updated EigenSolver to use .coeff / .coeffRef

1 files changed, 161 insertions, 161 deletions

diff --git a/Eigen/src/QR/EigenSolver.h b/Eigen/src/QR/EigenSolver.h
index cf3ea9c94..4e875757e 100644
--- a/Eigen/src/QR/EigenSolver.h
+++ b/Eigen/src/QR/EigenSolver.h
@@ -162,7 +162,7 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tridiagonalization(RealVectorType& e
 
     if (scale == 0.0)
     {
-      eivali[i] = eivalr[i-1];
+      eivali.coeffRef(i) = eivalr.coeff(i-1);
       eivalr.start(i) = m_eivec.row(i-1).start(i);
       m_eivec.corner(TopLeft, i, i) = m_eivec.corner(TopLeft, i, i).diagonal().asDiagonal();
     }
@@ -172,28 +172,28 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tridiagonalization(RealVectorType& e
       eivalr.start(i) /= scale;
       h = eivalr.start(i).cwiseAbs2().sum();
 
-      Scalar f = eivalr[i-1];
+      Scalar f = eivalr.coeff(i-1);
       Scalar g = ei_sqrt(h);
       if (f > 0)
         g = -g;
-      eivali[i] = scale * g;
+      eivali.coeffRef(i) = scale * g;
       h = h - f * g;
-      eivalr[i-1] = f - g;
+      eivalr.coeffRef(i-1) = f - g;
       eivali.start(i).setZero();
 
       // Apply similarity transformation to remaining columns.
       for (int j = 0; j < i; j++)
       {
-        f = eivalr[j];
-        m_eivec(j,i) = f;
-        g = eivali[j] + m_eivec(j,j) * f;
+        f = eivalr.coeff(j);
+        m_eivec.coeffRef(j,i) = f;
+        g = eivali.coeff(j) + m_eivec.coeff(j,j) * f;
         int bSize = i-j-1;
         if (bSize>0)
         {
           g += (m_eivec.col(j).block(j+1, bSize).transpose() * eivalr.block(j+1, bSize))(0,0);
           eivali.block(j+1, bSize) += m_eivec.col(j).block(j+1, bSize) * f;
         }
-        eivali[j] = g;
+        eivali.coeffRef(j) = g;
       }
 
       f = (eivali.start(i).transpose() * eivalr.start(i))(0,0);
@@ -206,15 +206,15 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tridiagonalization(RealVectorType& e
       eivalr.start(i) = m_eivec.row(i-1).start(i);
       m_eivec.row(i).start(i).setZero();
     }
-    eivalr[i] = h;
+    eivalr.coeffRef(i) = h;
   }
 
   // Accumulate transformations.
   for (int i = 0; i < n-1; i++)
   {
-    m_eivec(n-1,i) = m_eivec(i,i);
-    m_eivec(i,i) = 1.0;
-    Scalar h = eivalr[i+1];
+    m_eivec.coeffRef(n-1,i) = m_eivec.coeff(i,i);
+    m_eivec.coeffRef(i,i) = 1.0;
+    Scalar h = eivalr.coeff(i+1);
     // FIXME this does not looks very stable ;)
     if (h != 0.0)
     {
@@ -226,8 +226,8 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tridiagonalization(RealVectorType& e
   }
   eivalr = m_eivec.row(eivalr.size()-1);
   m_eivec.row(eivalr.size()-1).setZero();
-  m_eivec(n-1,n-1) = 1.0;
-  eivali[0] = 0.0;
+  m_eivec.coeffRef(n-1,n-1) = 1.0;
+  eivali.coeffRef(0) = 0.0;
 }
 
 
@@ -243,9 +243,9 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tql2(RealVectorType& eivalr, RealVec
   int n = eivalr.size();
 
   for (int i = 1; i < n; i++) {
-      eivali[i-1] = eivali[i];
+      eivali.coeffRef(i-1) = eivali.coeff(i);
   }
-  eivali[n-1] = 0.0;
+  eivali.coeffRef(n-1) = 0.0;
 
