the Index types change.

As discussed on the list (too long to explain here).

11 files changed, 96 insertions, 72 deletions

diff --git a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
index d75b1407c..aba31b238 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
@@ -56,6 +56,8 @@ template<typename FunctorType, typename Scalar=double>
 class HybridNonLinearSolver
 {
 public:
+    typedef DenseIndex Index;
+
     HybridNonLinearSolver(FunctorType &_functor)
         : functor(_functor) { nfev=njev=iter = 0;  fnorm= 0.; useExternalScaling=false;}
 
@@ -68,10 +70,10 @@ public:
             , nb_of_superdiagonals(-1)
             , epsfcn(Scalar(0.)) {}
         Scalar factor;
-        int maxfev;   // maximum number of function evaluation
+        Index maxfev;   // maximum number of function evaluation
         Scalar xtol;
-        int nb_of_subdiagonals;
-        int nb_of_superdiagonals;
+        Index nb_of_subdiagonals;
+        Index nb_of_superdiagonals;
         Scalar epsfcn;
     };
     typedef Matrix< Scalar, Dynamic, 1 > FVectorType;
@@ -102,24 +104,24 @@ public:
     FVectorType  fvec, qtf, diag;
     JacobianType fjac;
     UpperTriangularType R;
-    int nfev;
-    int njev;
-    int iter;
+    Index nfev;
+    Index njev;
+    Index iter;
     Scalar fnorm;
     bool useExternalScaling; 
 private:
     FunctorType &functor;
-    int n;
+    Index n;
     Scalar sum;
     bool sing;
     Scalar temp;
     Scalar delta;
     bool jeval;
-    int ncsuc;
+    Index ncsuc;
     Scalar ratio;
     Scalar pnorm, xnorm, fnorm1;
-    int nslow1, nslow2;
-    int ncfail;
+    Index nslow1, nslow2;
+    Index ncfail;
     Scalar actred, prered;
     FVectorType wa1, wa2, wa3, wa4;
 };
@@ -169,7 +171,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveInit(FVectorType  &x)
     if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. )
         return HybridNonLinearSolverSpace::ImproperInputParameters;
     if (useExternalScaling)
-        for (int j = 0; j < n; ++j)
+        for (Index j = 0; j < n; ++j)
             if (diag[j] <= 0.)
                 return HybridNonLinearSolverSpace::ImproperInputParameters;
 
@@ -196,7 +198,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
 {
     assert(x.size()==n); // check the caller is not cheating us
 
-    int j;
+    Index j;
     std::vector<PlanarRotation<Scalar> > v_givens(n), w_givens(n);
 
     jeval = true;
@@ -408,7 +410,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(FVectorType  &
     if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. )
         return HybridNonLinearSolverSpace::ImproperInputParameters;
     if (useExternalScaling)
-        for (int j = 0; j < n; ++j)
+        for (Index j = 0; j < n; ++j)
             if (diag[j] <= 0.)
                 return HybridNonLinearSolverSpace::ImproperInputParameters;
 
@@ -435,7 +437,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
 {
     assert(x.size()==n); // check the caller is not cheating us
 
-    int j;
+    Index j;
     std::vector<PlanarRotation<Scalar> > v_givens(n), w_givens(n);
 
     jeval = true;
diff --git a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
index 3d5b6ea70..63eb66738 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
@@ -63,6 +63,8 @@ public:
     LevenbergMarquardt(FunctorType &_functor)
         : functor(_functor) { nfev = njev = iter = 0;  fnorm = gnorm = 0.; useExternalScaling=false; }
 
+    typedef DenseIndex Index;
+
     struct Parameters {
         Parameters()
             : factor(Scalar(100.))
@@ -72,7 +74,7 @@ public:
             , gtol(Scalar(0.))
             , epsfcn(Scalar(0.)) {}
         Scalar factor;
-        int maxfev;   // maximum number of function evaluation
+        Index maxfev;   // maximum number of function evaluation
         Scalar ftol;
         Scalar xtol;
         Scalar gtol;
@@ -94,7 +96,7 @@ public:
     static LevenbergMarquardtSpace::Status lmdif1(
             FunctorType &functor,
             FVectorType &x,
-            int *nfev,
+            Index *nfev,
             const Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon())
             );
 
