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 /*
     pybind11/eigen/matrix.h: Transparent conversion for dense and sparse Eigen matrices
 
     Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>
 
     All rights reserved. Use of this source code is governed by a
     BSD-style license that can be found in the LICENSE file.
 */
 
 #pragma once
 
 #include "../numpy.h"
 
 /* HINT: To suppress warnings originating from the Eigen headers, use -isystem.
    See also:
        https://stackoverflow.com/questions/2579576/i-dir-vs-isystem-dir
        https://stackoverflow.com/questions/1741816/isystem-for-ms-visual-studio-c-compiler
 */
 PYBIND11_WARNING_PUSH
 PYBIND11_WARNING_DISABLE_MSVC(5054) // https://github.com/pybind/pybind11/pull/3741
 //       C5054: operator '&': deprecated between enumerations of different types
 PYBIND11_WARNING_DISABLE_GCC("-Wmaybe-uninitialized")
 
 #include <Eigen/Core>
 #include <Eigen/SparseCore>
 
 PYBIND11_WARNING_POP
 
 // Eigen prior to 3.2.7 doesn't have proper move constructors--but worse, some classes get implicit
 // move constructors that break things.  We could detect this an explicitly copy, but an extra copy
 // of matrices seems highly undesirable.
 static_assert(EIGEN_VERSION_AT_LEAST(3, 2, 7),
               "Eigen matrix support in pybind11 requires Eigen >= 3.2.7");
 
 PYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)
 
 PYBIND11_WARNING_DISABLE_MSVC(4127)
 
 // Provide a convenience alias for easier pass-by-ref usage with fully dynamic strides:
 using EigenDStride = Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic>;
 template <typename MatrixType>
 using EigenDRef = Eigen::Ref<MatrixType, 0, EigenDStride>;
 template <typename MatrixType>
 using EigenDMap = Eigen::Map<MatrixType, 0, EigenDStride>;
 
 PYBIND11_NAMESPACE_BEGIN(detail)
 
 #if EIGEN_VERSION_AT_LEAST(3, 3, 0)
 using EigenIndex = Eigen::Index;
 template <typename Scalar, int Flags, typename StorageIndex>
 using EigenMapSparseMatrix = Eigen::Map<Eigen::SparseMatrix<Scalar, Flags, StorageIndex>>;
 #else
 using EigenIndex = EIGEN_DEFAULT_DENSE_INDEX_TYPE;
 template <typename Scalar, int Flags, typename StorageIndex>
 using EigenMapSparseMatrix = Eigen::MappedSparseMatrix<Scalar, Flags, StorageIndex>;
 #endif
 
 // Matches Eigen::Map, Eigen::Ref, blocks, etc:
 template <typename T>
 using is_eigen_dense_map = all_of<is_template_base_of<Eigen::DenseBase, T>,
                                   std::is_base_of<Eigen::MapBase<T, Eigen::ReadOnlyAccessors>, T>>;
 template <typename T>
 using is_eigen_mutable_map = std::is_base_of<Eigen::MapBase<T, Eigen::WriteAccessors>, T>;
 template <typename T>
 using is_eigen_dense_plain
     = all_of<negation<is_eigen_dense_map<T>>, is_template_base_of<Eigen::PlainObjectBase, T>>;
 template <typename T>
 using is_eigen_sparse = is_template_base_of<Eigen::SparseMatrixBase, T>;
 // Test for objects inheriting from EigenBase<Derived> that aren't captured by the above.  This
 // basically covers anything that can be assigned to a dense matrix but that don't have a typical
 // matrix data layout that can be copied from their .data().  For example, DiagonalMatrix and
 // SelfAdjointView fall into this category.
 template <typename T>
 using is_eigen_other
     = all_of<is_template_base_of<Eigen::EigenBase, T>,
              negation<any_of<is_eigen_dense_map<T>, is_eigen_dense_plain<T>, is_eigen_sparse<T>>>>;
 
 // Captures numpy/eigen conformability status (returned by EigenProps::conformable()):
 template <bool EigenRowMajor>
 struct EigenConformable {
     bool conformable = false;
     EigenIndex rows = 0, cols = 0;
     EigenDStride stride{0, 0};    // Only valid if negativestrides is false!
     bool negativestrides = false; // If true, do not use stride!
 