   Scalar f = 0.0;
   Scalar tst1 = 0.0;
@@ -253,13 +253,13 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tql2(RealVectorType& eivalr, RealVec
   for (int l = 0; l < n; l++)
   {
     // Find small subdiagonal element
-    tst1 = std::max(tst1,ei_abs(eivalr[l]) + ei_abs(eivali[l]));
+    tst1 = std::max(tst1,ei_abs(eivalr.coeff(l)) + ei_abs(eivali.coeff(l)));
     int m = l;
 
-    while ( (m < n) && (ei_abs(eivali[m]) > eps*tst1) )
+    while ( (m < n) && (ei_abs(eivali.coeff(m)) > eps*tst1) )
       m++;
 
-    // If m == l, eivalr[l] is an eigenvalue,
+    // If m == l, eivalr.coeff(l) is an eigenvalue,
     // otherwise, iterate.
     if (m > l)
     {
@@ -269,26 +269,26 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tql2(RealVectorType& eivalr, RealVec
         iter = iter + 1;
 
         // Compute implicit shift
-        Scalar g = eivalr[l];
-        Scalar p = (eivalr[l+1] - g) / (2.0 * eivali[l]);
+        Scalar g = eivalr.coeff(l);
+        Scalar p = (eivalr.coeff(l+1) - g) / (2.0 * eivali.coeff(l));
         Scalar r = hypot(p,1.0);
         if (p < 0)
           r = -r;
 
-        eivalr[l] = eivali[l] / (p + r);
-        eivalr[l+1] = eivali[l] * (p + r);
-        Scalar dl1 = eivalr[l+1];
-        Scalar h = g - eivalr[l];
+        eivalr.coeffRef(l) = eivali.coeff(l) / (p + r);
+        eivalr.coeffRef(l+1) = eivali.coeff(l) * (p + r);
+        Scalar dl1 = eivalr.coeff(l+1);
+        Scalar h = g - eivalr.coeff(l);
         if (l+2<n)
           eivalr.end(n-l-2) -= RealVectorTypeX::constant(n-l-2, h);
         f = f + h;
 
         // Implicit QL transformation.
-        p = eivalr[m];
+        p = eivalr.coeff(m);
         Scalar c = 1.0;
         Scalar c2 = c;
         Scalar c3 = c;
-        Scalar el1 = eivali[l+1];
+        Scalar el1 = eivali.coeff(l+1);
         Scalar s = 0.0;
         Scalar s2 = 0.0;
         for (int i = m-1; i >= l; i--)
@@ -296,32 +296,32 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tql2(RealVectorType& eivalr, RealVec
           c3 = c2;
           c2 = c;
           s2 = s;
-          g = c * eivali[i];
+          g = c * eivali.coeff(i);
           h = c * p;
-          r = hypot(p,eivali[i]);
-          eivali[i+1] = s * r;
-          s = eivali[i] / r;
+          r = hypot(p,eivali.coeff(i));
+          eivali.coeffRef(i+1) = s * r;
+          s = eivali.coeff(i) / r;
           c = p / r;
-          p = c * eivalr[i] - s * g;
-          eivalr[i+1] = h + s * (c * g + s * eivalr[i]);
+          p = c * eivalr.coeff(i) - s * g;
+          eivalr.coeffRef(i+1) = h + s * (c * g + s * eivalr.coeff(i));
 
           // Accumulate transformation.
           for (int k = 0; k < n; k++)
           {
-            h = m_eivec(k,i+1);
-            m_eivec(k,i+1) = s * m_eivec(k,i) + c * h;
-            m_eivec(k,i) = c * m_eivec(k,i) - s * h;
+            h = m_eivec.coeff(k,i+1);
+            m_eivec.coeffRef(k,i+1) = s * m_eivec.coeff(k,i) + c * h;
+            m_eivec.coeffRef(k,i) = c * m_eivec.coeff(k,i) - s * h;
           }
         }
-        p = -s * s2 * c3 * el1 * eivali[l] / dl1;
-        eivali[l] = s * p;
-        eivalr[l] = c * p;
+        p = -s * s2 * c3 * el1 * eivali.coeff(l) / dl1;
+        eivali.coeffRef(l) = s * p;
+        eivalr.coeffRef(l) = c * p;
 
