eigen.h revision 14299:2fbea9df56d2
1/*
2    pybind11/eigen.h: Transparent conversion for dense and sparse Eigen matrices
3
4    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>
5
6    All rights reserved. Use of this source code is governed by a
7    BSD-style license that can be found in the LICENSE file.
8*/
9
10#pragma once
11
12#include "numpy.h"
13
14#if defined(__INTEL_COMPILER)
15#  pragma warning(disable: 1682) // implicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem)
16#elif defined(__GNUG__) || defined(__clang__)
17#  pragma GCC diagnostic push
18#  pragma GCC diagnostic ignored "-Wconversion"
19#  pragma GCC diagnostic ignored "-Wdeprecated-declarations"
20#  ifdef __clang__
21//   Eigen generates a bunch of implicit-copy-constructor-is-deprecated warnings with -Wdeprecated
22//   under Clang, so disable that warning here:
23#    pragma GCC diagnostic ignored "-Wdeprecated"
24#  endif
25#  if __GNUC__ >= 7
26#    pragma GCC diagnostic ignored "-Wint-in-bool-context"
27#  endif
28#endif
29
30#if defined(_MSC_VER)
31#  pragma warning(push)
32#  pragma warning(disable: 4127) // warning C4127: Conditional expression is constant
33#  pragma warning(disable: 4996) // warning C4996: std::unary_negate is deprecated in C++17
34#endif
35
36#include <Eigen/Core>
37#include <Eigen/SparseCore>
38
39// Eigen prior to 3.2.7 doesn't have proper move constructors--but worse, some classes get implicit
40// move constructors that break things.  We could detect this an explicitly copy, but an extra copy
41// of matrices seems highly undesirable.
42static_assert(EIGEN_VERSION_AT_LEAST(3,2,7), "Eigen support in pybind11 requires Eigen >= 3.2.7");
43
44NAMESPACE_BEGIN(PYBIND11_NAMESPACE)
45
46// Provide a convenience alias for easier pass-by-ref usage with fully dynamic strides:
47using EigenDStride = Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic>;
48template <typename MatrixType> using EigenDRef = Eigen::Ref<MatrixType, 0, EigenDStride>;
49template <typename MatrixType> using EigenDMap = Eigen::Map<MatrixType, 0, EigenDStride>;
50
51NAMESPACE_BEGIN(detail)
52
53#if EIGEN_VERSION_AT_LEAST(3,3,0)
54using EigenIndex = Eigen::Index;
55#else
56using EigenIndex = EIGEN_DEFAULT_DENSE_INDEX_TYPE;
57#endif
58
59// Matches Eigen::Map, Eigen::Ref, blocks, etc:
60template <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>>;
61template <typename T> using is_eigen_mutable_map = std::is_base_of<Eigen::MapBase<T, Eigen::WriteAccessors>, T>;
62template <typename T> using is_eigen_dense_plain = all_of<negation<is_eigen_dense_map<T>>, is_template_base_of<Eigen::PlainObjectBase, T>>;
63template <typename T> using is_eigen_sparse = is_template_base_of<Eigen::SparseMatrixBase, T>;
64// Test for objects inheriting from EigenBase<Derived> that aren't captured by the above.  This
65// basically covers anything that can be assigned to a dense matrix but that don't have a typical
66// matrix data layout that can be copied from their .data().  For example, DiagonalMatrix and
67// SelfAdjointView fall into this category.
68template <typename T> using is_eigen_other = all_of<
69    is_template_base_of<Eigen::EigenBase, T>,
70    negation<any_of<is_eigen_dense_map<T>, is_eigen_dense_plain<T>, is_eigen_sparse<T>>>
71>;
72
73// Captures numpy/eigen conformability status (returned by EigenProps::conformable()):
74template <bool EigenRowMajor> struct EigenConformable {
75    bool conformable = false;
76    EigenIndex rows = 0, cols = 0;
77    EigenDStride stride{0, 0};      // Only valid if negativestrides is false!
78    bool negativestrides = false;   // If true, do not use stride!
