+++ /dev/null
-/* $RCSfile$
- * $Author: egonw $
- * $Date: 2005-11-10 09:52:44f -0600 (Thu, 10 Nov 2005) $
- * $Revision: 4255 $
- *
- * Some portions of this file have been modified by Robert Hanson hansonr.at.stolaf.edu 2012-2017
- * for use in SwingJS via transpilation into JavaScript using Java2Script.
- *
- * Copyright (C) 2003-2005 Miguel, Jmol Development, www.jmol.org
- *
- * Contact: jmol-developers@lists.sf.net
- *
- * This library is free software; you can redistribute it and/or
- * modify it under the terms of the GNU Lesser General Public
- * License as published by the Free Software Foundation; either
- * version 2.1 of the License, or (at your option) any later version.
- *
- * This library is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public
- * License along with this library; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
- */
-
-package javajs.util;
-
-import javajs.api.EigenInterface;
-
-
-/**
- * Eigenvalues and eigenvectors of a real matrix.
- * See javajs.api.EigenInterface() as well.
- *
- * adapted by Bob Hanson from http://math.nist.gov/javanumerics/jama/ (public
- * domain); adding quaternion superimposition capability; removing
- * nonsymmetric reduction to Hessenberg form, which we do not need in Jmol.
- *
- * Output is as a set of double[n] columns, but for the EigenInterface
- * we return them as V3[3] and float[3] (or double[3]) values.
- *
- * Eigenvalues and eigenvectors are sorted from smallest to largest eigenvalue.
- *
- * <P>
- * If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal
- * and the eigenvector matrix V is orthogonal. I.e. A =
- * V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the
- * identity matrix.
- * <P>
- * If A is not symmetric, then the eigenvalue matrix D is block diagonal with
- * the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda +
- * i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent
- * the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals
- * V.times(D). The matrix V may be badly conditioned, or even singular, so the
- * validity of the equation A = V*D*inverse(V) depends upon V.cond().
- **/
-
-public class Eigen implements EigenInterface {
-
- /* ------------------------
- Public Methods
- * ------------------------ */
-
- public Eigen() {}
-
- public Eigen set(int n) {
- this.n = n;
- V = new double[n][n];
- d = new double[n];
- e = new double[n];
- return this;
- }
-
- @Override
- public Eigen setM(double[][] m) {
- set(m.length);
- calc(m);
- return this;
- }
-
- /**
- * return values sorted from smallest to largest value.
- */
- @Override
- public double[] getEigenvalues() {
- return d;
- }
-
- /**
- * Specifically for 3x3 systems, returns eigenVectors as V3[3]
- * and values as float[3]; sorted from smallest to largest value.
- *
- * @param eigenVectors returned vectors
- * @param eigenValues returned values
- *
- */
- @Override
- public void fillFloatArrays(V3[] eigenVectors, float[] eigenValues) {
- for (int i = 0; i < 3; i++) {
- if (eigenVectors != null) {
- if (eigenVectors[i] == null)
- eigenVectors[i] = new V3();
- eigenVectors[i].set((float) V[0][i], (float) V[1][i], (float) V[2][i]);
- }
- if (eigenValues != null)
- eigenValues[i] = (float) d[i];
- }
- }
-
- /**
- * Transpose V and turn into floats; sorted from smallest to largest value.
- *
- * @return ROWS of eigenvectors f[0], f[1], f[2], etc.
- */
- @Override
- public float[][] getEigenvectorsFloatTransposed() {
- float[][] f = new float[n][n];
- for (int i = n; --i >= 0;)
- for (int j = n; --j >= 0;)
- f[j][i] = (float) V[i][j];
- return f;
- }
-
-
- /**
- * Check for symmetry, then construct the eigenvalue decomposition
- *
- * @param A
- * Square matrix
- */
-
- public void calc(double[][] A) {
-
- /* Jmol only has need of symmetric solutions
- *
- issymmetric = true;
-
- for (int j = 0; (j < n) & issymmetric; j++) {
- for (int i = 0; (i < n) & issymmetric; i++) {
- issymmetric = (A[i][j] == A[j][i]);
- }
- }
-
- if (issymmetric) {
- */
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- V[i][j] = A[i][j];
- }
- }
-
- // Tridiagonalize.
