Importing release version 322 from old repos
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Marcel Kronfeld
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src/wsi/ra/math/Jama/QRDecomposition.java
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218
src/wsi/ra/math/Jama/QRDecomposition.java
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package wsi.ra.math.Jama;
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import wsi.ra.math.Jama.util.Maths;
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/** QR Decomposition.
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<P>
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For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
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orthogonal matrix Q and an n-by-n upper triangular matrix R so that
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A = Q*R.
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<P>
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The QR decompostion always exists, even if the matrix does not have
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full rank, so the constructor will never fail. The primary use of the
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QR decomposition is in the least squares solution of nonsquare systems
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of simultaneous linear equations. This will fail if isFullRank()
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returns false.
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*/
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public class QRDecomposition implements java.io.Serializable {
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/* ------------------------
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Class variables
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* ------------------------ */
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/** Array for internal storage of decomposition.
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@serial internal array storage.
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*/
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private double[][] QR;
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/** Row and column dimensions.
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@serial column dimension.
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@serial row dimension.
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*/
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private int m, n;
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/** Array for internal storage of diagonal of R.
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@serial diagonal of R.
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*/
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private double[] Rdiag;
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/* ------------------------
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Constructor
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* ------------------------ */
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/** QR Decomposition, computed by Householder reflections.
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@param A Rectangular matrix
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@return Structure to access R and the Householder vectors and compute Q.
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*/
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public QRDecomposition (Matrix A) {
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// Initialize.
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QR = A.getArrayCopy();
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m = A.getRowDimension();
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n = A.getColumnDimension();
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Rdiag = new double[n];
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// Main loop.
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for (int k = 0; k < n; k++) {
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// Compute 2-norm of k-th column without under/overflow.
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double nrm = 0;
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for (int i = k; i < m; i++) {
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nrm = Maths.hypot(nrm,QR[i][k]);
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}
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if (nrm != 0.0) {
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// Form k-th Householder vector.
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if (QR[k][k] < 0) {
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nrm = -nrm;
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}
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for (int i = k; i < m; i++) {
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QR[i][k] /= nrm;
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}
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QR[k][k] += 1.0;
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// Apply transformation to remaining columns.
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for (int j = k+1; j < n; j++) {
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double s = 0.0;
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for (int i = k; i < m; i++) {
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s += QR[i][k]*QR[i][j];
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}
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s = -s/QR[k][k];
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for (int i = k; i < m; i++) {
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QR[i][j] += s*QR[i][k];
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}
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}
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}
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Rdiag[k] = -nrm;
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}
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}
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/* ------------------------
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Public Methods
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* ------------------------ */
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/** Is the matrix full rank?
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@return true if R, and hence A, has full rank.
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*/
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public boolean isFullRank () {
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for (int j = 0; j < n; j++) {
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if (Rdiag[j] == 0)
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return false;
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}
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return true;
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}
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/** Return the Householder vectors
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@return Lower trapezoidal matrix whose columns define the reflections
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*/
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public Matrix getH () {
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Matrix X = new Matrix(m,n);
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double[][] H = X.getArray();
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for (int i = 0; i < m; i++) {
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for (int j = 0; j < n; j++) {
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if (i >= j) {
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H[i][j] = QR[i][j];
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} else {
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H[i][j] = 0.0;
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}
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}
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}
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return X;
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}
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/** Return the upper triangular factor
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@return R
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*/
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public Matrix getR () {
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Matrix X = new Matrix(n,n);
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double[][] R = X.getArray();
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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if (i < j) {
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R[i][j] = QR[i][j];
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} else if (i == j) {
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R[i][j] = Rdiag[i];
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} else {
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R[i][j] = 0.0;
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}
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}
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}
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return X;
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}
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/** Generate and return the (economy-sized) orthogonal factor
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@return Q
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*/
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public Matrix getQ () {
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Matrix X = new Matrix(m,n);
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double[][] Q = X.getArray();
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for (int k = n-1; k >= 0; k--) {
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for (int i = 0; i < m; i++) {
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Q[i][k] = 0.0;
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}
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Q[k][k] = 1.0;
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for (int j = k; j < n; j++) {
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if (QR[k][k] != 0) {
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double s = 0.0;
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for (int i = k; i < m; i++) {
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s += QR[i][k]*Q[i][j];
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}
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s = -s/QR[k][k];
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for (int i = k; i < m; i++) {
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Q[i][j] += s*QR[i][k];
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}
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}
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}
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}
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return X;
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}
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/** Least squares solution of A*X = B
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@param B A Matrix with as many rows as A and any number of columns.
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@return X that minimizes the two norm of Q*R*X-B.
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@exception IllegalArgumentException Matrix row dimensions must agree.
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@exception RuntimeException Matrix is rank deficient.
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*/
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public Matrix solve (Matrix B) {
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if (B.getRowDimension() != m) {
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throw new IllegalArgumentException("Matrix row dimensions must agree.");
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}
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if (!this.isFullRank()) {
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throw new RuntimeException("Matrix is rank deficient.");
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}
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// Copy right hand side
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int nx = B.getColumnDimension();
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double[][] X = B.getArrayCopy();
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// Compute Y = transpose(Q)*B
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for (int k = 0; k < n; k++) {
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for (int j = 0; j < nx; j++) {
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double s = 0.0;
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for (int i = k; i < m; i++) {
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s += QR[i][k]*X[i][j];
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}
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s = -s/QR[k][k];
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for (int i = k; i < m; i++) {
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X[i][j] += s*QR[i][k];
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}
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}
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}
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// Solve R*X = Y;
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for (int k = n-1; k >= 0; k--) {
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for (int j = 0; j < nx; j++) {
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X[k][j] /= Rdiag[k];
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}
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for (int i = 0; i < k; i++) {
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for (int j = 0; j < nx; j++) {
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X[i][j] -= X[k][j]*QR[i][k];
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}
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}
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}
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return (new Matrix(X,n,nx).getMatrix(0,n-1,0,nx-1));
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}
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}
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