Unify unit test for BDC and Jacobi SVD. This reveals some numerical issues in BDCSVD.

2 files changed, 473 insertions, 394 deletions

diff --git a/test/jacobisvd.cpp b/test/jacobisvd.cpp
index cd04db5be..bfcadce95 100644
--- a/test/jacobisvd.cpp
+++ b/test/jacobisvd.cpp
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
@@ -14,273 +14,47 @@
 #include "main.h"
 #include <Eigen/SVD>
 
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& svd)
-{
-  typedef typename MatrixType::Index Index;
-  Index rows = m.rows();
-  Index cols = m.cols();
-
-  enum {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = MatrixType::ColsAtCompileTime
-  };
-
-  typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
-  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
-
-  MatrixType sigma = MatrixType::Zero(rows,cols);
-  sigma.diagonal() = svd.singularValues().template cast<Scalar>();
-  MatrixUType u = svd.matrixU();
-  MatrixVType v = svd.matrixV();
-
-  VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
-  VERIFY_IS_UNITARY(u);
-  VERIFY_IS_UNITARY(v);
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_compare_to_full(const MatrixType& m,
-                               unsigned int computationOptions,
-                               const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd)
-{
-  typedef typename MatrixType::Index Index;
-  Index rows = m.rows();
-  Index cols = m.cols();
-  Index diagSize = (std::min)(rows, cols);
-
-  JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
-
-  VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
-  if(computationOptions & ComputeFullU)
-    VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
-  if(computationOptions & ComputeThinU)
-    VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
-  if(computationOptions & ComputeFullV)
-    VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
-  if(computationOptions & ComputeThinV)
-    VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_solve(const MatrixType& m, unsigned int computationOptions)
-{
-  typedef typename MatrixType::Scalar Scalar;
-  typedef typename MatrixType::RealScalar RealScalar;
-  typedef typename MatrixType::Index Index;
-  Index rows = m.rows();
-  Index cols = m.cols();
-
-  enum {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = MatrixType::ColsAtCompileTime
-  };
-
-  typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
-  typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
-
-  RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
-  JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
-
-       if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
-  else if(internal::is_same<RealScalar,float>::value)  svd.setThreshold(1e-4);
-  
-  SolutionType x = svd.solve(rhs);
-  
-  RealScalar residual = (m*x-rhs).norm();
-  // Check that there is no significantly better solution in the neighborhood of x
-  if(!test_isMuchSmallerThan(residual,rhs.norm()))
-  {
-    // If the residual is very small, then we have an exact solution, so we are already good.
-    for(int k=0;k<x.rows();++k)
-    {
-      SolutionType y(x);
-      y.row(k).array() += 2*NumTraits<RealScalar>::epsilon();
-      RealScalar residual_y = (m*y-rhs).norm();
-      VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
-      
-      y.row(k) = x.row(k).array() - 2*NumTraits<RealScalar>::epsilon();
-      residual_y = (m*y-rhs).norm();
-      VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
-    }
-  }
-  
-  // evaluate normal equation which works also for least-squares solutions
-  if(internal::is_same<RealScalar,double>::value)
-  {
-    // This test is not stable with single precision.
-    // This is probably because squaring m signicantly affects the precision.
-    VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
-  }
-  
-  // check minimal norm solutions
-  {
-    // generate a full-rank m x n problem with m<n
-    enum {
-      RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
-      RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
-    };
-    typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
-    typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
-    typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
-    Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
-    MatrixType2 m2(rank,cols);
-    int guard = 0;
-    do {
-      m2.setRandom();
-    } while(m2.jacobiSvd().setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
-    VERIFY(guard<10);
-    RhsType2 rhs2 = RhsType2::Random(rank);
-    // use QR to find a reference minimal norm solution
-    HouseholderQR<MatrixType2T> qr(m2.adjoint());
-    Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
-    tmp.conservativeResize(cols);
-    tmp.tail(cols-rank).setZero();
-    SolutionType x21 = qr.householderQ() * tmp;
-    // now check with SVD
-    JacobiSVD<MatrixType2, ColPivHouseholderQRPreconditioner> svd2(m2, computationOptions);
-    SolutionType x22 = svd2.solve(rhs2);
-    VERIFY_IS_APPROX(m2*x21, rhs2);
-    VERIFY_IS_APPROX(m2*x22, rhs2);
-    VERIFY_IS_APPROX(x21, x22);
-    
-    // Now check with a rank deficient matrix
-    typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
-    typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
-    Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
-    Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
-    MatrixType3 m3 = C * m2;
-    RhsType3 rhs3 = C * rhs2;
-    JacobiSVD<MatrixType3, ColPivHouseholderQRPreconditioner> svd3(m3, computationOptions);
-    SolutionType x3 = svd3.solve(rhs3);
-    VERIFY_IS_APPROX(m3*x3, rhs3);
-    VERIFY_IS_APPROX(m3*x21, rhs3);
-    VERIFY_IS_APPROX(m2*x3, rhs2);
-    
-    VERIFY_IS_APPROX(x21, x3);
-  }
-}
-
-template<typename MatrixType, int QRPreconditioner>
-void jacobisvd_test_all_computation_options(const MatrixType& m)
-{
-  if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
-    return;
-  JacobiSVD<MatrixType, QRPreconditioner> fullSvd(m, ComputeFullU|ComputeFullV);
-  CALL_SUBTEST(( jacobisvd_check_full(m, fullSvd) ));
-  CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeFullV) ));
-  
-  #if defined __INTEL_COMPILER
-  // remark #111: statement is unreachable
-  #pragma warning disable 111
-  #endif
-  if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
-    return;
-
-  CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU, fullSvd) ));
-  CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullV, fullSvd) ));
-  CALL_SUBTEST(( jacobisvd_compare_to_full(m, 0, fullSvd) ));
-
-  if (MatrixType::ColsAtCompileTime == Dynamic) {
-    // thin U/V are only available with dynamic number of columns
-    CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
-    CALL_SUBTEST(( jacobisvd_compare_to_full(m,              ComputeThinV, fullSvd) ));
-    CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
-    CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU             , fullSvd) ));
-    CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
-    CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeThinV) ));
-    CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeFullV) ));
-    CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeThinV) ));
-
-    // test reconstruction
-    typedef typename MatrixType::Index Index;
-    Index diagSize = (std::min)(m.rows(), m.cols());
-    JacobiSVD<MatrixType, QRPreconditioner> svd(m, ComputeThinU | ComputeThinV);
-    VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
-  }
-}
+#define SVD_DEFAULT(M) JacobiSVD<M>
+#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>
+#include "svd_common.h"
 
