/** * <p> * Computes the householder vector "u" for the first column of submatrix j. Note this is * a specialized householder for this problem. There is some protection against * overfloaw and underflow. * </p> * <p> * Q = I - γuu<sup>T</sup> * </p> * <p> * This function finds the values of 'u' and 'γ'. * </p> * * @param j Which submatrix to work off of. */ protected void householder(int j) { float[] u = dataQR[j]; // find the largest value in this column // this is used to normalize the column and mitigate overflow/underflow float max = QrHelperFunctions_CDRM.findMax(u, j, numRows - j); if (max == 0.0f) { gamma = 0; error = true; } else { // computes tau and gamma, and normalizes u by max gamma = QrHelperFunctions_CDRM.computeTauGammaAndDivide(j, numRows, u, max, tau); // divide u by u_0 // float u_0 = u[j] + tau; float real_u_0 = u[j * 2] + tau.real; float imag_u_0 = u[j * 2 + 1] + tau.imaginary; QrHelperFunctions_CDRM.divideElements(j + 1, numRows, u, 0, real_u_0, imag_u_0); tau.real *= max; tau.imaginary *= max; u[j * 2] = -tau.real; u[j * 2 + 1] = -tau.imaginary; } gammas[j] = gamma; }
/** * <p> * Computes the householder vector "u" for the first column of submatrix j. Note this is * a specialized householder for this problem. There is some protection against * overflow and underflow. * </p> * <p> * Q = I - γuu<sup>H</sup> * </p> * <p> * This function finds the values of 'u' and 'γ'. * </p> * * @param j Which submatrix to work off of. */ protected void householder(int j) { int startQR = j * numRows; int endQR = startQR + numRows; startQR += j; float max = QrHelperFunctions_CDRM.findMax(QR.data, startQR, numRows - j); if (max == 0.0f) { gamma = 0; error = true; } else { // computes tau and normalizes u by max gamma = QrHelperFunctions_CDRM.computeTauGammaAndDivide(startQR, endQR, QR.data, max, tau); // divide u by u_0 float realU0 = QR.data[startQR * 2] + tau.real; float imagU0 = QR.data[startQR * 2 + 1] + tau.imaginary; QrHelperFunctions_CDRM.divideElements(startQR + 1, endQR, QR.data, 0, realU0, imagU0); tau.real *= max; tau.imaginary *= max; QR.data[startQR * 2] = -tau.real; QR.data[startQR * 2 + 1] = -tau.imaginary; } gammas[j] = gamma; }