package Jama;
   import Jama.util.*;
   
   /** 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().
      @version $Id: EigenvalueDecomposition.java,v 1.1.1.1 2010/11/30 21:31:59 jeremy Exp $
  */
  
  public class EigenvalueDecomposition implements java.io.Serializable {
  
  /* ------------------------
     Class variables
   * ------------------------ */
  
     /** 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;
  
  /* ------------------------
     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 = 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.
 
    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;
          }
       }
    }
 
 
 /* ------------------------
    Constructor
  * ------------------------ */
 
    /** 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();
       }
    }
 
 /* ------------------------
    Public Methods
  * ------------------------ */
 
    /** 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;
    }
 }