+// Check all variants of JacobiSVD
 template<typename MatrixType>
 void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
 {
   MatrixType m = a;
   if(pickrandom)
-  {
-    typedef typename MatrixType::Scalar Scalar;
-    typedef typename MatrixType::RealScalar RealScalar;
-    typedef typename MatrixType::Index Index;
-    Index diagSize = (std::min)(a.rows(), a.cols());
-    RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
-    s = internal::random<RealScalar>(1,s);
-    Matrix<RealScalar,Dynamic,1> d =  Matrix<RealScalar,Dynamic,1>::Random(diagSize);
-    for(Index k=0; k<diagSize; ++k)
-      d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
-    m = Matrix<Scalar,Dynamic,Dynamic>::Random(a.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,a.cols());
-    // cancel some coeffs
-    Index n  = internal::random<Index>(0,m.size()-1);
-    for(Index i=0; i<n; ++i)
-      m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = Scalar(0);
-  }
+    svd_fill_random(m);
 
-  CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m) ));
-  CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m) ));
-  CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m) ));
-  CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m) ));
+  CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> >(m, true)  )); // check full only
+  CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>  >(m, false) ));
+  CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, HouseholderQRPreconditioner>        >(m, false) ));
+  if(m.rows()==m.cols())
+    CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, NoQRPreconditioner>               >(m, false) ));
 }
 
 template<typename MatrixType> void jacobisvd_verify_assert(const MatrixType& m)
 {
-  typedef typename MatrixType::Scalar Scalar;
+  svd_verify_assert<JacobiSVD<MatrixType> >(m);
   typedef typename MatrixType::Index Index;
   Index rows = m.rows();
   Index cols = m.cols();
 
   enum {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
     ColsAtCompileTime = MatrixType::ColsAtCompileTime
   };
 
-  typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
-
-  RhsType rhs(rows);
-
-  JacobiSVD<MatrixType> svd;
-  VERIFY_RAISES_ASSERT(svd.matrixU())
-  VERIFY_RAISES_ASSERT(svd.singularValues())
-  VERIFY_RAISES_ASSERT(svd.matrixV())
-  VERIFY_RAISES_ASSERT(svd.solve(rhs))
 
   MatrixType a = MatrixType::Zero(rows, cols);
   a.setZero();
-  svd.compute(a, 0);
-  VERIFY_RAISES_ASSERT(svd.matrixU())
-  VERIFY_RAISES_ASSERT(svd.matrixV())
-  svd.singularValues();
-  VERIFY_RAISES_ASSERT(svd.solve(rhs))
 
   if (ColsAtCompileTime == Dynamic)
   {
-    svd.compute(a, ComputeThinU);
-    svd.matrixU();
-    VERIFY_RAISES_ASSERT(svd.matrixV())
-    VERIFY_RAISES_ASSERT(svd.solve(rhs))
-
-    svd.compute(a, ComputeThinV);
-    svd.matrixV();
-    VERIFY_RAISES_ASSERT(svd.matrixU())
-    VERIFY_RAISES_ASSERT(svd.solve(rhs))
-
     JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;
     VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))
     VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))
     VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))
   }
-  else
-  {
-    VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
-    VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
-  }
 }
 
 template<typename MatrixType>
@@ -296,165 +70,17 @@ void jacobisvd_method()
   VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