@@ -113,17 +115,17 @@ public:
     FVectorType  fvec, qtf, diag;
     JacobianType fjac;
     PermutationMatrix<Dynamic,Dynamic> permutation;
-    int nfev;
-    int njev;
-    int iter;
+    Index nfev;
+    Index njev;
+    Index iter;
     Scalar fnorm, gnorm;
     bool useExternalScaling; 
 
     Scalar lm_param(void) { return par; }
 private:
     FunctorType &functor;
-    int n;
-    int m;
+    Index n;
+    Index m;
     FVectorType wa1, wa2, wa3, wa4;
 
     Scalar par, sum;
@@ -194,7 +196,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType  &x)
         return LevenbergMarquardtSpace::ImproperInputParameters;
 
     if (useExternalScaling)
-        for (int j = 0; j < n; ++j)
+        for (Index j = 0; j < n; ++j)
             if (diag[j] <= 0.)
                 return LevenbergMarquardtSpace::ImproperInputParameters;
 
@@ -219,7 +221,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
     assert(x.size()==n); // check the caller is not cheating us
 
     /* calculate the jacobian matrix. */
-    int df_ret = functor.df(x, fjac);
+    Index df_ret = functor.df(x, fjac);
     if (df_ret<0)
         return LevenbergMarquardtSpace::UserAsked;
     if (df_ret>0)
@@ -237,7 +239,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
     /* to the norms of the columns of the initial jacobian. */
     if (iter == 1) {
         if (!useExternalScaling)
-            for (int j = 0; j < n; ++j)
+            for (Index j = 0; j < n; ++j)
                 diag[j] = (wa2[j]==0.)? 1. : wa2[j];
 
         /* on the first iteration, calculate the norm of the scaled x */
@@ -257,7 +259,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
     /* compute the norm of the scaled gradient. */
     gnorm = 0.;
     if (fnorm != 0.)
-        for (int j = 0; j < n; ++j)
+        for (Index j = 0; j < n; ++j)
             if (wa2[permutation.indices()[j]] != 0.)
                 gnorm = std::max(gnorm, ei_abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
 
@@ -410,7 +412,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType
         return LevenbergMarquardtSpace::ImproperInputParameters;
 
     if (useExternalScaling)
-        for (int j = 0; j < n; ++j)
+        for (Index j = 0; j < n; ++j)
             if (diag[j] <= 0.)
                 return LevenbergMarquardtSpace::ImproperInputParameters;
 
@@ -435,7 +437,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
 {
     assert(x.size()==n); // check the caller is not cheating us
 
-    int i, j;
+    Index i, j;
     bool sing;
 
     /* compute the qr factorization of the jacobian matrix */
@@ -444,7 +446,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
     /* n components in qtf. */
     qtf.fill(0.);
     fjac.fill(0.);
-    int rownb = 2;
+    Index rownb = 2;
     for (i = 0; i < m; ++i) {
         if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked;
         ei_rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);
@@ -471,7 +473,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         fjac.diagonal() = qrfac.hCoeffs();
         permutation = qrfac.colsPermutation();
         // TODO : avoid this:
-        for(int ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
+        for(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
 
         for (j = 0; j < n; ++j) {
             if (fjac(j,j) != 0.) {
@@ -623,12 +625,12 @@ LevenbergMarquardtSpace::Status
 LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
         FunctorType &functor,
         FVectorType  &x,
-        int *nfev,
+        Index *nfev,
         const Scalar tol
         )
 {
-    int n = x.size();
-    int m = functor.values();
+    Index n = x.size();
+    Index m = functor.values();
 
