BasicUtils/SharedArray.hpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: SharedArray.hpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Scientific Computing and Imaging Institute,
// University of Utah (USA) and Department of Aeronautics, Imperial
// College London (UK).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description:
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILITIES_BASIC_UTILS_SHARED_ARRAY_HPP
#define NEKTAR_LIB_UTILITIES_BASIC_UTILS_SHARED_ARRAY_HPP
 
#include <LibUtilities/BasicUtils/ArrayPolicies.hpp>
#include <LibUtilities/BasicUtils/ErrorUtil.hpp>
#include <LibUtilities/BasicUtils/RealComparison.hpp>
#include <LibUtilities/LinearAlgebra/NekMatrixFwd.hpp>
#include <LibUtilities/LinearAlgebra/NekVectorFwd.hpp>
 
#include <boost/multi_array.hpp>
 
namespace Nektar
{
class LinearSystem;
 
enum ArrayWrapperType
{
    eArrayCopy,
    eArrayWrapper
};
 
// Forward declaration for a ConstArray constructor.
template <typename Dim, typename DataType> class Array;
 
/// \brief 1D Array of constant elements with garbage collection and bounds
/// checking.
template <typename DataType> class Array<OneD, const DataType>
{
#ifdef WITH_PYTHON
    struct PythonInfo
    {
        void *m_pyObject;           // Underlying PyObject pointer
        void (*m_callback)(void *); // Callback
    };
#endif
public:
    typedef DataType *ArrayType;
 
    typedef const DataType &const_reference;
    typedef DataType &reference;
 
    typedef const DataType *const_iterator;
    typedef DataType *iterator;
 
    typedef DataType element;
    typedef size_t size_type;
 
public:
    /// \brief Creates an empty array.
    Array()
        :
#ifdef WITH_PYTHON
          m_pythonInfo(nullptr),
#endif
          m_size(0), m_capacity(0), m_data(nullptr), m_count(nullptr),
          m_offset(0)
    {
        CreateStorage(m_capacity);
    }
 
    /// \brief Creates an array of size dim1Size.
    ///
    /// If DataType is a fundamental type (double, int, etc.), then the
    /// allocated array is uninitialized.  If it is any other type, each element
    /// is initialized with DataType's default constructor.
    explicit Array(size_type dim1Size)
        :
#ifdef WITH_PYTHON
          m_pythonInfo(nullptr),
#endif
          m_size(dim1Size), m_capacity(dim1Size), m_data(nullptr),
          m_count(nullptr), m_offset(0)
    {
        CreateStorage(m_capacity);
        ArrayInitializationPolicy<DataType>::Initialize(m_data, m_capacity);
    }
 
    /// \brief Creates a 1D array with each element
    /// initialized to an initial value.
    /// \param dim1Size The array's size.
    /// \param initValue Each element's initial value.
    ///
    /// If DataType is a fundamental type (double, int, etc.),
    /// then the initial value is copied directly into each
    /// element.  Otherwise, the DataType's copy constructor
    /// is used to initialize each element.
    Array(size_type dim1Size, const DataType &initValue)
        :
#ifdef WITH_PYTHON
          m_pythonInfo(nullptr),
#endif
          m_size(dim1Size), m_capacity(dim1Size), m_data(nullptr),
          m_count(nullptr), m_offset(0)
    {
        CreateStorage(m_capacity);
        ArrayInitializationPolicy<DataType>::Initialize(m_data, m_capacity,
                                                        initValue);
    }
 
    /// \brief Creates a 1D array a copies data into it.
    /// \param dim1Size the array's size.
    /// \param data The data to copy.
    ///
    /// If DataType is a fundamental type (double, int, etc.), then data is
    /// copied directly into the underlying storage.  Otherwise, the DataType's
    /// copy constructor is used to copy each element.
    Array(size_type dim1Size, const DataType *data)
        :
#ifdef WITH_PYTHON
          m_pythonInfo(nullptr),
#endif
          m_size(dim1Size), m_capacity(dim1Size), m_data(nullptr),
          m_count(nullptr), m_offset(0)
    {
        CreateStorage(m_capacity);
        ArrayInitializationPolicy<DataType>::Initialize(m_data, m_capacity,
                                                        data);
    }
 
