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umeyama.cpp
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Fri, Feb 21, 23:39

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;
bool 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());
}
EIGEN_DECLARE_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());
}

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