CoordinateSystem.cpp

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#include "CoordinateSystem.h"
 
#include <typeinfo>
 
#include "Parameter.h"
 
namespace ParameterLib
{
static double const tolerance = 1.e-15;
static const char* const error_info =
    "The determinant of the coordinate system transformation matrix is '{:g}', "
    "which is not sufficiently close to unity with the tolerance of '{:g}'. "
    "Please adjust the accuracy of the local system bases";
 
CoordinateSystem::CoordinateSystem(Parameter<double> const& e0,
                                   Parameter<double> const& e1)
    : _base{&e0, &e1, nullptr}
{
    if (typeid(_base[0]) != typeid(_base[1]))
    {
        OGS_FATAL(
            "The parameter types for the basis must be equal but they are "
            "'{:s}' and '{:s}'.",
            typeid(_base[0]).name(),
            typeid(_base[1]).name());
    }
    if (_base[0]->isTimeDependent() || _base[1]->isTimeDependent())
    {
        OGS_FATAL("The parameters for the basis must not be time dependent.");
    }
    if (_base[0]->getNumberOfGlobalComponents() != 2 ||
        _base[1]->getNumberOfGlobalComponents() != 2)
    {
        OGS_FATAL("The parameters for the 2D basis must have two components.");
    }
}
 
CoordinateSystem::CoordinateSystem(Parameter<double> const& e0,
                                   Parameter<double> const& e1,
                                   Parameter<double> const& e2)
    : _base{&e0, &e1, &e2}
{
    if ((typeid(_base[0]) != typeid(_base[1])) ||
        (typeid(_base[1]) != typeid(_base[2])) ||
        (typeid(_base[2]) != typeid(_base[0])))
    {
        OGS_FATAL(
            "The parameter types for the basis must be equal but they are "
            "'{:s}', '{:s}', and '{:s}'.",
            typeid(_base[0]).name(),
            typeid(_base[1]).name(),
            typeid(_base[2]).name());
    }
    if (_base[0]->isTimeDependent() || _base[1]->isTimeDependent(),
        _base[2]->isTimeDependent())
    {
        OGS_FATAL("The parameters for the basis must not be time dependent.");
    }
    if (_base[0]->getNumberOfGlobalComponents() != 3 ||
        _base[1]->getNumberOfGlobalComponents() != 3 ||
        _base[2]->getNumberOfGlobalComponents() != 3)
    {
        OGS_FATAL(
            "The parameters for the 3D basis must have three components.");
    }
}
 
template <>
Eigen::Matrix<double, 2, 2> CoordinateSystem::transformation<2>(
    SpatialPosition const& pos) const
{
    if (_base[2] != nullptr)
    {
        OGS_FATAL(
            "The coordinate system is 3D but a transformation for 2D case is "
            "requested.");
    }
 
    auto e0 = (*_base[0])(0 /* time independent */, pos);
    auto e1 = (*_base[1])(0 /* time independent */, pos);
    Eigen::Matrix<double, 2, 2> t;
    t << e0[0], e1[0], e0[1], e1[1];
 
#ifndef NDEBUG
    if (std::abs(t.determinant() - 1) > tolerance)
    {
        OGS_FATAL(error_info, t.determinant(), tolerance);
    }
#endif  // NDEBUG
    return t;
}
 
template <>
Eigen::Matrix<double, 3, 3> CoordinateSystem::transformation<3>(
    SpatialPosition const& pos) const
{
    if (_base[2] == nullptr)
    {
        OGS_FATAL(
            "The coordinate system is 2D but a transformation for 3D case is "
            "requested.");
    }
 
    auto e0 = (*_base[0])(0 /* time independent */, pos);
    auto e1 = (*_base[1])(0 /* time independent */, pos);
    auto e2 = (*_base[2])(0 /* time independent */, pos);
    Eigen::Matrix<double, 3, 3> t;
    t << e0[0], e1[0], e2[0], e0[1], e1[1], e2[1], e0[2], e1[2], e2[2];
 
#ifndef NDEBUG
    if (std::abs(t.determinant() - 1) > tolerance)
    {
        OGS_FATAL(error_info, t.determinant(), tolerance);
    }
#endif  // NDEBUG
    return t;
}
 
Eigen::Matrix<double, 3, 3> CoordinateSystem::transformation_3d(
    SpatialPosition const& pos) const
{
    if (_base[2] != nullptr)
    {
        return transformation<3>(pos);
    }
 
    auto e0 = (*_base[0])(0 /* time independent */, pos);
    auto e1 = (*_base[1])(0 /* time independent */, pos);
    Eigen::Matrix<double, 3, 3> t = Eigen::Matrix<double, 3, 3>::Identity();
    t.template topLeftCorner<2, 2>() << e0[0], e1[0], e0[1], e1[1];
 
#ifndef NDEBUG
    if (std::abs(t.determinant() - 1) > tolerance)
    {
        OGS_FATAL(error_info, t.determinant(), tolerance);
    }
#endif  // NDEBUG
    return t;
}
 
template <int Dimension>
Eigen::Matrix<double, Dimension, Dimension> CoordinateSystem::rotateTensor(
    std::vector<double> const& values, SpatialPosition const& pos) const
{
    assert(values.size() == Dimension * Dimension ||
           "Input vector has wrong dimension; expected 4 or 9 entries.");
    auto const tensor =
        Eigen::Map<Eigen::Matrix<double, Dimension, Dimension> const>(
            values.data(), Dimension, Dimension);
    auto const R = transformation<Dimension>(pos);
    return R * tensor * R.transpose();
}
 
template <int Dimension>
Eigen::Matrix<double, Dimension, Dimension>
CoordinateSystem::rotateDiagonalTensor(std::vector<double> const& values,
                                       SpatialPosition const& pos) const
{
    assert(values.size() == Dimension ||
           "Input vector has wrong dimension; expected 2 or 3 entries.");
    auto const tensor = Eigen::Map<Eigen::Matrix<double, Dimension, 1> const>(
        values.data(), Dimension, 1);
    auto const R = transformation<Dimension>(pos);
    return R * tensor.asDiagonal() * R.transpose();
}
 
template Eigen::Matrix<double, 2, 2> CoordinateSystem::rotateTensor<2>(
    std::vector<double> const& values, SpatialPosition const& pos) const;
template Eigen::Matrix<double, 3, 3> CoordinateSystem::rotateTensor<3>(
    std::vector<double> const& values, SpatialPosition const& pos) const;
template Eigen::Matrix<double, 2, 2> CoordinateSystem::rotateDiagonalTensor<2>(
    std::vector<double> const& values, SpatialPosition const& pos) const;
template Eigen::Matrix<double, 3, 3> CoordinateSystem::rotateDiagonalTensor<3>(
    std::vector<double> const& values, SpatialPosition const& pos) const;
}  // namespace ParameterLib