    /// \brief Create a 1D array that wrap around a given pointer.
    /// \param dim1Size The array's size.
    /// \param data The data to wrap around.
    /// \param wrap If true, the Array won't create new storage and copy
    ///  data. If false, it will create storage and copy data as usual.
    Array(size_type dim1Size, DataType *data,
          const ArrayWrapperType wrap = eArrayCopy)
        :
#ifdef WITH_PYTHON
          m_pythonInfo(nullptr),
#endif
          m_size(dim1Size), m_capacity(dim1Size), m_data(nullptr),
          m_count(nullptr), m_offset(0)
    {
        switch (wrap)
        {
            case eArrayCopy:
            {
                CreateStorage(m_capacity);
                ArrayInitializationPolicy<DataType>::Initialize(
                    m_data, m_capacity, data);
            }
            break;
            case eArrayWrapper:
            {
                m_data = data;
            }
        }
    }
 
    /// \brief Creates a 1D array that references rhs.
    /// \param dim1Size The size of the array.  This is useful
    ///                 when you want this array to reference
    ///                 a subset of the elements in rhs.
    /// \param rhs      Array to reference.
    /// This constructor creates an array that references rhs.
    /// Any changes to rhs will be reflected in this array.
    /// The memory for the array will only be deallocated when
    /// both rhs and this array have gone out of scope.
    Array(size_type dim1Size, const Array<OneD, const DataType> &rhs)
        :
#ifdef WITH_PYTHON
          m_pythonInfo(rhs.m_pythonInfo),
#endif
          m_size(dim1Size), m_capacity(rhs.m_capacity), m_data(rhs.m_data),
          m_count(rhs.m_count), m_offset(rhs.m_offset)
    {
        if (m_count != nullptr)
        {
            *m_count += 1;
        }
        ASSERTL0(m_size <= rhs.size(), "Requested size is \
                    larger than input array size.");
    }
 
#ifdef WITH_PYTHON
    /// \brief Creates a 1D array a copies data into it.
    /// \param dim1Size the array's size.
    /// \param data The data to reference.
    /// \param memory_pointer Pointer to the memory address of the array
    /// \param python_decrement Pointer to decrementer
    Array(size_type dim1Size, DataType *data, void *memory_pointer,
          void (*python_decrement)(void *))
        : m_size(dim1Size), m_capacity(dim1Size), m_data(data),
          m_count(nullptr), m_offset(0)
    {
        m_count  = new size_type();
        *m_count = 1;
 
        m_pythonInfo                = new PythonInfo *();
        *m_pythonInfo               = new PythonInfo();
        (*m_pythonInfo)->m_callback = python_decrement;
        (*m_pythonInfo)->m_pyObject = memory_pointer;
    }
#endif
 
    /// \brief Creates a reference to rhs.
    Array(const Array<OneD, const DataType> &rhs)
        :
#ifdef WITH_PYTHON
          m_pythonInfo(rhs.m_pythonInfo),
#endif
          m_size(rhs.m_size), m_capacity(rhs.m_capacity), m_data(rhs.m_data),
          m_count(rhs.m_count), m_offset(rhs.m_offset)
    {
        if (m_count != nullptr)
        {
            *m_count += 1;
        }
    }
 
// Disable use-after-free warning with these two functions as it appears to be
// incorrectly triggered in GCC 12.2.
#if __GNUC__ == 12 && __GNUC_MINOR__ == 2
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wuse-after-free"
#endif
    ~Array()
    {
        if (m_count == nullptr)
        {
            return;
        }
 
        *m_count -= 1;
        if (*m_count == 0)
        {
#ifdef WITH_PYTHON
            if (*m_pythonInfo == nullptr)
            {
                ArrayDestructionPolicy<DataType>::Destroy(m_data, m_capacity);
                MemoryManager<DataType>::RawDeallocate(m_data, m_capacity);
            }
            else
            {
                (*m_pythonInfo)->m_callback((*m_pythonInfo)->m_pyObject);
                delete *m_pythonInfo;
            }
 
            delete m_pythonInfo;
            m_pythonInfo = nullptr;
#else
 
            ArrayDestructionPolicy<DataType>::Destroy(m_data, m_capacity);
            MemoryManager<DataType>::RawDeallocate(m_data, m_capacity);
 
