Merged latest updates from the Eigen trunk.

Eigen/Core

@@ -42,7 +42,7 @@
   #define EIGEN_USING_STD_MATH(FUNC) using std::FUNC;
 #endif
 
-#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__)
+#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(EIGEN_EXCEPTIONS)
   #define EIGEN_EXCEPTIONS
 #endif
 

Eigen/SVD

@@ -21,6 +21,7 @@
   */
 
 #include "src/misc/Solve.h"
+#include "src/SVD/SVDBase.h"
 #include "src/SVD/JacobiSVD.h"
 #if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
 #include "src/SVD/JacobiSVD_MKL.h"

Eigen/src/Core/ArrayWrapper.h

@@ -29,6 +29,11 @@ struct traits<ArrayWrapper<ExpressionType> >
   : public traits<typename remove_all<typename ExpressionType::Nested>::type >
 {
   typedef ArrayXpr XprKind;
+  // Let's remove NestByRefBit
+  enum {
+    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
+    Flags = Flags0 & ~NestByRefBit
+  };
 };
 }
 
@@ -166,6 +171,11 @@ struct traits<MatrixWrapper<ExpressionType> >
  : public traits<typename remove_all<typename ExpressionType::Nested>::type >
 {
   typedef MatrixXpr XprKind;
+  // Let's remove NestByRefBit
+  enum {
+    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,
+    Flags = Flags0 & ~NestByRefBit
+  };
 };
 }
 

Eigen/src/Core/GeneralProduct.h

@@ -231,7 +231,7 @@ EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest&
   // FIXME not very good if rhs is real and lhs complex while alpha is real too
   const Index cols = dest.cols();
   for (Index j=0; j<cols; ++j)
-    func(dest.col(j), prod.rhs().coeff(j) * prod.lhs());
+    func(dest.col(j), prod.rhs().coeff(0,j) * prod.lhs());
 }
 
 // Row major
@@ -242,7 +242,7 @@ EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest&
   // FIXME not very good if lhs is real and rhs complex while alpha is real too
   const Index rows = dest.rows();
   for (Index i=0; i<rows; ++i)
-    func(dest.row(i), prod.lhs().coeff(i) * prod.rhs());
+    func(dest.row(i), prod.lhs().coeff(i,0) * prod.rhs());
 }
 
 template<typename Lhs, typename Rhs>

Eigen/src/Core/MathFunctions.h

@@ -12,6 +12,15 @@
 
 namespace Eigen {
 
+// On WINCE, std::abs is defined for int only, so let's defined our own overloads:
+// This issue has been confirmed with MSVC 2008 only, but the issue might exist for more recent versions too.
+#if defined(_WIN32_WCE) && defined(_MSC_VER) && _MSC_VER<=1500
+long        abs(long        x) { return (labs(x));  }
+double      abs(double      x) { return (fabs(x));  }
+float       abs(float       x) { return (fabsf(x)); }
+long double abs(long double x) { return (fabsl(x)); }
+#endif
+  
 namespace internal {
 
 /** \internal \struct global_math_functions_filtering_base
@@ -308,10 +317,17 @@ struct hypot_impl
     using std::sqrt;
     RealScalar _x = abs(x);
     RealScalar _y = abs(y);
-    RealScalar p = (max)(_x, _y);
+    Scalar p, qp;
-    if(p==RealScalar(0)) return 0;
+    if(_x>_y)
-    RealScalar q = (min)(_x, _y);
+    {
-    RealScalar qp = q/p;
+      p = _x;
+      qp = _y / p;
+    }
+    else
+    {
+      p = _y;
+      qp = _x / p;
+    }
     return p * sqrt(RealScalar(1) + qp*qp);
   }
 };

Eigen/src/Core/MatrixBase.h

@@ -81,6 +81,7 @@ template<typename Derived> class MatrixBase
     using Base::operator-=;
     using Base::operator*=;
     using Base::operator/=;
+    using Base::operator*;
 
     typedef typename Base::CoeffReturnType CoeffReturnType;
     typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;

Eigen/src/Core/Redux.h

@@ -207,7 +207,7 @@ struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
     const Index packetSize = packet_traits<Scalar>::size;
     const Index alignedStart = internal::first_aligned(mat);
     enum {
-      alignment = bool(Derived::Flags & DirectAccessBit) || bool(Derived::Flags & AlignedBit)
+      alignment = (bool(Derived::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) || bool(Derived::Flags & AlignedBit)
                 ? Aligned : Unaligned
     };
     const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);

Eigen/src/Core/SelfCwiseBinaryOp.h

@@ -209,15 +209,9 @@ inline Derived& ArrayBase<Derived>::operator-=(const Scalar& other)
 template<typename Derived>
 inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
 {
-  typedef typename internal::conditional<NumTraits<Scalar>::IsInteger,
-                                        internal::scalar_quotient_op<Scalar>,
-                                        internal::scalar_product_op<Scalar> >::type BinOp;
   typedef typename Derived::PlainObject PlainObject;
-  SelfCwiseBinaryOp<BinOp, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
+  SelfCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, Derived, typename PlainObject::ConstantReturnType> tmp(derived());
-  Scalar actual_other;
+  tmp = PlainObject::Constant(rows(),cols(), other);
-  if(NumTraits<Scalar>::IsInteger)  actual_other = other;
-  else                              actual_other = Scalar(1)/other;
-  tmp = PlainObject::Constant(rows(),cols(), actual_other);
   return derived();
 }
 

Eigen/src/Core/StableNorm.h

@@ -20,7 +20,7 @@ inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& sc
   using std::max;
   Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
   
-  if (maxCoeff>scale)
+  if(maxCoeff>scale)
   {
     ssq = ssq * numext::abs2(scale/maxCoeff);
     Scalar tmp = Scalar(1)/maxCoeff;
@@ -29,12 +29,21 @@ inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& sc
       invScale = NumTraits<Scalar>::highest();
       scale = Scalar(1)/invScale;
     }
+    else if(maxCoeff>NumTraits<Scalar>::highest()) // we got a INF
+    {
+      invScale = Scalar(1);
+      scale = maxCoeff;
+    }
     else
     {
       scale = maxCoeff;
       invScale = tmp;
     }
   }
+  else if(maxCoeff!=maxCoeff) // we got a NaN
+  {
+    scale = maxCoeff;
+  }
   
   // TODO if the maxCoeff is much much smaller than the current scale,
   // then we can neglect this sub vector
@@ -55,7 +64,7 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   using std::abs;
   const Derived& vec(_vec.derived());
   static bool initialized = false;
-  static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
+  static RealScalar b1, b2, s1m, s2m, rbig, relerr;
   if(!initialized)
   {
     int ibeta, it, iemin, iemax, iexp;
@@ -84,7 +93,6 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
     iexp  = - ((iemax+it)/2);
     s2m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for upper range
 
-    overfl  = rbig*s2m;                                             // overflow boundary for abig
     eps     = RealScalar(pow(double(ibeta), 1-it));
     relerr  = sqrt(eps);                                            // tolerance for neglecting asml
     initialized = true;
@@ -101,13 +109,13 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
     else if(ax < b1) asml += numext::abs2(ax*s1m);
     else             amed += numext::abs2(ax);
   }
+  if(amed!=amed)
+    return amed;  // we got a NaN
   if(abig > RealScalar(0))
   {
     abig = sqrt(abig);
-    if(abig > overfl)
+    if(abig > rbig) // overflow, or *this contains INF values
-    {
+      return abig;  // return INF
-      return rbig;
-    }
     if(amed > RealScalar(0))
     {
       abig = abig/s2m;

Eigen/src/Core/arch/AVX/PacketMath.h

@@ -143,7 +143,7 @@ template<> EIGEN_STRONG_INLINE Packet8f pmadd(const Packet8f& a, const Packet8f&
   // so let's enforce it to generate a vfmadd231ps instruction since the most common use case is to accumulate
   // the result of the product.
   Packet8f res = c;
-  asm("vfmadd231ps %[a], %[b], %[c]" : [c] "+x" (res) : [a] "x" (a), [b] "x" (b));
+  __asm__("vfmadd231ps %[a], %[b], %[c]" : [c] "+x" (res) : [a] "x" (a), [b] "x" (b));
   return res;
 #else
   return _mm256_fmadd_ps(a,b,c);
@@ -153,7 +153,7 @@ template<> EIGEN_STRONG_INLINE Packet4d pmadd(const Packet4d& a, const Packet4d&
 #if defined(__clang__) || defined(__GNUC__)
   // see above
   Packet4d res = c;
-  asm("vfmadd231pd %[a], %[b], %[c]" : [c] "+x" (res) : [a] "x" (a), [b] "x" (b));
+  __asm__("vfmadd231pd %[a], %[b], %[c]" : [c] "+x" (res) : [a] "x" (a), [b] "x" (b));
   return res;
 #else
   return _mm256_fmadd_pd(a,b,c);

Eigen/src/Core/arch/NEON/PacketMath.h

@@ -52,12 +52,12 @@ typedef uint32x4_t  Packet4ui;
 
 // arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
 // which available on LLVM and GCC (at least)
-#if (defined(__has_builtin) && __has_builtin(__builtin_prefetch)) || defined(__GNUC__)
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || defined(__GNUC__)
   #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
 #elif defined __pld
   #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
 #elif !defined(__aarch64__)
-  #define EIGEN_ARM_PREFETCH(ADDR) asm volatile ( "   pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+  #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ( "   pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
 #else
   // by default no explicit prefetching
   #define EIGEN_ARM_PREFETCH(ADDR)

Eigen/src/Core/functors/BinaryFunctors.h

@@ -167,9 +167,17 @@ template<typename Scalar> struct scalar_hypot_op {
     EIGEN_USING_STD_MATH(max);
     EIGEN_USING_STD_MATH(min);
     using std::sqrt;
-    Scalar p = (max)(_x, _y);
+    Scalar p, qp;
-    Scalar q = (min)(_x, _y);
+    if(_x>_y)
-    Scalar qp = q/p;
+    {
+      p = _x;
+      qp = _y / p;
+    }
+    else
+    {
+      p = _y;
+      qp = _x / p;
+    }
     return p * sqrt(Scalar(1) + qp*qp);
   }
 };

Eigen/src/Core/products/GeneralMatrixMatrix_MKL.h

@@ -53,6 +53,8 @@ template< \
   int RhsStorageOrder, bool ConjugateRhs> \
 struct general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor> \
 { \
+typedef gebp_traits<EIGTYPE,EIGTYPE> Traits; \
+\
 static void run(Index rows, Index cols, Index depth, \
   const EIGTYPE* _lhs, Index lhsStride, \
   const EIGTYPE* _rhs, Index rhsStride, \

Eigen/src/Core/products/TriangularMatrixMatrix_MKL.h

@@ -109,7 +109,7 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
    if (rows != depth) { \
 \
-     int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
+     int nthr = mkl_domain_get_max_threads(EIGEN_MKL_DOMAIN_BLAS); \
 \
      if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
      /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
@@ -223,7 +223,7 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
    if (cols != depth) { \
 \
-     int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
+     int nthr = mkl_domain_get_max_threads(EIGEN_MKL_DOMAIN_BLAS); \
 \
      if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
      /* Most likely no benefit to call TRMM or GEMM from MKL*/ \

Eigen/src/Core/util/MKL_support.h

@@ -76,6 +76,38 @@
 #include <mkl_lapacke.h>
 #define EIGEN_MKL_VML_THRESHOLD 128
 
+/* MKL_DOMAIN_BLAS, etc are defined only in 10.3 update 7 */
+/* MKL_BLAS, etc are not defined in 11.2 */
+#ifdef MKL_DOMAIN_ALL
+#define EIGEN_MKL_DOMAIN_ALL MKL_DOMAIN_ALL
+#else
+#define EIGEN_MKL_DOMAIN_ALL MKL_ALL
+#endif
+
+#ifdef MKL_DOMAIN_BLAS
+#define EIGEN_MKL_DOMAIN_BLAS MKL_DOMAIN_BLAS
+#else
+#define EIGEN_MKL_DOMAIN_BLAS MKL_BLAS
+#endif
+
+#ifdef MKL_DOMAIN_FFT
+#define EIGEN_MKL_DOMAIN_FFT MKL_DOMAIN_FFT
+#else
+#define EIGEN_MKL_DOMAIN_FFT MKL_FFT
+#endif
+
+#ifdef MKL_DOMAIN_VML
+#define EIGEN_MKL_DOMAIN_VML MKL_DOMAIN_VML
+#else
+#define EIGEN_MKL_DOMAIN_VML MKL_VML
+#endif
+
+#ifdef MKL_DOMAIN_PARDISO
+#define EIGEN_MKL_DOMAIN_PARDISO MKL_DOMAIN_PARDISO
+#else
+#define EIGEN_MKL_DOMAIN_PARDISO MKL_PARDISO
+#endif
+
 namespace Eigen {
 
 typedef std::complex<double> dcomplex;

Eigen/src/Core/util/Macros.h

@@ -107,6 +107,13 @@
 #define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
 #endif
 
+// Cross compiler wrapper around LLVM's __has_builtin
+#ifdef __has_builtin
+#  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
+#else
+#  define EIGEN_HAS_BUILTIN(x) 0
+#endif
+
 // A Clang feature extension to determine compiler features.
 // We use it to determine 'cxx_rvalue_references'
 #ifndef __has_feature
@@ -277,7 +284,7 @@ namespace Eigen {
 
 #if !defined(EIGEN_ASM_COMMENT)
   #if (defined __GNUC__) && ( defined(__i386__) || defined(__x86_64__) )
-    #define EIGEN_ASM_COMMENT(X)  asm("#" X)
+    #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
   #else
     #define EIGEN_ASM_COMMENT(X)
   #endif

Eigen/src/Core/util/Memory.h

@@ -64,7 +64,7 @@
 // Currently, let's include it only on unix systems:
 #if defined(__unix__) || defined(__unix)
   #include <unistd.h>
-  #if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
+  #if ((defined __QNXNTO__) || (defined _GNU_SOURCE) || (defined __PGI) || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
     #define EIGEN_HAS_POSIX_MEMALIGN 1
   #endif
 #endif