     // NOLINTNEXTLINE(google-explicit-constructor)
     EigenConformable(bool fits = false) : conformable{fits} {}
     // Matrix type:
     EigenConformable(EigenIndex r, EigenIndex c, EigenIndex rstride, EigenIndex cstride)
         : conformable{true}, rows{r}, cols{c},
           // TODO: when Eigen bug #747 is fixed, remove the tests for non-negativity.
           // http://eigen.tuxfamily.org/bz/show_bug.cgi?id=747
           stride{EigenRowMajor ? (rstride > 0 ? rstride : 0)
                                : (cstride > 0 ? cstride : 0) /* outer stride */,
                  EigenRowMajor ? (cstride > 0 ? cstride : 0)
                                : (rstride > 0 ? rstride : 0) /* inner stride */},
           negativestrides{rstride < 0 || cstride < 0} {}
     // Vector type:
     EigenConformable(EigenIndex r, EigenIndex c, EigenIndex stride)
         : EigenConformable(r, c, r == 1 ? c * stride : stride, c == 1 ? r : r * stride) {}
 
     template <typename props>
     bool stride_compatible() const {
         // To have compatible strides, we need (on both dimensions) one of fully dynamic strides,
         // matching strides, or a dimension size of 1 (in which case the stride value is
         // irrelevant). Alternatively, if any dimension size is 0, the strides are not relevant
         // (and numpy ≥ 1.23 sets the strides to 0 in that case, so we need to check explicitly).
         if (negativestrides) {
             return false;
         }
         if (rows == 0 || cols == 0) {
             return true;
         }
         return (props::inner_stride == Eigen::Dynamic || props::inner_stride == stride.inner()
                 || (EigenRowMajor ? cols : rows) == 1)
                && (props::outer_stride == Eigen::Dynamic || props::outer_stride == stride.outer()
                    || (EigenRowMajor ? rows : cols) == 1);
     }
     // NOLINTNEXTLINE(google-explicit-constructor)
     operator bool() const { return conformable; }
 };
 
 template <typename Type>
 struct eigen_extract_stride {
     using type = Type;
 };
 template <typename PlainObjectType, int MapOptions, typename StrideType>
 struct eigen_extract_stride<Eigen::Map<PlainObjectType, MapOptions, StrideType>> {
     using type = StrideType;
 };
 template <typename PlainObjectType, int Options, typename StrideType>
 struct eigen_extract_stride<Eigen::Ref<PlainObjectType, Options, StrideType>> {
     using type = StrideType;
 };
 
 // Helper struct for extracting information from an Eigen type
 template <typename Type_>
 struct EigenProps {
     using Type = Type_;
     using Scalar = typename Type::Scalar;
     using StrideType = typename eigen_extract_stride<Type>::type;
     static constexpr EigenIndex rows = Type::RowsAtCompileTime, cols = Type::ColsAtCompileTime,
                                 size = Type::SizeAtCompileTime;
     static constexpr bool row_major = Type::IsRowMajor,
                           vector
                           = Type::IsVectorAtCompileTime, // At least one dimension has fixed size 1
         fixed_rows = rows != Eigen::Dynamic, fixed_cols = cols != Eigen::Dynamic,
                           fixed = size != Eigen::Dynamic, // Fully-fixed size
         dynamic = !fixed_rows && !fixed_cols;             // Fully-dynamic size
 
     template <EigenIndex i, EigenIndex ifzero>
     using if_zero = std::integral_constant<EigenIndex, i == 0 ? ifzero : i>;
     static constexpr EigenIndex inner_stride
         = if_zero<StrideType::InnerStrideAtCompileTime, 1>::value,
         outer_stride = if_zero < StrideType::OuterStrideAtCompileTime,
         vector      ? size
         : row_major ? cols
                     : rows > ::value;
     static constexpr bool dynamic_stride
         = inner_stride == Eigen::Dynamic && outer_stride == Eigen::Dynamic;
     static constexpr bool requires_row_major
         = !dynamic_stride && !vector && (row_major ? inner_stride : outer_stride) == 1;
     static constexpr bool requires_col_major
         = !dynamic_stride && !vector && (row_major ? outer_stride : inner_stride) == 1;
 
     // Takes an input array and determines whether we can make it fit into the Eigen type.  If
     // the array is a vector, we attempt to fit it into either an Eigen 1xN or Nx1 vector
     // (preferring the latter if it will fit in either, i.e. for a fully dynamic matrix type).
     static EigenConformable<row_major> conformable(const array &a) {
         const auto dims = a.ndim();
         if (dims < 1 || dims > 2) {
             return false;
         }
 
         if (dims == 2) { // Matrix type: require exact match (or dynamic)
 