#endif
 
            delete m_count; // Clean up the memory used for the reference count.
            m_count = nullptr;
        }
    }
 
    /// \brief Creates a reference to rhs.
    Array<OneD, const DataType> &operator=(
        const Array<OneD, const DataType> &rhs)
    {
        if (m_count != nullptr)
        {
            *m_count -= 1;
        }
 
        if (m_count != nullptr && *m_count == 0)
        {
#ifdef WITH_PYTHON
            if (*m_pythonInfo == nullptr)
            {
                ArrayDestructionPolicy<DataType>::Destroy(m_data, m_capacity);
                MemoryManager<DataType>::RawDeallocate(m_data, m_capacity);
            }
            else if ((*rhs.m_pythonInfo) != nullptr &&
                     (*m_pythonInfo)->m_pyObject !=
                         (*rhs.m_pythonInfo)->m_pyObject)
            {
                (*m_pythonInfo)->m_callback((*m_pythonInfo)->m_pyObject);
                delete *m_pythonInfo;
            }
 
            delete m_pythonInfo;
            m_pythonInfo = nullptr;
#else
 
            ArrayDestructionPolicy<DataType>::Destroy(m_data, m_capacity);
            MemoryManager<DataType>::RawDeallocate(m_data, m_capacity);
#endif
            delete m_count; // Clean up the memory used for the reference count.
            m_count = nullptr;
        }
 
        m_data     = rhs.m_data;
        m_capacity = rhs.m_capacity;
        m_count    = rhs.m_count;
        if (m_count != nullptr)
        {
            *m_count += 1;
        }
        m_offset = rhs.m_offset;
        m_size   = rhs.m_size;
#ifdef WITH_PYTHON
        m_pythonInfo = rhs.m_pythonInfo;
#endif
        return *this;
    }
#if __GNUC__ == 12 && __GNUC_MINOR__ == 2
#pragma GCC diagnostic pop
#endif
 
    const_iterator begin() const
    {
        return m_data + m_offset;
    }
    const_iterator end() const
    {
        return m_data + m_offset + m_size;
    }
 
    const_reference operator[](size_type i) const
    {
        ASSERTL1(i < m_size,
                 std::string("Element ") + std::to_string(i) +
                     std::string(" requested in an array of size ") +
                     std::to_string(m_size));
        return *(m_data + i + m_offset);
    }
 
    /// \brief Returns a c-style pointer to the underlying array.
    [[deprecated("since 5.7.0, use data() instead")]] const element *get() const
    {
        return m_data + m_offset;
    }
 
    /// \brief Returns a c-style pointer to the underlying array.
    const element *data() const
    {
        return m_data + m_offset;
    }
 
    /// \brief Returns 1.
    size_type num_dimensions() const
    {
        return 1;
    }
 
    /// \brief Returns the array's size.
    size_type size() const
    {
        return m_size;
    }
 
    /// \brief Returns the array's size.
    /// Deprecated
    [[deprecated("since 5.1.0, use size() instead")]] size_type num_elements()
        const
    {
        WARNINGL1(false, "member function num_elements() is deprecated, "
                         "use size() instead.");
        return m_size;
    }
 
    /// \brief Returns the array's capacity.
    size_type capacity() const
    {
        return m_capacity;
    }
 
    /// \brief Returns the array's offset.
    size_type GetOffset() const
    {
        return m_offset;
    }
 
    /// \brief Returns the array's reference counter.
    size_type GetCount() const
    {
        return *m_count;
    }
 
    /// \brief Returns true is this array and rhs overlap.
    bool Overlaps(const Array<OneD, const DataType> &rhs) const
    {
        const element *start = data();
        const element *end   = start + m_size;
 
        const element *rhs_start = rhs.data();
        const element *rhs_end   = rhs_start + rhs.size();
 
        return (rhs_start >= start && rhs_start <= end) ||
               (rhs_end >= start && rhs_end <= end);
    }
 