         // Check for convergence.
-      } while (ei_abs(eivali[l]) > eps*tst1);
+      } while (ei_abs(eivali.coeff(l)) > eps*tst1);
     }
-    eivalr[l] = eivalr[l] + f;
-    eivali[l] = 0.0;
+    eivalr.coeffRef(l) = eivalr.coeff(l) + f;
+    eivali.coeffRef(l) = 0.0;
   }
 
   // Sort eigenvalues and corresponding vectors.
@@ -329,18 +329,18 @@ void EigenSolver<MatrixType,IsSelfadjoint>::tql2(RealVectorType& eivalr, RealVec
   for (int i = 0; i < n-1; i++)
   {
     int k = i;
-    Scalar minValue = eivalr[i];
+    Scalar minValue = eivalr.coeff(i);
     for (int j = i+1; j < n; j++)
     {
-      if (eivalr[j] < minValue)
+      if (eivalr.coeff(j) < minValue)
       {
         k = j;
-        minValue = eivalr[j];
+        minValue = eivalr.coeff(j);
       }
     }
     if (k != i)
     {
-      std::swap(eivalr[i], eivalr[k]);
+      std::swap(eivalr.coeffRef(i), eivalr.coeffRef(k));
       m_eivec.col(i).swap(m_eivec.col(k));
     }
   }
@@ -371,14 +371,14 @@ void EigenSolver<MatrixType,IsSelfadjoint>::orthes(MatrixType& matH, RealVectorT
       // FIXME could be rewritten, but this one looks better wrt cache
       for (int i = high; i >= m; i--)
       {
-        ort[i] = matH(i,m-1)/scale;
-        h += ort[i] * ort[i];
+        ort.coeffRef(i) = matH.coeff(i,m-1)/scale;
+        h += ort.coeff(i) * ort.coeff(i);
       }
       Scalar g = ei_sqrt(h);
-      if (ort[m] > 0)
+      if (ort.coeff(m) > 0)
         g = -g;
-      h = h - ort[m] * g;
-      ort[m] = ort[m] - g;
+      h = h - ort.coeff(m) * g;
+      ort.coeffRef(m) = ort.coeff(m) - g;
 
       // Apply Householder similarity transformation
       // H = (I-u*u'/h)*H*(I-u*u')/h)
@@ -389,8 +389,8 @@ void EigenSolver<MatrixType,IsSelfadjoint>::orthes(MatrixType& matH, RealVectorT
       matH.block(0, m, high+1, bSize) -= ((matH.block(0, m, high+1, bSize) * ort.block(m, bSize)).lazy()
         * (ort.block(m, bSize)/h).transpose()).lazy();
 
-      ort[m] = scale*ort[m];
-      matH(m,m-1) = scale*g;
+      ort.coeffRef(m) = scale*ort.coeff(m);
+      matH.coeffRef(m,m-1) = scale*g;
     }
   }
 
@@ -399,12 +399,12 @@ void EigenSolver<MatrixType,IsSelfadjoint>::orthes(MatrixType& matH, RealVectorT
 
   for (int m = high-1; m >= low+1; m--)
   {
-    if (matH(m,m-1) != 0.0)
+    if (matH.coeff(m,m-1) != 0.0)
     {
       ort.block(m+1, high-m) = matH.col(m-1).block(m+1, high-m);
 