 }
 
-// work around stupid msvc error when constructing at compile time an expression that involves
-// a division by zero, even if the numeric type has floating point
-template<typename Scalar>
-EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
-
-// workaround aggressive optimization in ICC
-template<typename T> EIGEN_DONT_INLINE  T sub(T a, T b) { return a - b; }
-
-template<typename MatrixType>
-void jacobisvd_inf_nan()
-{
-  // all this function does is verify we don't iterate infinitely on nan/inf values
-
-  JacobiSVD<MatrixType> svd;
-  typedef typename MatrixType::Scalar Scalar;
-  Scalar some_inf = Scalar(1) / zero<Scalar>();
-  VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
-  svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
-
-  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
-  VERIFY(nan != nan);
-  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)) = 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);
-}
-
-// Regression test for bug 286: JacobiSVD loops indefinitely with some
-// matrices containing denormal numbers.
-void jacobisvd_underoverflow()
-{
-#if defined __INTEL_COMPILER
-// shut up warning #239: floating point underflow
-#pragma warning push
-#pragma warning disable 239
-#endif
-  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
-  
-  // Check for overflow:
-  Matrix3d M3;
-  M3 << 4.4331978442502944e+307, -5.8585363752028680e+307,  6.4527017443412964e+307,
-        3.7841695601406358e+307,  2.4331702789740617e+306, -3.5235707140272905e+307,
-       -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
-
-  JacobiSVD<Matrix3d> svd3;
-  svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
-  jacobisvd_check_full(M3,svd3);
-}
-
-void jacobisvd_preallocate()
-{
-  Vector3f v(3.f, 2.f, 1.f);
-  MatrixXf m = v.asDiagonal();
-
-  internal::set_is_malloc_allowed(false);
-  VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
-  JacobiSVD<MatrixXf> svd;
-  internal::set_is_malloc_allowed(true);
-  svd.compute(m);
-  VERIFY_IS_APPROX(svd.singularValues(), v);
-
-  JacobiSVD<MatrixXf> svd2(3,3);
-  internal::set_is_malloc_allowed(false);
-  svd2.compute(m);
-  internal::set_is_malloc_allowed(true);
-  VERIFY_IS_APPROX(svd2.singularValues(), v);
-  VERIFY_RAISES_ASSERT(svd2.matrixU());
-  VERIFY_RAISES_ASSERT(svd2.matrixV());
-  svd2.compute(m, ComputeFullU | ComputeFullV);
-  VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
-  VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
-  internal::set_is_malloc_allowed(false);
-  svd2.compute(m);
-  internal::set_is_malloc_allowed(true);
-
-  JacobiSVD<MatrixXf> svd3(3,3,ComputeFullU|ComputeFullV);
-  internal::set_is_malloc_allowed(false);
-  svd2.compute(m);
-  internal::set_is_malloc_allowed(true);
-  VERIFY_IS_APPROX(svd2.singularValues(), v);
-  VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
-  VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
-  internal::set_is_malloc_allowed(false);
-  svd2.compute(m, ComputeFullU|ComputeFullV);
-  internal::set_is_malloc_allowed(true);
-}
-
 void test_jacobisvd()
 {
   CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
   CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) ));
   CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));
   CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));
+  
+  svd_all_trivial_2x2(jacobisvd<Matrix2cd>);
+  svd_all_trivial_2x2(jacobisvd<Matrix2d>);
 
