<p>
Takes the results from the householder computation and updates the 'A' matrix.<br>
<br>
A = (I - &gamma;*u*u<sup>H</sup>)A
</p>

@param w The submatrix.
497805
protected void updateA( final int w )
    {
//        int rowW = w*numRows;
//        int rowJ = rowW + numRows;
//
//        for( int j = w+1; j < numCols; j++ , rowJ += numRows) {
//            double val = QR.data[rowJ + w];
//
//            // val = gamma*u^T * A
//            for( int k = w+1; k < numRows; k++ ) {
//                val += QR.data[rowW + k]*QR.data[rowJ + k];
//            }
//            val *= gamma;
//
//            // A - val*u
//            QR.data[rowJ + w] -= val;
//            for( int i = w+1; i < numRows; i++ ) {
//                QR.data[rowJ + i] -= QR.data[rowW + i]*val;
//            }
//        }

        final double data[] = QR.data;
        int rowW = w*numRows + w + 1;
        int rowJ = rowW + numRows;
        final int rowJEnd = 2*(rowJ + (numCols-w-1)*numRows);
        final int indexWEnd = 2*(rowW + numRows - w - 1);

        rowJ = 2*rowJ;
        rowW = 2*rowW;

        for( ; rowJEnd != rowJ; rowJ += numRows*2) {
            // assume the first element in u is 1
            double realVal = data[rowJ - 2];
            double imagVal = data[rowJ - 1];

            int indexW = rowW;
            int indexJ = rowJ;

            while( indexW != indexWEnd ) {
                double realW = data[indexW++];
                double imagW = -data[indexW++];

                double realJ = data[indexJ++];
                double imagJ = data[indexJ++];

                realVal += realW*realJ - imagW*imagJ;
                imagVal += realW*imagJ + imagW*realJ;
            }
            realVal *= gamma;
            imagVal *= gamma;

            data[rowJ - 2] -= realVal;
            data[rowJ - 1] -= imagVal;

            indexW = rowW;
            indexJ = rowJ;
            while( indexW != indexWEnd ) {
                double realW = data[indexW++];
                double imagW = data[indexW++];

                data[indexJ++] -= realW*realVal - imagW*imagVal;
                data[indexJ++] -= realW*imagVal + imagW*realVal;
            }
        }
    }
989132
public static final DoubleMatrix2D diagonalMatrixMult(final DoubleMatrix1D diagonalU, DoubleMatrix2D A, final DoubleMatrix1D diagonalV){
		int r = A.rows();
		int c = A.columns();
		final DoubleMatrix2D ret;
		if (A instanceof SparseDoubleMatrix2D) {
			ret = DoubleFactory2D.sparse.make(r, c);
			A.forEachNonZero(new IntIntDoubleFunction() {
				@Override
				public double apply(int i, int j, double aij) {
					ret.setQuick(i, j, aij * diagonalU.getQuick(i) * diagonalV.getQuick(j));
					return aij;
				}
			});
		} else {
			ret = DoubleFactory2D.dense.make(r, c);
			for (int i = 0; i < r; i++) {
				for (int j = 0; j < c; j++) {
					ret.setQuick(i, j, A.getQuick(i, j) * diagonalU.getQuick(i)	* diagonalV.getQuick(j));
				}
			}
		}

		return ret;
	}
116220
void initialize(DMatrixSparseCSC A) {
        m = A.numRows;
        n = A.numCols;
        int s = 4*n + (ata ? (n+m+1) : 0);

        gw.reshape(s);
        w = gw.data;

        // compute the transpose of A
        At.reshape(A.numCols,A.numRows,A.nz_length);
        CommonOps_DSCC.transpose(A,At,gw);

        // initialize w
        Arrays.fill(w,0,s,-1); // assign all values in workspace to -1

        ancestor = 0;
        maxfirst = n;
        prevleaf = 2*n;
        first    = 3*n;
    }
1259908
public void plus(LinearSparseVector sv, float w) {
		if (sv == null)
			return;
		for (int i = 0; i < sv.length; i++) {
			float val = (float) sv.data[i] * w;
			add(sv.index[i], val);
		}
	}
362156
protected void upgradeSolution( DMatrixRMaj X ) {
        DMatrixRMaj z = Y; // recycle Y

        // compute the z which will minimize the 2-norm of X
        // because of the identity matrix tacked onto the end 'A' should never be singular
        if( !internalSolver.setA(W) )
            throw new RuntimeException("This should never happen.  Is input NaN?");
        z.reshape(numCols-rank,1);
        internalSolver.solve(X, z);

