[]` `getDoublePivot()`
Return pivot permutation vector as a one-dimensional double array
`Matrix` `getL()`
Return lower triangular factor
`int[]` `getPivot()`
Return pivot permutation vector
`Matrix` `getU()`
Return upper triangular factor
`boolean` `isNonsingular()`
Is the matrix nonsingular?
`Matrix` `solve(Matrix 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(Matrix 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 Matrix getL()`
Return lower triangular factor
Returns:
L
• #### getU

`public Matrix getU()`
Return upper triangular factor
Returns:
U
• #### getPivot

`public int[] getPivot()`
Return pivot permutation vector
Returns:
piv
• #### getDoublePivot

`public double[] getDoublePivot()`
Return pivot permutation vector as a one-dimensional double array
Returns:
(double) piv
• #### det

`public double det()`
Determinant
Returns:
det(A)
Throws:
`IllegalArgumentException` - Matrix must be square
• #### solve

`public Matrix solve(Matrix 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.