/*
* This software is a cooperative product of The MathWorks and the National
* Institute of Standards and Technology (NIST) which has been released to the
* public domain. Neither The MathWorks nor NIST assumes any responsibility
* whatsoever for its use by other parties, and makes no guarantees, expressed
* or implied, about its quality, reliability, or any other characteristic.
*/
/*
* LUDecomposition.java
* Copyright (C) 1999 The Mathworks and NIST
*
*/
package weka.core.matrix;
import weka.core.RevisionHandler;
import weka.core.RevisionUtils;
import java.io.Serializable;
/**
* LU Decomposition.
* <P>
* 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.
* <P>
* 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.
* <p/>
* Adapted from the <a href="http://math.nist.gov/javanumerics/jama/" target="_blank">JAMA</a> package.
*
* @author The Mathworks and NIST
* @author Fracpete (fracpete at waikato dot ac dot nz)
* @version $Revision: 5953 $
*/
public class LUDecomposition
implements Serializable, RevisionHandler {
/** for serialization */
private static final long serialVersionUID = -2731022568037808629L;
/**
* Array for internal storage of decomposition.
* @serial internal array storage.
*/
private double[][] LU;
/**
* Row and column dimensions, and pivot sign.
* @serial column dimension.
* @serial row dimension.
* @serial pivot sign.
*/
private int m, n, pivsign;
/**
* Internal storage of pivot vector.
* @serial pivot vector.
*/
private int[] piv;
/**
* LU Decomposition
* @param A Rectangular matrix
*/
public LUDecomposition(Matrix A) {
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = A.getArrayCopy();
m = A.getRowDimension();
n = A.getColumnDimension();
piv = new int[m];
for (int i = 0; i < m; i++) {
piv[i] = i;
}
pivsign = 1;
double[] LUrowi;
double[] LUcolj = new double[m];
// Outer loop.
for (int j = 0; j < n; j++) {
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++) {
LUcolj[i] = LU[i][j];
}
// Apply previous transformations.
for (int i = 0; i < m; i++) {
LUrowi = LU[i];
// Most of the time is spent in the following dot product.
int kmax = Math.min(i,j);
double s = 0.0;
for (int k = 0; k < kmax; k++) {
s += LUrowi[k]*LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j+1; i < m; i++) {
if (Math.abs(LUcolj[i]) > Math.abs(LUcolj[p])) {
p = i;
}
}
if (p != j) {
for (int k = 0; k < n; k++) {
double t = LU[p][k]; LU[p][k] = LU[j][k]; LU[j][k] = t;
}
int k = piv[p]; piv[p] = piv[j]; piv[j] = k;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m & LU[j][j] != 0.0) {
for (int i = j+1; i < m; i++) {
LU[i][j] /= LU[j][j];
}
}
}
}
/**
* Is the matrix nonsingular?
* @return true if U, and hence A, is nonsingular.
*/
public boolean isNonsingular() {
for (int j = 0; j < n; j++) {
if (LU[j][j] == 0)
return false;
}
return true;
}
/**
* Return lower triangular factor
* @return L
*/
public Matrix getL() {
Matrix X = new Matrix(m,n);
double[][] L = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i > j) {
L[i][j] = LU[i][j];
} else if (i == j) {
L[i][j] = 1.0;
} else {
L[i][j] = 0.0;
}
}
}
return X;
}
/**
* Return upper triangular factor
* @return U
*/
public Matrix getU() {
Matrix X = new Matrix(n,n);
double[][] U = X.getArray();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i <= j) {
U[i][j] = LU[i][j];
} else {
U[i][j] = 0.0;
}
}
}
return X;
}
/**
* Return pivot permutation vector
* @return piv
*/
public int[] getPivot() {
int[] p = new int[m];
for (int i = 0; i < m; i++) {
p[i] = piv[i];
}
return p;
}
/**
* Return pivot permutation vector as a one-dimensional double array
* @return (double) piv
*/
public double[] getDoublePivot() {
double[] vals = new double[m];
for (int i = 0; i < m; i++) {
vals[i] = (double) piv[i];
}
return vals;
}
/**
* Determinant
* @return det(A)
* @exception IllegalArgumentException Matrix must be square
*/
public double det() {
if (m != n) {
throw new IllegalArgumentException("Matrix must be square.");
}
double d = (double) pivsign;
for (int j = 0; j < n; j++) {
d *= LU[j][j];
}
return d;
}
/**
* Solve A*X = B
* @param B A Matrix with as many rows as A and any number of columns.
* @return X so that L*U*X = B(piv,:)
* @exception IllegalArgumentException Matrix row dimensions must agree.
* @exception RuntimeException Matrix is singular.
*/
public Matrix solve(Matrix B) {
if (B.getRowDimension() != m) {
throw new IllegalArgumentException("Matrix row dimensions must agree.");
}
if (!this.isNonsingular()) {
throw new RuntimeException("Matrix is singular.");
}
// Copy right hand side with pivoting
int nx = B.getColumnDimension();
Matrix Xmat = B.getMatrix(piv,0,nx-1);
double[][] X = Xmat.getArray();
// Solve L*Y = B(piv,:)
for (int k = 0; k < n; k++) {
for (int i = k+1; i < n; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j]*LU[i][k];
}
}
}
// Solve U*X = Y;
for (int k = n-1; k >= 0; k--) {
for (int j = 0; j < nx; j++) {
X[k][j] /= LU[k][k];
}
for (int i = 0; i < k; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j]*LU[i][k];
}
}
}
return Xmat;
}
/**
* Returns the revision string.
*
* @return the revision
*/
public String getRevision() {
return RevisionUtils.extract("$Revision: 5953 $");
}
}