Eigen/src/Core/util/XprHelper.h

@@ -383,13 +383,21 @@ struct special_scalar_op_base<Derived,Scalar,OtherScalar,true>  : public DenseCo
   const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
   operator*(const OtherScalar& scalar) const
   {
+#ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
+    EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
+#endif
     return CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
       (*static_cast<const Derived*>(this), scalar_multiple2_op<Scalar,OtherScalar>(scalar));
   }
 
   inline friend const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
   operator*(const OtherScalar& scalar, const Derived& matrix)
-  { return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar); }
+  {
+#ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
+    EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
+#endif
+    return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar);
+  }
 };
 
 template<typename XprType, typename CastType> struct cast_return_type

Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h

@@ -605,7 +605,6 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
     if(computeEigenvectors)
     {
       Scalar safeNorm2 = Eigen::NumTraits<Scalar>::epsilon();
-      safeNorm2 *= safeNorm2;
       if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())
       {
         eivecs.setIdentity();
@@ -619,7 +618,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
         Scalar d0 = eivals(2) - eivals(1);
         Scalar d1 = eivals(1) - eivals(0);
         int k =  d0 > d1 ? 2 : 0;
-        d0 = d0 > d1 ? d1 : d0;
+        d0 = d0 > d1 ? d0 : d1;
 
         tmp.diagonal().array () -= eivals(k);
         VectorType cross;
@@ -627,19 +626,25 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
         n = (cross = tmp.row(0).cross(tmp.row(1))).squaredNorm();
 
         if(n>safeNorm2)
+        {
           eivecs.col(k) = cross / sqrt(n);
+        }
         else
         {
           n = (cross = tmp.row(0).cross(tmp.row(2))).squaredNorm();
 
           if(n>safeNorm2)
+          {
             eivecs.col(k) = cross / sqrt(n);
+          }
           else
           {
             n = (cross = tmp.row(1).cross(tmp.row(2))).squaredNorm();
 
             if(n>safeNorm2)
+            {
               eivecs.col(k) = cross / sqrt(n);
+            }
             else
             {
               // the input matrix and/or the eigenvaues probably contains some inf/NaN,
@@ -659,12 +664,16 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
         tmp.diagonal().array() -= eivals(1);
 
         if(d0<=Eigen::NumTraits<Scalar>::epsilon())
+        {
           eivecs.col(1) = eivecs.col(k).unitOrthogonal();
+        }
         else
         {
-          n = (cross = eivecs.col(k).cross(tmp.row(0).normalized())).squaredNorm();
+          n = (cross = eivecs.col(k).cross(tmp.row(0))).squaredNorm();
           if(n>safeNorm2)
+          {
             eivecs.col(1) = cross / sqrt(n);
+          }
           else
           {
             n = (cross = eivecs.col(k).cross(tmp.row(1))).squaredNorm();
@@ -678,13 +687,14 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
               else
               {
                 // we should never reach this point,
-                // if so the last two eigenvalues are likely to ve very closed to each other
+                // if so the last two eigenvalues are likely to be very close to each other
                 eivecs.col(1) = eivecs.col(k).unitOrthogonal();
               }
             }
           }
 
           // make sure that eivecs[1] is orthogonal to eivecs[2]
+          // FIXME: this step should not be needed
           Scalar d = eivecs.col(1).dot(eivecs.col(k));
           eivecs.col(1) = (eivecs.col(1) - d * eivecs.col(k)).normalized();
         }

Eigen/src/Geometry/Homogeneous.h

@@ -120,7 +120,7 @@ template<typename MatrixType,int _Direction> class Homogeneous
   * Example: \include MatrixBase_homogeneous.cpp
   * Output: \verbinclude MatrixBase_homogeneous.out
   *
-  * \sa class Homogeneous
+  * \sa VectorwiseOp::homogeneous(), class Homogeneous
   */
 template<typename Derived>
 inline typename MatrixBase<Derived>::HomogeneousReturnType
@@ -137,7 +137,7 @@ MatrixBase<Derived>::homogeneous() const
   * Example: \include VectorwiseOp_homogeneous.cpp
   * Output: \verbinclude VectorwiseOp_homogeneous.out
   *
-  * \sa MatrixBase::homogeneous() */
+  * \sa MatrixBase::homogeneous(), class Homogeneous */
 template<typename ExpressionType, int Direction>
 inline Homogeneous<ExpressionType,Direction>
 VectorwiseOp<ExpressionType,Direction>::homogeneous() const

Eigen/src/IterativeLinearSolvers/BiCGSTAB.h

@@ -39,7 +39,6 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
   int maxIters = iters;
 
   int n = mat.cols();
-  x = precond.solve(x);
   VectorType r  = rhs - mat * x;
   VectorType r0 = r;
   

Eigen/src/SVD/JacobiSVD.h

@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -424,24 +425,31 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   JacobiRotation<RealScalar> rot1;
   RealScalar t = m.coeff(0,0) + m.coeff(1,1);
   RealScalar d = m.coeff(1,0) - m.coeff(0,1);
-  if(t == RealScalar(0))
+  
+  if(d == RealScalar(0))
   {
-    rot1.c() = RealScalar(0);
+    rot1.s() = RealScalar(0);
-    rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
+    rot1.c() = RealScalar(1);
   }
   else
   {
-    RealScalar t2d2 = numext::hypot(t,d);
+    // If d!=0, then t/d cannot overflow because the magnitude of the
-    rot1.c() = abs(t)/t2d2;
+    // entries forming d are not too small compared to the ones forming t.
-    rot1.s() = d/t2d2;
+    RealScalar u = t / d;
-    if(t<RealScalar(0))
+    rot1.s() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
-      rot1.s() = -rot1.s();
+    rot1.c() = rot1.s() * u;
   }
   m.applyOnTheLeft(0,1,rot1);
   j_right->makeJacobi(m,0,1);
   *j_left  = rot1 * j_right->transpose();
 }
 
+template<typename _MatrixType, int QRPreconditioner> 
+struct traits<JacobiSVD<_MatrixType,QRPreconditioner> >
+{
+  typedef _MatrixType MatrixType;
+};
+
 } // end namespace internal
 
 /** \ingroup SVD_Module
@@ -498,7 +506,9 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   * \sa MatrixBase::jacobiSvd()
   */
 template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
+ : public SVDBase<JacobiSVD<_MatrixType,QRPreconditioner> >
 {
+    typedef SVDBase<JacobiSVD> Base;
   public:
 
     typedef _MatrixType MatrixType;
@@ -515,13 +525,10 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       MatrixOptions = MatrixType::Options
     };
 
-    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
+    typedef typename Base::MatrixUType MatrixUType;
-                   MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
+    typedef typename Base::MatrixVType MatrixVType;
-            MatrixUType;
+    typedef typename Base::SingularValuesType SingularValuesType;
-    typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
+    
-                   MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
-            MatrixVType;
-    typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
     typedef typename internal::plain_row_type<MatrixType>::type RowType;
     typedef typename internal::plain_col_type<MatrixType>::type ColType;
     typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
@@ -534,11 +541,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       * perform decompositions via JacobiSVD::compute(const MatrixType&).
       */
     JacobiSVD()
-      : m_isInitialized(false),
-        m_isAllocated(false),
-        m_usePrescribedThreshold(false),
-        m_computationOptions(0),
-        m_rows(-1), m_cols(-1), m_diagSize(0)
     {}
 
 
@@ -549,11 +551,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       * \sa JacobiSVD()
       */
     JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
-      : m_isInitialized(false),
-        m_isAllocated(false),
-        m_usePrescribedThreshold(false),
-        m_computationOptions(0),
-        m_rows(-1), m_cols(-1)
     {
       allocate(rows, cols, computationOptions);
     }
@@ -569,11 +566,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
      * available with the (non-default) FullPivHouseholderQR preconditioner.
      */
     JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
-      : m_isInitialized(false),
-        m_isAllocated(false),
-        m_usePrescribedThreshold(false),
-        m_computationOptions(0),
-        m_rows(-1), m_cols(-1)
     {
       compute(matrix, computationOptions);
     }
@@ -601,54 +593,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       return compute(matrix, m_computationOptions);
     }
 
-    /** \returns the \a U matrix.
-     *
-     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
-     * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
-     *
-     * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
-     *
-     * This method asserts that you asked for \a U to be computed.
-     */
-    const MatrixUType& matrixU() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
-      return m_matrixU;
-    }
-
-    /** \returns the \a V matrix.
-     *
-     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
-     * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
-     *
-     * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
-     *
-     * This method asserts that you asked for \a V to be computed.
-     */
-    const MatrixVType& matrixV() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
-      return m_matrixV;
-    }
-
-    /** \returns the vector of singular values.
-     *
-     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
-     * returned vector has size \a m.  Singular values are always sorted in decreasing order.
-     */
-    const SingularValuesType& singularValues() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      return m_singularValues;
-    }
-
-    /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
-    inline bool computeU() const { return m_computeFullU || m_computeThinU; }
-    /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
-    inline bool computeV() const { return m_computeFullV || m_computeThinV; }
-
     /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
       *
       * \param b the right-hand-side of the equation to solve.
@@ -667,93 +611,30 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
     }
     
-    /** \returns the number of singular values that are not exactly 0 */
+    using Base::computeU;
-    Index nonzeroSingularValues() const
+    using Base::computeV;
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      return m_nonzeroSingularValues;
-    }
-    
-    /** \returns the rank of the matrix of which \c *this is the SVD.
-      *
-      * \note This method has to determine which singular values should be considered nonzero.
-      *       For that, it uses the threshold value that you can control by calling
-      *       setThreshold(const RealScalar&).
-      */
-    inline Index rank() const
-    {
-      using std::abs;
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      if(m_singularValues.size()==0) return 0;
-      RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
-      Index i = m_nonzeroSingularValues-1;
-      while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
-      return i+1;
-    }
-    
-    /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
-      * which need to determine when singular values are to be considered nonzero.
-      * This is not used for the SVD decomposition itself.
-      *
-      * When it needs to get the threshold value, Eigen calls threshold().
-      * The default is \c NumTraits<Scalar>::epsilon()
-      *
-      * \param threshold The new value to use as the threshold.
-      *
-      * A singular value will be considered nonzero if its value is strictly greater than
-      *  \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
-      *
-      * If you want to come back to the default behavior, call setThreshold(Default_t)
-      */
-    JacobiSVD& setThreshold(const RealScalar& threshold)
-    {
-      m_usePrescribedThreshold = true;
-      m_prescribedThreshold = threshold;
-      return *this;
-    }
-
-    /** Allows to come back to the default behavior, letting Eigen use its default formula for
-      * determining the threshold.
-      *
-      * You should pass the special object Eigen::Default as parameter here.
-      * \code svd.setThreshold(Eigen::Default); \endcode
-      *
-      * See the documentation of setThreshold(const RealScalar&).
-      */
-    JacobiSVD& setThreshold(Default_t)
-    {
-      m_usePrescribedThreshold = false;
-      return *this;
-    }
-
-    /** Returns the threshold that will be used by certain methods such as rank().
-      *
-      * See the documentation of setThreshold(const RealScalar&).
-      */
-    RealScalar threshold() const
-    {
-      eigen_assert(m_isInitialized || m_usePrescribedThreshold);
-      return m_usePrescribedThreshold ? m_prescribedThreshold
-                                      : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
-    }
-
-    inline Index rows() const { return m_rows; }
-    inline Index cols() const { return m_cols; }
     
   private:
     void allocate(Index rows, Index cols, unsigned int computationOptions);
 
   protected:
-    MatrixUType m_matrixU;
+    using Base::m_matrixU;
-    MatrixVType m_matrixV;
+    using Base::m_matrixV;
-    SingularValuesType m_singularValues;
+    using Base::m_singularValues;
+    using Base::m_isInitialized;
+    using Base::m_isAllocated;
+    using Base::m_usePrescribedThreshold;
+    using Base::m_computeFullU;
+    using Base::m_computeThinU;
+    using Base::m_computeFullV;
+    using Base::m_computeThinV;
+    using Base::m_computationOptions;
+    using Base::m_nonzeroSingularValues;
+    using Base::m_rows;
+    using Base::m_cols;
+    using Base::m_diagSize;
+    using Base::m_prescribedThreshold;
     WorkMatrixType m_workMatrix;
-    bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
-    bool m_computeFullU, m_computeThinU;
-    bool m_computeFullV, m_computeThinV;
-    unsigned int m_computationOptions;
-    Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
-    RealScalar m_prescribedThreshold;
 
     template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
     friend struct internal::svd_precondition_2x2_block_to_be_real;
@@ -861,7 +742,8 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
         EIGEN_USING_STD_MATH(max);
         RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
                                                                        abs(m_workMatrix.coeff(q,q))));
-        if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)
+        // We compare both values to threshold instead of calling max to be robust to NaN (See bug 791)
+        if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
         {
           finished = false;
 

Eigen/src/SVD/SVDBase.h

@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
 // Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
@@ -12,8 +13,8 @@
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
-#ifndef EIGEN_SVD_H
+#ifndef EIGEN_SVDBASE_H
-#define EIGEN_SVD_H
+#define EIGEN_SVDBASE_H
 
 namespace Eigen {
 /** \ingroup SVD_Module
@@ -21,9 +22,10 @@ namespace Eigen {
  *
  * \class SVDBase
  *
- * \brief Mother class of SVD classes algorithms
+ * \brief Base class of SVD algorithms
+ *
+ * \tparam Derived the type of the actual SVD decomposition
  *
- * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
  * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
  *   \f[ A = U S V^* \f]
  * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
@@ -42,12 +44,12 @@ namespace Eigen {
  * terminate in finite (and reasonable) time.
  * \sa MatrixBase::genericSvd()
  */
-template<typename _MatrixType> 
+template<typename Derived>
 class SVDBase
 {
 
 public:
-  typedef _MatrixType MatrixType;
+  typedef typename internal::traits<Derived>::MatrixType MatrixType;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
   typedef typename MatrixType::Index Index;
@@ -61,46 +63,16 @@ public:
     MatrixOptions = MatrixType::Options
   };
 
-  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
+  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixUType;
-		 MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
+  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> MatrixVType;
-  MatrixUType;
-  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
-		 MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
-  MatrixVType;
   typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
-  typedef typename internal::plain_row_type<MatrixType>::type RowType;
-  typedef typename internal::plain_col_type<MatrixType>::type ColType;
-  typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
-		 MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
-  WorkMatrixType;
   
-
+  Derived& derived() { return *static_cast<Derived*>(this); }
-
+  const Derived& derived() const { return *static_cast<const Derived*>(this); }
-
-  /** \brief Method performing the decomposition of given matrix using custom options.
-   *
-   * \param matrix the matrix to decompose
-   * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
-   *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
-   *                           #ComputeFullV, #ComputeThinV.
-   *
-   * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
-   * available with the (non-default) FullPivHouseholderQR preconditioner.
-   */
-  SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions);
-
-  /** \brief Method performing the decomposition of given matrix using current options.
-   *
-   * \param matrix the matrix to decompose
-   *
-   * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
-   */
-  //virtual SVDBase& compute(const MatrixType& matrix) = 0;
-  SVDBase& compute(const MatrixType& matrix);
 