- tred2();
-
- // Diagonalize.
- tql2();
- /*
- } else {
- H = new double[n][n];
- ort = new double[n];
-
- for (int j = 0; j < n; j++) {
- for (int i = 0; i < n; i++) {
- H[i][j] = A[i][j];
- }
- }
-
- // Reduce to Hessenberg form.
- orthes();
-
- // Reduce Hessenberg to real Schur form.
- hqr2();
- }
- */
-
- }
-
- /**
- * Return the real parts of the eigenvalues
- *
- * @return real(diag(D))
- */
-
- public double[] getRealEigenvalues() {
- return d;
- }
-
- /**
- * Return the imaginary parts of the eigenvalues
- *
- * @return imag(diag(D))
- */
-
- public double[] getImagEigenvalues() {
- return e;
- }
-
- /* ------------------------
- Class variables
- * ------------------------ */
-
- /**
- * Row and column dimension (square matrix).
- *
- * @serial matrix dimension.
- */
- private int n = 3;
-
- /**
- * Symmetry flag.
- *
- * @serial internal symmetry flag.
- */
- //private boolean issymmetric = true;
-
- /**
- * Arrays for internal storage of eigenvalues.
- *
- * @serial internal storage of eigenvalues.
- */
- private double[] d, e;
-
- /**
- * Array for internal storage of eigenvectors.
- *
- * @serial internal storage of eigenvectors.
- */
- private double[][] V;
-
- /**
- * Array for internal storage of nonsymmetric Hessenberg form.
- *
- * @serial internal storage of nonsymmetric Hessenberg form.
- */
- //private double[][] H;
-
- /**
- * Working storage for nonsymmetric algorithm.
- *
- * @serial working storage for nonsymmetric algorithm.
- */
- //private double[] ort;
-
- /* ------------------------
- Private Methods
- * ------------------------ */
-
- // Symmetric Householder reduction to tridiagonal form.
-
- private void tred2() {
-
- // This is derived from the Algol procedures tred2 by
- // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
- // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutine in EISPACK.
-
- for (int j = 0; j < n; j++) {
- d[j] = V[n - 1][j];
- }
-
- // Householder reduction to tridiagonal form.
-
- for (int i = n - 1; i > 0; i--) {
-
- // Scale to avoid under/overflow.
-
- double scale = 0.0;
- double h = 0.0;
- for (int k = 0; k < i; k++) {
- scale = scale + Math.abs(d[k]);
- }
- if (scale == 0.0) {
- e[i] = d[i - 1];
- for (int j = 0; j < i; j++) {
- d[j] = V[i - 1][j];
- V[i][j] = 0.0;
- V[j][i] = 0.0;
- }
- } else {
-
- // Generate Householder vector.
-
- for (int k = 0; k < i; k++) {
- d[k] /= scale;
- h += d[k] * d[k];
- }
- double f = d[i - 1];
- double g = Math.sqrt(h);
- if (f > 0) {
- g = -g;
- }
- e[i] = scale * g;
- h = h - f * g;
- d[i - 1] = f - g;
- for (int j = 0; j < i; j++) {
- e[j] = 0.0;
- }
-
- // Apply similarity transformation to remaining columns.
-
- for (int j = 0; j < i; j++) {
- f = d[j];
- V[j][i] = f;
- g = e[j] + V[j][j] * f;
- for (int k = j + 1; k <= i - 1; k++) {
- g += V[k][j] * d[k];
- e[k] += V[k][j] * f;
- }
- e[j] = g;
- }
- f = 0.0;
- for (int j = 0; j < i; j++) {
- e[j] /= h;
- f += e[j] * d[j];
- }
- double hh = f / (h + h);
- for (int j = 0; j < i; j++) {
- e[j] -= hh * d[j];
- }
- for (int j = 0; j < i; j++) {
- f = d[j];
- g = e[j];
- for (int k = j; k <= i - 1; k++) {
- V[k][j] -= (f * e[k] + g * d[k]);
- }
- d[j] = V[i - 1][j];
- V[i][j] = 0.0;
- }
- }
- d[i] = h;
- }
-
- // Accumulate transformations.