   for(int i = 0; i < g_repeat; i++) {
-    Matrix2cd m;
-    m << 0, 1,
-         0, 1;
-    CALL_SUBTEST_1(( jacobisvd(m, false) ));
-    m << 1, 0,
-         1, 0;
-    CALL_SUBTEST_1(( jacobisvd(m, false) ));
-
-    Matrix2d n;
-    n << 0, 0,
-         0, 0;
-    CALL_SUBTEST_2(( jacobisvd(n, false) ));
-    n << 0, 0,
-         0, 1;
-    CALL_SUBTEST_2(( jacobisvd(n, false) ));
-    
     CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));
     CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));
     CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));
@@ -473,8 +99,8 @@ void test_jacobisvd()
     (void) c;
 
     // Test on inf/nan matrix
-    CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
-    CALL_SUBTEST_10( jacobisvd_inf_nan<MatrixXd>() );
+    CALL_SUBTEST_7(  (svd_inf_nan<JacobiSVD<MatrixXf>, MatrixXf>()) );
+    CALL_SUBTEST_10( (svd_inf_nan<JacobiSVD<MatrixXd>, 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))) ));
@@ -488,8 +114,7 @@ void test_jacobisvd()
   CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
 
   // Check that preallocation avoids subsequent mallocs
-  CALL_SUBTEST_9( jacobisvd_preallocate() );
+  CALL_SUBTEST_9( svd_preallocate() );
 