   /** \returns the \a U matrix.
    *
-   * For the SVDBase decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+   * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
    * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
    *
    * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
@@ -141,8 +113,6 @@ public:
     return m_singularValues;
   }
 
-  
-
   /** \returns the number of singular values that are not exactly 0 */
   Index nonzeroSingularValues() const
   {
@@ -150,17 +120,77 @@ public:
     return m_nonzeroSingularValues;
   }
   
+  /** \returns the rank of the matrix of which \c *this is the SVD.
+    *
+    * \note This method has to determine which singular values should be considered nonzero.
+    *       For that, it uses the threshold value that you can control by calling
+    *       setThreshold(const RealScalar&).
+    */
+  inline Index rank() const
+  {
+    using std::abs;
+    eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+    if(m_singularValues.size()==0) return 0;
+    RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
+    Index i = m_nonzeroSingularValues-1;
+    while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
+    return i+1;
+  }
+  
+  /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
+    * which need to determine when singular values are to be considered nonzero.
+    * This is not used for the SVD decomposition itself.
+    *
+    * When it needs to get the threshold value, Eigen calls threshold().
+    * The default is \c NumTraits<Scalar>::epsilon()
+    *
+    * \param threshold The new value to use as the threshold.
+    *
+    * A singular value will be considered nonzero if its value is strictly greater than
+    *  \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
+    *
+    * If you want to come back to the default behavior, call setThreshold(Default_t)
+    */
+  Derived& setThreshold(const RealScalar& threshold)
+  {
+    m_usePrescribedThreshold = true;
+    m_prescribedThreshold = threshold;
+    return derived();
+  }
+
+  /** Allows to come back to the default behavior, letting Eigen use its default formula for
+    * determining the threshold.
+    *
+    * You should pass the special object Eigen::Default as parameter here.
+    * \code svd.setThreshold(Eigen::Default); \endcode
+    *
+    * See the documentation of setThreshold(const RealScalar&).
+    */
+  Derived& setThreshold(Default_t)
+  {
+    m_usePrescribedThreshold = false;
+    return derived();
+  }
+
+  /** Returns the threshold that will be used by certain methods such as rank().
+    *
+    * See the documentation of setThreshold(const RealScalar&).
+    */
+  RealScalar threshold() const
+  {
+    eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+    return m_usePrescribedThreshold ? m_prescribedThreshold
+                                    : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
+  }
 
   /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
   inline bool computeU() const { return m_computeFullU || m_computeThinU; }
   /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
   inline bool computeV() const { return m_computeFullV || m_computeThinV; }
 
-
   inline Index rows() const { return m_rows; }
   inline Index cols() const { return m_cols; }
 
-
 protected:
   // return true if already allocated
   bool allocate(Index rows, Index cols, unsigned int computationOptions) ;
@@ -168,12 +198,12 @@ protected:
   MatrixUType m_matrixU;
   MatrixVType m_matrixV;
   SingularValuesType m_singularValues;
-  bool m_isInitialized, m_isAllocated;
+  bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
   bool m_computeFullU, m_computeThinU;
   bool m_computeFullV, m_computeThinV;
   unsigned int m_computationOptions;
   Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
-
+  RealScalar m_prescribedThreshold;
 
   /** \brief Default Constructor.
    *
@@ -182,8 +212,9 @@ protected:
   SVDBase()
     : m_isInitialized(false),
       m_isAllocated(false),
+      m_usePrescribedThreshold(false),
       m_computationOptions(0),
-      m_rows(-1), m_cols(-1)
+      m_rows(-1), m_cols(-1), m_diagSize(0)
   {}
 
 
@@ -220,17 +251,13 @@ bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computat
   m_diagSize = (std::min)(m_rows, m_cols);
   m_singularValues.resize(m_diagSize);
   if(RowsAtCompileTime==Dynamic)
-    m_matrixU.resize(m_rows, m_computeFullU ? m_rows
+    m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);
-		     : m_computeThinU ? m_diagSize
-		     : 0);
   if(ColsAtCompileTime==Dynamic)
-    m_matrixV.resize(m_cols, m_computeFullV ? m_cols
+    m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
-		     : m_computeThinV ? m_diagSize
-		     : 0);
 
   return false;
 }
 
 }// end namespace
 
-#endif // EIGEN_SVD_H
+#endif // EIGEN_SVDBASE_H

Eigen/src/SVD/UpperBidiagonalization.h

@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -153,14 +154,19 @@ void upperbidiagonalization_blocked_helper(MatrixType& A,
                                            typename MatrixType::RealScalar *diagonal,
                                            typename MatrixType::RealScalar *upper_diagonal,
                                            typename MatrixType::Index bs,
-                                           Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic> > X,
+                                           Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,
-                                           Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic> > Y)
+                                                      traits<MatrixType>::Flags & RowMajorBit> > X,
+                                           Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,
+                                                      traits<MatrixType>::Flags & RowMajorBit> > Y)
 {
   typedef typename MatrixType::Index Index;
   typedef typename MatrixType::Scalar Scalar;
-  typedef Ref<Matrix<Scalar, Dynamic, 1> >                    SubColumnType;
+  enum { StorageOrder = traits<MatrixType>::Flags & RowMajorBit };
-  typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, InnerStride<> >  SubRowType;
+  typedef InnerStride<int(StorageOrder) == int(ColMajor) ? 1 : Dynamic> ColInnerStride;
-  typedef Ref<Matrix<Scalar, Dynamic, Dynamic> >              SubMatType;
+  typedef InnerStride<int(StorageOrder) == int(ColMajor) ? Dynamic : 1> RowInnerStride;
+  typedef Ref<Matrix<Scalar, Dynamic, 1>, 0, ColInnerStride>    SubColumnType;
+  typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, RowInnerStride>    SubRowType;
+  typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder > > SubMatType;
   
   Index brows = A.rows();
   Index bcols = A.cols();
@@ -287,8 +293,18 @@ void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagona
   Index cols = A.cols();
   Index size = (std::min)(rows, cols);
 
-  Matrix<Scalar,MatrixType::RowsAtCompileTime,Dynamic,ColMajor,MatrixType::MaxRowsAtCompileTime> X(rows,maxBlockSize);
+  // X and Y are work space
-  Matrix<Scalar,MatrixType::ColsAtCompileTime,Dynamic,ColMajor,MatrixType::MaxColsAtCompileTime> Y(cols,maxBlockSize);
+  enum { StorageOrder = traits<MatrixType>::Flags & RowMajorBit };
+  Matrix<Scalar,
+         MatrixType::RowsAtCompileTime,
+         Dynamic,
+         StorageOrder,
+         MatrixType::MaxRowsAtCompileTime> X(rows,maxBlockSize);
+  Matrix<Scalar,
+         MatrixType::ColsAtCompileTime,
+         Dynamic,
+         StorageOrder,
+         MatrixType::MaxColsAtCompileTime> Y(cols,maxBlockSize);
   Index blockSize = (std::min)(maxBlockSize,size);
 
   Index k = 0;

Eigen/src/SparseCore/ConservativeSparseSparseProduct.h

@@ -15,7 +15,7 @@ namespace Eigen {
 namespace internal {
 
 template<typename Lhs, typename Rhs, typename ResultType>
-static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res, bool sortedInsertion = false)
 {
   typedef typename remove_all<Lhs>::type::Scalar Scalar;
   typedef typename remove_all<Lhs>::type::Index Index;
@@ -25,9 +25,11 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
   Index cols = rhs.outerSize();
   eigen_assert(lhs.outerSize() == rhs.innerSize());
   
-  std::vector<bool> mask(rows,false);
+  ei_declare_aligned_stack_constructed_variable(bool,   mask,     rows, 0);
-  Matrix<Scalar,Dynamic,1> values(rows);
+  ei_declare_aligned_stack_constructed_variable(Scalar, values,   rows, 0);
-  Matrix<Index,Dynamic,1>  indices(rows);
+  ei_declare_aligned_stack_constructed_variable(Index,  indices,  rows, 0);
+  
+  std::memset(mask,0,sizeof(bool)*rows);
 
   // estimate the number of non zero entries
   // given a rhs column containing Y non zeros, we assume that the respective Y columns
@@ -64,7 +66,8 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
           values[i] += x * y;
       }
     }
-
+    if(!sortedInsertion)
+    {
       // unordered insertion
       for(Index k=0; k<nnz; ++k)
       {
@@ -72,24 +75,22 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
         res.insertBackByOuterInnerUnordered(j,i) = values[i];
         mask[i] = false;
       }
-
+    }
-#if 0
+    else
+    {
       // alternative ordered insertion code:
-
+      const Index t200 = rows/11; // 11 == (log2(200)*1.39)
-    Index t200 = rows/(log2(200)*1.39);
+      const Index t = (rows*100)/139;
-    Index t = (rows*100)/139;
 
       // FIXME reserve nnz non zeros
-    // FIXME implement fast sort algorithms for very small nnz
+      // FIXME implement faster sorting algorithms for very small nnz
       // if the result is sparse enough => use a quick sort
       // otherwise => loop through the entire vector
       // In order to avoid to perform an expensive log2 when the
       // result is clearly very sparse we use a linear bound up to 200.
-    //if((nnz<200 && nnz<t200) || nnz * log2(nnz) < t)
+      if((nnz<200 && nnz<t200) || nnz * log2(nnz) < t)
-    //res.startVec(j);
-    if(true)
       {
-      if(nnz>1) std::sort(indices.data(),indices.data()+nnz);
+        if(nnz>1) std::sort(indices,indices+nnz);
         for(Index k=0; k<nnz; ++k)
         {
           Index i = indices[k];
@@ -109,8 +110,7 @@ static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& r
           }
         }
       }
-#endif
+    }
-
   }
   res.finalize();
 }
@@ -135,12 +135,25 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,C
   static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
   {
     typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::Index> RowMajorMatrix;
-    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrix;
+    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrixAux;
+    typedef typename sparse_eval<ColMajorMatrixAux,ResultType::RowsAtCompileTime,ResultType::ColsAtCompileTime>::type ColMajorMatrix;
+    
+    // FIXME, the following heuristic is probably not very good.
+    if(lhs.rows()>=rhs.cols())
+    {
       ColMajorMatrix resCol(lhs.rows(),rhs.cols());
-    internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol);
+      // perform sorted insertion
-    // sort the non zeros:
+      internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol, true);
+      res = resCol.markAsRValue();
+    }
+    else
+    {
+      ColMajorMatrixAux resCol(lhs.rows(),rhs.cols());
+      // ressort to transpose to sort the entries
+      internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrixAux>(lhs, rhs, resCol, false);
       RowMajorMatrix resRow(resCol);
-    res = resRow;
+      res = resRow.markAsRValue();
+    }
   }
 };
 

Eigen/src/SparseCore/SparseDenseProduct.h

@@ -318,15 +318,6 @@ class DenseTimeSparseProduct
     DenseTimeSparseProduct& operator=(const DenseTimeSparseProduct&);
 };
 
-// sparse * dense
-template<typename Derived>
-template<typename OtherDerived>
-inline const typename SparseDenseProductReturnType<Derived,OtherDerived>::Type
-SparseMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
-{
-  return typename SparseDenseProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
-}
-
 } // end namespace Eigen
 
 #endif // EIGEN_SPARSEDENSEPRODUCT_H

Eigen/src/SparseCore/SparseMatrixBase.h

@@ -358,7 +358,8 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
     /** sparse * dense (returns a dense object unless it is an outer product) */
     template<typename OtherDerived>
     const typename SparseDenseProductReturnType<Derived,OtherDerived>::Type
-    operator*(const MatrixBase<OtherDerived> &other) const;
+    operator*(const MatrixBase<OtherDerived> &other) const
+    { return typename SparseDenseProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived()); }
     
      /** \returns an expression of P H P^-1 where H is the matrix represented by \c *this */
     SparseSymmetricPermutationProduct<Derived,Upper|Lower> twistedBy(const PermutationMatrix<Dynamic,Dynamic,Index>& perm) const

Eigen/src/SparseCore/SparseVector.h

@@ -109,7 +109,7 @@ class SparseVector
     inline Scalar& coeffRef(Index row, Index col)
     {
       eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
-      return coeff(IsColVector ? row : col);
+      return coeffRef(IsColVector ? row : col);
     }
 
     /** \returns a reference to the coefficient value at given index \a i
@@ -152,6 +152,18 @@ class SparseVector
       return m_data.value(m_data.size()-1);
     }
     
+    Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)
+    {
+      EIGEN_UNUSED_VARIABLE(outer);
+      eigen_assert(outer==0);
+      return insertBackUnordered(inner);
+    }
+    inline Scalar& insertBackUnordered(Index i)
+    {
+      m_data.append(0, i);
+      return m_data.value(m_data.size()-1);
+    }
+
     inline Scalar& insert(Index row, Index col)
     {
       eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));

Eigen/src/SparseQR/SparseQR.h

@@ -75,7 +75,7 @@ class SparseQR
     typedef Matrix<Scalar, Dynamic, 1> ScalarVector;
     typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
   public:
-    SparseQR () : m_isInitialized(false), m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false)
+    SparseQR () : m_isInitialized(false), m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
     { }
     
     /** Construct a QR factorization of the matrix \a mat.
@@ -84,7 +84,7 @@ class SparseQR
       * 
       * \sa compute()
       */
-    SparseQR(const MatrixType& mat) : m_isInitialized(false), m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false)
+    SparseQR(const MatrixType& mat) : m_isInitialized(false), m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
     {
       compute(mat);
     }
@@ -262,6 +262,7 @@ class SparseQR
     IndexVector m_etree;            // Column elimination tree
     IndexVector m_firstRowElt;      // First element in each row
     bool m_isQSorted;               // whether Q is sorted or not
+    bool m_isEtreeOk;               // whether the elimination tree match the initial input matrix
     
     template <typename, typename > friend struct SparseQR_QProduct;
     template <typename > friend struct SparseQRMatrixQReturnType;
@@ -297,6 +298,7 @@ void SparseQR<MatrixType,OrderingType>::analyzePattern(const MatrixType& mat)
   // Compute the column elimination tree of the permuted matrix
   m_outputPerm_c = m_perm_c.inverse();
   internal::coletree(mat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());
+  m_isEtreeOk = true;
   
   m_R.resize(m, n);
   m_Q.resize(m, diagSize);
@@ -331,6 +333,15 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
   ScalarVector tval(m);                                     // The dense vector used to compute the current column
   RealScalar pivotThreshold = m_threshold;
   