             EigenIndex np_rows = a.shape(0), np_cols = a.shape(1),
                        np_rstride = a.strides(0) / static_cast<ssize_t>(sizeof(Scalar)),
                        np_cstride = a.strides(1) / static_cast<ssize_t>(sizeof(Scalar));
             if ((fixed_rows && np_rows != rows) || (fixed_cols && np_cols != cols)) {
                 return false;
             }
 
             return {np_rows, np_cols, np_rstride, np_cstride};
         }
 
         // Otherwise we're storing an n-vector.  Only one of the strides will be used, but
         // whichever is used, we want the (single) numpy stride value.
         const EigenIndex n = a.shape(0),
                          stride = a.strides(0) / static_cast<ssize_t>(sizeof(Scalar));
 
         if (vector) { // Eigen type is a compile-time vector
             if (fixed && size != n) {
                 return false; // Vector size mismatch
             }
             return {rows == 1 ? 1 : n, cols == 1 ? 1 : n, stride};
         }
         if (fixed) {
             // The type has a fixed size, but is not a vector: abort
             return false;
         }
         if (fixed_cols) {
             // Since this isn't a vector, cols must be != 1.  We allow this only if it exactly
             // equals the number of elements (rows is Dynamic, and so 1 row is allowed).
             if (cols != n) {
                 return false;
             }
             return {1, n, stride};
         } // Otherwise it's either fully dynamic, or column dynamic; both become a column vector
         if (fixed_rows && rows != n) {
             return false;
         }
         return {n, 1, stride};
     }
 
     static constexpr bool show_writeable
         = is_eigen_dense_map<Type>::value && is_eigen_mutable_map<Type>::value;
     static constexpr bool show_order = is_eigen_dense_map<Type>::value;
     static constexpr bool show_c_contiguous = show_order && requires_row_major;
     static constexpr bool show_f_contiguous
         = !show_c_contiguous && show_order && requires_col_major;
 
     static constexpr auto descriptor
         = const_name("numpy.ndarray[") + npy_format_descriptor<Scalar>::name + const_name("[")
           + const_name<fixed_rows>(const_name<(size_t) rows>(), const_name("m")) + const_name(", ")
           + const_name<fixed_cols>(const_name<(size_t) cols>(), const_name("n")) + const_name("]")
           +
           // For a reference type (e.g. Ref<MatrixXd>) we have other constraints that might need to
           // be satisfied: writeable=True (for a mutable reference), and, depending on the map's
           // stride options, possibly f_contiguous or c_contiguous.  We include them in the
           // descriptor output to provide some hint as to why a TypeError is occurring (otherwise
           // it can be confusing to see that a function accepts a 'numpy.ndarray[float64[3,2]]' and
           // an error message that you *gave* a numpy.ndarray of the right type and dimensions.
           const_name<show_writeable>(", flags.writeable", "")
           + const_name<show_c_contiguous>(", flags.c_contiguous", "")
           + const_name<show_f_contiguous>(", flags.f_contiguous", "") + const_name("]");
 };
 
 // Casts an Eigen type to numpy array.  If given a base, the numpy array references the src data,
 // otherwise it'll make a copy.  writeable lets you turn off the writeable flag for the array.
 template <typename props>
 handle
 eigen_array_cast(typename props::Type const &src, handle base = handle(), bool writeable = true) {
     constexpr ssize_t elem_size = sizeof(typename props::Scalar);
     array a;
     if (props::vector) {
         a = array({src.size()}, {elem_size * src.innerStride()}, src.data(), base);
     } else {
         a = array({src.rows(), src.cols()},
                   {elem_size * src.rowStride(), elem_size * src.colStride()},
                   src.data(),
                   base);
     }
 
     if (!writeable) {
         array_proxy(a.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;
     }
 
     return a.release();
 }
 
 // Takes an lvalue ref to some Eigen type and a (python) base object, creating a numpy array that
 // reference the Eigen object's data with `base` as the python-registered base class (if omitted,
 // the base will be set to None, and lifetime management is up to the caller).  The numpy array is
 // non-writeable if the given type is const.
 template <typename props, typename Type>
 handle eigen_ref_array(Type &src, handle parent = none()) {
     // none here is to get past array's should-we-copy detection, which currently always
     // copies when there is no base.  Setting the base to None should be harmless.
     return eigen_array_cast<props>(src, parent, !std::is_const<Type>::value);
 }
 