-  // Regression check for bug 286
-  CALL_SUBTEST_2( jacobisvd_underoverflow() );
+  CALL_SUBTEST_2( svd_underoverflow() );
 }
diff --git a/test/svd_common.h b/test/svd_common.h
new file mode 100644
index 000000000..4631939e5
--- /dev/null
+++ b/test/svd_common.h
@@ -0,0 +1,454 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 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 SVD_DEFAULT
+#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+#ifndef SVD_FOR_MIN_NORM
+#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+// Check that the matrix m is properly reconstructed and that the U and V factors are unitary
+// The SVD must have already been computed.
+template<typename SvdType, typename MatrixType>
+void svd_check_full(const MatrixType& m, const SvdType& svd)
+{
+  typedef typename MatrixType::Index Index;
+  Index rows = m.rows();
+  Index cols = m.cols();
+
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime
+  };
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
+  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
+
+  MatrixType sigma = MatrixType::Zero(rows,cols);
+  sigma.diagonal() = svd.singularValues().template cast<Scalar>();
+  MatrixUType u = svd.matrixU();
+  MatrixVType v = svd.matrixV();
+
+  VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
+  VERIFY_IS_UNITARY(u);
+  VERIFY_IS_UNITARY(v);
+}
+
+// Compare partial SVD defined by computationOptions to a full SVD referenceSvd
+template<typename SvdType, typename MatrixType>
+void svd_compare_to_full(const MatrixType& m,
+                         unsigned int computationOptions,
+                         const SvdType& referenceSvd)
+{
+  typedef typename MatrixType::Index Index;
+  Index rows = m.rows();
+  Index cols = m.cols();
+  Index diagSize = (std::min)(rows, cols);
+
+  SvdType svd(m, computationOptions);
+
+  VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
+  if(computationOptions & ComputeFullU)  VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
+  if(computationOptions & ComputeThinU)  VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
+  if(computationOptions & ComputeFullV)  VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
+  if(computationOptions & ComputeThinV)  VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
+}
+
+//
+template<typename SvdType, typename MatrixType>
+void svd_least_square(const MatrixType& m, unsigned int computationOptions)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  typedef typename MatrixType::Index Index;
+  Index rows = m.rows();
+  Index cols = m.cols();
+
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime
+  };
+
+  typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
+  typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+  RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
+  SvdType svd(m, computationOptions);
+
+       if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
+  else if(internal::is_same<RealScalar,float>::value)  svd.setThreshold(1e-4);
+  
+  SolutionType x = svd.solve(rhs);
+  
+  RealScalar residual = (m*x-rhs).norm();
+  // Check that there is no significantly better solution in the neighborhood of x
+  if(!test_isMuchSmallerThan(residual,rhs.norm()))
+  {
+    // If the residual is very small, then we have an exact solution, so we are already good.
+    for(int k=0;k<x.rows();++k)
+    {
+      SolutionType y(x);
+      y.row(k).array() += 2*NumTraits<RealScalar>::epsilon();
+      RealScalar residual_y = (m*y-rhs).norm();
+      VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+      
+      y.row(k) = x.row(k).array() - 2*NumTraits<RealScalar>::epsilon();
+      residual_y = (m*y-rhs).norm();
+      VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+    }
+  }
+  
+  // evaluate normal equation which works also for least-squares solutions
+  if(internal::is_same<RealScalar,double>::value)
+  {
+    // This test is not stable with single precision.
+    // This is probably because squaring m signicantly affects the precision.
+    VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
+  }
+}
+
+// check minimal norm solutions, the inoput matrix m is only used to recover problem size
+template<typename MatrixType>
+void svd_min_norm(const MatrixType& m, unsigned int computationOptions)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::Index Index;
+  Index cols = m.cols();
+
+  enum {
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime
+  };
+
+  typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+  // generate a full-rank m x n problem with m<n
+  enum {
+    RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
+    RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