+  m_R.setZero();
+  m_Q.setZero();
+  if(!m_isEtreeOk)
+  {
+    m_outputPerm_c = m_perm_c.inverse();
+    internal::coletree(mat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());
+    m_isEtreeOk = true;
+  }
+    
   m_pmat = mat;
   m_pmat.uncompress(); // To have the innerNonZeroPtr allocated
   // Apply the fill-in reducing permutation lazily:
@@ -447,7 +458,7 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
       }
     } // End update current column
     
-    Scalar tau;
+    Scalar tau = RealScalar(0);
     RealScalar beta = 0;
     
     if(nonzeroCol < diagSize)
@@ -461,7 +472,6 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
       for (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));
       if(sqrNorm == RealScalar(0) && numext::imag(c0) == RealScalar(0))
       {
-        tau = RealScalar(0);
         beta = numext::real(c0);
         tval(Qidx(0)) = 1;
       }
@@ -514,6 +524,7 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
       
       // Recompute the column elimination tree
       internal::coletree(m_pmat, m_etree, m_firstRowElt, m_pivotperm.indices().data());
+      m_isEtreeOk = false;
     }
   }
   

Eigen/src/plugins/ArrayCwiseUnaryOps.h

@@ -29,6 +29,9 @@ abs2() const
 }
 
 /** \returns an expression of the coefficient-wise exponential of *this.
+  *
+  * This function computes the coefficient-wise exponential. The function MatrixBase::exp() in the
+  * unsupported module MatrixFunctions computes the matrix exponential.
   *
   * Example: \include Cwise_exp.cpp
   * Output: \verbinclude Cwise_exp.out
@@ -43,6 +46,9 @@ exp() const
 }
 
 /** \returns an expression of the coefficient-wise logarithm of *this.
+  *
+  * This function computes the coefficient-wise logarithm. The function MatrixBase::log() in the
+  * unsupported module MatrixFunctions computes the matrix logarithm.
   *
   * Example: \include Cwise_log.cpp
   * Output: \verbinclude Cwise_log.out
@@ -57,6 +63,9 @@ log() const
 }
 
 /** \returns an expression of the coefficient-wise square root of *this.
+  *
+  * This function computes the coefficient-wise square root. The function MatrixBase::sqrt() in the
+  * unsupported module MatrixFunctions computes the matrix square root.
   *
   * Example: \include Cwise_sqrt.cpp
   * Output: \verbinclude Cwise_sqrt.out
@@ -71,6 +80,9 @@ sqrt() const
 }
 
 /** \returns an expression of the coefficient-wise cosine of *this.
+  *
+  * This function computes the coefficient-wise cosine. The function MatrixBase::cos() in the
+  * unsupported module MatrixFunctions computes the matrix cosine.
   *
   * Example: \include Cwise_cos.cpp
   * Output: \verbinclude Cwise_cos.out
@@ -86,6 +98,9 @@ cos() const
 
 
 /** \returns an expression of the coefficient-wise sine of *this.
+  *
+  * This function computes the coefficient-wise sine. The function MatrixBase::sin() in the
+  * unsupported module MatrixFunctions computes the matrix sine.
   *
   * Example: \include Cwise_sin.cpp
   * Output: \verbinclude Cwise_sin.out
@@ -155,6 +170,9 @@ atan() const
 }
 
 /** \returns an expression of the coefficient-wise power of *this to the given exponent.
+  *
+  * This function computes the coefficient-wise power. The function MatrixBase::pow() in the
+  * unsupported module MatrixFunctions computes the matrix power.
   *
   * Example: \include Cwise_pow.cpp
   * Output: \verbinclude Cwise_pow.out

bench/bench_norm.cpp

@@ -6,19 +6,25 @@ using namespace Eigen;
 using namespace std;
 
 template<typename T>
-EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(const T& v)
+EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(T& v)
 {
   return v.norm();
 }
 
 template<typename T>
-EIGEN_DONT_INLINE typename T::Scalar hypotNorm(const T& v)
+EIGEN_DONT_INLINE typename T::Scalar stableNorm(T& v)
+{
+  return v.stableNorm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar hypotNorm(T& v)
 {
   return v.hypotNorm();
 }
 
 template<typename T>
-EIGEN_DONT_INLINE typename T::Scalar blueNorm(const T& v)
+EIGEN_DONT_INLINE typename T::Scalar blueNorm(T& v)
 {
   return v.blueNorm();
 }
@@ -217,20 +223,21 @@ EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
 }
 
 #define BENCH_PERF(NRM) { \
+  float af = 0; double ad = 0; std::complex<float> ac = 0; \
   Eigen::BenchTimer tf, td, tcf; tf.reset(); td.reset(); tcf.reset();\
   for (int k=0; k<tries; ++k) { \
     tf.start(); \
-    for (int i=0; i<iters; ++i) NRM(vf); \
+    for (int i=0; i<iters; ++i) { af += NRM(vf); } \
     tf.stop(); \
   } \
   for (int k=0; k<tries; ++k) { \
     td.start(); \
-    for (int i=0; i<iters; ++i) NRM(vd); \
+    for (int i=0; i<iters; ++i) { ad += NRM(vd); } \
     td.stop(); \
   } \
   /*for (int k=0; k<std::max(1,tries/3); ++k) { \
     tcf.start(); \
-    for (int i=0; i<iters; ++i) NRM(vcf); \
+    for (int i=0; i<iters; ++i) { ac += NRM(vcf); } \
     tcf.stop(); \
   } */\
   std::cout << #NRM << "\t" << tf.value() << "   " << td.value() <<  "    " << tcf.value() << "\n"; \
@@ -316,14 +323,17 @@ int main(int argc, char** argv)
     std::cout << "\n";
   }
 
+  y = 1;
   std::cout.precision(4);
-  std::cerr << "Performance (out of cache):\n";
+  int s1 = 1024*1024*32;
+  std::cerr << "Performance (out of cache, " << s1 << "):\n";
   {
     int iters = 1;
-    VectorXf vf = VectorXf::Random(1024*1024*32) * y;
+    VectorXf vf = VectorXf::Random(s1) * y;
-    VectorXd vd = VectorXd::Random(1024*1024*32) * y;
+    VectorXd vd = VectorXd::Random(s1) * y;
-    VectorXcf vcf = VectorXcf::Random(1024*1024*32) * y;
+    VectorXcf vcf = VectorXcf::Random(s1) * y;
     BENCH_PERF(sqsumNorm);
+    BENCH_PERF(stableNorm);
     BENCH_PERF(blueNorm);
     BENCH_PERF(pblueNorm);
     BENCH_PERF(lapackNorm);
@@ -332,13 +342,14 @@ int main(int argc, char** argv)
     BENCH_PERF(bl2passNorm);
   }
 
-  std::cerr << "\nPerformance (in cache):\n";
+  std::cerr << "\nPerformance (in cache, " << 512 << "):\n";
   {
     int iters = 100000;
     VectorXf vf = VectorXf::Random(512) * y;
     VectorXd vd = VectorXd::Random(512) * y;
     VectorXcf vcf = VectorXcf::Random(512) * y;
     BENCH_PERF(sqsumNorm);
+    BENCH_PERF(stableNorm);
     BENCH_PERF(blueNorm);
     BENCH_PERF(pblueNorm);
     BENCH_PERF(lapackNorm);

cmake/FindEigen3.cmake

@@ -9,6 +9,12 @@
 #  EIGEN3_FOUND - system has eigen lib with correct version
 #  EIGEN3_INCLUDE_DIR - the eigen include directory
 #  EIGEN3_VERSION - eigen version
+#
+# This module reads hints about search locations from 
+# the following enviroment variables:
+#
+# EIGEN3_ROOT
+# EIGEN3_ROOT_DIR
 
 # Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>
 # Copyright (c) 2008, 2009 Gael Guennebaud, <g.gael@free.fr>
@@ -62,6 +68,9 @@ if (EIGEN3_INCLUDE_DIR)
 else (EIGEN3_INCLUDE_DIR)
 
   find_path(EIGEN3_INCLUDE_DIR NAMES signature_of_eigen3_matrix_library
+      HINTS
+      ENV EIGEN3_ROOT 
+      ENV EIGEN3_ROOT_DIR
       PATHS
       ${CMAKE_INSTALL_PREFIX}/include
       ${KDE4_INCLUDE_DIR}

doc/CMakeLists.txt

@@ -97,6 +97,7 @@ add_dependencies(doc-unsupported-prerequisites unsupported_snippets unsupported_
 add_custom_target(doc ALL
   COMMAND doxygen
   COMMAND doxygen Doxyfile-unsupported
+  COMMAND ${CMAKE_COMMAND} -E copy ${Eigen_BINARY_DIR}/doc/html/group__TopicUnalignedArrayAssert.html ${Eigen_BINARY_DIR}/doc/html/TopicUnalignedArrayAssert.html
   COMMAND ${CMAKE_COMMAND} -E rename html eigen-doc
   COMMAND ${CMAKE_COMMAND} -E remove eigen-doc/eigen-doc.tgz
   COMMAND ${CMAKE_COMMAND} -E tar cfz eigen-doc/eigen-doc.tgz eigen-doc

doc/examples/CMakeLists.txt

@@ -6,12 +6,10 @@ foreach(example_src ${examples_SRCS})
   if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
     target_link_libraries(${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
   endif()
-  get_target_property(example_executable
-                      ${example} LOCATION)
   add_custom_command(
     TARGET ${example}
     POST_BUILD
-    COMMAND ${example_executable}
+    COMMAND ${example}
     ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out
   )
   add_dependencies(all_examples ${example})

doc/snippets/CMakeLists.txt

@@ -14,12 +14,10 @@ foreach(snippet_src ${snippets_SRCS})
   if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
     target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
   endif()
-  get_target_property(compile_snippet_executable
-                      ${compile_snippet_target} LOCATION)
   add_custom_command(
     TARGET ${compile_snippet_target}
     POST_BUILD
-    COMMAND ${compile_snippet_executable}
+    COMMAND ${compile_snippet_target}
     ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out
   )
   add_dependencies(all_snippets ${compile_snippet_target})

doc/snippets/DirectionWise_hnormalized.cpp

@@ -0,0 +1,7 @@
+typedef Matrix<double,4,Dynamic> Matrix4Xd;
+Matrix4Xd M = Matrix4Xd::Random(4,5);
+Projective3d P(Matrix4d::Random());
+cout << "The matrix M is:" << endl << M << endl << endl;
+cout << "M.colwise().hnormalized():" << endl << M.colwise().hnormalized() << endl << endl;
+cout << "P*M:" << endl << P*M << endl << endl;
+cout << "(P*M).colwise().hnormalized():" << endl << (P*M).colwise().hnormalized() << endl << endl;

doc/snippets/MatrixBase_hnormalized.cpp

@@ -0,0 +1,6 @@
+Vector4d v = Vector4d::Random();
+Projective3d P(Matrix4d::Random());
+cout << "v                   = " << v.transpose() << "]^T" << endl;
+cout << "v.hnormalized()     = " << v.hnormalized().transpose() << "]^T" << endl;
+cout << "P*v                 = " << (P*v).transpose() << "]^T" << endl;
+cout << "(P*v).hnormalized() = " << (P*v).hnormalized().transpose() << "]^T" << endl;

doc/snippets/MatrixBase_homogeneous.cpp

@@ -0,0 +1,6 @@
+Vector3d v = Vector3d::Random(), w;
+Projective3d P(Matrix4d::Random());
+cout << "v                                   = [" << v.transpose() << "]^T" << endl;
+cout << "h.homogeneous()                     = [" << v.homogeneous().transpose() << "]^T" << endl;
+cout << "(P * v.homogeneous())               = [" << (P * v.homogeneous()).transpose() << "]^T" << endl;
+cout << "(P * v.homogeneous()).hnormalized() = [" << (P * v.homogeneous()).eval().hnormalized().transpose() << "]^T" << endl;

doc/snippets/VectorwiseOp_homogeneous.cpp

@@ -0,0 +1,7 @@
+typedef Matrix<double,3,Dynamic> Matrix3Xd;
+Matrix3Xd M = Matrix3Xd::Random(3,5);
+Projective3d P(Matrix4d::Random());
+cout << "The matrix M is:" << endl << M << endl << endl;
+cout << "M.colwise().homogeneous():" << endl << M.colwise().homogeneous() << endl << endl;
+cout << "P * M.colwise().homogeneous():" << endl << P * M.colwise().homogeneous() << endl << endl;
+cout << "P * M.colwise().homogeneous().hnormalized(): " << endl << (P * M.colwise().homogeneous()).colwise().hnormalized() << endl << endl;

doc/special_examples/CMakeLists.txt

@@ -1,4 +1,3 @@
-
 if(NOT EIGEN_TEST_NOQT)
   find_package(Qt4)
   if(QT4_FOUND)
@@ -6,7 +5,6 @@ if(NOT EIGEN_TEST_NOQT)
   endif()
 endif(NOT EIGEN_TEST_NOQT)
 
-
 if(QT4_FOUND)
   add_executable(Tutorial_sparse_example Tutorial_sparse_example.cpp Tutorial_sparse_example_details.cpp)
   target_link_libraries(Tutorial_sparse_example ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY})
@@ -27,14 +25,10 @@ if(EIGEN_COMPILER_SUPPORT_CPP11)
   add_dependencies(all_examples random_cpp11)
   ei_add_target_property(random_cpp11 COMPILE_FLAGS "-std=c++11")
 
-  get_target_property(random_cpp11_exec
-                      random_cpp11 LOCATION)
   add_custom_command(
     TARGET random_cpp11
     POST_BUILD
-    COMMAND ${random_cpp11_exec}
+    COMMAND random_cpp11
     ARGS >${CMAKE_CURRENT_BINARY_DIR}/random_cpp11.out
   )
-  
-  
 endif()

test/eigensolver_selfadjoint.cpp

@@ -29,7 +29,21 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
   MatrixType a = MatrixType::Random(rows,cols);
   MatrixType a1 = MatrixType::Random(rows,cols);
   MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
+  MatrixType symmC = symmA;
+  
+  // randomly nullify some rows/columns
+  {
+    Index count = 1;//internal::random<Index>(-cols,cols);
+    for(Index k=0; k<count; ++k)
+    {
+      Index i = internal::random<Index>(0,cols-1);
+      symmA.row(i).setZero();
+      symmA.col(i).setZero();
+    }
+  }
+  
   symmA.template triangularView<StrictlyUpper>().setZero();
+  symmC.template triangularView<StrictlyUpper>().setZero();
 
