cart-elc

Source code for CART-ELC
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Tensor.h (21269B)


      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
      5 // Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     10 
     11 #ifndef EIGEN_CXX11_TENSOR_TENSOR_H
     12 #define EIGEN_CXX11_TENSOR_TENSOR_H
     13 
     14 namespace Eigen {
     15 
     16 /** \class Tensor
     17   * \ingroup CXX11_Tensor_Module
     18   *
     19   * \brief The tensor class.
     20   *
     21   * The %Tensor class is the work-horse for all \em dense tensors within Eigen.
     22   *
     23   * The %Tensor class encompasses only dynamic-size objects so far.
     24   *
     25   * The first two template parameters are required:
     26   * \tparam Scalar_  Numeric type, e.g. float, double, int or `std::complex<float>`.
     27   *                 User defined scalar types are supported as well (see \ref user_defined_scalars "here").
     28   * \tparam NumIndices_ Number of indices (i.e. rank of the tensor)
     29   *
     30   * The remaining template parameters are optional -- in most cases you don't have to worry about them.
     31   * \tparam Options_  A combination of either \b #RowMajor or \b #ColMajor, and of either
     32   *                 \b #AutoAlign or \b #DontAlign.
     33   *                 The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
     34   *                 for vectorization. It defaults to aligning tensors. Note that tensors currently do not support any operations that profit from vectorization.
     35   *                 Support for such operations (i.e. adding two tensors etc.) is planned.
     36   *
     37   * You can access elements of tensors using normal subscripting:
     38   *
     39   * \code
     40   * Eigen::Tensor<double, 4> t(10, 10, 10, 10);
     41   * t(0, 1, 2, 3) = 42.0;
     42   * \endcode
     43   *
     44   * This class can be extended with the help of the plugin mechanism described on the page
     45   * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_TENSOR_PLUGIN.
     46   *
     47   * <i><b>Some notes:</b></i>
     48   *
     49   * <dl>
     50   * <dt><b>Relation to other parts of Eigen:</b></dt>
     51   * <dd>The midterm development goal for this class is to have a similar hierarchy as Eigen uses for matrices, so that
     52   * taking blocks or using tensors in expressions is easily possible, including an interface with the vector/matrix code
     53   * by providing .asMatrix() and .asVector() (or similar) methods for rank 2 and 1 tensors. However, currently, the %Tensor
     54   * class does not provide any of these features and is only available as a stand-alone class that just allows for
     55   * coefficient access. Also, when fixed-size tensors are implemented, the number of template arguments is likely to
     56   * change dramatically.</dd>
     57   * </dl>
     58   *
     59   * \ref TopicStorageOrders
     60   */
     61 
     62 template<typename Scalar_, int NumIndices_, int Options_, typename IndexType_>
     63 class Tensor : public TensorBase<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >
     64 {
     65   public:
     66     typedef Tensor<Scalar_, NumIndices_, Options_, IndexType_> Self;
     67     typedef TensorBase<Tensor<Scalar_, NumIndices_, Options_, IndexType_> > Base;
     68     typedef typename Eigen::internal::nested<Self>::type Nested;
     69     typedef typename internal::traits<Self>::StorageKind StorageKind;
     70     typedef typename internal::traits<Self>::Index Index;
     71     typedef Scalar_ Scalar;
     72     typedef typename NumTraits<Scalar>::Real RealScalar;
     73     typedef typename Base::CoeffReturnType CoeffReturnType;
     74 
     75     enum {
     76       IsAligned = bool(EIGEN_MAX_ALIGN_BYTES>0) & !(Options_&DontAlign),
     77       Layout = Options_ & RowMajor ? RowMajor : ColMajor,
     78       CoordAccess = true,
     79       RawAccess = true
     80     };
     81 
     82     static const int Options = Options_;
     83     static const int NumIndices = NumIndices_;
     84     typedef DSizes<Index, NumIndices_> Dimensions;
     85 
     86   protected:
     87     TensorStorage<Scalar, Dimensions, Options> m_storage;
     88 
     89 #ifdef EIGEN_HAS_SFINAE
     90     template<typename CustomIndices>
     91     struct isOfNormalIndex{
     92       static const bool is_array = internal::is_base_of<array<Index, NumIndices>, CustomIndices>::value;
     93       static const bool is_int = NumTraits<CustomIndices>::IsInteger;
     94       static const bool value = is_array | is_int;
     95     };
     96 #endif
     97 
     98   public:
     99     // Metadata
    100     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                         rank()                   const { return NumIndices; }
    101     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                         dimension(std::size_t n) const { return m_storage.dimensions()[n]; }
    102     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions&             dimensions()             const { return m_storage.dimensions(); }
    103     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                         size()                   const { return m_storage.size(); }
    104     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar                        *data()                        { return m_storage.data(); }
    105     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar                  *data()                  const { return m_storage.data(); }
    106 
    107     // This makes EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
    108     // work, because that uses base().coeffRef() - and we don't yet
    109     // implement a similar class hierarchy