+  };
+  typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
+  typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
+  typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
+  Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
+  MatrixType2 m2(rank,cols);
+  int guard = 0;
+  do {
+    m2.setRandom();
+  } while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
+  VERIFY(guard<10);
+  RhsType2 rhs2 = RhsType2::Random(rank);
+  // use QR to find a reference minimal norm solution
+  HouseholderQR<MatrixType2T> qr(m2.adjoint());
+  Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
+  tmp.conservativeResize(cols);
+  tmp.tail(cols-rank).setZero();
+  SolutionType x21 = qr.householderQ() * tmp;
+  // now check with SVD
+  SVD_FOR_MIN_NORM(MatrixType2) svd2(m2, computationOptions);
+  SolutionType x22 = svd2.solve(rhs2);
+  VERIFY_IS_APPROX(m2*x21, rhs2);
+  VERIFY_IS_APPROX(m2*x22, rhs2);
+  VERIFY_IS_APPROX(x21, x22);
+  
+  // Now check with a rank deficient matrix
+  typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
+  typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
+  Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
+  Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
+  MatrixType3 m3 = C * m2;
+  RhsType3 rhs3 = C * rhs2;
+  SVD_FOR_MIN_NORM(MatrixType3) svd3(m3, computationOptions);
+  SolutionType x3 = svd3.solve(rhs3);
+  VERIFY_IS_APPROX(m3*x3, rhs3);
+  VERIFY_IS_APPROX(m3*x21, rhs3);
+  VERIFY_IS_APPROX(m2*x3, rhs2);
+  
+  VERIFY_IS_APPROX(x21, x3);
+}
+
+// Check full, compare_to_full, least_square, and min_norm for all possible compute-options
+template<typename SvdType, typename MatrixType>
+void svd_test_all_computation_options(const MatrixType& m, bool full_only)
+{
+//   if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
+//     return;
+  SvdType fullSvd(m, ComputeFullU|ComputeFullV);
+  CALL_SUBTEST(( svd_check_full(m, fullSvd) ));
+  CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeFullV) ));
+  CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeFullV) ));
+  
+  #if defined __INTEL_COMPILER
+  // remark #111: statement is unreachable
+  #pragma warning disable 111
+  #endif
+  if(full_only)
+    return;
+
+  CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU, fullSvd) ));
+  CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullV, fullSvd) ));
+  CALL_SUBTEST(( svd_compare_to_full(m, 0, fullSvd) ));
+
+  if (MatrixType::ColsAtCompileTime == Dynamic) {
+    // thin U/V are only available with dynamic number of columns
+    CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
+    CALL_SUBTEST(( svd_compare_to_full(m,              ComputeThinV, fullSvd) ));
+    CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
+    CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU             , fullSvd) ));
+    CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
+    
+    CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeThinV) ));
+    CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeFullV) ));
+    CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeThinV) ));
+    
+    CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeThinV) ));
+    CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeFullV) ));
+    CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeThinV) ));
+
+    // test reconstruction
+    typedef typename MatrixType::Index Index;
+    Index diagSize = (std::min)(m.rows(), m.cols());
+    SvdType svd(m, ComputeThinU | ComputeThinV);
+    VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
+  }
+}
+
+template<typename MatrixType>
+void svd_fill_random(MatrixType &m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  typedef typename MatrixType::Index Index;
+  Index diagSize = (std::min)(m.rows(), m.cols());
+  RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
+  s = internal::random<RealScalar>(1,s);
+  Matrix<RealScalar,Dynamic,1> d =  Matrix<RealScalar,Dynamic,1>::Random(diagSize);
+  for(Index k=0; k<diagSize; ++k)
+    d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
+  m = Matrix<Scalar,Dynamic,Dynamic>::Random(m.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,m.cols());
+  // cancel some coeffs
+  Index n  = internal::random<Index>(0,m.size()-1);
+  for(Index i=0; i<n; ++i)
+    m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = Scalar(0);
+}
+
+
+// work around stupid msvc error when constructing at compile time an expression that involves
+// a division by zero, even if the numeric type has floating point
+template<typename Scalar>
+EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
+
+// workaround aggressive optimization in ICC