   MatrixType b = MatrixType::Random(rows,cols);
   MatrixType b1 = MatrixType::Random(rows,cols);
@@ -40,7 +54,7 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
   SelfAdjointEigenSolver<MatrixType> eiDirect;
   eiDirect.computeDirect(symmA);
   // generalized eigen pb
-  GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
+  GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
 
   VERIFY_IS_EQUAL(eiSymm.info(), Success);
   VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
@@ -57,27 +71,28 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
   VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
   
   // generalized eigen problem Ax = lBx
-  eiSymmGen.compute(symmA, symmB,Ax_lBx);
+  eiSymmGen.compute(symmC, symmB,Ax_lBx);
   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
-  VERIFY((symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
+  VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
           symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
 
   // generalized eigen problem BAx = lx
-  eiSymmGen.compute(symmA, symmB,BAx_lx);
+  eiSymmGen.compute(symmC, symmB,BAx_lx);
   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
-  VERIFY((symmB.template selfadjointView<Lower>() * (symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+  VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
          (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
 
   // generalized eigen problem ABx = lx
-  eiSymmGen.compute(symmA, symmB,ABx_lx);
+  eiSymmGen.compute(symmC, symmB,ABx_lx);
   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
-  VERIFY((symmA.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+  VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
          (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
 
 
+  eiSymm.compute(symmC);
   MatrixType sqrtSymmA = eiSymm.operatorSqrt();
-  VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
+  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
-  VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
+  VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
 
   MatrixType id = MatrixType::Identity(rows, cols);
   VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
@@ -95,9 +110,9 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
 
   // test Tridiagonalization's methods
-  Tridiagonalization<MatrixType> tridiag(symmA);
+  Tridiagonalization<MatrixType> tridiag(symmC);
   // FIXME tridiag.matrixQ().adjoint() does not work
-  VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
+  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
   
   // Test computation of eigenvalues from tridiagonal matrix
   if(rows > 1)
@@ -111,8 +126,8 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
   if (rows > 1)
   {
     // Test matrix with NaN
-    symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+    symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
-    SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA);
+    SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
     VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
   }
 }
@@ -122,8 +137,10 @@ void test_eigensolver_selfadjoint()
   int s = 0;
   for(int i = 0; i < g_repeat; i++) {
     // very important to test 3x3 and 2x2 matrices since we provide special paths for them
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) );
     CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) );
     CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) );
     CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
     CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );

test/jacobisvd.cpp

@@ -315,16 +315,30 @@ void jacobisvd_inf_nan()
   VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
   svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
 
-  Scalar some_nan = zero<Scalar>() / zero<Scalar>();
+  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
-  VERIFY(some_nan != some_nan);
+  VERIFY(nan != nan);
-  svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV);
+  svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);
 
   MatrixType m = MatrixType::Zero(10,10);
   m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
   svd.compute(m, ComputeFullU | ComputeFullV);
 
   m = MatrixType::Zero(10,10);
-  m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_nan;
+  m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
+  svd.compute(m, ComputeFullU | ComputeFullV);
+  
+  // regression test for bug 791
+  m.resize(3,3);
+  m << 0,    2*NumTraits<Scalar>::epsilon(),  0.5,
+       0,   -0.5,                             0,
+       nan,  0,                               0;
+  svd.compute(m, ComputeFullU | ComputeFullV);
+  
+  m.resize(4,4);
+  m <<  1, 0, 0, 0,
+        0, 3, 1, 2e-308,
+        1, 0, 1, nan,
+        0, nan, nan, 0;
   svd.compute(m, ComputeFullU | ComputeFullV);
 }
 
@@ -340,11 +354,33 @@ void jacobisvd_underoverflow()
   Matrix2d M;
   M << -7.90884e-313, -4.94e-324,
                  0, 5.60844e-313;
+  JacobiSVD<Matrix2d> svd;
+  svd.compute(M,ComputeFullU|ComputeFullV);
+  jacobisvd_check_full(M,svd);
+  
+  VectorXd value_set(9);
+  value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
+  Array4i id(0,0,0,0);
+  int k = 0;
+  do
+  {
+    M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+    svd.compute(M,ComputeFullU|ComputeFullV);
+    jacobisvd_check_full(M,svd);
+    
+    id(k)++;
+    if(id(k)>=value_set.size())
+    {
+      while(k<3 && id(k)>=value_set.size()) id(++k)++;
+      id.head(k).setZero();
+      k=0;
+    }
+    
+  } while((id<int(value_set.size())).all());
+  
 #if defined __INTEL_COMPILER
 #pragma warning pop
 #endif
-  JacobiSVD<Matrix2d> svd;
-  svd.compute(M); // just check we don't loop indefinitely
   
   // Check for overflow:
   Matrix3d M3;
@@ -353,7 +389,8 @@ void jacobisvd_underoverflow()
        -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
 
   JacobiSVD<Matrix3d> svd3;
-  svd3.compute(M3); // just check we don't loop indefinitely
+  svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
+  jacobisvd_check_full(M3,svd3);
 }
 
 void jacobisvd_preallocate()
@@ -437,6 +474,7 @@ void test_jacobisvd()
 
     // Test on inf/nan matrix
     CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
+    CALL_SUBTEST_10( jacobisvd_inf_nan<MatrixXd>() );
   }
 
   CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));

test/linearstructure.cpp

@@ -2,11 +2,16 @@
 // for linear algebra.
 //
 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
+static bool g_called;
+
+#define EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN { g_called = true; }
+
 #include "main.h"
 
 template<typename MatrixType> void linearStructure(const MatrixType& m)
@@ -68,6 +73,24 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
   VERIFY_IS_APPROX(m1.block(0,0,rows,cols) * s1, m1 * s1);
 }
 
+// Make sure that complex * real and real * complex are properly optimized
+template<typename MatrixType> void real_complex(DenseIndex rows = MatrixType::RowsAtCompileTime, DenseIndex cols = MatrixType::ColsAtCompileTime)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  
+  RealScalar s = internal::random<RealScalar>();
+  MatrixType m1 = MatrixType::Random(rows, cols);
+  
+  g_called = false;
+  VERIFY_IS_APPROX(s*m1, Scalar(s)*m1);
+  VERIFY(g_called && "real * matrix<complex> not properly optimized");
+  
+  g_called = false;
+  VERIFY_IS_APPROX(m1*s, m1*Scalar(s));
+  VERIFY(g_called && "matrix<complex> * real not properly optimized");
+}
+
 void test_linearstructure()
 {
   for(int i = 0; i < g_repeat; i++) {
@@ -80,5 +103,8 @@ void test_linearstructure()
     CALL_SUBTEST_7( linearStructure(MatrixXi (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
     CALL_SUBTEST_8( linearStructure(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
     CALL_SUBTEST_9( linearStructure(ArrayXXf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+    
+    CALL_SUBTEST_10( real_complex<Matrix4cd>() );
+    CALL_SUBTEST_10( real_complex<MatrixXcf>(10,10) );
   }
 }

test/main.h

@@ -17,13 +17,36 @@
 #include <sstream>
 #include <vector>
 #include <typeinfo>
+
+// The following includes of STL headers have to be done _before_ the
+// definition of macros min() and max().  The reason is that many STL
+// implementations will not work properly as the min and max symbols collide
+// with the STL functions std:min() and std::max().  The STL headers may check
+// for the macro definition of min/max and issue a warning or undefine the
+// macros.
+//
+// Still, Windows defines min() and max() in windef.h as part of the regular
+// Windows system interfaces and many other Windows APIs depend on these
+// macros being available.  To prevent the macro expansion of min/max and to
+// make Eigen compatible with the Windows environment all function calls of
+// std::min() and std::max() have to be written with parenthesis around the
+// function name.
+//
+// All STL headers used by Eigen should be included here.  Because main.h is
+// included before any Eigen header and because the STL headers are guarded
+// against multiple inclusions, no STL header will see our own min/max macro
+// definitions.
 #include <limits>
 #include <algorithm>
-#include <sstream>
 #include <complex>
 #include <deque>
 #include <queue>
+#include <list>
 
+// To test that all calls from Eigen code to std::min() and std::max() are
+// protected by parenthesis against macro expansion, the min()/max() macros
+// are defined here and any not-parenthesized min/max call will cause a
+// compiler error.
 #define min(A,B) please_protect_your_min_with_parentheses
 #define max(A,B) please_protect_your_max_with_parentheses
 
@@ -76,6 +99,10 @@ namespace Eigen
 
 #define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, "  ", "\n", "", "", "", "")
 
+#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__)
+  #define EIGEN_EXCEPTIONS
+#endif
+
 #ifndef EIGEN_NO_ASSERTION_CHECKING
 
   namespace Eigen
@@ -172,7 +199,7 @@ namespace Eigen
 
 #ifndef VERIFY_RAISES_ASSERT
   #define VERIFY_RAISES_ASSERT(a) \
-    std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled";
+    std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled\n";
 #endif
     
   #if !defined(__CUDACC__)

test/product.h

@@ -139,4 +139,12 @@ template<typename MatrixType> void product(const MatrixType& m)
   // inner product
   Scalar x = square2.row(c) * square2.col(c2);
   VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
+  
+  // outer product
+  VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose());
+  VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));  
 }

test/sparseqr.cpp

@@ -54,6 +54,8 @@ template<typename Scalar> void test_sparseqr_scalar()
   
   b = dA * DenseVector::Random(A.cols());
   solver.compute(A);
+  if(internal::random<float>(0,1)>0.5)
+    solver.factorize(A);  // this checks that calling analyzePattern is not needed if the pattern do not change.
   if (solver.info() != Success)
   {
     std::cerr << "sparse QR factorization failed\n";

test/stable_norm.cpp

@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -14,6 +14,21 @@ template<typename T> bool isNotNaN(const T& x)
   return x==x;
 }
 
+template<typename T> bool isNaN(const T& x)
+{
+  return x!=x;
+}
+
+template<typename T> bool isInf(const T& x)
+{
+  return x > NumTraits<T>::highest();
+}
+
+template<typename T> bool isMinusInf(const T& x)
+{
+  return x < NumTraits<T>::lowest();
+}
+
 // workaround aggressive optimization in ICC
 template<typename T> EIGEN_DONT_INLINE  T sub(T a, T b) { return a - b; }
 
@@ -106,6 +121,58 @@ template<typename MatrixType> void stable_norm(const MatrixType& m)
   VERIFY_IS_APPROX(vrand.rowwise().stableNorm(),      vrand.rowwise().norm());
   VERIFY_IS_APPROX(vrand.rowwise().blueNorm(),        vrand.rowwise().norm());
   VERIFY_IS_APPROX(vrand.rowwise().hypotNorm(),       vrand.rowwise().norm());
+  
+  // test NaN, +inf, -inf 
+  MatrixType v;
+  Index i = internal::random<Index>(0,rows-1);
+  Index j = internal::random<Index>(0,cols-1);
+
+  // NaN
+  {
+    v = vrand;
+    v(i,j) = RealScalar(0)/RealScalar(0);
+    VERIFY(!isFinite(v.squaredNorm()));   VERIFY(isNaN(v.squaredNorm()));
+    VERIFY(!isFinite(v.norm()));          VERIFY(isNaN(v.norm()));
+    VERIFY(!isFinite(v.stableNorm()));    VERIFY(isNaN(v.stableNorm()));
+    VERIFY(!isFinite(v.blueNorm()));      VERIFY(isNaN(v.blueNorm()));
+    VERIFY(!isFinite(v.hypotNorm()));     VERIFY(isNaN(v.hypotNorm()));
+  }
+  
+  // +inf
+  {
+    v = vrand;
+    v(i,j) = RealScalar(1)/RealScalar(0);
+    VERIFY(!isFinite(v.squaredNorm()));   VERIFY(isInf(v.squaredNorm()));
+    VERIFY(!isFinite(v.norm()));          VERIFY(isInf(v.norm()));
+    VERIFY(!isFinite(v.stableNorm()));    VERIFY(isInf(v.stableNorm()));
+    VERIFY(!isFinite(v.blueNorm()));      VERIFY(isInf(v.blueNorm()));
+    VERIFY(!isFinite(v.hypotNorm()));     VERIFY(isInf(v.hypotNorm()));
+  }
+  
+  // -inf
+  {
+    v = vrand;
+    v(i,j) = RealScalar(-1)/RealScalar(0);
+    VERIFY(!isFinite(v.squaredNorm()));   VERIFY(isInf(v.squaredNorm()));
+    VERIFY(!isFinite(v.norm()));          VERIFY(isInf(v.norm()));
+    VERIFY(!isFinite(v.stableNorm()));    VERIFY(isInf(v.stableNorm()));
+    VERIFY(!isFinite(v.blueNorm()));      VERIFY(isInf(v.blueNorm()));
+    VERIFY(!isFinite(v.hypotNorm()));     VERIFY(isInf(v.hypotNorm()));
+  }
+  
+  // mix
+  {
+    Index i2 = internal::random<Index>(0,rows-1);
+    Index j2 = internal::random<Index>(0,cols-1);
+    v = vrand;
+    v(i,j) = RealScalar(-1)/RealScalar(0);
+    v(i2,j2) = RealScalar(0)/RealScalar(0);
+    VERIFY(!isFinite(v.squaredNorm()));   VERIFY(isNaN(v.squaredNorm()));
+    VERIFY(!isFinite(v.norm()));          VERIFY(isNaN(v.norm()));
+    VERIFY(!isFinite(v.stableNorm()));    VERIFY(isNaN(v.stableNorm()));
+    VERIFY(!isFinite(v.blueNorm()));      VERIFY(isNaN(v.blueNorm()));
+    VERIFY(!isFinite(v.hypotNorm()));     VERIFY(isNaN(v.hypotNorm()));
+  }
 }
 
 void test_stable_norm()

test/upperbidiagonalization.cpp

@@ -35,7 +35,7 @@ void test_upperbidiagonalization()
    CALL_SUBTEST_1( upperbidiag(MatrixXf(3,3)) );
    CALL_SUBTEST_2( upperbidiag(MatrixXd(17,12)) );
    CALL_SUBTEST_3( upperbidiag(MatrixXcf(20,20)) );
-   CALL_SUBTEST_4( upperbidiag(MatrixXcd(16,15)) );
+   CALL_SUBTEST_4( upperbidiag(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(16,15)) );
    CALL_SUBTEST_5( upperbidiag(Matrix<float,6,4>()) );
    CALL_SUBTEST_6( upperbidiag(Matrix<float,5,5>()) );
    CALL_SUBTEST_7( upperbidiag(Matrix<double,4,3>()) );

unsupported/Eigen/BDCSVD

@@ -0,0 +1,26 @@
+#ifndef EIGEN_BDCSVD_MODULE_H
+#define EIGEN_BDCSVD_MODULE_H
+
+#include <Eigen/SVD>
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup BDCSVD_Module BDCSVD module
+  *
+  *
+  *
+  * This module provides Divide & Conquer SVD decomposition for matrices (both real and complex).
+  * This decomposition is accessible via the following MatrixBase method:
+  *  - MatrixBase::bdcSvd()
+  *
+  * \code
+  * #include <Eigen/BDCSVD>
+  * \endcode
+  */
+
+#include "src/BDCSVD/BDCSVD.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_BDCSVD_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */

unsupported/Eigen/MatrixFunctions

@@ -82,7 +82,9 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
 \param[in]  M  a square matrix.
 \returns  expression representing \f$ \cos(M) \f$.
 
