X-Git-Url: http://gitweb.fperrin.net/?p=GpsPrune.git;a=blobdiff_plain;f=src%2Ftim%2Fprune%2Ffunction%2Festimate%2Fjama%2FQRDecomposition.java;fp=src%2Ftim%2Fprune%2Ffunction%2Festimate%2Fjama%2FQRDecomposition.java;h=199c67e5ef1df774b62834aa13db481ac1aa7a57;hp=0000000000000000000000000000000000000000;hb=ce6f2161b8596f7018d6a76bff79bc9e571f35fd;hpb=2d8cb72e84d5cc1089ce77baf1e34ea3ea2f8465

diff --git a/src/tim/prune/function/estimate/jama/QRDecomposition.java b/src/tim/prune/function/estimate/jama/QRDecomposition.java
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+package tim.prune.function.estimate.jama;
+
+/**
+ * QR Decomposition.
+ *
+ * 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.
+ *
+ * The QR decomposition 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.
+ *
+ * Original authors The MathWorks, Inc. and the National Institute of Standards and Technology
+ * The original public domain code has now been modified and reduced,
+ * and is placed under GPL2 with the rest of the GpsPrune code.
+ */
+public class QRDecomposition
+{
+
+	/** Array for internal storage of decomposition */
+	private double[][] _QR;
+
+	/** Row and column dimensions */
+	private int _m, _n;
+
+	/** Array for internal storage of diagonal of R */
+	private double[] _Rdiag;
+
+
+	/**
+	 * QR Decomposition, computed by Householder reflections.
+	 *
+	 * @param inA   Rectangular matrix
+	 * @return Structure to access R and the Householder vectors and compute Q.
+	 */
+	public QRDecomposition(Matrix inA)
+	{
+		// Initialize.
+		_QR = inA.getArrayCopy();
+		_m = inA.getNumRows();
+		_n = inA.getNumColumns();
+		_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.pythag(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;
+		}
+	}
+
+	/*
+	 * ------------------------ Public Methods ------------------------
+	 */
+
+	/**
+	 * 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;
+	}
+
+
+	/**
+	 * 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 if matrix dimensions don't agree
+	 * @exception RuntimeException         if Matrix is rank deficient.
+	 */
+	public Matrix solve(Matrix B)
+	{
+		if (B.getNumRows() != _m) {
+			throw new IllegalArgumentException("Matrix row dimensions must agree.");
+		}
+		if (!isFullRank()) {
+			throw new RuntimeException("Matrix is rank deficient.");
+		}
+
+		// Copy right hand side
+		int nx = B.getNumColumns();
+		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));
+	}
+}