 // Takes a pointer to some dense, plain Eigen type, builds a capsule around it, then returns a
 // numpy array that references the encapsulated data with a python-side reference to the capsule to
 // tie its destruction to that of any dependent python objects.  Const-ness is determined by
 // whether or not the Type of the pointer given is const.
 template <typename props, typename Type, typename = enable_if_t<is_eigen_dense_plain<Type>::value>>
 handle eigen_encapsulate(Type *src) {
     capsule base(src, [](void *o) { delete static_cast<Type *>(o); });
     return eigen_ref_array<props>(*src, base);
 }
 
 // Type caster for regular, dense matrix types (e.g. MatrixXd), but not maps/refs/etc. of dense
 // types.
 template <typename Type>
 struct type_caster<Type, enable_if_t<is_eigen_dense_plain<Type>::value>> {
     using Scalar = typename Type::Scalar;
     using props = EigenProps<Type>;
 
     bool load(handle src, bool convert) {
         // If we're in no-convert mode, only load if given an array of the correct type
         if (!convert && !isinstance<array_t<Scalar>>(src)) {
             return false;
         }
 
         // Coerce into an array, but don't do type conversion yet; the copy below handles it.
         auto buf = array::ensure(src);
 
         if (!buf) {
             return false;
         }
 
         auto dims = buf.ndim();
         if (dims < 1 || dims > 2) {
             return false;
         }
 
         auto fits = props::conformable(buf);
         if (!fits) {
             return false;
         }
 
         // Allocate the new type, then build a numpy reference into it
         value = Type(fits.rows, fits.cols);
         auto ref = reinterpret_steal<array>(eigen_ref_array<props>(value));
         if (dims == 1) {
             ref = ref.squeeze();
         } else if (ref.ndim() == 1) {
             buf = buf.squeeze();
         }
 
         int result = detail::npy_api::get().PyArray_CopyInto_(ref.ptr(), buf.ptr());
 
         if (result < 0) { // Copy failed!
             PyErr_Clear();
             return false;
         }
 
         return true;
     }
 
 private:
     // Cast implementation
     template <typename CType>
     static handle cast_impl(CType *src, return_value_policy policy, handle parent) {
         switch (policy) {
             case return_value_policy::take_ownership:
             case return_value_policy::automatic:
                 return eigen_encapsulate<props>(src);
             case return_value_policy::move:
                 return eigen_encapsulate<props>(new CType(std::move(*src)));
             case return_value_policy::copy:
                 return eigen_array_cast<props>(*src);
             case return_value_policy::reference:
             case return_value_policy::automatic_reference:
                 return eigen_ref_array<props>(*src);
             case return_value_policy::reference_internal:
                 return eigen_ref_array<props>(*src, parent);
             default:
                 throw cast_error("unhandled return_value_policy: should not happen!");
         };
     }
 
 public:
     // Normal returned non-reference, non-const value:
     static handle cast(Type &&src, return_value_policy /* policy */, handle parent) {
         return cast_impl(&src, return_value_policy::move, parent);
     }
     // If you return a non-reference const, we mark the numpy array readonly:
     static handle cast(const Type &&src, return_value_policy /* policy */, handle parent) {
         return cast_impl(&src, return_value_policy::move, parent);
     }
     // lvalue reference return; default (automatic) becomes copy
     static handle cast(Type &src, return_value_policy policy, handle parent) {
         if (policy == return_value_policy::automatic
             || policy == return_value_policy::automatic_reference) {
             policy = return_value_policy::copy;
         }
         return cast_impl(&src, policy, parent);
     }
     // const lvalue reference return; default (automatic) becomes copy
     static handle cast(const Type &src, return_value_policy policy, handle parent) {
         if (policy == return_value_policy::automatic
             || policy == return_value_policy::automatic_reference) {
             policy = return_value_policy::copy;
         }
         return cast(&src, policy, parent);
     }
     // non-const pointer return
     static handle cast(Type *src, return_value_policy policy, handle parent) {
         return cast_impl(src, policy, parent);
     }
     // const pointer return
     static handle cast(const Type *src, return_value_policy policy, handle parent) {
         return cast_impl(src, policy, parent);
     }
 
     static constexpr auto name = props::descriptor;
 