       int bSize = high-m+1;
-      m_eivec.block(m, m, bSize, bSize) += ( (ort.block(m, bSize) /  (matH(m,m-1) * ort[m] ) )
+      m_eivec.block(m, m, bSize, bSize) += ( (ort.block(m, bSize) /  (matH.coeff(m,m-1) * ort.coeff(m) ) )
         * (ort.block(m, bSize).transpose() * m_eivec.block(m, m, bSize, bSize)).lazy());
     }
   }
@@ -458,8 +458,8 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
     // FIXME what's the purpose of the following since the condition is always false
     if ((j < low) || (j > high))
     {
-      m_eivalues[j].real() = matH(j,j);
-      m_eivalues[j].imag() = 0.0;
+      m_eivalues.coeffRef(j).real() = matH.coeff(j,j);
+      m_eivalues.coeffRef(j).imag() = 0.0;
     }
     norm += matH.col(j).start(std::min(j+1,nn)).cwiseAbs().sum();
   }
@@ -472,10 +472,10 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
     int l = n;
     while (l > low)
     {
-      s = ei_abs(matH(l-1,l-1)) + ei_abs(matH(l,l));
+      s = ei_abs(matH.coeff(l-1,l-1)) + ei_abs(matH.coeff(l,l));
       if (s == 0.0)
           s = norm;
-      if (ei_abs(matH(l,l-1)) < eps * s)
+      if (ei_abs(matH.coeff(l,l-1)) < eps * s)
         break;
       l--;
     }
@@ -484,21 +484,21 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
     // One root found
     if (l == n)
     {
-      matH(n,n) = matH(n,n) + exshift;
-      m_eivalues[n].real() = matH(n,n);
-      m_eivalues[n].imag() = 0.0;
+      matH.coeffRef(n,n) = matH.coeff(n,n) + exshift;
+      m_eivalues.coeffRef(n).real() = matH.coeff(n,n);
+      m_eivalues.coeffRef(n).imag() = 0.0;
       n--;
       iter = 0;
     }
     else if (l == n-1) // Two roots found
     {
-      w = matH(n,n-1) * matH(n-1,n);
-      p = (matH(n-1,n-1) - matH(n,n)) / 2.0;
+      w = matH.coeff(n,n-1) * matH.coeff(n-1,n);
+      p = (matH.coeff(n-1,n-1) - matH.coeff(n,n)) / 2.0;
       q = p * p + w;
       z = ei_sqrt(ei_abs(q));
-      matH(n,n) = matH(n,n) + exshift;
-      matH(n-1,n-1) = matH(n-1,n-1) + exshift;
-      x = matH(n,n);
+      matH.coeffRef(n,n) = matH.coeff(n,n) + exshift;
+      matH.coeffRef(n-1,n-1) = matH.coeff(n-1,n-1) + exshift;
+      x = matH.coeff(n,n);
 
       // Scalar pair
       if (q >= 0)
@@ -508,14 +508,14 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
         else
           z = p - z;
 
-        m_eivalues[n-1].real() = x + z;
-        m_eivalues[n].real() = m_eivalues[n-1].real();
+        m_eivalues.coeffRef(n-1).real() = x + z;
+        m_eivalues.coeffRef(n).real() = m_eivalues.coeff(n-1).real();
         if (z != 0.0)
-          m_eivalues[n].real() = x - w / z;
+          m_eivalues.coeffRef(n).real() = x - w / z;
 
-        m_eivalues[n-1].imag() = 0.0;
-        m_eivalues[n].imag() = 0.0;
-        x = matH(n,n-1);
+        m_eivalues.coeffRef(n-1).imag() = 0.0;
+        m_eivalues.coeffRef(n).imag() = 0.0;
+        x = matH.coeff(n,n-1);
         s = ei_abs(x) + ei_abs(z);
         p = x / s;
         q = z / s;
@@ -526,33 +526,33 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
         // Row modification
         for (int j = n-1; j < nn; j++)
         {
-          z = matH(n-1,j);
-          matH(n-1,j) = q * z + p * matH(n,j);
-          matH(n,j) = q * matH(n,j) - p * z;
+          z = matH.coeff(n-1,j);
+          matH.coeffRef(n-1,j) = q * z + p * matH.coeff(n,j);
+          matH.coeffRef(n,j) = q * matH.coeff(n,j) - p * z;
         }
 