#ifdef WITH_PYTHON
    bool IsPythonArray()
    {
        return *m_pythonInfo != nullptr;
    }
 
    void ToPythonArray(void *memory_pointer, void (*python_decrement)(void *))
    {
        *m_pythonInfo               = new PythonInfo();
        (*m_pythonInfo)->m_callback = python_decrement;
        (*m_pythonInfo)->m_pyObject = memory_pointer;
    }
#endif
 
    /// \brief Creates an array with a specified offset.
    ///
    /// The return value will reference the same array as lhs,
    /// but with an offset.
    ///
    /// For example, in the following:
    /// \code
    /// Array<OneD, const double> result = anArray + 10;
    /// \endcode
    /// result[0] == anArray[10];
    template <typename T>
    friend Array<OneD, T> operator+(const Array<OneD, T> &lhs,
                                    typename Array<OneD, T>::size_type offset);
 
    template <typename T>
    friend Array<OneD, T> operator+(typename Array<OneD, T>::size_type offset,
                                    const Array<OneD, T> &rhs);
 
protected:
#ifdef WITH_PYTHON
    PythonInfo **m_pythonInfo;
#endif
 
    size_type m_size;
    size_type m_capacity;
    DataType *m_data;
 
    // m_count points to an integer used as a reference count to this array's
    // data (m_data). Previously, the reference count was stored in the first 4
    // bytes of the m_data array.
    size_type *m_count;
 
    size_type m_offset;
 
private:
    void CreateStorage(size_type size)
    {
        DataType *storage = MemoryManager<DataType>::RawAllocate(size);
        m_data            = storage;
 
        // Allocate an integer to hold the reference count.  Note 1, all arrays
        // that share this array's data (ie, point to m_data) will also share
        // the m_count data.  Note 2, previously m_count pointed to "(unsigned
        // int*)storage".
        m_count  = new size_type();
        *m_count = 1;
#ifdef WITH_PYTHON
        m_pythonInfo  = new PythonInfo *();
        *m_pythonInfo = nullptr;
#endif
    }
 
    template <typename T>
    static Array<OneD, T> CreateWithOffset(const Array<OneD, T> &rhs,
                                           size_type offset)
    {
        Array<OneD, T> result(rhs);
        result.m_offset += offset;
        result.m_size = rhs.m_size - offset;
        return result;
    }
};
 
/// \brief 2D array with garbage collection and bounds checking.
template <typename DataType> class Array<TwoD, const DataType>
{
public:
    typedef boost::multi_array_ref<DataType, 2> ArrayType;
 
    typedef typename ArrayType::const_reference const_reference;
    typedef typename ArrayType::reference reference;
 
    typedef typename ArrayType::index index;
    typedef typename ArrayType::const_iterator const_iterator;
    typedef typename ArrayType::iterator iterator;
 
    typedef typename ArrayType::element element;
    typedef typename ArrayType::size_type size_type;
 
public:
    Array() : m_data(CreateStorage<DataType>(0, 0))
    {
    }
 
    /// \brief Constructs a 2 dimensional array.  The elements of the array are
    /// not initialized.
    Array(size_type dim1Size, size_type dim2Size)
        : m_data(CreateStorage<DataType>(dim1Size, dim2Size))
    {
        ArrayInitializationPolicy<DataType>::Initialize(m_data->data(),
                                                        m_data->num_elements());
    }
 
    Array(size_type dim1Size, size_type dim2Size, const DataType &initValue)
        : m_data(CreateStorage<DataType>(dim1Size, dim2Size))
    {
        ArrayInitializationPolicy<DataType>::Initialize(
            m_data->data(), m_data->num_elements(), initValue);
    }
 
    Array(size_type dim1Size, size_type dim2Size, const DataType *data)
        : m_data(CreateStorage<DataType>(dim1Size, dim2Size))
    {
        ArrayInitializationPolicy<DataType>::Initialize(
            m_data->data(), m_data->num_elements(), data);
    }
 
