content: /*
   * This software is a cooperative product of The MathWorks and the National
   * Institute of Standards and Technology (NIST) which has been released to the
   * public domain. Neither The MathWorks nor NIST assumes any responsibility
   * whatsoever for its use by other parties, and makes no guarantees, expressed
   * or implied, about its quality, reliability, or any other characteristic.
   */
  
  /*
   * EigenvalueDecomposition.java
   * Copyright (C) 1999 The Mathworks and NIST
   *
   */
  
  package weka.core.matrix;
  
  import weka.core.RevisionHandler;
  import weka.core.RevisionUtils;
  
  import java.io.Serializable;
  
  /** 
   * Eigenvalues and eigenvectors of a real matrix. 
   * <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().
   * <p/>
   * Adapted from the <a href="http://math.nist.gov/javanumerics/jama/" target="_blank">JAMA</a> package.
   *
   * @author The Mathworks and NIST 
   * @author Fracpete (fracpete at waikato dot ac dot nz)
   * @version $Revision: 5953 $
   */
  public class EigenvalueDecomposition 
    implements Serializable, RevisionHandler {
  
    /** for serialization */
    private static final long serialVersionUID = 4011654467211422319L;
  
    /** 
     * Row and column dimension (square matrix).
     * @serial matrix dimension.
     */
    private int n;
  
    /** 
     * Symmetry flag.
     * @serial internal symmetry flag.
     */
    private boolean issymmetric;
  
    /** 
     * 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;
  
    /**
     * helper variables for the comples scalar division
     * @see #cdiv(double,double,double,double)
     */
    private transient double cdivr, cdivi;
  
    /** 
     * Symmetric Householder reduction to tridiagonal form.
     * <p/>
     * 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.
     */
    private void tred2() {
  
      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.
     * <p/>
     * 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.
     */
    private void tql2() {
  
      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 = Maths.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 = Maths.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;
          }
        }
      }
    }
  
    /**
     * Nonsymmetric reduction to Hessenberg form.
     * <p/>
     * 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.
     */
    private void orthes() {
  
      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 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.
     * <p/>
     * 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.
     */
    private void hqr2() {
  
      // 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;
        }
      }
    }
  
  
    /** 
     * Check for symmetry, then construct the eigenvalue decomposition
     *
     * @param Arg    Square matrix
     */
    public EigenvalueDecomposition(Matrix Arg) {
      double[][] A = Arg.getArray();
      n = Arg.getColumnDimension();
      V = new double[n][n];
      d = new double[n];
      e = new double[n];
  
      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 eigenvector matrix
     * @return     V
     */
    public Matrix getV() {
      return new Matrix(V,n,n);
    }
  
    /** 
     * 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;
    }
  
    /** 
     * Return the block diagonal eigenvalue matrix
     * @return     D
     */
    public Matrix getD() {
      Matrix X = new Matrix(n,n);
      double[][] D = X.getArray();
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
          D[i][j] = 0.0;
        }
        D[i][i] = d[i];
        if (e[i] > 0) {
          D[i][i+1] = e[i];
        } else if (e[i] < 0) {
          D[i][i-1] = e[i];
        }
      }
      return X;
    }
    
    /**
     * Returns the revision string.
     * 
     * @return		the revision
     */
    public String getRevision() {
      return RevisionUtils.extract("$Revision: 5953 $");
    }
  }
  