79
80    EigenConformable(bool fits = false) : conformable{fits} {}
81    // Matrix type:
82    EigenConformable(EigenIndex r, EigenIndex c,
83            EigenIndex rstride, EigenIndex cstride) :
84        conformable{true}, rows{r}, cols{c} {
85        // TODO: when Eigen bug #747 is fixed, remove the tests for non-negativity. http://eigen.tuxfamily.org/bz/show_bug.cgi?id=747
86        if (rstride < 0 || cstride < 0) {
87            negativestrides = true;
88        } else {
89            stride = {EigenRowMajor ? rstride : cstride /* outer stride */,
90                      EigenRowMajor ? cstride : rstride /* inner stride */ };
91        }
92    }
93    // Vector type:
94    EigenConformable(EigenIndex r, EigenIndex c, EigenIndex stride)
95        : EigenConformable(r, c, r == 1 ? c*stride : stride, c == 1 ? r : r*stride) {}
96
97    template <typename props> bool stride_compatible() const {
98        // To have compatible strides, we need (on both dimensions) one of fully dynamic strides,
99        // matching strides, or a dimension size of 1 (in which case the stride value is irrelevant)
100        return
101            !negativestrides &&
102            (props::inner_stride == Eigen::Dynamic || props::inner_stride == stride.inner() ||
103                (EigenRowMajor ? cols : rows) == 1) &&
104            (props::outer_stride == Eigen::Dynamic || props::outer_stride == stride.outer() ||
105                (EigenRowMajor ? rows : cols) == 1);
106    }
107    operator bool() const { return conformable; }
108};
109
110template <typename Type> struct eigen_extract_stride { using type = Type; };
111template <typename PlainObjectType, int MapOptions, typename StrideType>
112struct eigen_extract_stride<Eigen::Map<PlainObjectType, MapOptions, StrideType>> { using type = StrideType; };
113template <typename PlainObjectType, int Options, typename StrideType>
114struct eigen_extract_stride<Eigen::Ref<PlainObjectType, Options, StrideType>> { using type = StrideType; };
115
116// Helper struct for extracting information from an Eigen type
117template <typename Type_> struct EigenProps {
118    using Type = Type_;
119    using Scalar = typename Type::Scalar;
120    using StrideType = typename eigen_extract_stride<Type>::type;
121    static constexpr EigenIndex
122        rows = Type::RowsAtCompileTime,
123        cols = Type::ColsAtCompileTime,
124        size = Type::SizeAtCompileTime;
125    static constexpr bool
126        row_major = Type::IsRowMajor,
127        vector = Type::IsVectorAtCompileTime, // At least one dimension has fixed size 1
128        fixed_rows = rows != Eigen::Dynamic,
129        fixed_cols = cols != Eigen::Dynamic,
130        fixed = size != Eigen::Dynamic, // Fully-fixed size
131        dynamic = !fixed_rows && !fixed_cols; // Fully-dynamic size
132
133    template <EigenIndex i, EigenIndex ifzero> using if_zero = std::integral_constant<EigenIndex, i == 0 ? ifzero : i>;
134    static constexpr EigenIndex inner_stride = if_zero<StrideType::InnerStrideAtCompileTime, 1>::value,
135                                outer_stride = if_zero<StrideType::OuterStrideAtCompileTime,
136                                                       vector ? size : row_major ? cols : rows>::value;
137    static constexpr bool dynamic_stride = inner_stride == Eigen::Dynamic && outer_stride == Eigen::Dynamic;
138    static constexpr bool requires_row_major = !dynamic_stride && !vector && (row_major ? inner_stride : outer_stride) == 1;
139    static constexpr bool requires_col_major = !dynamic_stride && !vector && (row_major ? outer_stride : inner_stride) == 1;
140
141    // Takes an input array and determines whether we can make it fit into the Eigen type.  If
142    // the array is a vector, we attempt to fit it into either an Eigen 1xN or Nx1 vector
143    // (preferring the latter if it will fit in either, i.e. for a fully dynamic matrix type).