    Array(const Array<TwoD, const DataType> &rhs) : m_data(rhs.m_data)
    {
    }
 
    Array<TwoD, const DataType> &operator=(
        const Array<TwoD, const DataType> &rhs)
    {
        m_data = rhs.m_data;
        return *this;
    }
 
    const_iterator begin() const
    {
        return m_data->begin();
    }
    const_iterator end() const
    {
        return m_data->end();
    }
    const_reference operator[](index i) const
    {
        return (*m_data)[i];
    }
    [[deprecated("since 5.7.0, use data() instead")]] const element *get() const
    {
        return m_data->data();
    }
    const element *data() const
    {
        return m_data->data();
    }
    size_type num_dimensions() const
    {
        return m_data->num_dimensions();
    }
    const size_type *shape() const
    {
        return m_data->shape();
    }
    // m_data is a shared_ptr to a boost::multi_array_ref
    size_type size() const
    {
        return m_data->num_elements();
    }
 
    size_type GetRows() const
    {
        return m_data->shape()[0];
    }
    size_type GetColumns() const
    {
        return m_data->shape()[1];
    }
 
protected:
    std::shared_ptr<ArrayType> m_data;
 
private:
};
 
/// \brief 1D Array
///
/// \ref pageNekArrays
///
/// Misc notes.
///
/// Through out the 1D Array class you will see things like "using
/// BaseType::begin" and "using BaseType::end".  This is necessary to bring the
/// methods from the ConstArray into scope in Array class.  Typically this is
/// not necessary, but since we have method names which match those in the base
/// class, the base class names are hidden. Therefore, we have to explicitly
/// bring them into scope to use them.
template <typename DataType>
class Array<OneD, DataType> : public Array<OneD, const DataType>
{
public:
    typedef Array<OneD, const DataType> BaseType;
    typedef typename BaseType::iterator iterator;
    typedef typename BaseType::reference reference;
    typedef typename BaseType::size_type size_type;
    typedef typename BaseType::element element;
 
public:
    Array() : BaseType()
    {
    }
 
    explicit Array(size_type dim1Size) : BaseType(dim1Size)
    {
    }
 
    Array(size_type dim1Size, const DataType &initValue)
        : BaseType(dim1Size, initValue)
    {
    }
 
    Array(size_type dim1Size, const DataType *data) : BaseType(dim1Size, data)
    {
    }
 
    Array(size_type dim1Size, DataType *data,
          const ArrayWrapperType wrap = eArrayCopy)
        : BaseType(dim1Size, data, wrap)
    {
    }
 
    Array(size_type dim1Size, const Array<OneD, DataType> &rhs)
        : BaseType(dim1Size, rhs)
    {
    }
 
    Array(size_type dim1Size, const Array<OneD, const DataType> &rhs)
        : BaseType(dim1Size, rhs.data())
    {
    }
 
    Array(const Array<OneD, DataType> &rhs) : BaseType(rhs)
    {
    }
 
    Array(const Array<OneD, const DataType> &rhs)
        : BaseType(rhs.size(), rhs.data())
    {
    }
 
#ifdef WITH_PYTHON
    Array(size_type dim1Size, DataType *data, void *memory_pointer,
          void (*python_decrement)(void *))
        : BaseType(dim1Size, data, memory_pointer, python_decrement)
    {
    }
 
    void ToPythonArray(void *memory_pointer, void (*python_decrement)(void *))
    {
        BaseType::ToPythonArray(memory_pointer, python_decrement);
    }
#endif
 