    110     inline Self& base()             { return *this; }
    111     inline const Self& base() const { return *this; }
    112 
    113 #if EIGEN_HAS_VARIADIC_TEMPLATES
    114     template<typename... IndexTypes>
    115     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const
    116     {
    117       // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
    118       EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    119       return coeff(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
    120     }
    121 #endif
    122 
    123     // normal indices
    124     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(const array<Index, NumIndices>& indices) const
    125     {
    126       eigen_internal_assert(checkIndexRange(indices));
    127       return m_storage.data()[linearizedIndex(indices)];
    128     }
    129 
    130     // custom indices
    131 #ifdef EIGEN_HAS_SFINAE
    132     template<typename CustomIndices,
    133              EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
    134     >
    135     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(CustomIndices& indices) const
    136     {
    137         return coeff(internal::customIndices2Array<Index,NumIndices>(indices));
    138     }
    139 #endif
    140 
    141     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff() const
    142     {
    143       EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
    144       return m_storage.data()[0];
    145     }
    146 
    147     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
    148     {
    149       eigen_internal_assert(index >= 0 && index < size());
    150       return m_storage.data()[index];
    151     }
    152 
    153 #if EIGEN_HAS_VARIADIC_TEMPLATES
    154     template<typename... IndexTypes>
    155     inline Scalar& coeffRef(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)
    156     {
    157       // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
    158       EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    159       return coeffRef(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
    160     }
    161 #endif
    162 
    163     // normal indices
    164     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)
    165     {
    166       eigen_internal_assert(checkIndexRange(indices));
    167       return m_storage.data()[linearizedIndex(indices)];
    168     }
    169 
    170     // custom indices
    171 #ifdef EIGEN_HAS_SFINAE
    172     template<typename CustomIndices,
    173              EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
    174              >
    175     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(CustomIndices& indices)
    176     {
    177         return coeffRef(internal::customIndices2Array<Index,NumIndices>(indices));
    178     }
    179 #endif
    180 
    181     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef()
    182     {
    183       EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
    184       return m_storage.data()[0];
    185     }
    186 
    187     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
    188     {
    189       eigen_internal_assert(index >= 0 && index < size());
    190       return m_storage.data()[index];
    191     }
    192 
    193 #if EIGEN_HAS_VARIADIC_TEMPLATES
    194     template<typename... IndexTypes>
    195     inline const Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const
    196     {
    197       // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
    198       EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    199       return this->operator()(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
    200     }
    201 #else
    202     EIGEN_DEVICE_FUNC
    203     EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1) const
    204     {
    205       return coeff(array<Index, 2>(i0, i1));
    206     }
    207     EIGEN_DEVICE_FUNC
    208     EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2) const
    209     {
    210       return coeff(array<Index, 3>(i0, i1, i2));
    211     }
    212     EIGEN_DEVICE_FUNC
    213     EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3) const
    214     {
    215       return coeff(array<Index, 4>(i0, i1, i2, i3));
    216     }
    217     EIGEN_DEVICE_FUNC
    218     EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4) const
    219     {
    220       return coeff(array<Index, 5>(i0, i1, i2, i3, i4));
    221     }
    222 #endif
    223 
    224     // custom indices
    225 #ifdef EIGEN_HAS_SFINAE
    226     template<typename CustomIndices,
    227              EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
    228     >
    229     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(CustomIndices& indices) const
    230     {
    231         return coeff(internal::customIndices2Array<Index,NumIndices>(indices));
    232     }
    233 #endif
    234 
    235     // normal indices
    236     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(const array<Index, NumIndices>& indices) const
    237     {
    238       return coeff(indices);
    239     }
    240 
    241     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(Index index) const
    242     {
    243       eigen_internal_assert(index >= 0 && index < size());
    244       return coeff(index);
    245     }
    246 
    247     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()() const
    248     {
    249       EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
    250       return coeff();
    251     }
    252 
    253     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator[](Index index) const
    254     {
    255       // The bracket operator is only for vectors, use the parenthesis operator instead.