         // Column modification
         for (int i = 0; i <= n; i++)
         {
-          z = matH(i,n-1);
-          matH(i,n-1) = q * z + p * matH(i,n);
-          matH(i,n) = q * matH(i,n) - p * z;
+          z = matH.coeff(i,n-1);
+          matH.coeffRef(i,n-1) = q * z + p * matH.coeff(i,n);
+          matH.coeffRef(i,n) = q * matH.coeff(i,n) - p * z;
         }
 
         // Accumulate transformations
         for (int i = low; i <= high; i++)
         {
-          z = m_eivec(i,n-1);
-          m_eivec(i,n-1) = q * z + p * m_eivec(i,n);
-          m_eivec(i,n) = q * m_eivec(i,n) - p * z;
+          z = m_eivec.coeff(i,n-1);
+          m_eivec.coeffRef(i,n-1) = q * z + p * m_eivec.coeff(i,n);
+          m_eivec.coeffRef(i,n) = q * m_eivec.coeff(i,n) - p * z;
         }
       }
       else // Complex pair
       {
-        m_eivalues[n-1].real() = x + p;
-        m_eivalues[n].real() = x + p;
-        m_eivalues[n-1].imag() = z;
-        m_eivalues[n].imag() = -z;
+        m_eivalues.coeffRef(n-1).real() = x + p;
+        m_eivalues.coeffRef(n).real() = x + p;
+        m_eivalues.coeffRef(n-1).imag() = z;
+        m_eivalues.coeffRef(n).imag() = -z;
       }
       n = n - 2;
       iter = 0;
@@ -560,13 +560,13 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
     else // No convergence yet
     {
       // Form shift
-      x = matH(n,n);
+      x = matH.coeff(n,n);
       y = 0.0;
       w = 0.0;
       if (l < n)
       {
-          y = matH(n-1,n-1);
-          w = matH(n,n-1) * matH(n-1,n);
+          y = matH.coeff(n-1,n-1);
+          w = matH.coeff(n,n-1) * matH.coeff(n-1,n);
       }
 
       // Wilkinson's original ad hoc shift
@@ -574,8 +574,8 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
       {
         exshift += x;
         for (int i = low; i <= n; i++)
-          matH(i,i) -= x;
-        s = ei_abs(matH(n,n-1)) + ei_abs(matH(n-1,n-2));
+          matH.coeffRef(i,i) -= x;
+        s = ei_abs(matH.coeff(n,n-1)) + ei_abs(matH.coeff(n-1,n-2));
         x = y = 0.75 * s;
         w = -0.4375 * s * s;
       }
@@ -592,7 +592,7 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
             s = -s;
           s = x - w / ((y - x) / 2.0 + s);
           for (int i = low; i <= n; i++)
-            matH(i,i) -= s;
+            matH.coeffRef(i,i) -= s;
           exshift += s;
           x = y = w = 0.964;
         }
@@ -604,12 +604,12 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
       int m = n-2;
       while (m >= l)
       {
-        z = matH(m,m);
+        z = matH.coeff(m,m);
         r = x - z;
         s = y - z;
-        p = (r * s - w) / matH(m+1,m) + matH(m,m+1);
-        q = matH(m+1,m+1) - z - r - s;
-        r = matH(m+2,m+1);
+        p = (r * s - w) / matH.coeff(m+1,m) + matH.coeff(m,m+1);
+        q = matH.coeff(m+1,m+1) - z - r - s;
+        r = matH.coeff(m+2,m+1);
         s = ei_abs(p) + ei_abs(q) + ei_abs(r);
         p = p / s;
         q = q / s;
@@ -617,9 +617,9 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
         if (m == l) {
           break;
         }
-        if (ei_abs(matH(m,m-1)) * (ei_abs(q) + ei_abs(r)) <
-          eps * (ei_abs(p) * (ei_abs(matH(m-1,m-1)) + ei_abs(z) +
-          ei_abs(matH(m+1,m+1)))))
+        if (ei_abs(matH.coeff(m,m-1)) * (ei_abs(q) + ei_abs(r)) <
+          eps * (ei_abs(p) * (ei_abs(matH.coeff(m-1,m-1)) + ei_abs(z) +
+          ei_abs(matH.coeff(m+1,m+1)))))
         {
           break;
         }
@@ -628,9 +628,9 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
 