    Array<OneD, DataType> &operator=(const Array<OneD, DataType> &rhs)
    {
        BaseType::operator=(rhs);
        return *this;
    }
 
    static Array<OneD, DataType> CreateWithOffset(
        const Array<OneD, DataType> &rhs, unsigned int offset)
    {
        Array<OneD, DataType> result(rhs);
        result.m_offset += offset;
        result.m_size = rhs.m_size - offset;
        return result;
    }
 
    typename Array<OneD, const DataType>::const_iterator begin() const
    {
        return Array<OneD, const DataType>::begin();
    }
    iterator begin()
    {
        return this->m_data + this->m_offset;
    }
 
    using BaseType::end;
    iterator end()
    {
        return this->m_data + this->m_offset + this->m_size;
    }
 
    using BaseType::operator[];
    reference operator[](size_type i)
    {
        ASSERTL1(static_cast<size_type>(i) < this->size(),
                 std::string("Element ") + std::to_string(i) +
                     std::string(" requested in an array of size ") +
                     std::to_string(this->size()));
        return (data())[i];
    }
 
    using BaseType::get;
    [[deprecated("since 5.7.0, use data() instead")]] element *get()
    {
        return this->m_data + this->m_offset;
    }
 
    using BaseType::data;
    element *data()
    {
        return this->m_data + this->m_offset;
    }
 
    template <typename T1> friend class NekVector;
 
    template <typename T1, typename T3> friend class NekMatrix;
 
    friend class LinearSystem;
 
protected:
    void ChangeSize(size_type newSize)
    {
        ASSERTL1(newSize <= this->m_capacity,
                 "Can't change an array size to something larger than its "
                 "capacity.");
        this->m_size = newSize;
    }
 
private:
};
 
/// \brief A 2D array.
template <typename DataType>
class Array<TwoD, DataType> : public Array<TwoD, const DataType>
{
public:
    typedef Array<TwoD, const DataType> BaseType;
    typedef typename BaseType::iterator iterator;
    typedef typename BaseType::reference reference;
    typedef typename BaseType::index index;
    typedef typename BaseType::size_type size_type;
    typedef typename BaseType::element element;
 
public:
    Array() : BaseType()
    {
    }
 
    Array(size_type dim1Size, size_type dim2Size) : BaseType(dim1Size, dim2Size)
    {
    }
 
    Array(size_type dim1Size, size_type dim2Size, const DataType &initValue)
        : BaseType(dim1Size, dim2Size, initValue)
    {
    }
 
    Array(size_type dim1Size, size_type dim2Size, const DataType *data)
        : BaseType(dim1Size, dim2Size, data)
    {
    }
 
    Array(const Array<TwoD, DataType> &rhs) : BaseType(rhs)
    {
    }
 
    Array<TwoD, DataType> &operator=(const Array<TwoD, DataType> &rhs)
    {
        BaseType::operator=(rhs);
        return *this;
    }
 
    using BaseType::begin;
    iterator begin()
    {
        return this->m_data->begin();
    }
 
    using BaseType::end;
    iterator end()
    {
        return this->m_data->end();
    }
 
    using BaseType::operator[];
    reference operator[](index i)
    {
        return (*this->m_data)[i];
    }
 
    using BaseType::get;
    [[deprecated("since 5.7.0, use data() instead")]] element *get()
    {
        return this->m_data->data();
    }
 
    using BaseType::data;
    element *data()
    {
        return this->m_data->data();
    }
 
private:
};
 
// compare whatever
template <typename T>
inline bool IsEqualImpl(const T &lhs, const T &rhs, std::false_type)
{
    return lhs == rhs;
}
 
// compare floating point value
template <typename T>
inline bool IsEqualImpl(const T &lhs, const T &rhs, std::true_type)
{
    return LibUtilities::IsRealEqual(lhs, rhs);
}
 
template <typename T> inline bool IsEqual(const T &lhs, const T &rhs)
{
    return IsEqualImpl(lhs, rhs, std::is_floating_point<T>());
}
 
template <typename T1, typename T2>
bool operator==(const Array<OneD, T1> &lhs, const Array<OneD, T2> &rhs)
{
    if (lhs.size() != rhs.size())
    {
        return false;
    }
 
    if (lhs.data() == rhs.data())
    {
        return true;
    }
 
    typename Array<OneD, T1>::size_type size_value(lhs.size());
    for (typename Array<OneD, T1>::size_type i = 0; i < size_value; ++i)
    {
        if (!IsEqual(lhs[i], rhs[i]))
        {
            return false;
        }
    }
 
