matrix.h

/*
    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 <pybind11/numpy.h>

#include "common.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
#if defined(__MINGW32__)
PYBIND11_WARNING_DISABLE_GCC("-Wmaybe-uninitialized")
#endif

#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("typing.Annotated[")
          + io_name("numpy.typing.ArrayLike, ", "numpy.typing.NDArray[")
          + npy_format_descriptor<Scalar>::name + io_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
          // 'typing.Annotated[numpy.typing.NDArray[numpy.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;
    static_assert(!std::is_pointer<Scalar>::value,
                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);
    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;
        }

        PYBIND11_WARNING_PUSH
        PYBIND11_WARNING_DISABLE_GCC("-Wmaybe-uninitialized") // See PR #5516
        // Allocate the new type, then build a numpy reference into it
        value = Type(fits.rows, fits.cols);
        PYBIND11_WARNING_POP
        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 {
    static_assert(!std::is_pointer<typename MapType::Scalar>::value,
                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);

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");
        }
    }

    // return_descr forces the use of NDArray instead of ArrayLike in args
    // since Ref<...> args can only accept arrays.
    static constexpr auto name = return_descr(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;
    static_assert(!std::is_pointer<Scalar>::value,
                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);
    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>> {
    static_assert(!std::is_pointer<typename Type::Scalar>::value,
                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);

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;
    static_assert(!std::is_pointer<Scalar>::value,
                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);
    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)