       for (int i = m+2; i <= n; i++)
       {
-        matH(i,i-2) = 0.0;
+        matH.coeffRef(i,i-2) = 0.0;
         if (i > m+2)
-          matH(i,i-3) = 0.0;
+          matH.coeffRef(i,i-3) = 0.0;
       }
 
       // Double QR step involving rows l:n and columns m:n
@@ -638,9 +638,9 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
       {
         int notlast = (k != n-1);
         if (k != m) {
-          p = matH(k,k-1);
-          q = matH(k+1,k-1);
-          r = (notlast ? matH(k+2,k-1) : 0.0);
+          p = matH.coeff(k,k-1);
+          q = matH.coeff(k+1,k-1);
+          r = (notlast ? matH.coeff(k+2,k-1) : 0.0);
           x = ei_abs(p) + ei_abs(q) + ei_abs(r);
           if (x != 0.0)
           {
@@ -661,9 +661,9 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
         if (s != 0)
         {
           if (k != m)
-            matH(k,k-1) = -s * x;
+            matH.coeffRef(k,k-1) = -s * x;
           else if (l != m)
-            matH(k,k-1) = -matH(k,k-1);
+            matH.coeffRef(k,k-1) = -matH.coeff(k,k-1);
 
           p = p + s;
           x = p / s;
@@ -675,40 +675,40 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
           // Row modification
           for (int j = k; j < nn; j++)
           {
-            p = matH(k,j) + q * matH(k+1,j);
+            p = matH.coeff(k,j) + q * matH.coeff(k+1,j);
             if (notlast)
             {
-              p = p + r * matH(k+2,j);
-              matH(k+2,j) = matH(k+2,j) - p * z;
+              p = p + r * matH.coeff(k+2,j);
+              matH.coeffRef(k+2,j) = matH.coeff(k+2,j) - p * z;
             }
-            matH(k,j) = matH(k,j) - p * x;
-            matH(k+1,j) = matH(k+1,j) - p * y;
+            matH.coeffRef(k,j) = matH.coeff(k,j) - p * x;
+            matH.coeffRef(k+1,j) = matH.coeff(k+1,j) - p * y;
           }
 
           // Column modification
           for (int i = 0; i <= std::min(n,k+3); i++)
           {
-            p = x * matH(i,k) + y * matH(i,k+1);
+            p = x * matH.coeff(i,k) + y * matH.coeff(i,k+1);
             if (notlast)
             {
-              p = p + z * matH(i,k+2);
-              matH(i,k+2) = matH(i,k+2) - p * r;
+              p = p + z * matH.coeff(i,k+2);
+              matH.coeffRef(i,k+2) = matH.coeff(i,k+2) - p * r;
             }
-            matH(i,k) = matH(i,k) - p;
-            matH(i,k+1) = matH(i,k+1) - p * q;
+            matH.coeffRef(i,k) = matH.coeff(i,k) - p;
+            matH.coeffRef(i,k+1) = matH.coeff(i,k+1) - p * q;
           }
 