    return true;
}
 
template <typename T1, typename T2>
bool operator!=(const Array<OneD, T1> &lhs, const Array<OneD, T2> &rhs)
{
    return !(lhs == rhs);
}
 
template <typename DataType>
Array<OneD, DataType> operator+(
    const Array<OneD, DataType> &lhs,
    typename Array<OneD, DataType>::size_type offset)
{
    return Array<OneD, const DataType>::CreateWithOffset(lhs, offset);
}
 
template <typename DataType>
Array<OneD, DataType> operator+(
    typename Array<OneD, DataType>::size_type offset,
    const Array<OneD, DataType> &rhs)
{
    return Array<OneD, const DataType>::CreateWithOffset(rhs, offset);
}
 
template <typename ConstDataType, typename DataType>
void CopyArray(const Array<OneD, ConstDataType> &source,
               Array<OneD, DataType> &dest)
{
    if (dest.size() != source.size())
    {
        dest = Array<OneD, DataType>(source.size());
    }
 
    std::copy(source.data(), source.data() + source.size(), dest.data());
}
 
template <typename ConstDataType, typename DataType>
void CopyArrayN(const Array<OneD, ConstDataType> &source,
                Array<OneD, DataType> &dest,
                typename Array<OneD, DataType>::size_type n)
{
    if (dest.size() != n)
    {
        dest = Array<OneD, DataType>(n);
    }
 
    std::copy(source.data(), source.data() + n, dest.data());
}
 
static Array<OneD, int> NullInt1DArray;
static Array<OneD, NekDouble> NullNekDouble1DArray;
static Array<OneD, Array<OneD, NekDouble>> NullNekDoubleArrayOfArray;
static Array<OneD, Array<OneD, Array<OneD, NekDouble>>>
    NullNekDoubleTensorOfArray3D;
 
// Temporary alias for 2D nested array.
template <class T> using TensorOfArray2D = Array<OneD, Array<OneD, T>>;
// Temporary alias for 3D nested array. Please note that the inner arrays
// are not const declared. It is therefore suggested to use this alias with
// caution.
template <class T>
using TensorOfArray3D = Array<OneD, Array<OneD, Array<OneD, T>>>;
// Temporary alias for 4D nested array. Please note that the inner arrays
// are not const declared. It is therefore suggested to use this alias with
// caution.
template <class T>
using TensorOfArray4D = Array<OneD, Array<OneD, Array<OneD, Array<OneD, T>>>>;
// Temporary alias for 5D nested array. Please note that the inner arrays
// are not const declared. It is therefore suggested to use this alias with
// caution.
template <class T>
using TensorOfArray5D =
    Array<OneD, Array<OneD, Array<OneD, Array<OneD, Array<OneD, T>>>>>;
 
template <typename T1, typename T2>
bool operator==(const Array<TwoD, T1> &lhs, const Array<TwoD, T2> &rhs)
{
    if ((lhs.GetRows() != rhs.GetRows()) ||
        (lhs.GetColumns() != rhs.GetColumns()))
    {
        return false;
    }
 
    if (lhs.data() == rhs.data())
    {
        return true;
    }
 
    for (typename Array<OneD, T1>::size_type i = 0; i < lhs.GetRows(); ++i)
    {
        for (typename Array<OneD, T1>::size_type j = 0; j < lhs.GetColumns();
             ++j)
        {
            if (!IsEqual(lhs[i][j], rhs[i][j]))
            {
                return false;
            }
        }
    }
 
    return true;
}
 
template <typename T1, typename T2>
bool operator!=(const Array<TwoD, T1> &lhs, const Array<TwoD, T2> &rhs)
{
    return !(lhs == rhs);
}
 
namespace LibUtilities
{
static std::vector<NekDouble> NullNekDoubleVector;
static std::vector<unsigned int> NullUnsignedIntVector;
static std::vector<std::vector<NekDouble>> NullVectorNekDoubleVector = {
    NullNekDoubleVector};
} // namespace LibUtilities
} // namespace Nektar
 
#endif // NEKTAR_LIB_UTILITIES_BASIC_UTILS_SHARED_ARRAY_HPP