-
- for (int i = 0; i < n - 1; i++) {
- V[n - 1][i] = V[i][i];
- V[i][i] = 1.0;
- double h = d[i + 1];
- if (h != 0.0) {
- for (int k = 0; k <= i; k++) {
- d[k] = V[k][i + 1] / h;
- }
- for (int j = 0; j <= i; j++) {
- double g = 0.0;
- for (int k = 0; k <= i; k++) {
- g += V[k][i + 1] * V[k][j];
- }
- for (int k = 0; k <= i; k++) {
- V[k][j] -= g * d[k];
- }
- }
- }
- for (int k = 0; k <= i; k++) {
- V[k][i + 1] = 0.0;
- }
- }
- for (int j = 0; j < n; j++) {
- d[j] = V[n - 1][j];
- V[n - 1][j] = 0.0;
- }
- V[n - 1][n - 1] = 1.0;
- e[0] = 0.0;
- }
-
- // Symmetric tridiagonal QL algorithm.
-
- private void tql2() {
-
- // This is derived from the Algol procedures tql2, by
- // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
- // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutine in EISPACK.
-
- for (int i = 1; i < n; i++) {
- e[i - 1] = e[i];
- }
- e[n - 1] = 0.0;
-
- double f = 0.0;
- double tst1 = 0.0;
- double eps = Math.pow(2.0, -52.0);
- for (int l = 0; l < n; l++) {
-
- // Find small subdiagonal element
-
- tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
- int m = l;
- while (m < n) {
- if (Math.abs(e[m]) <= eps * tst1) {
- break;
- }
- m++;
- }
-
- // If m == l, d[l] is an eigenvalue,
- // otherwise, iterate.
-
- if (m > l) {
- int iter = 0;
- do {
- iter = iter + 1; // (Could check iteration count here.)
-
- // Compute implicit shift
-
- double g = d[l];
- double p = (d[l + 1] - g) / (2.0 * e[l]);
- double r = hypot(p, 1.0);
- if (p < 0) {
- r = -r;
- }
- d[l] = e[l] / (p + r);
- d[l + 1] = e[l] * (p + r);
- double dl1 = d[l + 1];
- double h = g - d[l];
- for (int i = l + 2; i < n; i++) {
- d[i] -= h;
- }
- f = f + h;
-
- // Implicit QL transformation.
-
- p = d[m];
- double c = 1.0;
- double c2 = c;
- double c3 = c;
- double el1 = e[l + 1];
- double s = 0.0;
- double s2 = 0.0;
- for (int i = m - 1; i >= l; i--) {
- c3 = c2;
- c2 = c;
- s2 = s;
- g = c * e[i];
- h = c * p;
- r = hypot(p, e[i]);
- e[i + 1] = s * r;
- s = e[i] / r;
- c = p / r;
- p = c * d[i] - s * g;
- d[i + 1] = h + s * (c * g + s * d[i]);
-
- // Accumulate transformation.
-
- for (int k = 0; k < n; k++) {
- h = V[k][i + 1];
- V[k][i + 1] = s * V[k][i] + c * h;
- V[k][i] = c * V[k][i] - s * h;
- }
- }
- p = -s * s2 * c3 * el1 * e[l] / dl1;
- e[l] = s * p;
- d[l] = c * p;
-
- // Check for convergence.
-
- } while (Math.abs(e[l]) > eps * tst1);
- }
- d[l] = d[l] + f;
- e[l] = 0.0;
- }
-
- // Sort eigenvalues and corresponding vectors.