-This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
+This function computes the matrix cosine. Use ArrayBase::cos() for computing the entry-wise cosine.
+
+The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
 
 \sa \ref matrixbase_sin "sin()" for an example.
 
@@ -123,6 +125,9 @@ differential equations: the solution of \f$ y' = My \f$ with the
 initial condition \f$ y(0) = y_0 \f$ is given by
 \f$ y(t) = \exp(M) y_0 \f$.
 
+The matrix exponential is different from applying the exp function to all the entries in the matrix.
+Use ArrayBase::exp() if you want to do the latter.
+
 The cost of the computation is approximately \f$ 20 n^3 \f$ for
 matrices of size \f$ n \f$. The number 20 depends weakly on the
 norm of the matrix.
@@ -177,6 +182,9 @@ the scalar logarithm, the equation \f$ \exp(X) = M \f$ may have
 multiple solutions; this function returns a matrix whose eigenvalues
 have imaginary part in the interval \f$ (-\pi,\pi] \f$.
 
+The matrix logarithm is different from applying the log function to all the entries in the matrix.
+Use ArrayBase::log() if you want to do the latter.
+
 In the real case, the matrix \f$ M \f$ should be invertible and
 it should have no eigenvalues which are real and negative (pairs of
 complex conjugate eigenvalues are allowed). In the complex case, it
@@ -232,7 +240,8 @@ const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(RealScalar p) con
 
 The matrix power \f$ M^p \f$ is defined as \f$ \exp(p \log(M)) \f$,
 where exp denotes the matrix exponential, and log denotes the matrix
-logarithm.
+logarithm. This is different from raising all the entries in the matrix
+to the p-th power. Use ArrayBase::pow() if you want to do the latter.
 
 If \p p is complex, the scalar type of \p M should be the type of \p
 p . \f$ M^p \f$ simply evaluates into \f$ \exp(p \log(M)) \f$.
@@ -391,7 +400,9 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
 \param[in]  M  a square matrix.
 \returns  expression representing \f$ \sin(M) \f$.
 
-This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
+This function computes the matrix sine. Use ArrayBase::sin() for computing the entry-wise sine.
+
+The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
 
 Example: \include MatrixSine.cpp
 Output: \verbinclude MatrixSine.out
@@ -428,7 +439,9 @@ const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const
 
 The matrix square root of \f$ M \f$ is the matrix \f$ M^{1/2} \f$
 whose square is the original matrix; so if \f$ S = M^{1/2} \f$ then
-\f$ S^2 = M \f$. 
+\f$ S^2 = M \f$. This is different from taking the square root of all
+the entries in the matrix; use ArrayBase::sqrt() if you want to do the
+latter.
 
 In the <b>real case</b>, the matrix \f$ M \f$ should be invertible and
 it should have no eigenvalues which are real and negative (pairs of

unsupported/Eigen/SVD

@@ -1,35 +0,0 @@
-#ifndef EIGEN_SVD_MODULE_H
-#define EIGEN_SVD_MODULE_H
-
-#include <Eigen/QR>
-#include <Eigen/Householder>
-#include <Eigen/Jacobi>
-
-#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
-
-/** \defgroup SVD_Module SVD module
-  *
-  *
-  *
-  * This module provides SVD decomposition for matrices (both real and complex).
-  * This decomposition is accessible via the following MatrixBase method:
-  *  - MatrixBase::jacobiSvd()
-  *
-  * \code
-  * #include <Eigen/SVD>
-  * \endcode
-  */
-
-#include "../../Eigen/src/misc/Solve.h"
-#include "../../Eigen/src/SVD/UpperBidiagonalization.h"
-#include "src/SVD/SVDBase.h"
-#include "src/SVD/JacobiSVD.h"
-#include "src/SVD/BDCSVD.h"
-#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
-#include "../../Eigen/src/SVD/JacobiSVD_MKL.h"
-#endif
-
-#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
-
-#endif // EIGEN_SVD_MODULE_H
-/* vim: set filetype=cpp et sw=2 ts=2 ai: */

unsupported/Eigen/src/BDCSVD/BDCSVD.h

@@ -24,6 +24,20 @@
 #define ALGOSWAP 16
 
 namespace Eigen {
+
+template<typename _MatrixType> class BDCSVD;
+
+namespace internal {
+
+template<typename _MatrixType> 
+struct traits<BDCSVD<_MatrixType> >
+{
+  typedef _MatrixType MatrixType;
+};  
+
+} // end namespace internal
+  
+  
 /** \ingroup SVD_Module
  *
  *
@@ -36,9 +50,9 @@ namespace Eigen {
  * It should be used to speed up the calcul of SVD for big matrices. 
  */
 template<typename _MatrixType> 
-class BDCSVD : public SVDBase<_MatrixType>
+class BDCSVD : public SVDBase<BDCSVD<_MatrixType> >
 {
-  typedef SVDBase<_MatrixType> Base;
+  typedef SVDBase<BDCSVD> Base;
     
 public:
   using Base::rows;
@@ -77,9 +91,7 @@ public:
    * The default constructor is useful in cases in which the user intends to
    * perform decompositions via BDCSVD::compute(const MatrixType&).
    */
-  BDCSVD()
+  BDCSVD() : algoswap(ALGOSWAP), m_numIters(0)
-    : SVDBase<_MatrixType>::SVDBase(), 
-      algoswap(ALGOSWAP), m_numIters(0)
   {}
 
 
@@ -90,8 +102,7 @@ public:
    * \sa BDCSVD()
    */
   BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0)
-    : SVDBase<_MatrixType>::SVDBase(), 
+    : algoswap(ALGOSWAP), m_numIters(0)
-      algoswap(ALGOSWAP), m_numIters(0)
   {
     allocate(rows, cols, computationOptions);
   }
@@ -107,8 +118,7 @@ public:
    * available with the (non - default) FullPivHouseholderQR preconditioner.
    */
   BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
-    : SVDBase<_MatrixType>::SVDBase(), 
+    : algoswap(ALGOSWAP), m_numIters(0)
-      algoswap(ALGOSWAP), m_numIters(0)
   {
     compute(matrix, computationOptions);
   }
@@ -116,6 +126,7 @@ public:
   ~BDCSVD() 
   {
   }
+  
   /** \brief Method performing the decomposition of given matrix using custom options.
    *
    * \param matrix the matrix to decompose
@@ -126,7 +137,7 @@ public:
    * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
    * available with the (non - default) FullPivHouseholderQR preconditioner.
    */
-  SVDBase<MatrixType>& compute(const MatrixType& matrix, unsigned int computationOptions);
+  BDCSVD& compute(const MatrixType& matrix, unsigned int computationOptions);
 
   /** \brief Method performing the decomposition of given matrix using current options.
    *
@@ -134,7 +145,7 @@ public:
    *
    * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
    */
-  SVDBase<MatrixType>& compute(const MatrixType& matrix)
+  BDCSVD& compute(const MatrixType& matrix)
   {
     return compute(matrix, this->m_computationOptions);
   }
@@ -160,7 +171,7 @@ public:
   solve(const MatrixBase<Rhs>& b) const
   {
     eigen_assert(this->m_isInitialized && "BDCSVD is not initialized.");
-    eigen_assert(SVDBase<_MatrixType>::computeU() && SVDBase<_MatrixType>::computeV() && 
+    eigen_assert(computeU() && computeV() && 
                  "BDCSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
     return internal::solve_retval<BDCSVD, Rhs>(*this, b.derived());
   }
@@ -196,6 +207,9 @@ public:
     }
   }
   
+  using Base::computeU;
+  using Base::computeV;
+ 
 private:
   void allocate(Index rows, Index cols, unsigned int computationOptions);
   void divide(Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift);
@@ -229,7 +243,7 @@ template<typename MatrixType>
 void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
 {
   isTranspose = (cols > rows);
-  if (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) return;
+  if (Base::allocate(rows, cols, computationOptions)) return;
   m_computed = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize );
   if (isTranspose){
     compU = this->computeU();
@@ -262,8 +276,7 @@ void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computati
 
 // Methode which compute the BDCSVD for the int
 template<>
-SVDBase<Matrix<int, Dynamic, Dynamic> >&
+BDCSVD<Matrix<int, Dynamic, Dynamic> >& BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) {
-BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) {
   allocate(matrix.rows(), matrix.cols(), computationOptions);
   this->m_nonzeroSingularValues = 0;
   m_computed = Matrix<int, Dynamic, Dynamic>::Zero(rows(), cols());
@@ -279,8 +292,7 @@ BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsign
 
 // Methode which compute the BDCSVD
 template<typename MatrixType>
-SVDBase<MatrixType>&
+BDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions) 
-BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions) 
 {
   allocate(matrix.rows(), matrix.cols(), computationOptions);
   using std::abs;

unsupported/Eigen/src/BDCSVD/CMakeLists.txt

@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_BDCSVD_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_BDCSVD_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/BDCSVD COMPONENT Devel
+  )

unsupported/Eigen/src/CMakeLists.txt

@@ -12,3 +12,4 @@ ADD_SUBDIRECTORY(Skyline)
 ADD_SUBDIRECTORY(SparseExtra)
 ADD_SUBDIRECTORY(KroneckerProduct)
 ADD_SUBDIRECTORY(Splines)
+ADD_SUBDIRECTORY(BDCSVD)

unsupported/Eigen/src/IterativeSolvers/GMRES.h

@@ -27,7 +27,7 @@ namespace internal {
  *  \param iters     on input: maximum number of iterations to perform
  *                   on output: number of iterations performed
  *  \param restart   number of iterations for a restart
- *  \param tol_error on input: residual tolerance
+ *  \param tol_error on input: relative residual tolerance
  *                   on output: residuum achieved
  *
  * \sa IterativeMethods::bicgstab()
@@ -70,18 +70,24 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
 
 	const int m = mat.rows();
 
-	VectorType p0 = rhs - mat*x;
+	// residual and preconditioned residual
+	const VectorType p0 = rhs - mat*x;
 	VectorType r0 = precond.solve(p0);
 
+	const RealScalar r0Norm = r0.norm();
+
 	// is initial guess already good enough?
-	if(abs(r0.norm()) < tol) {
+	if(r0Norm == 0) {
+		tol_error=0;
 		return true;
 	}
 
+	// storage for Hessenberg matrix and Householder data
+	FMatrixType H = FMatrixType::Zero(m, restart + 1);
 	VectorType w = VectorType::Zero(restart + 1);
-
-	FMatrixType H = FMatrixType::Zero(m, restart + 1); // Hessenberg matrix
 	VectorType tau = VectorType::Zero(restart + 1);
+
+	// storage for Jacobi rotations
 	std::vector < JacobiRotation < Scalar > > G(restart);
 
 	// generate first Householder vector
@@ -112,7 +118,6 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
 		}
 
 		if (v.tail(m - k).norm() != 0.0) {
-
 			if (k <= restart) {
 
 				// generate new Householder vector
@@ -135,19 +140,19 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
 		}
 
 		if (k<m && v(k) != (Scalar) 0) {
+
 			// determine next Givens rotation
 			G[k - 1].makeGivens(v(k - 1), v(k));
 
 			// apply Givens rotation to v and w
 			v.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());
 			w.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());
-
 		}
 
 		// insert coefficients into upper matrix triangle
 		H.col(k - 1).head(k) = v.head(k);
 
-                bool stop=(k==m || abs(w(k)) < tol || iters == maxIters);
+		bool stop=(k==m || abs(w(k)) < tol * r0Norm || iters == maxIters);
 
 		if (stop || k == restart) {
 
@@ -174,13 +179,13 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
 			} else {
 				k=0;
 
-                                // reset data for a restart  r0 = rhs - mat * x;
+				// reset data for restart
-                                VectorType p0=mat*x;
+				const VectorType p0 = rhs - mat*x;
-                                VectorType p1=precond.solve(p0);
+				r0 = precond.solve(p0);
-                                r0 = rhs - p1;
+
-//                                 r0_sqnorm = r0.squaredNorm();
+				// clear Hessenberg matrix and Householder data
-                                w = VectorType::Zero(restart + 1);
 				H = FMatrixType::Zero(m, restart + 1);
+				w = VectorType::Zero(restart + 1);
 				tau = VectorType::Zero(restart + 1);
 
 				// generate first Householder vector
@@ -194,7 +199,6 @@ bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Precondition
 		}
 
 
-
 	}
 
 	return false;

unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h

@@ -145,10 +145,12 @@ class LevenbergMarquardt : internal::no_assignment_operator
     /** Sets the default parameters */
     void resetParameters() 
     {
+      using std::sqrt;        
+
       m_factor = 100.; 
       m_maxfev = 400; 
-      m_ftol = std::sqrt(NumTraits<RealScalar>::epsilon());
+      m_ftol = sqrt(NumTraits<RealScalar>::epsilon());
-      m_xtol = std::sqrt(NumTraits<RealScalar>::epsilon());
+      m_xtol = sqrt(NumTraits<RealScalar>::epsilon());
       m_gtol = 0. ; 
       m_epsfcn = 0. ;
     }

unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h

@@ -45,6 +45,12 @@ namespace LevenbergMarquardtSpace {
 template<typename FunctorType, typename Scalar=double>
 class LevenbergMarquardt
 {
+    static Scalar sqrt_epsilon()
+    {
+      using std::sqrt;
+      return sqrt(NumTraits<Scalar>::epsilon());
+    }
+    
 public:
     LevenbergMarquardt(FunctorType &_functor)
         : functor(_functor) { nfev = njev = iter = 0;  fnorm = gnorm = 0.; useExternalScaling=false; }
@@ -55,8 +61,8 @@ public:
         Parameters()
             : factor(Scalar(100.))
             , maxfev(400)
-            , ftol(std::sqrt(NumTraits<Scalar>::epsilon()))
+            , ftol(sqrt_epsilon())
-            , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
+            , xtol(sqrt_epsilon())
             , gtol(Scalar(0.))
             , epsfcn(Scalar(0.)) {}
         Scalar factor;
@@ -72,7 +78,7 @@ public:
 
