/** * Frobenius norm * * @return sqrt of sum of squares of all elements. */ public double normF() { double f = 0; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { f = Maths.hypot(f, A[i][j]); } } return f; }
/** * QR Decomposition, computed by Householder reflections. * * @param A Rectangular matrix * @return Structure to access R and the Householder vectors and compute Q. */ 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; } }