+template<typename T> EIGEN_DONT_INLINE  T sub(T a, T b) { return a - b; }
+
+// all this function does is verify we don't iterate infinitely on nan/inf values
+template<typename SvdType, typename MatrixType>
+void svd_inf_nan()
+{
+  SvdType svd;
+  typedef typename MatrixType::Scalar Scalar;
+  Scalar some_inf = Scalar(1) / zero<Scalar>();
+  VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
+  svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
+
+  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+  VERIFY(nan != nan);
+  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)) = 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);
+}
+
+// Regression test for bug 286: JacobiSVD loops indefinitely with some
+// matrices containing denormal numbers.
+void svd_underoverflow()
+{
+#if defined __INTEL_COMPILER
+// shut up warning #239: floating point underflow
+#pragma warning push
+#pragma warning disable 239
+#endif
+  Matrix2d M;
+  M << -7.90884e-313, -4.94e-324,
+                 0, 5.60844e-313;
+  SVD_DEFAULT(Matrix2d) svd;
+  svd.compute(M,ComputeFullU|ComputeFullV);
+  svd_check_full(M,svd);
+  
+  // Check all 2x2 matrices made with the following coefficients:
+  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);
+    svd_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
+  
+  // Check for overflow:
+  Matrix3d M3;
+  M3 << 4.4331978442502944e+307, -5.8585363752028680e+307,  6.4527017443412964e+307,
+        3.7841695601406358e+307,  2.4331702789740617e+306, -3.5235707140272905e+307,
+       -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
+
+  SVD_DEFAULT(Matrix3d) svd3;
+  svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
+  svd_check_full(M3,svd3);
+}
+
+// void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
+
+template<typename MatrixType>
+void svd_all_trivial_2x2( void (*cb)(const MatrixType&,bool) )
+{
+  MatrixType M;
+  VectorXd value_set(3);
+  value_set << 0, 1, -1;
+  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));
+    
+    cb(M,false);
+    
+    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());
+}
+
+void svd_preallocate()
+{
+  Vector3f v(3.f, 2.f, 1.f);
+  MatrixXf m = v.asDiagonal();
+
+  internal::set_is_malloc_allowed(false);
+  VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
+  SVD_DEFAULT(MatrixXf) svd;
+  internal::set_is_malloc_allowed(true);
+  svd.compute(m);
+  VERIFY_IS_APPROX(svd.singularValues(), v);
+
+  SVD_DEFAULT(MatrixXf) svd2(3,3);
+  internal::set_is_malloc_allowed(false);
+  svd2.compute(m);
+  internal::set_is_malloc_allowed(true);
+  VERIFY_IS_APPROX(svd2.singularValues(), v);
+  VERIFY_RAISES_ASSERT(svd2.matrixU());
+  VERIFY_RAISES_ASSERT(svd2.matrixV());
+  svd2.compute(m, ComputeFullU | ComputeFullV);
+  VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+  VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+  internal::set_is_malloc_allowed(false);
+  svd2.compute(m);
+  internal::set_is_malloc_allowed(true);
+
+  SVD_DEFAULT(MatrixXf) svd3(3,3,ComputeFullU|ComputeFullV);
+  internal::set_is_malloc_allowed(false);
+  svd2.compute(m);
+  internal::set_is_malloc_allowed(true);
+  VERIFY_IS_APPROX(svd2.singularValues(), v);
+  VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+  VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+  internal::set_is_malloc_allowed(false);
+  svd2.compute(m, ComputeFullU|ComputeFullV);
+  internal::set_is_malloc_allowed(true);
+}
+
+template<typename SvdType,typename MatrixType> 
+void svd_verify_assert(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::Index Index;
+  Index rows = m.rows();
+  Index cols = m.cols();
+
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime
+  };
+
+  typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
+  RhsType rhs(rows);
+  SvdType svd;
+  VERIFY_RAISES_ASSERT(svd.matrixU())
+  VERIFY_RAISES_ASSERT(svd.singularValues())
+  VERIFY_RAISES_ASSERT(svd.matrixV())
+  VERIFY_RAISES_ASSERT(svd.solve(rhs))
+  MatrixType a = MatrixType::Zero(rows, cols);
+  a.setZero();
+  svd.compute(a, 0);
+  VERIFY_RAISES_ASSERT(svd.matrixU())
+  VERIFY_RAISES_ASSERT(svd.matrixV())
+  svd.singularValues();
+  VERIFY_RAISES_ASSERT(svd.solve(rhs))
+    
+  if (ColsAtCompileTime == Dynamic)
+  {
+    svd.compute(a, ComputeThinU);
+    svd.matrixU();
+    VERIFY_RAISES_ASSERT(svd.matrixV())
+    VERIFY_RAISES_ASSERT(svd.solve(rhs))
+    svd.compute(a, ComputeThinV);
+    svd.matrixV();
+    VERIFY_RAISES_ASSERT(svd.matrixU())
+    VERIFY_RAISES_ASSERT(svd.solve(rhs))
+  }
+  else
+  {
+    VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
+    VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
+  }
+}
+
+#undef SVD_DEFAULT
+#undef SVD_FOR_MIN_NORM