     LevenbergMarquardtSpace::Status lmder1(
             FVectorType &x,
-            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = sqrt_epsilon()
             );
 
     LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@@ -83,12 +89,12 @@ public:
             FunctorType &functor,
             FVectorType &x,
             Index *nfev,
-            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = sqrt_epsilon()
             );
 
     LevenbergMarquardtSpace::Status lmstr1(
             FVectorType  &x,
-            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = sqrt_epsilon()
             );
 
     LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType  &x);
@@ -109,6 +115,7 @@ public:
 
     Scalar lm_param(void) { return par; }
 private:
+    
     FunctorType &functor;
     Index n;
     Index m;

unsupported/Eigen/src/SVD/CMakeLists.txt

@@ -1,6 +0,0 @@
-FILE(GLOB Eigen_SVD_SRCS "*.h")
-
-INSTALL(FILES
-  ${Eigen_SVD_SRCS}
-  DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/SVD COMPONENT Devel
-  )

unsupported/Eigen/src/SVD/JacobiSVD.h

@@ -1,782 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN_JACOBISVD_H
-#define EIGEN_JACOBISVD_H
-
-namespace Eigen { 
-
-namespace internal {
-// forward declaration (needed by ICC)
-// the empty body is required by MSVC
-template<typename MatrixType, int QRPreconditioner,
-         bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
-struct svd_precondition_2x2_block_to_be_real {};
-
-/*** QR preconditioners (R-SVD)
- ***
- *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
- *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
- *** JacobiSVD which by itself is only able to work on square matrices.
- ***/
-
-enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
-
-template<typename MatrixType, int QRPreconditioner, int Case>
-struct qr_preconditioner_should_do_anything
-{
-  enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
-             MatrixType::ColsAtCompileTime != Dynamic &&
-             MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
-         b = MatrixType::RowsAtCompileTime != Dynamic &&
-             MatrixType::ColsAtCompileTime != Dynamic &&
-             MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
-         ret = !( (QRPreconditioner == NoQRPreconditioner) ||
-                  (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
-                  (Case == PreconditionIfMoreRowsThanCols && bool(b)) )
-  };
-};
-
-template<typename MatrixType, int QRPreconditioner, int Case,
-         bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret
-> struct qr_preconditioner_impl {};
-
-template<typename MatrixType, int QRPreconditioner, int Case>
-class qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>
-{
-public:
-  typedef typename MatrixType::Index Index;
-  void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}
-  bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)
-  {
-    return false;
-  }
-};
-
-/*** preconditioner using FullPivHouseholderQR ***/
-
-template<typename MatrixType>
-class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
-{
-public:
-  typedef typename MatrixType::Index Index;
-  typedef typename MatrixType::Scalar Scalar;
-  enum
-  {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
-  };
-  typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;
-
-  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
-  {
-    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
-    {
-      m_qr.~QRType();
-      ::new (&m_qr) QRType(svd.rows(), svd.cols());
-    }
-    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
-  }
-
-  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
-  {
-    if(matrix.rows() > matrix.cols())
-    {
-      m_qr.compute(matrix);
-      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
-      if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
-      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
-      return true;
-    }
-    return false;
-  }
-private:
-  typedef FullPivHouseholderQR<MatrixType> QRType;
-  QRType m_qr;
-  WorkspaceType m_workspace;
-};
-
-template<typename MatrixType>
-class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
-{
-public:
-  typedef typename MatrixType::Index Index;
-  typedef typename MatrixType::Scalar Scalar;
-  enum
-  {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
-    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    Options = MatrixType::Options
-  };
-  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
-          TransposeTypeWithSameStorageOrder;
-
-  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
-  {
-    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
-    {
-      m_qr.~QRType();
-      ::new (&m_qr) QRType(svd.cols(), svd.rows());
-    }
-    m_adjoint.resize(svd.cols(), svd.rows());
-    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
-  }
-
-  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
-  {
-    if(matrix.cols() > matrix.rows())
-    {
-      m_adjoint = matrix.adjoint();
-      m_qr.compute(m_adjoint);
-      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
-      if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
-      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
-      return true;
-    }
-    else return false;
-  }
-private:
-  typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
-  QRType m_qr;
-  TransposeTypeWithSameStorageOrder m_adjoint;
-  typename internal::plain_row_type<MatrixType>::type m_workspace;
-};
-
-/*** preconditioner using ColPivHouseholderQR ***/
-
-template<typename MatrixType>
-class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
-{
-public:
-  typedef typename MatrixType::Index Index;
-
-  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
-  {
-    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
-    {
-      m_qr.~QRType();
-      ::new (&m_qr) QRType(svd.rows(), svd.cols());
-    }
-    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
-    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
-  }
-
-  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
-  {
-    if(matrix.rows() > matrix.cols())
-    {
-      m_qr.compute(matrix);
-      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
-      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
-      else if(svd.m_computeThinU)
-      {
-        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
-        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
-      }
-      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
-      return true;
-    }
-    return false;
-  }
-
-private:
-  typedef ColPivHouseholderQR<MatrixType> QRType;
-  QRType m_qr;
-  typename internal::plain_col_type<MatrixType>::type m_workspace;
-};
-
-template<typename MatrixType>
-class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
-{
-public:
-  typedef typename MatrixType::Index Index;
-  typedef typename MatrixType::Scalar Scalar;
-  enum
-  {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
-    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    Options = MatrixType::Options
-  };
-
-  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
-          TransposeTypeWithSameStorageOrder;
-
-  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
-  {
-    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
-    {
-      m_qr.~QRType();
-      ::new (&m_qr) QRType(svd.cols(), svd.rows());
-    }
-    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
-    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
-    m_adjoint.resize(svd.cols(), svd.rows());
-  }
-
-  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
-  {
-    if(matrix.cols() > matrix.rows())
-    {
-      m_adjoint = matrix.adjoint();
-      m_qr.compute(m_adjoint);
-
-      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
-      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
-      else if(svd.m_computeThinV)
-      {
-        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
-        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
-      }
-      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
-      return true;
-    }
-    else return false;
-  }
-
-private:
-  typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
-  QRType m_qr;
-  TransposeTypeWithSameStorageOrder m_adjoint;
-  typename internal::plain_row_type<MatrixType>::type m_workspace;
-};
-
-/*** preconditioner using HouseholderQR ***/
-
-template<typename MatrixType>
-class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
-{
-public:
-  typedef typename MatrixType::Index Index;
-
-  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
-  {
-    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
-    {
-      m_qr.~QRType();
-      ::new (&m_qr) QRType(svd.rows(), svd.cols());
-    }
-    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
-    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
-  }
-
-  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
-  {
-    if(matrix.rows() > matrix.cols())
-    {
-      m_qr.compute(matrix);
-      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
-      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
-      else if(svd.m_computeThinU)
-      {
-        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
-        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
-      }
-      if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
-      return true;
-    }
-    return false;
-  }
-private:
-  typedef HouseholderQR<MatrixType> QRType;
-  QRType m_qr;
-  typename internal::plain_col_type<MatrixType>::type m_workspace;
-};
-
-template<typename MatrixType>
-class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
-{
-public:
-  typedef typename MatrixType::Index Index;
-  typedef typename MatrixType::Scalar Scalar;
-  enum
-  {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
-    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    Options = MatrixType::Options
-  };
-
-  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
-          TransposeTypeWithSameStorageOrder;
-
-  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
-  {
-    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
-    {
-      m_qr.~QRType();
-      ::new (&m_qr) QRType(svd.cols(), svd.rows());
-    }
-    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
-    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
-    m_adjoint.resize(svd.cols(), svd.rows());
-  }
-
-  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
-  {
-    if(matrix.cols() > matrix.rows())
-    {
-      m_adjoint = matrix.adjoint();
-      m_qr.compute(m_adjoint);
-
-      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
-      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
-      else if(svd.m_computeThinV)
-      {
-        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
-        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
-      }
-      if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
-      return true;
-    }
-    else return false;
-  }
-
-private:
-  typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
-  QRType m_qr;
-  TransposeTypeWithSameStorageOrder m_adjoint;
-  typename internal::plain_row_type<MatrixType>::type m_workspace;
-};
-
-/*** 2x2 SVD implementation
- ***
- *** JacobiSVD consists in performing a series of 2x2 SVD subproblems
- ***/
-
-template<typename MatrixType, int QRPreconditioner>
-struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
-{
-  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
-  typedef typename SVD::Index Index;
-  static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {}
-};
-
-template<typename MatrixType, int QRPreconditioner>
-struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
-{
-  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
-  typedef typename MatrixType::Scalar Scalar;
-  typedef typename MatrixType::RealScalar RealScalar;
-  typedef typename SVD::Index Index;
-  static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
-  {
-    using std::sqrt;
-    Scalar z;
-    JacobiRotation<Scalar> rot;
-    RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
-    if(n==0)
-    {
-      z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
-      work_matrix.row(p) *= z;
-      if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
-      z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
-      work_matrix.row(q) *= z;
-      if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
-    }
-    else
-    {
-      rot.c() = conj(work_matrix.coeff(p,p)) / n;
-      rot.s() = work_matrix.coeff(q,p) / n;
-      work_matrix.applyOnTheLeft(p,q,rot);
-      if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
-      if(work_matrix.coeff(p,q) != Scalar(0))
-      {
-        Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
-        work_matrix.col(q) *= z;
-        if(svd.computeV()) svd.m_matrixV.col(q) *= z;
-      }
-      if(work_matrix.coeff(q,q) != Scalar(0))
-      {
-        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
-        work_matrix.row(q) *= z;
-        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
-      }
-    }
-  }
-};
-
-template<typename MatrixType, typename RealScalar, typename Index>
-void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
-                            JacobiRotation<RealScalar> *j_left,
-                            JacobiRotation<RealScalar> *j_right)
-{
-  using std::sqrt;
-  Matrix<RealScalar,2,2> m;
-  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
-       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
-  JacobiRotation<RealScalar> rot1;
-  RealScalar t = m.coeff(0,0) + m.coeff(1,1);
-  RealScalar d = m.coeff(1,0) - m.coeff(0,1);
-  if(t == RealScalar(0))
-  {
-    rot1.c() = RealScalar(0);
-    rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
-  }
-  else
-  {
-    RealScalar u = d / t;
-    rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
-    rot1.s() = rot1.c() * u;
-  }
-  m.applyOnTheLeft(0,1,rot1);
-  j_right->makeJacobi(m,0,1);
-  *j_left  = rot1 * j_right->transpose();
-}
-
-} // end namespace internal
-
-/** \ingroup SVD_Module
-  *
-  *
-  * \class JacobiSVD
-  *
-  * \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
-  *
-  * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
-  * \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally
-  *                        for the R-SVD step for non-square matrices. See discussion of possible values below.
-  *
-  * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
-  *   \f[ A = U S V^* \f]
-  * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
-  * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
-  * and right \em singular \em vectors of \a A respectively.
-  *
-  * Singular values are always sorted in decreasing order.
-  *
-  * This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask for them explicitly.
-  *
-  * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
-  * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
-  * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
-  * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
-  *
-  * Here's an example demonstrating basic usage:
-  * \include JacobiSVD_basic.cpp
-  * Output: \verbinclude JacobiSVD_basic.out
-  *
-  * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than
-  * bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \f$ O(n^2p) \f$ where \a n is the smaller dimension and
-  * \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.
-  * In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
-  *
-  * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
-  * terminate in finite (and reasonable) time.
-  *
-  * The possible values for QRPreconditioner are:
-  * \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
-  * \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
-  *     Contrary to other QRs, it doesn't allow computing thin unitaries.
-  * \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.
-  *     This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization
-  *     is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive
-  *     process is more reliable than the optimized bidiagonal SVD iterations.
-  * \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing
-  *     JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in
-  *     faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking
-  *     if QR preconditioning is needed before applying it anyway.
-  *
-  * \sa MatrixBase::jacobiSvd()
-  */
-template<typename _MatrixType, int QRPreconditioner> 
-class JacobiSVD : public SVDBase<_MatrixType>
-{
-  public:
-
-    typedef _MatrixType MatrixType;
-    typedef typename MatrixType::Scalar Scalar;
-    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    typedef typename MatrixType::Index Index;
-    enum {
-      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-      DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
-      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
-      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-      MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
-      MatrixOptions = MatrixType::Options
-    };
-
-    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
-                   MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
-            MatrixUType;
-    typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
-                   MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
-            MatrixVType;
-    typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
-    typedef typename internal::plain_row_type<MatrixType>::type RowType;
-    typedef typename internal::plain_col_type<MatrixType>::type ColType;
-    typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
-                   MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
-            WorkMatrixType;
-
-    /** \brief Default Constructor.
-      *
-      * The default constructor is useful in cases in which the user intends to
-      * perform decompositions via JacobiSVD::compute(const MatrixType&).
-      */
-    JacobiSVD()
-      : SVDBase<_MatrixType>::SVDBase()
-    {}
-
-
-    /** \brief Default Constructor with memory preallocation
-      *
-      * Like the default constructor but with preallocation of the internal data
-      * according to the specified problem size.
-      * \sa JacobiSVD()
-      */
-    JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
-      : SVDBase<_MatrixType>::SVDBase() 
-    {
-      allocate(rows, cols, computationOptions);
-    }
-
-    /** \brief Constructor performing the decomposition of given matrix.
-     *
-     * \param matrix the matrix to decompose
-     * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
-     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
-     *                           #ComputeFullV, #ComputeThinV.
-     *
-     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
-     * available with the (non-default) FullPivHouseholderQR preconditioner.
-     */
-    JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
-      : SVDBase<_MatrixType>::SVDBase()
-    {
-      compute(matrix, computationOptions);
-    }
-
-    /** \brief Method performing the decomposition of given matrix using custom options.
-     *
-     * \param matrix the matrix to decompose
-     * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
-     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
-     *                           #ComputeFullV, #ComputeThinV.
-     *
-     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
-     * available with the (non-default) FullPivHouseholderQR preconditioner.
-     */
-    SVDBase<MatrixType>& compute(const MatrixType& matrix, unsigned int computationOptions);
-
-    /** \brief Method performing the decomposition of given matrix using current options.
-     *
-     * \param matrix the matrix to decompose
-     *
-     * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
-     */
-    SVDBase<MatrixType>& compute(const MatrixType& matrix)
-    {
-      return compute(matrix, this->m_computationOptions);
-    }
-    
-    /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
-      *
-      * \param b the right-hand-side of the equation to solve.
-      *
-      * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
-      *
-      * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
-      * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
-      */
-    template<typename Rhs>
-    inline const internal::solve_retval<JacobiSVD, Rhs>
-    solve(const MatrixBase<Rhs>& b) const
-    {
-      eigen_assert(this->m_isInitialized && "JacobiSVD is not initialized.");
-      eigen_assert(SVDBase<MatrixType>::computeU() && SVDBase<MatrixType>::computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
-      return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
-    }
-
-    
-
-  private:
-    void allocate(Index rows, Index cols, unsigned int computationOptions);
-
-  protected:
-    WorkMatrixType m_workMatrix;
-   
-    template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
-    friend struct internal::svd_precondition_2x2_block_to_be_real;
-    template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything>
-    friend struct internal::qr_preconditioner_impl;
-
-    internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;
-    internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;
-};
-
-template<typename MatrixType, int QRPreconditioner>
-void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions)
-{
-  if (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) return;
-
-  if (QRPreconditioner == FullPivHouseholderQRPreconditioner)
-  {
-      eigen_assert(!(this->m_computeThinU || this->m_computeThinV) &&
-              "JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
-              "Use the ColPivHouseholderQR preconditioner instead.");
-  }
-
-  m_workMatrix.resize(this->m_diagSize, this->m_diagSize);
-  
-  if(this->m_cols>this->m_rows) m_qr_precond_morecols.allocate(*this);
-  if(this->m_rows>this->m_cols) m_qr_precond_morerows.allocate(*this);
-}
-
-template<typename MatrixType, int QRPreconditioner>
-SVDBase<MatrixType>&
-JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
-{
-  using std::abs;
-  allocate(matrix.rows(), matrix.cols(), computationOptions);
-
-  // currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
-  // only worsening the precision of U and V as we accumulate more rotations
-  const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
-
-  // limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
-  const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
-
-  /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
-
-  if(!m_qr_precond_morecols.run(*this, matrix) && !m_qr_precond_morerows.run(*this, matrix))
-  {
-    m_workMatrix = matrix.block(0,0,this->m_diagSize,this->m_diagSize);
-    if(this->m_computeFullU) this->m_matrixU.setIdentity(this->m_rows,this->m_rows);
-    if(this->m_computeThinU) this->m_matrixU.setIdentity(this->m_rows,this->m_diagSize);
-    if(this->m_computeFullV) this->m_matrixV.setIdentity(this->m_cols,this->m_cols);
-    if(this->m_computeThinV) this->m_matrixV.setIdentity(this->m_cols, this->m_diagSize);
-  }
-
-  /*** step 2. The main Jacobi SVD iteration. ***/
-
-  bool finished = false;
-  while(!finished)
-  {
-    finished = true;
-
-    // do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
-
-    for(Index p = 1; p < this->m_diagSize; ++p)
-    {
-      for(Index q = 0; q < p; ++q)
-      {
-        // if this 2x2 sub-matrix is not diagonal already...
-        // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
-        // keep us iterating forever. Similarly, small denormal numbers are considered zero.
-        using std::max;
-        RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
-                                                                       abs(m_workMatrix.coeff(q,q))));
-        if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)
-        {
-          finished = false;
-
-          // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
-          internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q);
-          JacobiRotation<RealScalar> j_left, j_right;
-          internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
-
-          // accumulate resulting Jacobi rotations
-          m_workMatrix.applyOnTheLeft(p,q,j_left);
-          if(SVDBase<MatrixType>::computeU()) this->m_matrixU.applyOnTheRight(p,q,j_left.transpose());
-
-          m_workMatrix.applyOnTheRight(p,q,j_right);
-          if(SVDBase<MatrixType>::computeV()) this->m_matrixV.applyOnTheRight(p,q,j_right);
-        }
-      }
-    }
-  }
-
-  /*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
-
-  for(Index i = 0; i < this->m_diagSize; ++i)
-  {
-    RealScalar a = abs(m_workMatrix.coeff(i,i));
-    this->m_singularValues.coeffRef(i) = a;
-    if(SVDBase<MatrixType>::computeU() && (a!=RealScalar(0))) this->m_matrixU.col(i) *= this->m_workMatrix.coeff(i,i)/a;
-  }
-
-  /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
-
-  this->m_nonzeroSingularValues = this->m_diagSize;
-  for(Index i = 0; i < this->m_diagSize; i++)
-  {
-    Index pos;
-    RealScalar maxRemainingSingularValue = this->m_singularValues.tail(this->m_diagSize-i).maxCoeff(&pos);
-    if(maxRemainingSingularValue == RealScalar(0))
-    {
-      this->m_nonzeroSingularValues = i;
-      break;
-    }
-    if(pos)
-    {
-      pos += i;
-      std::swap(this->m_singularValues.coeffRef(i), this->m_singularValues.coeffRef(pos));
-      if(SVDBase<MatrixType>::computeU()) this->m_matrixU.col(pos).swap(this->m_matrixU.col(i));
-      if(SVDBase<MatrixType>::computeV()) this->m_matrixV.col(pos).swap(this->m_matrixV.col(i));
-    }
-  }
-
-  this->m_isInitialized = true;
-  return *this;
-}
-
-namespace internal {
-template<typename _MatrixType, int QRPreconditioner, typename Rhs>
-struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
-  : solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
-{
-  typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType;
-  EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs)
-
-  template<typename Dest> void evalTo(Dest& dst) const
-  {
-    eigen_assert(rhs().rows() == dec().rows());
-
-    // A = U S V^*
-    // So A^{-1} = V S^{-1} U^*
-
-    Index diagSize = (std::min)(dec().rows(), dec().cols());
-    typename JacobiSVDType::SingularValuesType invertedSingVals(diagSize);
-
-    Index nonzeroSingVals = dec().nonzeroSingularValues();
-    invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();
-    invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();
-
-    dst = dec().matrixV().leftCols(diagSize)
-        * invertedSingVals.asDiagonal()
-        * dec().matrixU().leftCols(diagSize).adjoint()
-        * rhs();
-  }
-};
-} // end namespace internal
-
-/** \svd_module
-  *
-  * \return the singular value decomposition of \c *this computed by two-sided
-  * Jacobi transformations.
-  *
-  * \sa class JacobiSVD
-  */
-template<typename Derived>
-JacobiSVD<typename MatrixBase<Derived>::PlainObject>
-MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const
-{
-  return JacobiSVD<PlainObject>(*this, computationOptions);
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_JACOBISVD_H