     // NOLINTNEXTLINE(google-explicit-constructor)
     operator Type *() { return &value; }
     // NOLINTNEXTLINE(google-explicit-constructor)
     operator Type &() { return value; }
     // NOLINTNEXTLINE(google-explicit-constructor)
     operator Type &&() && { return std::move(value); }
     template <typename T>
     using cast_op_type = movable_cast_op_type<T>;
 
 private:
     Type value;
 };
 
 // Base class for casting reference/map/block/etc. objects back to python.
 template <typename MapType>
 struct eigen_map_caster {
 private:
     using props = EigenProps<MapType>;
 
 public:
     // Directly referencing a ref/map's data is a bit dangerous (whatever the map/ref points to has
     // to stay around), but we'll allow it under the assumption that you know what you're doing
     // (and have an appropriate keep_alive in place).  We return a numpy array pointing directly at
     // the ref's data (The numpy array ends up read-only if the ref was to a const matrix type.)
     // Note that this means you need to ensure you don't destroy the object in some other way (e.g.
     // with an appropriate keep_alive, or with a reference to a statically allocated matrix).
     static handle cast(const MapType &src, return_value_policy policy, handle parent) {
         switch (policy) {
             case return_value_policy::copy:
                 return eigen_array_cast<props>(src);
             case return_value_policy::reference_internal:
                 return eigen_array_cast<props>(src, parent, is_eigen_mutable_map<MapType>::value);
             case return_value_policy::reference:
             case return_value_policy::automatic:
             case return_value_policy::automatic_reference:
                 return eigen_array_cast<props>(src, none(), is_eigen_mutable_map<MapType>::value);
             default:
                 // move, take_ownership don't make any sense for a ref/map:
                 pybind11_fail("Invalid return_value_policy for Eigen Map/Ref/Block type");
         }
     }
 
     static constexpr auto name = props::descriptor;
 
     // Explicitly delete these: support python -> C++ conversion on these (i.e. these can be return
     // types but not bound arguments).  We still provide them (with an explicitly delete) so that
     // you end up here if you try anyway.
     bool load(handle, bool) = delete;
     operator MapType() = delete;
     template <typename>
     using cast_op_type = MapType;
 };
 
 // We can return any map-like object (but can only load Refs, specialized next):
 template <typename Type>
 struct type_caster<Type, enable_if_t<is_eigen_dense_map<Type>::value>> : eigen_map_caster<Type> {};
 
 // Loader for Ref<...> arguments.  See the documentation for info on how to make this work without
 // copying (it requires some extra effort in many cases).
 template <typename PlainObjectType, typename StrideType>
 struct type_caster<
     Eigen::Ref<PlainObjectType, 0, StrideType>,
     enable_if_t<is_eigen_dense_map<Eigen::Ref<PlainObjectType, 0, StrideType>>::value>>
     : public eigen_map_caster<Eigen::Ref<PlainObjectType, 0, StrideType>> {
 private:
     using Type = Eigen::Ref<PlainObjectType, 0, StrideType>;
     using props = EigenProps<Type>;
     using Scalar = typename props::Scalar;
     using MapType = Eigen::Map<PlainObjectType, 0, StrideType>;
     using Array
         = array_t<Scalar,
                   array::forcecast
                       | ((props::row_major ? props::inner_stride : props::outer_stride) == 1
                              ? array::c_style
                          : (props::row_major ? props::outer_stride : props::inner_stride) == 1
                              ? array::f_style
                              : 0)>;
     static constexpr bool need_writeable = is_eigen_mutable_map<Type>::value;
     // Delay construction (these have no default constructor)
     std::unique_ptr<MapType> map;
     std::unique_ptr<Type> ref;
     // Our array.  When possible, this is just a numpy array pointing to the source data, but
     // sometimes we can't avoid copying (e.g. input is not a numpy array at all, has an
     // incompatible layout, or is an array of a type that needs to be converted).  Using a numpy
     // temporary (rather than an Eigen temporary) saves an extra copy when we need both type
     // conversion and storage order conversion.  (Note that we refuse to use this temporary copy
     // when loading an argument for a Ref<M> with M non-const, i.e. a read-write reference).
     Array copy_or_ref;
 
 public:
     bool load(handle src, bool convert) {
         // First check whether what we have is already an array of the right type.  If not, we
         // can't avoid a copy (because the copy is also going to do type conversion).
         bool need_copy = !isinstance<Array>(src);
 