        // compute X by tweaking the original
        CommonOps_DDRM.multAdd(-1, W, z, X);
    }
575910
public void put(double x, double y, double w) {
    if(w == 0.) {
      return;
    }
    if(sumWe <= 0.) {
      sumX = x * w;
      sumY = y * w;
      sumWe = w;
      return;
    }
    // Delta to previous mean
    final double deltaX = x * sumWe - sumX;
    final double deltaY = y * sumWe - sumY;
    final double oldWe = sumWe;
    // Incremental update
    sumWe += w;
    final double f = w / (sumWe * oldWe);
    // Update
    sumXX += f * deltaX * deltaX;
    sumYY += f * deltaY * deltaY;
    // should equal weight * deltaY * neltaX!
    sumXY += f * deltaX * deltaY;
    // Update means
    sumX += x * w;
    sumY += y * w;
  }
802870
public void setMatrix(int[] r, int j0, int j1, Matrix X)
    {
        try
        {
            for (int i = 0; i < r.length; i++)
            {
                for (int j = j0; j <= j1; j++)
                {
                    A[r[i]][j] = X.get(i, j - j0);
                }
            }
        }
        catch (ArrayIndexOutOfBoundsException e)
        {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
    }
1138019
public static void transpose(DMatrixSparseCSC A , DMatrixSparseCSC C , @Nullable IGrowArray gw ) {
        int []work = adjust(gw,A.numRows,A.numRows);
        C.reshape(A.numCols,A.numRows,A.nz_length);

        // compute the histogram for each row in 'a'
        int idx0 = A.col_idx[0];
        for (int j = 1; j <= A.numCols; j++) {
            int idx1 = A.col_idx[j];
            for (int i = idx0; i < idx1; i++) {
                if( A.nz_rows.length <= i)
                    throw new RuntimeException("Egads");
                work[A.nz_rows[i]]++;
            }
            idx0 = idx1;
        }

        // construct col_idx in the transposed matrix
        C.histogramToStructure(work);
        System.arraycopy(C.col_idx,0,work,0,C.numCols);

        // fill in the row indexes
        idx0 = A.col_idx[0];
        for (int j = 1; j <= A.numCols; j++) {
            int col = j-1;
            int idx1 = A.col_idx[j];
            for (int i = idx0; i < idx1; i++) {
                int row = A.nz_rows[i];
                int index = work[row]++;
                C.nz_rows[index] = col;
                C.nz_values[index] = A.nz_values[i];
            }
            idx0 = idx1;
        }
    }
964415
@Override
    public boolean setA(DMatrixRMaj A) {
        blockA.reshape(A.numRows,A.numCols,false);
        MatrixOps_DDRB.convert(A,blockA);

        return alg.setA(blockA);
    }
241819
public static void symmLowerToFull( DMatrixSparseCSC A , DMatrixSparseCSC B , @Nullable IGrowArray gw )
    {
        if( A.numCols != A.numRows )
            throw new IllegalArgumentException("Must be a lower triangular square matrix");

        int N = A.numCols;
        int w[] = adjust(gw,N,N);
        B.reshape(N,N,A.nz_length*2);
        B.indicesSorted = false;

        //=== determine the row counts of the full matrix
        for (int col = 0; col < N; col++) {
            int idx0 = A.col_idx[col];
            int idx1 = A.col_idx[col+1];

            // We know the length of the lower part of this column already
            w[col] += idx1 - idx0;

            // add elements to the top of the other columns along row with index 'col'
            for (int i = idx0; i < idx1; i++) {
                int row = A.nz_rows[i];
                if( row > col ) {
                    w[row]++;
                }
            }
        }

        // Update the structure of B
        B.histogramToStructure(w);

        // Zero W again. It's being used to keep track of how many elements have been added to a column already
        Arrays.fill(w,0,N,0);
        // Fill in matrix
        for (int col = 0; col < N; col++) {

            int idx0 = A.col_idx[col];
            int idx1 = A.col_idx[col+1];

            int lengthA = idx1 - idx0;
            int lengthB = B.col_idx[col+1] - B.col_idx[col];

            // Copy the non-zero values from A into B along the columns while taking in account the upper
            // elements already copied
            System.arraycopy(A.nz_values,idx0,B.nz_values,B.col_idx[col]+lengthB-lengthA,lengthA);
            System.arraycopy(A.nz_rows,idx0,B.nz_rows,B.col_idx[col]+lengthB-lengthA,lengthA);

            // Copy this column into the upper portion of B
            for (int i = idx0; i < idx1; i++) {
                int row = A.nz_rows[i];
                if( row > col ) {
                    int indexB = B.col_idx[row] + w[row]++;
                    B.nz_rows[indexB] = col;
                    B.nz_values[indexB] = A.nz_values[i];
                }
            }
        }

    }
72031
public void householderSymmetric( int row , double gamma )
    {
        int startU = (row-1)*N;