-
- for (int i = 0; i < n - 1; i++) {
- int k = i;
- double p = d[i];
- for (int j = i + 1; j < n; j++) {
- if (d[j] < p) {
- k = j;
- p = d[j];
- }
- }
- if (k != i) {
- d[k] = d[i];
- d[i] = p;
- for (int j = 0; j < n; j++) {
- p = V[j][i];
- V[j][i] = V[j][k];
- V[j][k] = p;
- }
- }
- }
- }
-
- private static double hypot(double a, double b) {
-
- // sqrt(a^2 + b^2) without under/overflow.
-
- double r;
- if (Math.abs(a) > Math.abs(b)) {
- r = b / a;
- r = Math.abs(a) * Math.sqrt(1 + r * r);
- } else if (b != 0) {
- r = a / b;
- r = Math.abs(b) * Math.sqrt(1 + r * r);
- } else {
- r = 0.0;
- }
- return r;
- }
-
- // Nonsymmetric reduction to Hessenberg form.
-
- /*
- private void orthes() {
-
- // This is derived from the Algol procedures orthes and ortran,
- // by Martin and Wilkinson, Handbook for Auto. Comp.,
- // Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutines in EISPACK.
-
- int low = 0;
- int high = n - 1;
-
- for (int m = low + 1; m <= high - 1; m++) {
-
- // Scale column.
-
- double scale = 0.0;
- for (int i = m; i <= high; i++) {
- scale = scale + Math.abs(H[i][m - 1]);
- }
- if (scale != 0.0) {
-
- // Compute Householder transformation.
-
- double h = 0.0;
- for (int i = high; i >= m; i--) {
- ort[i] = H[i][m - 1] / scale;
- h += ort[i] * ort[i];
- }
- double g = Math.sqrt(h);
- if (ort[m] > 0) {
- g = -g;
- }
- h = h - ort[m] * g;
- ort[m] = ort[m] - g;
-
- // Apply Householder similarity transformation
- // H = (I-u*u'/h)*H*(I-u*u')/h)
-
- for (int j = m; j < n; j++) {
- double f = 0.0;
- for (int i = high; i >= m; i--) {
- f += ort[i] * H[i][j];
- }
- f = f / h;
- for (int i = m; i <= high; i++) {
- H[i][j] -= f * ort[i];
- }
- }
-
- for (int i = 0; i <= high; i++) {
- double f = 0.0;
- for (int j = high; j >= m; j--) {
- f += ort[j] * H[i][j];
- }
- f = f / h;
- for (int j = m; j <= high; j++) {
- H[i][j] -= f * ort[j];
- }
- }
- ort[m] = scale * ort[m];
- H[m][m - 1] = scale * g;
- }
- }
-
- // Accumulate transformations (Algol's ortran).
-
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- V[i][j] = (i == j ? 1.0 : 0.0);
- }
- }
-
- for (int m = high - 1; m >= low + 1; m--) {
- if (H[m][m - 1] != 0.0) {
- for (int i = m + 1; i <= high; i++) {
- ort[i] = H[i][m - 1];
- }
- for (int j = m; j <= high; j++) {
- double g = 0.0;
- for (int i = m; i <= high; i++) {
- g += ort[i] * V[i][j];
- }
- // Double division avoids possible underflow
- g = (g / ort[m]) / H[m][m - 1];
- for (int i = m; i <= high; i++) {
- V[i][j] += g * ort[i];
- }
- }
- }
- }
- }
-
- // Complex scalar division.
-
- private transient double cdivr, cdivi;
-
- private void cdiv(double xr, double xi, double yr, double yi) {
- double r, d;
- if (Math.abs(yr) > Math.abs(yi)) {
- r = yi / yr;
- d = yr + r * yi;
- cdivr = (xr + r * xi) / d;
- cdivi = (xi - r * xr) / d;
- } else {
- r = yr / yi;
- d = yi + r * yr;
- cdivr = (r * xr + xi) / d;
- cdivi = (r * xi - xr) / d;
- }
- }
-
- // Nonsymmetric reduction from Hessenberg to real Schur form.
-
- private void hqr2() {
-
- // This is derived from the Algol procedure hqr2,
- // by Martin and Wilkinson, Handbook for Auto. Comp.,
- // Vol.ii-Linear Algebra, and the corresponding
- // Fortran subroutine in EISPACK.