         EigenConformable<props::row_major> fits;
         if (!need_copy) {
             // We don't need a converting copy, but we also need to check whether the strides are
             // compatible with the Ref's stride requirements
             auto aref = reinterpret_borrow<Array>(src);
 
             if (aref && (!need_writeable || aref.writeable())) {
                 fits = props::conformable(aref);
                 if (!fits) {
                     return false; // Incompatible dimensions
                 }
                 if (!fits.template stride_compatible<props>()) {
                     need_copy = true;
                 } else {
                     copy_or_ref = std::move(aref);
                 }
             } else {
                 need_copy = true;
             }
         }
 
         if (need_copy) {
             // We need to copy: If we need a mutable reference, or we're not supposed to convert
             // (either because we're in the no-convert overload pass, or because we're explicitly
             // instructed not to copy (via `py::arg().noconvert()`) we have to fail loading.
             if (!convert || need_writeable) {
                 return false;
             }
 
             Array copy = Array::ensure(src);
             if (!copy) {
                 return false;
             }
             fits = props::conformable(copy);
             if (!fits || !fits.template stride_compatible<props>()) {
                 return false;
             }
             copy_or_ref = std::move(copy);
             loader_life_support::add_patient(copy_or_ref);
         }
 
         ref.reset();
         map.reset(new MapType(data(copy_or_ref),
                               fits.rows,
                               fits.cols,
                               make_stride(fits.stride.outer(), fits.stride.inner())));
         ref.reset(new Type(*map));
 
         return true;
     }
 
     // NOLINTNEXTLINE(google-explicit-constructor)
     operator Type *() { return ref.get(); }
     // NOLINTNEXTLINE(google-explicit-constructor)
     operator Type &() { return *ref; }
     template <typename _T>
     using cast_op_type = pybind11::detail::cast_op_type<_T>;
 
 private:
     template <typename T = Type, enable_if_t<is_eigen_mutable_map<T>::value, int> = 0>
     Scalar *data(Array &a) {
         return a.mutable_data();
     }
 
     template <typename T = Type, enable_if_t<!is_eigen_mutable_map<T>::value, int> = 0>
     const Scalar *data(Array &a) {
         return a.data();
     }
 
     // Attempt to figure out a constructor of `Stride` that will work.
     // If both strides are fixed, use a default constructor:
     template <typename S>
     using stride_ctor_default = bool_constant<S::InnerStrideAtCompileTime != Eigen::Dynamic
                                               && S::OuterStrideAtCompileTime != Eigen::Dynamic
                                               && std::is_default_constructible<S>::value>;
     // Otherwise, if there is a two-index constructor, assume it is (outer,inner) like
     // Eigen::Stride, and use it:
     template <typename S>
     using stride_ctor_dual
         = bool_constant<!stride_ctor_default<S>::value
                         && std::is_constructible<S, EigenIndex, EigenIndex>::value>;
     // Otherwise, if there is a one-index constructor, and just one of the strides is dynamic, use
     // it (passing whichever stride is dynamic).
     template <typename S>
     using stride_ctor_outer
         = bool_constant<!any_of<stride_ctor_default<S>, stride_ctor_dual<S>>::value
                         && S::OuterStrideAtCompileTime == Eigen::Dynamic
                         && S::InnerStrideAtCompileTime != Eigen::Dynamic
                         && std::is_constructible<S, EigenIndex>::value>;
     template <typename S>
     using stride_ctor_inner
         = bool_constant<!any_of<stride_ctor_default<S>, stride_ctor_dual<S>>::value
                         && S::InnerStrideAtCompileTime == Eigen::Dynamic
                         && S::OuterStrideAtCompileTime != Eigen::Dynamic
                         && std::is_constructible<S, EigenIndex>::value>;
 
     template <typename S = StrideType, enable_if_t<stride_ctor_default<S>::value, int> = 0>
     static S make_stride(EigenIndex, EigenIndex) {
         return S();
     }
     template <typename S = StrideType, enable_if_t<stride_ctor_dual<S>::value, int> = 0>
     static S make_stride(EigenIndex outer, EigenIndex inner) {
         return S(outer, inner);
     }
     template <typename S = StrideType, enable_if_t<stride_ctor_outer<S>::value, int> = 0>
     static S make_stride(EigenIndex outer, EigenIndex) {
         return S(outer);
     }
     template <typename S = StrideType, enable_if_t<stride_ctor_inner<S>::value, int> = 0>
     static S make_stride(EigenIndex, EigenIndex inner) {
         return S(inner);
     }
 };
 