    256       EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE);
    257       return coeff(index);
    258     }
    259 
    260 #if EIGEN_HAS_VARIADIC_TEMPLATES
    261     template<typename... IndexTypes>
    262     inline Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)
    263     {
    264       // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
    265       EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    266       return operator()(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
    267     }
    268 #else
    269     EIGEN_DEVICE_FUNC
    270     EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1)
    271     {
    272       return coeffRef(array<Index, 2>(i0, i1));
    273     }
    274     EIGEN_DEVICE_FUNC
    275     EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2)
    276     {
    277       return coeffRef(array<Index, 3>(i0, i1, i2));
    278     }
    279     EIGEN_DEVICE_FUNC
    280     EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3)
    281     {
    282       return coeffRef(array<Index, 4>(i0, i1, i2, i3));
    283     }
    284     EIGEN_DEVICE_FUNC
    285     EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4)
    286     {
    287       return coeffRef(array<Index, 5>(i0, i1, i2, i3, i4));
    288     }
    289 #endif
    290 
    291     // normal indices
    292     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(const array<Index, NumIndices>& indices)
    293     {
    294       return coeffRef(indices);
    295     }
    296 
    297     // custom indices
    298 #ifdef EIGEN_HAS_SFINAE
    299     template<typename CustomIndices,
    300              EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
    301     >
    302     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(CustomIndices& indices)
    303     {
    304       return coeffRef(internal::customIndices2Array<Index,NumIndices>(indices));
    305     }
    306 #endif
    307 
    308     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(Index index)
    309     {
    310       eigen_assert(index >= 0 && index < size());
    311       return coeffRef(index);
    312     }
    313 
    314     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()()
    315     {
    316       EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
    317       return coeffRef();
    318     }
    319 
    320     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator[](Index index)
    321     {
    322       // The bracket operator is only for vectors, use the parenthesis operator instead
    323       EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE)
    324       return coeffRef(index);
    325     }
    326 
    327     EIGEN_DEVICE_FUNC
    328     EIGEN_STRONG_INLINE Tensor()
    329       : m_storage()
    330     {
    331     }
    332 
    333     EIGEN_DEVICE_FUNC
    334     EIGEN_STRONG_INLINE Tensor(const Self& other)
    335       : m_storage(other.m_storage)
    336     {
    337     }
    338 
    339 #if EIGEN_HAS_VARIADIC_TEMPLATES
    340     template<typename... IndexTypes>
    341     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index firstDimension, IndexTypes... otherDimensions)
    342         : m_storage(firstDimension, otherDimensions...)
    343     {
    344       // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.
