/*
* 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.
*/
/*
* QRDecomposition.java
* Copyright (C) 1999 The Mathworks and NIST
*
*/
package weka.core.matrix;
import weka.core.RevisionHandler;
import weka.core.RevisionUtils;
import java.io.Serializable;
/**
* QR Decomposition.
* <P>
* For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
* orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.
* <P>
* The QR decompostion always exists, even if the matrix does not have full
* rank, so the constructor will never fail. The primary use of the QR
* decomposition is in the least squares solution of nonsquare systems of
* simultaneous linear equations. This will fail if isFullRank() 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 QRDecomposition
implements Serializable, RevisionHandler {
/** for serialization */
private static final long serialVersionUID = -5013090736132211418L;
/**
* Array for internal storage of decomposition.
* @serial internal array storage.
*/
private double[][] QR;
/**
* Row and column dimensions.
* @serial column dimension.
* @serial row dimension.
*/
private int m, n;
/**
* Array for internal storage of diagonal of R.
* @serial diagonal of R.
*/
private double[] Rdiag;
/**
* QR Decomposition, computed by Householder reflections.
* @param A Rectangular matrix
*/
public QRDecomposition(Matrix A) {
// Initialize.
QR = A.getArrayCopy();
m = A.getRowDimension();
n = A.getColumnDimension();
Rdiag = new double[n];
// Main loop.
for (int k = 0; k < n; k++) {
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
for (int i = k; i < m; i++) {
nrm = Maths.hypot(nrm,QR[i][k]);
}
if (nrm != 0.0) {
// Form k-th Householder vector.
if (QR[k][k] < 0) {
nrm = -nrm;
}
for (int i = k; i < m; i++) {
QR[i][k] /= nrm;
}
QR[k][k] += 1.0;
// Apply transformation to remaining columns.
for (int j = k+1; j < n; j++) {
double s = 0.0;
for (int i = k; i < m; i++) {
s += QR[i][k]*QR[i][j];
}
s = -s/QR[k][k];
for (int i = k; i < m; i++) {
QR[i][j] += s*QR[i][k];
}
}
}
Rdiag[k] = -nrm;
}
}
/**
* Is the matrix full rank?
* @return true if R, and hence A, has full rank.
*/
public boolean isFullRank() {
for (int j = 0; j < n; j++) {
if (Rdiag[j] == 0)
return false;
}
return true;
}
/**
* Return the Householder vectors
* @return Lower trapezoidal matrix whose columns define the reflections
*/
public Matrix getH() {
Matrix X = new Matrix(m,n);
double[][] H = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i >= j) {
H[i][j] = QR[i][j];
} else {
H[i][j] = 0.0;
}
}
}
return X;
}
/**
* Return the upper triangular factor
* @return R
*/
public Matrix getR() {
Matrix X = new Matrix(n,n);
double[][] R = X.getArray();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i < j) {
R[i][j] = QR[i][j];
} else if (i == j) {
R[i][j] = Rdiag[i];
} else {
R[i][j] = 0.0;
}
}
}
return X;
}
/**
* Generate and return the (economy-sized) orthogonal factor
* @return Q
*/
public Matrix getQ() {
Matrix X = new Matrix(m,n);
double[][] Q = X.getArray();
for (int k = n-1; k >= 0; k--) {
for (int i = 0; i < m; i++) {
Q[i][k] = 0.0;
}
Q[k][k] = 1.0;
for (int j = k; j < n; j++) {
if (QR[k][k] != 0) {
double s = 0.0;
for (int i = k; i < m; i++) {
s += QR[i][k]*Q[i][j];
}
s = -s/QR[k][k];
for (int i = k; i < m; i++) {
Q[i][j] += s*QR[i][k];
}
}
}
}
return X;
}
/**
* Least squares solution of A*X = B
* @param B A Matrix with as many rows as A and any number of columns.
* @return X that minimizes the two norm of Q*R*X-B.
* @exception IllegalArgumentException Matrix row dimensions must agree.
* @exception RuntimeException Matrix is rank deficient.
*/
public Matrix solve(Matrix B) {
if (B.getRowDimension() != m) {
throw new IllegalArgumentException("Matrix row dimensions must agree.");
}
if (!this.isFullRank()) {
throw new RuntimeException("Matrix is rank deficient.");
}
// Copy right hand side
int nx = B.getColumnDimension();
double[][] X = B.getArrayCopy();
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++) {
for (int j = 0; j < nx; j++) {
double s = 0.0;
for (int i = k; i < m; i++) {
s += QR[i][k]*X[i][j];
}
s = -s/QR[k][k];
for (int i = k; i < m; i++) {
X[i][j] += s*QR[i][k];
}
}
}
// Solve R*X = Y;
for (int k = n-1; k >= 0; k--) {
for (int j = 0; j < nx; j++) {
X[k][j] /= Rdiag[k];
}
for (int i = 0; i < k; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j]*QR[i][k];
}
}
}
return (new Matrix(X,n,nx).getMatrix(0,n-1,0,nx-1));
}
/**
* Returns the revision string.
*
* @return the revision
*/
public String getRevision() {
return RevisionUtils.extract("$Revision: 5953 $");
}
}