smile.math.matrix

Class Matrix.LU

java.lang.Object

smile.math.matrix.Matrix.LU

All Implemented Interfaces:

java.io.Serializable

Enclosing class:

Matrix

public static class Matrix.LU
extends java.lang.Object
implements java.io.Serializable

The 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 decomposition with pivoting always exists, even if the matrix is singular. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations if it is not singular. The decomposition can also be used to calculate the determinant.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	info If info = 0, the LU decomposition was successful.
int[]	ipiv The pivot vector.
Matrix	lu The LU decomposition.

Constructor Summary

Constructors

Constructor and Description
LU(Matrix lu, int[] ipiv, int info) Constructor.

Method Summary

Modifier and Type	Method and Description
double	det() Returns the matrix determinant.
Matrix	inverse() Returns the matrix inverse.
boolean	isSingular() Returns if the matrix is singular.
double[]	solve(double[] b) Solve A * x = b.
void	solve(Matrix B) Solve A * X = B.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

lu

public final Matrix lu

The LU decomposition.

ipiv

public final int[] ipiv

The pivot vector.

info

public final int info

If info = 0, the LU decomposition was successful. If info = i > 0, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Constructor Detail

LU

public LU(Matrix lu,
          int[] ipiv,
          int info)

Constructor.

Parameters:

lu - LU decomposition matrix

ipiv - the pivot vector

info - info > 0 if the matrix is singular

Method Detail

isSingular

public boolean isSingular()

Returns if the matrix is singular.

det

public double det()

Returns the matrix determinant.

inverse

public Matrix inverse()

Returns the matrix inverse. For pseudo inverse, use QRDecomposition.

solve

public double[] solve(double[] b)

Solve A * x = b.

Parameters:

b - right hand side of linear system. On output, b will be overwritten with the solution matrix.

Throws:

java.lang.RuntimeException - if matrix is singular.

solve

public void solve(Matrix B)

Solve A * X = B. B will be overwritten with the solution matrix on output.

Parameters:

B - right hand side of linear system. On output, B will be overwritten with the solution matrix.

Throws:

java.lang.RuntimeException - if matrix is singular.