    345       EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    346     }
    347 #else
    348     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Tensor(Index dim1)
    349       : m_storage(dim1, array<Index, 1>(dim1))
    350     {
    351       EIGEN_STATIC_ASSERT(1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    352     }
    353     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2)
    354       : m_storage(dim1*dim2, array<Index, 2>(dim1, dim2))
    355     {
    356       EIGEN_STATIC_ASSERT(2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    357     }
    358     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2, Index dim3)
    359       : m_storage(dim1*dim2*dim3, array<Index, 3>(dim1, dim2, dim3))
    360     {
    361       EIGEN_STATIC_ASSERT(3 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    362     }
    363     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2, Index dim3, Index dim4)
    364       : m_storage(dim1*dim2*dim3*dim4, array<Index, 4>(dim1, dim2, dim3, dim4))
    365     {
    366       EIGEN_STATIC_ASSERT(4 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    367     }
    368     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2, Index dim3, Index dim4, Index dim5)
    369       : m_storage(dim1*dim2*dim3*dim4*dim5, array<Index, 5>(dim1, dim2, dim3, dim4, dim5))
    370     {
    371       EIGEN_STATIC_ASSERT(5 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    372     }
    373 #endif
    374 
    375     /** Normal Dimension */
    376     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Tensor(const array<Index, NumIndices>& dimensions)
    377         : m_storage(internal::array_prod(dimensions), dimensions)
    378     {
    379       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
    380     }
    381 
    382     template<typename OtherDerived>
    383     EIGEN_DEVICE_FUNC
    384     EIGEN_STRONG_INLINE Tensor(const TensorBase<OtherDerived, ReadOnlyAccessors>& other)
    385     {
    386       typedef TensorAssignOp<Tensor, const OtherDerived> Assign;
    387       Assign assign(*this, other.derived());
    388       resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
    389       internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
    390     }
    391 
    392     template<typename OtherDerived>
    393     EIGEN_DEVICE_FUNC
    394     EIGEN_STRONG_INLINE Tensor(const TensorBase<OtherDerived, WriteAccessors>& other)
    395     {
    396       typedef TensorAssignOp<Tensor, const OtherDerived> Assign;
    397       Assign assign(*this, other.derived());
    398       resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
    399       internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
    400     }
    401 
    402     #if EIGEN_HAS_RVALUE_REFERENCES
    403     EIGEN_DEVICE_FUNC
    404     EIGEN_STRONG_INLINE Tensor(Self&& other)
    405       : m_storage(std::move(other.m_storage))
    406     {
    407     }
    408     EIGEN_DEVICE_FUNC
    409     EIGEN_STRONG_INLINE Tensor& operator=(Self&& other)
    410     {
    411       m_storage = std::move(other.m_storage);
    412       return *this;
    413     }
    414     #endif
    415 
    416     EIGEN_DEVICE_FUNC
    417     EIGEN_STRONG_INLINE Tensor& operator=(const Tensor& other)
    418     {
    419       typedef TensorAssignOp<Tensor, const Tensor> Assign;
    420       Assign assign(*this, other);
    421       resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
    422       internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
    423       return *this;
    424     }
    425     template<typename OtherDerived>
    426     EIGEN_DEVICE_FUNC
    427     EIGEN_STRONG_INLINE Tensor& operator=(const OtherDerived& other)
    428     {
    429       typedef TensorAssignOp<Tensor, const OtherDerived> Assign;
    430       Assign assign(*this, other);
    431       resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
    432       internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
    433       return *this;
    434     }
    435 
    436 #if EIGEN_HAS_VARIADIC_TEMPLATES
    437     template<typename... IndexTypes> EIGEN_DEVICE_FUNC
    438     void resize(Index firstDimension, IndexTypes... otherDimensions)
    439     {
    440       // The number of dimensions used to resize a tensor must be equal to the rank of the tensor.