           // Accumulate transformations
           for (int i = low; i <= high; i++)
           {
-            p = x * m_eivec(i,k) + y * m_eivec(i,k+1);
+            p = x * m_eivec.coeff(i,k) + y * m_eivec.coeff(i,k+1);
             if (notlast)
             {
-              p = p + z * m_eivec(i,k+2);
-              m_eivec(i,k+2) = m_eivec(i,k+2) - p * r;
+              p = p + z * m_eivec.coeff(i,k+2);
+              m_eivec.coeffRef(i,k+2) = m_eivec.coeff(i,k+2) - p * r;
             }
-            m_eivec(i,k) = m_eivec(i,k) - p;
-            m_eivec(i,k+1) = m_eivec(i,k+1) - p * q;
+            m_eivec.coeffRef(i,k) = m_eivec.coeff(i,k) - p;
+            m_eivec.coeffRef(i,k+1) = m_eivec.coeff(i,k+1) - p * q;
           }
         }  // (s != 0)
       }  // k loop
@@ -723,20 +723,20 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
 
   for (n = nn-1; n >= 0; n--)
   {
-    p = m_eivalues[n].real();
-    q = m_eivalues[n].imag();
+    p = m_eivalues.coeff(n).real();
+    q = m_eivalues.coeff(n).imag();
 
     // Scalar vector
     if (q == 0)
     {
       int l = n;
-      matH(n,n) = 1.0;
+      matH.coeffRef(n,n) = 1.0;
       for (int i = n-1; i >= 0; i--)
       {
-        w = matH(i,i) - p;
+        w = matH.coeff(i,i) - p;
         r = (matH.row(i).end(nn-l) * matH.col(n).end(nn-l))(0,0);
 
-        if (m_eivalues[i].imag() < 0.0)
+        if (m_eivalues.coeff(i).imag() < 0.0)
         {
           z = w;
           s = r;
@@ -744,28 +744,28 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
         else
         {
           l = i;
-          if (m_eivalues[i].imag() == 0.0)
+          if (m_eivalues.coeff(i).imag() == 0.0)
           {
             if (w != 0.0)
-              matH(i,n) = -r / w;
+              matH.coeffRef(i,n) = -r / w;
             else
-              matH(i,n) = -r / (eps * norm);
+              matH.coeffRef(i,n) = -r / (eps * norm);
           }
           else // Solve real equations
           {
-            x = matH(i,i+1);
-            y = matH(i+1,i);
-            q = (m_eivalues[i].real() - p) * (m_eivalues[i].real() - p) + m_eivalues[i].imag() * m_eivalues[i].imag();
+            x = matH.coeff(i,i+1);
+            y = matH.coeff(i+1,i);
+            q = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();
             t = (x * s - z * r) / q;
-            matH(i,n) = t;
+            matH.coeffRef(i,n) = t;
             if (ei_abs(x) > ei_abs(z))
-              matH(i+1,n) = (-r - w * t) / x;
+              matH.coeffRef(i+1,n) = (-r - w * t) / x;
             else
-              matH(i+1,n) = (-s - y * t) / z;
+              matH.coeffRef(i+1,n) = (-s - y * t) / z;
           }
 
           // Overflow control
-          t = ei_abs(matH(i,n));
+          t = ei_abs(matH.coeff(i,n));
           if ((eps * t) * t > 1)
             matH.col(n).end(nn-i) /= t;
         }
@@ -777,27 +777,27 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
       int l = n-1;
 
       // Last vector component imaginary so matrix is triangular
-      if (ei_abs(matH(n,n-1)) > ei_abs(matH(n-1,n)))
+      if (ei_abs(matH.coeff(n,n-1)) > ei_abs(matH.coeff(n-1,n)))
       {
-        matH(n-1,n-1) = q / matH(n,n-1);
-        matH(n-1,n) = -(matH(n,n) - p) / matH(n,n-1);
+        matH.coeffRef(n-1,n-1) = q / matH.coeff(n,n-1);
+        matH.coeffRef(n-1,n) = -(matH.coeff(n,n) - p) / matH.coeff(n,n-1);
       }
       else
       {
-        cc = cdiv<Scalar>(0.0,-matH(n-1,n),matH(n-1,n-1)-p,q);
-        matH(n-1,n-1) = ei_real(cc);
-        matH(n-1,n) = ei_imag(cc);
+        cc = cdiv<Scalar>(0.0,-matH.coeff(n-1,n),matH.coeff(n-1,n-1)-p,q);
+        matH.coeffRef(n-1,n-1) = ei_real(cc);
+        matH.coeffRef(n-1,n) = ei_imag(cc);
       }
-      matH(n,n-1) = 0.0;
-      matH(n,n) = 1.0;
+      matH.coeffRef(n,n-1) = 0.0;
+      matH.coeffRef(n,n) = 1.0;
       for (int i = n-2; i >= 0; i--)
       {
         Scalar ra,sa,vr,vi;
         ra = (matH.row(i).end(nn-l) * matH.col(n-1).end(nn-l)).lazy()(0,0);
         sa = (matH.row(i).end(nn-l) * matH.col(n).end(nn-l)).lazy()(0,0);
-        w = matH(i,i) - p;
+        w = matH.coeff(i,i) - p;
 