-
- // Initialize
-
- int nn = this.n;
- int n = nn - 1;
- int low = 0;
- int high = nn - 1;
- double eps = Math.pow(2.0, -52.0);
- double exshift = 0.0;
- double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
-
- // Store roots isolated by balanc and compute matrix norm
-
- double norm = 0.0;
- for (int i = 0; i < nn; i++) {
- if (i < low || i > high) {
- d[i] = H[i][i];
- e[i] = 0.0;
- }
- for (int j = Math.max(i - 1, 0); j < nn; j++) {
- norm = norm + Math.abs(H[i][j]);
- }
- }
-
- // Outer loop over eigenvalue index
-
- int iter = 0;
- while (n >= low) {
-
- // Look for single small sub-diagonal element
-
- int l = n;
- while (l > low) {
- s = Math.abs(H[l - 1][l - 1]) + Math.abs(H[l][l]);
- if (s == 0.0) {
- s = norm;
- }
- if (Math.abs(H[l][l - 1]) < eps * s) {
- break;
- }
- l--;
- }
-
- // Check for convergence
- // One root found
-
- if (l == n) {
- H[n][n] = H[n][n] + exshift;
- d[n] = H[n][n];
- e[n] = 0.0;
- n--;
- iter = 0;
-
- // Two roots found
-
- } else if (l == n - 1) {
- w = H[n][n - 1] * H[n - 1][n];
- p = (H[n - 1][n - 1] - H[n][n]) / 2.0;
- q = p * p + w;
- z = Math.sqrt(Math.abs(q));
- H[n][n] = H[n][n] + exshift;
- H[n - 1][n - 1] = H[n - 1][n - 1] + exshift;
- x = H[n][n];
-
- // Real pair
-
- if (q >= 0) {
- if (p >= 0) {
- z = p + z;
- } else {
- z = p - z;
- }
- d[n - 1] = x + z;
- d[n] = d[n - 1];
- if (z != 0.0) {
- d[n] = x - w / z;
- }
- e[n - 1] = 0.0;
- e[n] = 0.0;
- x = H[n][n - 1];
- s = Math.abs(x) + Math.abs(z);
- p = x / s;
- q = z / s;
- r = Math.sqrt(p * p + q * q);
- p = p / r;
- q = q / r;
-
- // Row modification
-
- for (int j = n - 1; j < nn; j++) {
- z = H[n - 1][j];
- H[n - 1][j] = q * z + p * H[n][j];
- H[n][j] = q * H[n][j] - p * z;
- }
-
- // Column modification
-
- for (int i = 0; i <= n; i++) {
- z = H[i][n - 1];
- H[i][n - 1] = q * z + p * H[i][n];
- H[i][n] = q * H[i][n] - p * z;
- }
-
- // Accumulate transformations
-
- for (int i = low; i <= high; i++) {
- z = V[i][n - 1];
- V[i][n - 1] = q * z + p * V[i][n];
- V[i][n] = q * V[i][n] - p * z;
- }
-
- // Complex pair
-
- } else {
- d[n - 1] = x + p;
- d[n] = x + p;
- e[n - 1] = z;
- e[n] = -z;
- }
- n = n - 2;
- iter = 0;
-
- // No convergence yet
-
- } else {
-
- // Form shift
-
- x = H[n][n];
- y = 0.0;
- w = 0.0;
- if (l < n) {
- y = H[n - 1][n - 1];
- w = H[n][n - 1] * H[n - 1][n];
- }
-
- // Wilkinson's original ad hoc shift
-
- if (iter == 10) {
- exshift += x;
- for (int i = low; i <= n; i++) {
- H[i][i] -= x;
- }
- s = Math.abs(H[n][n - 1]) + Math.abs(H[n - 1][n - 2]);
- x = y = 0.75 * s;
- w = -0.4375 * s * s;
- }
-
- // MATLAB's new ad hoc shift
-
- if (iter == 30) {
- s = (y - x) / 2.0;
- s = s * s + w;
- if (s > 0) {
- s = Math.sqrt(s);
- if (y < x) {
- s = -s;
- }
- s = x - w / ((y - x) / 2.0 + s);
- for (int i = low; i <= n; i++) {
- H[i][i] -= s;
- }
- exshift += s;
- x = y = w = 0.964;
- }
- }
-
- iter = iter + 1; // (Could check iteration count here.)