unsupported/doc/examples/CMakeLists.txt

@@ -10,12 +10,10 @@ FOREACH(example_src ${examples_SRCS})
   if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
     target_link_libraries(example_${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
   endif()
-  GET_TARGET_PROPERTY(example_executable
-                      example_${example} LOCATION)
   ADD_CUSTOM_COMMAND(
     TARGET example_${example}
     POST_BUILD
-    COMMAND ${example_executable}
+    COMMAND example_${example}
     ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out
   )
   ADD_DEPENDENCIES(unsupported_examples example_${example})

unsupported/doc/snippets/CMakeLists.txt

@@ -14,12 +14,10 @@ FOREACH(snippet_src ${snippets_SRCS})
   if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
     target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
   endif()
-  GET_TARGET_PROPERTY(compile_snippet_executable
-                      ${compile_snippet_target} LOCATION)
   ADD_CUSTOM_COMMAND(
     TARGET ${compile_snippet_target}
     POST_BUILD
-    COMMAND ${compile_snippet_executable}
+    COMMAND ${compile_snippet_target}
     ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out
   )
   ADD_DEPENDENCIES(unsupported_snippets ${compile_snippet_target})

unsupported/test/NonLinearOptimization.cpp

@@ -1022,7 +1022,8 @@ void testNistLanczos1(void)
   VERIFY_IS_EQUAL(lm.nfev, 79);
   VERIFY_IS_EQUAL(lm.njev, 72);
   // check norm^2
-  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.430899764097e-25);  // should be 1.4307867721E-25, but nist results are on 128-bit floats
+  std::cout.precision(30);
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4290986055242372e-25);  // should be 1.4307867721E-25, but nist results are on 128-bit floats
   // check x
   VERIFY_IS_APPROX(x[0], 9.5100000027E-02);
   VERIFY_IS_APPROX(x[1], 1.0000000001E+00);
@@ -1043,7 +1044,7 @@ void testNistLanczos1(void)
   VERIFY_IS_EQUAL(lm.nfev, 9);
   VERIFY_IS_EQUAL(lm.njev, 8);
   // check norm^2
-  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.428595533845e-25);  // should be 1.4307867721E-25, but nist results are on 128-bit floats
+  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.430571737783119393e-25);  // should be 1.4307867721E-25, but nist results are on 128-bit floats
   // check x
   VERIFY_IS_APPROX(x[0], 9.5100000027E-02);
   VERIFY_IS_APPROX(x[1], 1.0000000001E+00);
@@ -1262,8 +1263,8 @@ void testNistBoxBOD(void)
 
   // check return value
   VERIFY_IS_EQUAL(info, 1);
-  VERIFY_IS_EQUAL(lm.nfev, 31);
+  VERIFY(lm.nfev < 31); // 31
-  VERIFY_IS_EQUAL(lm.njev, 25);
+  VERIFY(lm.njev < 25); // 25
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);
   // check x
@@ -1342,10 +1343,6 @@ void testNistMGH17(void)
   lm.parameters.maxfev = 1000;
   info = lm.minimize(x);
 
-  // check return value
-  VERIFY_IS_EQUAL(info, 2); 
-  VERIFY_IS_EQUAL(lm.nfev, 602 ); 
-  VERIFY_IS_EQUAL(lm.njev, 545 ); 
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);
   // check x
@@ -1355,6 +1352,11 @@ void testNistMGH17(void)
   VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
   VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
   
+  // check return value
+  VERIFY_IS_EQUAL(info, 2); 
+  VERIFY(lm.nfev < 650);  // 602
+  VERIFY(lm.njev < 600);  // 545
+
   /*
    * Second try
    */
@@ -1832,8 +1834,8 @@ void test_NonLinearOptimization()
     // NIST tests, level of difficulty = "Average"
     CALL_SUBTEST/*_5*/(testNistHahn1());
     CALL_SUBTEST/*_6*/(testNistMisra1d());
-//     CALL_SUBTEST/*_7*/(testNistMGH17());
+    CALL_SUBTEST/*_7*/(testNistMGH17());
-//     CALL_SUBTEST/*_8*/(testNistLanczos1());
+    CALL_SUBTEST/*_8*/(testNistLanczos1());
 
 //     // NIST tests, level of difficulty = "Higher"
     CALL_SUBTEST/*_9*/(testNistRat42());

unsupported/test/levenberg_marquardt.cpp

@@ -787,10 +787,6 @@ void testNistMGH10(void)
   LevenbergMarquardt<MGH10_functor> lm(functor);
   info = lm.minimize(x);
 
-  // check return value
-  VERIFY_IS_EQUAL(info, 1); 
-  VERIFY_IS_EQUAL(lm.nfev(), 284 ); 
-  VERIFY_IS_EQUAL(lm.njev(), 249 ); 
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01);
   // check x
@@ -798,6 +794,11 @@ void testNistMGH10(void)
   VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
   VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
   
+  // check return value
+  //VERIFY_IS_EQUAL(info, 1);
+  VERIFY_IS_EQUAL(lm.nfev(), 284 );
+  VERIFY_IS_EQUAL(lm.njev(), 249 );
+
   /*
    * Second try
    */
@@ -805,16 +806,17 @@ void testNistMGH10(void)
   // do the computation
   info = lm.minimize(x);
 
-  // check return value
-  VERIFY_IS_EQUAL(info, 1);
-  VERIFY_IS_EQUAL(lm.nfev(), 126);
-  VERIFY_IS_EQUAL(lm.njev(), 116);
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01);
   // check x
   VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
   VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
   VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+  
+  // check return value
+  //VERIFY_IS_EQUAL(info, 1);
+  VERIFY_IS_EQUAL(lm.nfev(), 126);
+  VERIFY_IS_EQUAL(lm.njev(), 116);
 }
 
 
@@ -866,16 +868,17 @@ void testNistBoxBOD(void)
   lm.setFactor(10);
   info = lm.minimize(x);
 
-  // check return value
-  VERIFY_IS_EQUAL(info, 1);
-  VERIFY_IS_EQUAL(lm.nfev(), 31);
-  VERIFY_IS_EQUAL(lm.njev(), 25);
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03);
   // check x
   VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
   VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
   
+  // check return value
+  VERIFY_IS_EQUAL(info, 1);
+  VERIFY(lm.nfev() < 31); // 31
+  VERIFY(lm.njev() < 25); // 25
+
   /*
    * Second try
    */
@@ -948,10 +951,6 @@ void testNistMGH17(void)
   lm.setMaxfev(1000);
   info = lm.minimize(x);
 
-  // check return value
-//   VERIFY_IS_EQUAL(info, 2);  //FIXME Use (lm.info() == Success)
-//   VERIFY_IS_EQUAL(lm.nfev(), 602 ); 
-  VERIFY_IS_EQUAL(lm.njev(), 545 ); 
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05);
   // check x
@@ -961,6 +960,11 @@ void testNistMGH17(void)
   VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
   VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
   
+    // check return value
+//   VERIFY_IS_EQUAL(info, 2);  //FIXME Use (lm.info() == Success)
+  VERIFY(lm.nfev() < 700 ); // 602
+  VERIFY(lm.njev() < 600 ); // 545
+
   /*
    * Second try
    */
@@ -1035,10 +1039,6 @@ void testNistMGH09(void)
   lm.setMaxfev(1000);
   info = lm.minimize(x);
 
-  // check return value
-  VERIFY_IS_EQUAL(info, 1); 
-  VERIFY_IS_EQUAL(lm.nfev(), 490 ); 
-  VERIFY_IS_EQUAL(lm.njev(), 376 ); 
   // check norm^2
   VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04);
   // check x
@@ -1046,6 +1046,10 @@ void testNistMGH09(void)
   VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01
   VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01
   VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01
+  // check return value
+  VERIFY_IS_EQUAL(info, 1); 
+  VERIFY(lm.nfev() < 510 ); // 490
+  VERIFY(lm.njev() < 400 ); // 376
 
   /*
    * Second try

unsupported/test/svd_common.h

@@ -18,7 +18,7 @@
 #define EIGEN_RUNTIME_NO_MALLOC
 
 #include "main.h"
-#include <unsupported/Eigen/SVD>
+#include <unsupported/Eigen/BDCSVD>
 #include <Eigen/LU>