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diff --git a/eigen/test/umeyama.cpp b/eigen/test/umeyama.cpp
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@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/.
+
+#include "main.h"
+
+#include <Eigen/Core>
+#include <Eigen/Geometry>
+
+#include <Eigen/LU> // required for MatrixBase::determinant
+#include <Eigen/SVD> // required for SVD
+
+using namespace Eigen;
+
+//  Constructs a random matrix from the unitary group U(size).
+template <typename T>
+Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixUnitary(int size)
+{
+  typedef T Scalar;
+  typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;
+
+  MatrixType Q;
+
+  int max_tries = 40;
+  double is_unitary = false;
+
+  while (!is_unitary && max_tries > 0)
+  {
+    // initialize random matrix
+    Q = MatrixType::Random(size, size);
+
+    // orthogonalize columns using the Gram-Schmidt algorithm
+    for (int col = 0; col < size; ++col)
+    {
+      typename MatrixType::ColXpr colVec = Q.col(col);
+      for (int prevCol = 0; prevCol < col; ++prevCol)
+      {
+        typename MatrixType::ColXpr prevColVec = Q.col(prevCol);
+        colVec -= colVec.dot(prevColVec)*prevColVec;
+      }
+      Q.col(col) = colVec.normalized();
+    }
+
+    // this additional orthogonalization is not necessary in theory but should enhance
+    // the numerical orthogonality of the matrix
+    for (int row = 0; row < size; ++row)
+    {
+      typename MatrixType::RowXpr rowVec = Q.row(row);
+      for (int prevRow = 0; prevRow < row; ++prevRow)
+      {
+        typename MatrixType::RowXpr prevRowVec = Q.row(prevRow);
+        rowVec -= rowVec.dot(prevRowVec)*prevRowVec;
+      }
+      Q.row(row) = rowVec.normalized();
+    }
+
+    // final check
+    is_unitary = Q.isUnitary();
+    --max_tries;
+  }
+
+  if (max_tries == 0)
+    eigen_assert(false && "randMatrixUnitary: Could not construct unitary matrix!");
+
+  return Q;
+}
+
+//  Constructs a random matrix from the special unitary group SU(size).
+template <typename T>
+Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixSpecialUnitary(int size)
+{
+  typedef T Scalar;
+
+  typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;
+
+  // initialize unitary matrix
+  MatrixType Q = randMatrixUnitary<Scalar>(size);
+
+  // tweak the first column to make the determinant be 1
+  Q.col(0) *= numext::conj(Q.determinant());
+
+  return Q;
+}
+
+template <typename MatrixType>
+void run_test(int dim, int num_elements)
+{
+  using std::abs;
+  typedef typename internal::traits<MatrixType>::Scalar Scalar;
+  typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
+  typedef Matrix<Scalar, Eigen::Dynamic, 1> VectorX;
+
+  // MUST be positive because in any other case det(cR_t) may become negative for
+  // odd dimensions!
+  const Scalar c = abs(internal::random<Scalar>());
+
+  MatrixX R = randMatrixSpecialUnitary<Scalar>(dim);
+  VectorX t = Scalar(50)*VectorX::Random(dim,1);
+
+  MatrixX cR_t = MatrixX::Identity(dim+1,dim+1);
+  cR_t.block(0,0,dim,dim) = c*R;
+  cR_t.block(0,dim,dim,1) = t;
+
+  MatrixX src = MatrixX::Random(dim+1, num_elements);
+  src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));
+
+  MatrixX dst = cR_t*src;
+
+  MatrixX cR_t_umeyama = umeyama(src.block(0,0,dim,num_elements), dst.block(0,0,dim,num_elements));
+
+  const Scalar error = ( cR_t_umeyama*src - dst ).norm() / dst.norm();
+  VERIFY(error < Scalar(40)*std::numeric_limits<Scalar>::epsilon());
+}
+
+template<typename Scalar, int Dimension>
+void run_fixed_size_test(int num_elements)
+{
+  using std::abs;
+  typedef Matrix<Scalar, Dimension+1, Dynamic> MatrixX;
+  typedef Matrix<Scalar, Dimension+1, Dimension+1> HomMatrix;
+  typedef Matrix<Scalar, Dimension, Dimension> FixedMatrix;
+  typedef Matrix<Scalar, Dimension, 1> FixedVector;
+
+  const int dim = Dimension;
+
+  // MUST be positive because in any other case det(cR_t) may become negative for
+  // odd dimensions!
+  // Also if c is to small compared to t.norm(), problem is ill-posed (cf. Bug 744)
+  const Scalar c = internal::random<Scalar>(0.5, 2.0);
+
+  FixedMatrix R = randMatrixSpecialUnitary<Scalar>(dim);
+  FixedVector t = Scalar(32)*FixedVector::Random(dim,1);
+
+  HomMatrix cR_t = HomMatrix::Identity(dim+1,dim+1);
+  cR_t.block(0,0,dim,dim) = c*R;
+  cR_t.block(0,dim,dim,1) = t;
+
+  MatrixX src = MatrixX::Random(dim+1, num_elements);
+  src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));
+
+  MatrixX dst = cR_t*src;
+
+  Block<MatrixX, Dimension, Dynamic> src_block(src,0,0,dim,num_elements);
+  Block<MatrixX, Dimension, Dynamic> dst_block(dst,0,0,dim,num_elements);
+
+  HomMatrix cR_t_umeyama = umeyama(src_block, dst_block);
+
+  const Scalar error = ( cR_t_umeyama*src - dst ).squaredNorm();
+
+  VERIFY(error < Scalar(16)*std::numeric_limits<Scalar>::epsilon());
+}
+
+void test_umeyama()
+{
+  for (int i=0; i<g_repeat; ++i)
+  {
+    const int num_elements = internal::random<int>(40,500);
+
+    // works also for dimensions bigger than 3...
+    for (int dim=2; dim<8; ++dim)
+    {
+      CALL_SUBTEST_1(run_test<MatrixXd>(dim, num_elements));
+      CALL_SUBTEST_2(run_test<MatrixXf>(dim, num_elements));
+    }
+
+    CALL_SUBTEST_3((run_fixed_size_test<float, 2>(num_elements)));
+    CALL_SUBTEST_4((run_fixed_size_test<float, 3>(num_elements)));
+    CALL_SUBTEST_5((run_fixed_size_test<float, 4>(num_elements)));
+
+    CALL_SUBTEST_6((run_fixed_size_test<double, 2>(num_elements)));
+    CALL_SUBTEST_7((run_fixed_size_test<double, 3>(num_elements)));
+    CALL_SUBTEST_8((run_fixed_size_test<double, 4>(num_elements)));
+  }
+
+  // Those two calls don't compile and result in meaningful error messages!
+  // umeyama(MatrixXcf(),MatrixXcf());
+  // umeyama(MatrixXcd(),MatrixXcd());
+}