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

1 files changed, 454 insertions, 0 deletions

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