     /* check the input parameters for errors. */
     if (n <= 0 || m < n || tol < 0.)
diff --git a/unsupported/Eigen/src/NonLinearOptimization/chkder.h b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
index 591e8bef7..4cb4fbdef 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/chkder.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
@@ -13,17 +13,19 @@ void ei_chkder(
         Matrix< Scalar, Dynamic, 1 >  &err
         )
 {
+    typedef DenseIndex Index;
+
     const Scalar eps = ei_sqrt(NumTraits<Scalar>::epsilon());
     const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon();
     const Scalar epslog = chkder_log10e * ei_log(eps);
     Scalar temp;
 
-    const int m = fvec.size(), n = x.size();
+    const Index m = fvec.size(), n = x.size();
 
     if (mode != 2) {
         /* mode = 1. */
         xp.resize(n);
-        for (int j = 0; j < n; ++j) {
+        for (Index j = 0; j < n; ++j) {
             temp = eps * ei_abs(x[j]);
             if (temp == 0.)
                 temp = eps;
@@ -33,13 +35,13 @@ void ei_chkder(
     else {
         /* mode = 2. */
         err.setZero(m); 
-        for (int j = 0; j < n; ++j) {
+        for (Index j = 0; j < n; ++j) {
             temp = ei_abs(x[j]);
             if (temp == 0.)
                 temp = 1.;
             err += temp * fjac.col(j);
         }
-        for (int i = 0; i < m; ++i) {
+        for (Index i = 0; i < m; ++i) {
             temp = 1.;
             if (fvec[i] != 0. && fvecp[i] != 0. && ei_abs(fvecp[i] - fvec[i]) >= epsf * ei_abs(fvec[i]))
                 temp = eps * ei_abs((fvecp[i] - fvec[i]) / eps - err[i]) / (ei_abs(fvec[i]) + ei_abs(fvecp[i]));
diff --git a/unsupported/Eigen/src/NonLinearOptimization/covar.h b/unsupported/Eigen/src/NonLinearOptimization/covar.h
index 7cfaa22d4..104898a30 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/covar.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/covar.h
@@ -5,13 +5,15 @@ void ei_covar(
         const VectorXi &ipvt,
         Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon()) )
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
-    int i, j, k, l, ii, jj;
-    int sing;
+    Index i, j, k, l, ii, jj;
+    bool sing;
     Scalar temp;
 
     /* Function Body */
-    const int n = r.cols();
+    const Index n = r.cols();
     const Scalar tolr = tol * ei_abs(r(0,0));
     Matrix< Scalar, Dynamic, 1 > wa(n);
     assert(ipvt.size()==n);
diff --git a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
index 9c1d38dea..ab01d5c47 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
@@ -7,15 +7,17 @@ void ei_dogleg(
         Scalar delta,
         Matrix< Scalar, Dynamic, 1 >  &x)
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
-    int i, j;
+    Index i, j;
     Scalar sum, temp, alpha, bnorm;
     Scalar gnorm, qnorm;
     Scalar sgnorm;
 
     /* Function Body */
     const Scalar epsmch = NumTraits<Scalar>::epsilon();
-    const int n = qrfac.cols();
+    const Index n = qrfac.cols();
     assert(n==qtb.size());
     assert(n==x.size());
     assert(n==diag.size());
diff --git a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
index 3dc1e8070..74cf53b90 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
@@ -1,24 +1,26 @@
 
 template<typename FunctorType, typename Scalar>
-int ei_fdjac1(
+DenseIndex ei_fdjac1(
         const FunctorType &Functor,
         Matrix< Scalar, Dynamic, 1 >  &x,
         Matrix< Scalar, Dynamic, 1 >  &fvec,
         Matrix< Scalar, Dynamic, Dynamic > &fjac,
-        int ml, int mu,
+        DenseIndex ml, DenseIndex mu,
         Scalar epsfcn)
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
     Scalar h;
-    int j, k;
+    Index j, k;
     Scalar eps, temp;
-    int msum;
+    Index msum;
     int iflag;
-    int start, length;
+    Index start, length;
 