 // type_caster for special matrix types (e.g. DiagonalMatrix), which are EigenBase, but not
 // EigenDense (i.e. they don't have a data(), at least not with the usual matrix layout).
 // load() is not supported, but we can cast them into the python domain by first copying to a
 // regular Eigen::Matrix, then casting that.
 template <typename Type>
 struct type_caster<Type, enable_if_t<is_eigen_other<Type>::value>> {
 protected:
     using Matrix
         = Eigen::Matrix<typename Type::Scalar, Type::RowsAtCompileTime, Type::ColsAtCompileTime>;
     using props = EigenProps<Matrix>;
 
 public:
     static handle cast(const Type &src, return_value_policy /* policy */, handle /* parent */) {
         handle h = eigen_encapsulate<props>(new Matrix(src));
         return h;
     }
     static handle cast(const Type *src, return_value_policy policy, handle parent) {
         return cast(*src, policy, parent);
     }
 
     static constexpr auto name = props::descriptor;
 
     // Explicitly delete these: support python -> C++ conversion on these (i.e. these can be return
     // types but not bound arguments).  We still provide them (with an explicitly delete) so that
     // you end up here if you try anyway.
     bool load(handle, bool) = delete;
     operator Type() = delete;
     template <typename>
     using cast_op_type = Type;
 };
 
 template <typename Type>
 struct type_caster<Type, enable_if_t<is_eigen_sparse<Type>::value>> {
     using Scalar = typename Type::Scalar;
     using StorageIndex = remove_reference_t<decltype(*std::declval<Type>().outerIndexPtr())>;
     using Index = typename Type::Index;
     static constexpr bool rowMajor = Type::IsRowMajor;
 
     bool load(handle src, bool) {
         if (!src) {
             return false;
         }
 
         auto obj = reinterpret_borrow<object>(src);
         object sparse_module = module_::import("scipy.sparse");
         object matrix_type = sparse_module.attr(rowMajor ? "csr_matrix" : "csc_matrix");
 
         if (!type::handle_of(obj).is(matrix_type)) {
             try {
                 obj = matrix_type(obj);
             } catch (const error_already_set &) {
                 return false;
             }
         }
 
         auto values = array_t<Scalar>((object) obj.attr("data"));
         auto innerIndices = array_t<StorageIndex>((object) obj.attr("indices"));
         auto outerIndices = array_t<StorageIndex>((object) obj.attr("indptr"));
         auto shape = pybind11::tuple((pybind11::object) obj.attr("shape"));
         auto nnz = obj.attr("nnz").cast<Index>();
 
         if (!values || !innerIndices || !outerIndices) {
             return false;
         }
 
         value = EigenMapSparseMatrix<Scalar,
                                      Type::Flags &(Eigen::RowMajor | Eigen::ColMajor),
                                      StorageIndex>(shape[0].cast<Index>(),
                                                    shape[1].cast<Index>(),
                                                    std::move(nnz),
                                                    outerIndices.mutable_data(),
                                                    innerIndices.mutable_data(),
                                                    values.mutable_data());
 
         return true;
     }
 
     static handle cast(const Type &src, return_value_policy /* policy */, handle /* parent */) {
         const_cast<Type &>(src).makeCompressed();
 
         object matrix_type
             = module_::import("scipy.sparse").attr(rowMajor ? "csr_matrix" : "csc_matrix");
 
         array data(src.nonZeros(), src.valuePtr());
         array outerIndices((rowMajor ? src.rows() : src.cols()) + 1, src.outerIndexPtr());
         array innerIndices(src.nonZeros(), src.innerIndexPtr());
 
         return matrix_type(pybind11::make_tuple(
                                std::move(data), std::move(innerIndices), std::move(outerIndices)),
                            pybind11::make_tuple(src.rows(), src.cols()))
             .release();
     }
 
     PYBIND11_TYPE_CASTER(Type,
                          const_name<(Type::IsRowMajor) != 0>("scipy.sparse.csr_matrix[",
                                                              "scipy.sparse.csc_matrix[")
                              + npy_format_descriptor<Scalar>::name + const_name("]"));
 };
 
 PYBIND11_NAMESPACE_END(detail)
 PYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)

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