-
- // Look for two consecutive small sub-diagonal elements
-
- int m = n - 2;
- while (m >= l) {
- z = H[m][m];
- r = x - z;
- s = y - z;
- p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
- q = H[m + 1][m + 1] - z - r - s;
- r = H[m + 2][m + 1];
- s = Math.abs(p) + Math.abs(q) + Math.abs(r);
- p = p / s;
- q = q / s;
- r = r / s;
- if (m == l) {
- break;
- }
- if (Math.abs(H[m][m - 1]) * (Math.abs(q) + Math.abs(r)) < eps
- * (Math.abs(p) * (Math.abs(H[m - 1][m - 1]) + Math.abs(z) + Math
- .abs(H[m + 1][m + 1])))) {
- break;
- }
- m--;
- }
-
- for (int i = m + 2; i <= n; i++) {
- H[i][i - 2] = 0.0;
- if (i > m + 2) {
- H[i][i - 3] = 0.0;
- }
- }
-
- // Double QR step involving rows l:n and columns m:n
-
- for (int k = m; k <= n - 1; k++) {
- boolean notlast = (k != n - 1);
- if (k != m) {
- p = H[k][k - 1];
- q = H[k + 1][k - 1];
- r = (notlast ? H[k + 2][k - 1] : 0.0);
- x = Math.abs(p) + Math.abs(q) + Math.abs(r);
- if (x != 0.0) {
- p = p / x;
- q = q / x;
- r = r / x;
- }
- }
- if (x == 0.0) {
- break;
- }
- s = Math.sqrt(p * p + q * q + r * r);
- if (p < 0) {
- s = -s;
- }
- if (s != 0) {
- if (k != m) {
- H[k][k - 1] = -s * x;
- } else if (l != m) {
- H[k][k - 1] = -H[k][k - 1];
- }
- p = p + s;
- x = p / s;
- y = q / s;
- z = r / s;
- q = q / p;
- r = r / p;
-
- // Row modification
-
- for (int j = k; j < nn; j++) {
- p = H[k][j] + q * H[k + 1][j];
- if (notlast) {
- p = p + r * H[k + 2][j];
- H[k + 2][j] = H[k + 2][j] - p * z;
- }
- H[k][j] = H[k][j] - p * x;
- H[k + 1][j] = H[k + 1][j] - p * y;
- }
-
- // Column modification
-
- for (int i = 0; i <= Math.min(n, k + 3); i++) {
- p = x * H[i][k] + y * H[i][k + 1];
- if (notlast) {
- p = p + z * H[i][k + 2];
- H[i][k + 2] = H[i][k + 2] - p * r;
- }
- H[i][k] = H[i][k] - p;
- H[i][k + 1] = H[i][k + 1] - p * q;
- }
-
- // Accumulate transformations
-
- for (int i = low; i <= high; i++) {
- p = x * V[i][k] + y * V[i][k + 1];
- if (notlast) {
- p = p + z * V[i][k + 2];
- V[i][k + 2] = V[i][k + 2] - p * r;
- }
- V[i][k] = V[i][k] - p;
- V[i][k + 1] = V[i][k + 1] - p * q;
- }
- } // (s != 0)
- } // k loop
- } // check convergence
- } // while (n >= low)
-
- // Backsubstitute to find vectors of upper triangular form
-
- if (norm == 0.0) {
- return;
- }
-
- for (n = nn - 1; n >= 0; n--) {
- p = d[n];
- q = e[n];
-
- // Real vector
-
- if (q == 0) {
- int l = n;
- H[n][n] = 1.0;
- for (int i = n - 1; i >= 0; i--) {
- w = H[i][i] - p;
- r = 0.0;
- for (int j = l; j <= n; j++) {
- r = r + H[i][j] * H[j][n];
- }
- if (e[i] < 0.0) {
- z = w;
- s = r;
- } else {
- l = i;
- if (e[i] == 0.0) {
- if (w != 0.0) {
- H[i][n] = -r / w;
- } else {
- H[i][n] = -r / (eps * norm);
- }
-