     /* Function Body */
     const Scalar epsmch = NumTraits<Scalar>::epsilon();
-    const int n = x.size();
+    const Index n = x.size();
     assert(fvec.size()==n);
     Matrix< Scalar, Dynamic, 1 >  wa1(n);
     Matrix< Scalar, Dynamic, 1 >  wa2(n);
@@ -57,7 +59,7 @@ int ei_fdjac1(
                 h = eps * ei_abs(wa2[j]);
                 if (h == 0.) h = eps;
                 fjac.col(j).setZero();
-                start = std::max(0,j-mu);
+                start = std::max<Index>(0,j-mu);
                 length = std::min(n-1, j+ml) - start + 1;
                 fjac.col(j).segment(start, length) = ( wa1.segment(start, length)-fvec.segment(start, length))/h;
             }
diff --git a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
index 850011912..27138de96 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
@@ -9,11 +9,13 @@ void ei_lmpar(
         Scalar &par,
         Matrix< Scalar, Dynamic, 1 >  &x)
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
-    int i, j, l;
+    Index i, j, l;
     Scalar fp;
     Scalar parc, parl;
-    int iter;
+    Index iter;
     Scalar temp, paru;
     Scalar gnorm;
     Scalar dxnorm;
@@ -21,7 +23,7 @@ void ei_lmpar(
 
     /* Function Body */
     const Scalar dwarf = std::numeric_limits<Scalar>::min();
-    const int n = r.cols();
+    const Index n = r.cols();
     assert(n==diag.size());
     assert(n==qtb.size());
     assert(n==x.size());
@@ -30,7 +32,7 @@ void ei_lmpar(
 
     /* compute and store in x the gauss-newton direction. if the */
     /* jacobian is rank-deficient, obtain a least squares solution. */
-    int nsing = n-1;
+    Index nsing = n-1;
     wa1 = qtb;
     for (j = 0; j < n; ++j) {
         if (r(j,j) == 0. && nsing == n-1)
@@ -163,11 +165,13 @@ void ei_lmpar2(
         Matrix< Scalar, Dynamic, 1 >  &x)
 
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
-    int j;
+    Index j;
     Scalar fp;
     Scalar parc, parl;
-    int iter;
+    Index iter;
     Scalar temp, paru;
     Scalar gnorm;
     Scalar dxnorm;
@@ -175,7 +179,7 @@ void ei_lmpar2(
 
     /* Function Body */
     const Scalar dwarf = std::numeric_limits<Scalar>::min();
-    const int n = qr.matrixQR().cols();
+    const Index n = qr.matrixQR().cols();
     assert(n==diag.size());
     assert(n==qtb.size());
 
@@ -184,8 +188,8 @@ void ei_lmpar2(
     /* compute and store in x the gauss-newton direction. if the */
     /* jacobian is rank-deficient, obtain a least squares solution. */
 
-//    const int rank = qr.nonzeroPivots(); // exactly double(0.)
-    const int rank = qr.rank(); // use a threshold
+//    const Index rank = qr.nonzeroPivots(); // exactly double(0.)
+    const Index rank = qr.rank(); // use a threshold
     wa1 = qtb;
     wa1.tail(n-rank).setZero();
     qr.matrixQR().topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(wa1.head(rank));
@@ -262,7 +266,7 @@ void ei_lmpar2(
         for (j = 0; j < n; ++j) {
             wa1[j] /= sdiag[j];
             temp = wa1[j];
-            for (int i = j+1; i < n; ++i)
+            for (Index i = j+1; i < n; ++i)
                 wa1[i] -= s(i,j) * temp;
         }
         temp = wa1.blueNorm();
diff --git a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
index 205d934bd..bce8a4441 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
@@ -11,10 +11,12 @@ void ei_qrsolv(
         Matrix< Scalar, Dynamic, 1 >  &sdiag)
 