    441       EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
    442       resize(array<Index, NumIndices>{{firstDimension, otherDimensions...}});
    443     }
    444 #endif
    445 
    446     /** Normal Dimension */
    447     EIGEN_DEVICE_FUNC void resize(const array<Index, NumIndices>& dimensions)
    448     {
    449       int i;
    450       Index size = Index(1);
    451       for (i = 0; i < NumIndices; i++) {
    452         internal::check_rows_cols_for_overflow<Dynamic>::run(size, dimensions[i]);
    453         size *= dimensions[i];
    454       }
    455       #ifdef EIGEN_INITIALIZE_COEFFS
    456         bool size_changed = size != this->size();
    457         m_storage.resize(size, dimensions);
    458         if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
    459       #else
    460         m_storage.resize(size, dimensions);
    461       #endif
    462     }
    463 
    464     // Why this overload, DSizes is derived from array ??? //
    465     EIGEN_DEVICE_FUNC void resize(const DSizes<Index, NumIndices>& dimensions) {
    466       array<Index, NumIndices> dims;
    467       for (int i = 0; i < NumIndices; ++i) {
    468         dims[i] = dimensions[i];
    469       }
    470       resize(dims);
    471     }
    472 
    473     EIGEN_DEVICE_FUNC
    474     void resize()
    475     {
    476       EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
    477       // Nothing to do: rank 0 tensors have fixed size
    478     }
    479 
    480 #ifdef EIGEN_HAS_INDEX_LIST
    481     template <typename FirstType, typename... OtherTypes>
    482     EIGEN_DEVICE_FUNC
    483     void resize(const Eigen::IndexList<FirstType, OtherTypes...>& dimensions) {
    484       array<Index, NumIndices> dims;
    485       for (int i = 0; i < NumIndices; ++i) {
    486         dims[i] = static_cast<Index>(dimensions[i]);
    487       }
    488       resize(dims);
    489     }
    490 #endif
    491 
    492     /** Custom Dimension */
    493 #ifdef EIGEN_HAS_SFINAE
    494     template<typename CustomDimension,
    495              EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomDimension>::value) )
    496     >
    497     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(CustomDimension& dimensions)
    498     {
    499       resize(internal::customIndices2Array<Index,NumIndices>(dimensions));
    500     }
    501 #endif
    502 
    503 #ifndef EIGEN_EMULATE_CXX11_META_H
    504     template <typename std::ptrdiff_t... Indices>
    505     EIGEN_DEVICE_FUNC
    506     void resize(const Sizes<Indices...>& dimensions) {
    507       array<Index, NumIndices> dims;
    508       for (int i = 0; i < NumIndices; ++i) {
    509         dims[i] = static_cast<Index>(dimensions[i]);
    510       }
    511       resize(dims);
    512     }
    513 #else
    514     template <std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5>
    515     EIGEN_DEVICE_FUNC
    516     void resize(const Sizes<V1, V2, V3, V4, V5>& dimensions) {
    517       array<Index, NumIndices> dims;
    518       for (int i = 0; i < NumIndices; ++i) {
    519         dims[i] = static_cast<Index>(dimensions[i]);
    520       }
    521       resize(dims);
    522     }
    523 #endif
    524 
    525   protected:
    526 
    527     bool checkIndexRange(const array<Index, NumIndices>& indices) const
    528     {
    529       using internal::array_apply_and_reduce;
    530       using internal::array_zip_and_reduce;
    531       using internal::greater_equal_zero_op;
    532       using internal::logical_and_op;
    533       using internal::lesser_op;
    534 
    535       return
    536         // check whether the indices are all >= 0
    537         array_apply_and_reduce<logical_and_op, greater_equal_zero_op>(indices) &&
    538         // check whether the indices fit in the dimensions
    539         array_zip_and_reduce<logical_and_op, lesser_op>(indices, m_storage.dimensions());
    540     }
    541 
    542     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index linearizedIndex(const array<Index, NumIndices>& indices) const
    543     {
    544       if (Options&RowMajor) {
    545         return m_storage.dimensions().IndexOfRowMajor(indices);
    546       } else {
    547         return m_storage.dimensions().IndexOfColMajor(indices);
    548       }
    549     }
    550 };
    551 
    552 } // end namespace Eigen
    553 
    554 #endif // EIGEN_CXX11_TENSOR_TENSOR_H