-        if (m_eivalues[i].imag() < 0.0)
+        if (m_eivalues.coeff(i).imag() < 0.0)
         {
           z = w;
           r = ra;
@@ -806,40 +806,40 @@ void EigenSolver<MatrixType,IsSelfadjoint>::hqr2(MatrixType& matH)
         else
         {
           l = i;
-          if (m_eivalues[i].imag() == 0)
+          if (m_eivalues.coeff(i).imag() == 0)
           {
             cc = cdiv(-ra,-sa,w,q);
-            matH(i,n-1) = ei_real(cc);
-            matH(i,n) = ei_imag(cc);
+            matH.coeffRef(i,n-1) = ei_real(cc);
+            matH.coeffRef(i,n) = ei_imag(cc);
           }
           else
           {
             // Solve complex equations
-            x = matH(i,i+1);
-            y = matH(i+1,i);
-            vr = (m_eivalues[i].real() - p) * (m_eivalues[i].real() - p) + m_eivalues[i].imag() * m_eivalues[i].imag() - q * q;
-            vi = (m_eivalues[i].real() - p) * 2.0 * q;
+            x = matH.coeff(i,i+1);
+            y = matH.coeff(i+1,i);
+            vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;
+            vi = (m_eivalues.coeff(i).real() - p) * 2.0 * q;
             if ((vr == 0.0) && (vi == 0.0))
               vr = eps * norm * (ei_abs(w) + ei_abs(q) + ei_abs(x) + ei_abs(y) + ei_abs(z));
 
             cc= cdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
-            matH(i,n-1) = ei_real(cc);
-            matH(i,n) = ei_imag(cc);
+            matH.coeffRef(i,n-1) = ei_real(cc);
+            matH.coeffRef(i,n) = ei_imag(cc);
             if (ei_abs(x) > (ei_abs(z) + ei_abs(q)))
             {
-              matH(i+1,n-1) = (-ra - w * matH(i,n-1) + q * matH(i,n)) / x;
-              matH(i+1,n) = (-sa - w * matH(i,n) - q * matH(i,n-1)) / x;
+              matH.coeffRef(i+1,n-1) = (-ra - w * matH.coeff(i,n-1) + q * matH.coeff(i,n)) / x;
+              matH.coeffRef(i+1,n) = (-sa - w * matH.coeff(i,n) - q * matH.coeff(i,n-1)) / x;
             }
             else
             {
-              cc = cdiv(-r-y*matH(i,n-1),-s-y*matH(i,n),z,q);
-              matH(i+1,n-1) = ei_real(cc);
-              matH(i+1,n) = ei_imag(cc);
+              cc = cdiv(-r-y*matH.coeff(i,n-1),-s-y*matH.coeff(i,n),z,q);
+              matH.coeffRef(i+1,n-1) = ei_real(cc);
+              matH.coeffRef(i+1,n) = ei_imag(cc);
             }
           }
 
           // Overflow control
-          t = std::max(ei_abs(matH(i,n-1)),ei_abs(matH(i,n)));
+          t = std::max(ei_abs(matH.coeff(i,n-1)),ei_abs(matH.coeff(i,n)));
           if ((eps * t) * t > 1)
             matH.block(i, n-1, nn-i, 2) /= t;