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
-    int i, j, k, l;
+    Index i, j, k, l;
     Scalar temp;
-    int n = s.cols();
+    Index n = s.cols();
     Matrix< Scalar, Dynamic, 1 >  wa(n);
     PlanarRotation<Scalar> givens;
 
@@ -67,7 +69,7 @@ void ei_qrsolv(
 
     /*     solve the triangular system for z. if the system is */
     /*     singular, then obtain a least squares solution. */
-    int nsing;
+    Index nsing;
     for (nsing=0; nsing<n && sdiag[nsing]!=0; nsing++);
 
     wa.tail(n-nsing).setZero();
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
index 855cb7a1b..ad319d9eb 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
@@ -2,18 +2,20 @@
 // TODO : move this to GivensQR once there's such a thing in Eigen
 
 template <typename Scalar>
-void ei_r1mpyq(int m, int n, Scalar *a, const std::vector<PlanarRotation<Scalar> > &v_givens, const std::vector<PlanarRotation<Scalar> > &w_givens)
+void ei_r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<PlanarRotation<Scalar> > &v_givens, const std::vector<PlanarRotation<Scalar> > &w_givens)
 {
+    typedef DenseIndex Index;
+
     /*     apply the first set of givens rotations to a. */
-    for (int j = n-2; j>=0; --j)
-        for (int i = 0; i<m; ++i) {
+    for (Index j = n-2; j>=0; --j)
+        for (Index i = 0; i<m; ++i) {
             Scalar temp = v_givens[j].c() * a[i+m*j] - v_givens[j].s() * a[i+m*(n-1)];
             a[i+m*(n-1)] = v_givens[j].s() * a[i+m*j] + v_givens[j].c() * a[i+m*(n-1)];
             a[i+m*j] = temp;
         }
     /*     apply the second set of givens rotations to a. */
-    for (int j = 0; j<n-1; ++j)
-        for (int i = 0; i<m; ++i) {
+    for (Index j = 0; j<n-1; ++j)
+        for (Index i = 0; i<m; ++i) {
             Scalar temp = w_givens[j].c() * a[i+m*j] + w_givens[j].s() * a[i+m*(n-1)];
             a[i+m*(n-1)] = -w_givens[j].s() * a[i+m*j] + w_givens[j].c() * a[i+m*(n-1)];
             a[i+m*j] = temp;
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
index 3d8978837..e01d02910 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
@@ -9,10 +9,12 @@ void ei_r1updt(
         Matrix< Scalar, Dynamic, 1> &w,
         bool *sing)
 {
+    typedef DenseIndex Index;
+
     /* Local variables */
-    const int m = s.rows();
-    const int n = s.cols();
-    int i, j=1;
+    const Index m = s.rows();
+    const Index n = s.cols();
+    Index i, j=1;
     Scalar temp;
     PlanarRotation<Scalar> givens;
 
diff --git a/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
index b0bf72923..aa0bf7d0f 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
@@ -6,7 +6,9 @@ void ei_rwupdt(
         Matrix< Scalar, Dynamic, 1>  &b,
         Scalar alpha)
 {
-    const int n = r.cols();
+    typedef DenseIndex Index;
+
+    const Index n = r.cols();
     assert(r.rows()>=n);
     std::vector<PlanarRotation<Scalar> > givens(n);
 
@@ -14,12 +16,12 @@ void ei_rwupdt(
     Scalar temp, rowj;
 
     /* Function Body */
-    for (int j = 0; j < n; ++j) {
+    for (Index j = 0; j < n; ++j) {
         rowj = w[j];
 
         /* apply the previous transformations to */
         /* r(i,j), i=0,1,...,j-1, and to w(j). */
-        for (int i = 0; i < j; ++i) {
+        for (Index i = 0; i < j; ++i) {
             temp = givens[i].c() * r(i,j) + givens[i].s() * rowj;
             rowj = -givens[i].s() * r(i,j) + givens[i].c() * rowj;
             r(i,j) = temp;