        // compute v = -gamma*A*u
        for( int i = row; i < N; i++ ) {
            double total = 0;
            for( int j = row; j < N; j++ ) {
                total += QT.data[i*N+j]*QT.data[startU+j];
            }
            w[i] = -gamma*total;
//            System.out.println("y["+i+"] = "+w[i]);
        }
        // alpha = -0.5*gamma*u^T*v
        double alpha = 0;

        for( int i = row; i < N; i++ ) {
            alpha += QT.data[startU+i]*w[i];
        }
        alpha *= -0.5*gamma;

        // w = v + alpha*u
        for( int i = row; i < N; i++ ) {
            w[i] += alpha*QT.data[startU+i];
//            System.out.println("w["+i+"] = "+w[i]);
        }
        // A = A + w*u^T + u*w^T
        for( int i = row; i < N; i++ ) {

            double ww = w[i];
            double uu = QT.data[startU+i];
//            System.out.println("u["+i+"] = "+uu);

            for( int j = i; j < N; j++ ) {
                QT.data[j*N+i] = QT.data[i*N+j] += ww*QT.data[startU+j] + w[j]*uu;
            }
        }

    }
259553
protected void convertToColumnMajor(DMatrixRMaj A) {
        for( int x = 0; x < numCols; x++ ) {
            double colQ[] = dataQR[x];
            for( int y = 0; y < numRows; y++ ) {
                colQ[y] = A.data[y*A.numCols+x];
            }
        }
    }
912904
public static void multRow(Matrix A, int i, double[] c)
    {
        if(A.cols() != c.length)
            throw new ArithmeticException("Can not perform row update, length miss match " + A.cols() + " and " + c.length);
        multRow(A, i, 0, c.length, c);
    }
738390
protected void updateA( int w )
    {
        final double u[] = dataQR[w];

        for( int j = w+1; j < numCols; j++ ) {

            final double colQ[] = dataQR[j];
            double val = colQ[w];

            for( int k = w+1; k < numRows; k++ ) {
                val += u[k]*colQ[k];
            }
            val *= gamma;

            colQ[w] -= val;
            for( int i = w+1; i < numRows; i++ ) {
                colQ[i] -= u[i]*val;
            }
        }
    }
619428
private void hqr2 (double[][] V, double[][] H) {
   
      //  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;
         }
      }
   }
447213
function householderTransform (x) {
  // Based on "Matrix Computations" by Golub, Van Loan
  const n = x.dimension;
  const v = x.clone();
  v.x = 1;
  let sigma = 0;
  for (let i = 1; i < n; ++i) {
    const vi = v.getComponent(i);
    sigma += vi * vi;
  }
  let beta = 0;
  if (sigma !== 0) {
    const x1 = x.x;
    const mu = _Math.sqrt(x1 * x1 + sigma);
    const v1 = (x1 <= 0 ? x1 - mu : -sigma / (x1 + mu));
    v.x = v1;
    beta = 2 * v1 * v1 / (sigma + v1 * v1);
    v.multiplyScalar(1.0 / v1);
  }
  return {
    v,
    beta
  };
}
57043
private void orthes() {
    // FIXME: does this fail on NaN/inf values?

    // 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.

    final int low = 0, 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 += abs(H[i][m - 1]);
      }
      if(scale > 0.0 || scale < 0.0) {
        // Compute Householder transformation.
        double h = 0.0;
        for(int i = high; i >= m; i--) {
          double oi = ort[i] = H[i][m - 1] / scale;
          h += oi * oi;
        }
        double g = FastMath.sqrt(h), om = ort[m];
        g = (om > 0) ? -g : g;
        h -= om * g;
        ort[m] = om - 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 /= h;
          for(int i = m; i <= high; i++) {
            H[i][j] -= f * ort[i];
          }
        }

        for(int i = 0; i <= high; i++) {
          final double[] Hi = H[i];
          double f = 0.0;
          for(int j = high; j >= m; j--) {
            f += ort[j] * Hi[j];
          }
          f /= h;
          for(int j = m; j <= high; j++) {
            Hi[j] -= f * ort[j];
          }
        }
        ort[m] *= scale;
        H[m][m - 1] = scale * g;
      }
    }

    // Accumulate transformations (Algol's ortran).
    for(int i = 0; i < n; i++) {
      Arrays.fill(V[i], 0.);
      V[i][i] = 1.;
    }

    for(int m = high - 1; m >= low + 1; m--) {
      final double[] H_m = H[m];
      if(H_m[m - 1] != 0.0) {
        for(int i = m + 1; i <= high; i++) {
          ort[i] = H[i][m - 1];
        }
        final double ort_m = ort[m];
        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];
          }
        }
      }
    }
  }