- // Solve real equations
-
- } else {
- x = H[i][i + 1];
- y = H[i + 1][i];
- q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
- t = (x * s - z * r) / q;
- H[i][n] = t;
- if (Math.abs(x) > Math.abs(z)) {
- H[i + 1][n] = (-r - w * t) / x;
- } else {
- H[i + 1][n] = (-s - y * t) / z;
- }
- }
-
- // Overflow control
-
- t = Math.abs(H[i][n]);
- if ((eps * t) * t > 1) {
- for (int j = i; j <= n; j++) {
- H[j][n] = H[j][n] / t;
- }
- }
- }
- }
-
- // Complex vector
-
- } else if (q < 0) {
- int l = n - 1;
-
- // Last vector component imaginary so matrix is triangular
-
- if (Math.abs(H[n][n - 1]) > Math.abs(H[n - 1][n])) {
- H[n - 1][n - 1] = q / H[n][n - 1];
- H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
- } else {
- cdiv(0.0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
- H[n - 1][n - 1] = cdivr;
- H[n - 1][n] = cdivi;
- }
- H[n][n - 1] = 0.0;
- H[n][n] = 1.0;
- for (int i = n - 2; i >= 0; i--) {
- double ra, sa, vr, vi;
- ra = 0.0;
- sa = 0.0;
- for (int j = l; j <= n; j++) {
- ra = ra + H[i][j] * H[j][n - 1];
- sa = sa + H[i][j] * H[j][n];
- }
- w = H[i][i] - p;
-
- if (e[i] < 0.0) {
- z = w;
- r = ra;
- s = sa;
- } else {
- l = i;
- if (e[i] == 0) {
- cdiv(-ra, -sa, w, q);
- H[i][n - 1] = cdivr;
- H[i][n] = cdivi;
- } else {
-
- // Solve complex equations
-
- x = H[i][i + 1];
- y = H[i + 1][i];
- vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
- vi = (d[i] - p) * 2.0 * q;
- if (vr == 0.0 & vi == 0.0) {
- vr = eps
- * norm
- * (Math.abs(w) + Math.abs(q) + Math.abs(x) + Math.abs(y) + Math
- .abs(z));
- }
- cdiv(x * r - z * ra + q * sa, x * s - z * sa - q * ra, vr, vi);
- H[i][n - 1] = cdivr;
- H[i][n] = cdivi;
- if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
- H[i + 1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
- H[i + 1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
- } else {
- cdiv(-r - y * H[i][n - 1], -s - y * H[i][n], z, q);
- H[i + 1][n - 1] = cdivr;
- H[i + 1][n] = cdivi;
- }
- }
-
- // Overflow control
-
- t = Math.max(Math.abs(H[i][n - 1]), Math.abs(H[i][n]));
- if ((eps * t) * t > 1) {
- for (int j = i; j <= n; j++) {
- H[j][n - 1] = H[j][n - 1] / t;
- H[j][n] = H[j][n] / t;
- }
- }
- }
- }
- }
- }
-
- // Vectors of isolated roots
-
- for (int i = 0; i < nn; i++) {
- if (i < low || i > high) {
- for (int j = i; j < nn; j++) {
- V[i][j] = H[i][j];
- }
- }
- }
-
- // Back transformation to get eigenvectors of original matrix
-
- for (int j = nn - 1; j >= low; j--) {
- for (int i = low; i <= high; i++) {
- z = 0.0;
- for (int k = low; k <= Math.min(j, high); k++) {
- z = z + V[i][k] * H[k][j];
- }
- V[i][j] = z;
- }
- }
- }
- */
-
-
-}
git://source.jalview.org / jalview.git / blobdiff