144    static EigenConformable<row_major> conformable(const array &a) {
145        const auto dims = a.ndim();
146        if (dims < 1 || dims > 2)
147            return false;
148
149        if (dims == 2) { // Matrix type: require exact match (or dynamic)
150
151            EigenIndex
152                np_rows = a.shape(0),
153                np_cols = a.shape(1),
154                np_rstride = a.strides(0) / static_cast<ssize_t>(sizeof(Scalar)),
155                np_cstride = a.strides(1) / static_cast<ssize_t>(sizeof(Scalar));
156            if ((fixed_rows && np_rows != rows) || (fixed_cols && np_cols != cols))
157                return false;
158
159            return {np_rows, np_cols, np_rstride, np_cstride};
160        }
161
162        // Otherwise we're storing an n-vector.  Only one of the strides will be used, but whichever
163        // is used, we want the (single) numpy stride value.
164        const EigenIndex n = a.shape(0),
165              stride = a.strides(0) / static_cast<ssize_t>(sizeof(Scalar));
166
167        if (vector) { // Eigen type is a compile-time vector
168            if (fixed && size != n)
169                return false; // Vector size mismatch
170            return {rows == 1 ? 1 : n, cols == 1 ? 1 : n, stride};
171        }
172        else if (fixed) {
173            // The type has a fixed size, but is not a vector: abort
174            return false;
175        }
176        else if (fixed_cols) {
177            // Since this isn't a vector, cols must be != 1.  We allow this only if it exactly
178            // equals the number of elements (rows is Dynamic, and so 1 row is allowed).
179            if (cols != n) return false;
180            return {1, n, stride};
181        }
182        else {
183            // Otherwise it's either fully dynamic, or column dynamic; both become a column vector
184            if (fixed_rows && rows != n) return false;
185            return {n, 1, stride};
186        }
187    }
188
189    static constexpr bool show_writeable = is_eigen_dense_map<Type>::value && is_eigen_mutable_map<Type>::value;
190    static constexpr bool show_order = is_eigen_dense_map<Type>::value;
191    static constexpr bool show_c_contiguous = show_order && requires_row_major;
192    static constexpr bool show_f_contiguous = !show_c_contiguous && show_order && requires_col_major;
193
194    static constexpr auto descriptor =
195        _("numpy.ndarray[") + npy_format_descriptor<Scalar>::name +
196        _("[")  + _<fixed_rows>(_<(size_t) rows>(), _("m")) +
197        _(", ") + _<fixed_cols>(_<(size_t) cols>(), _("n")) +
198        _("]") +
199        // For a reference type (e.g. Ref<MatrixXd>) we have other constraints that might need to be
200        // satisfied: writeable=True (for a mutable reference), and, depending on the map's stride
201        // options, possibly f_contiguous or c_contiguous.  We include them in the descriptor output
202        // to provide some hint as to why a TypeError is occurring (otherwise it can be confusing to
203        // see that a function accepts a 'numpy.ndarray[float64[3,2]]' and an error message that you
204        // *gave* a numpy.ndarray of the right type and dimensions.
205        _<show_writeable>(", flags.writeable", "") +
206        _<show_c_contiguous>(", flags.c_contiguous", "") +
207        _<show_f_contiguous>(", flags.f_contiguous", "") +
208        _("]");
209};
210
211// Casts an Eigen type to numpy array.  If given a base, the numpy array references the src data,
212// otherwise it'll make a copy.  writeable lets you turn off the writeable flag for the array.
213template <typename props> handle eigen_array_cast(typename props::Type const &src, handle base = handle(), bool writeable = true) {
214    constexpr ssize_t elem_size = sizeof(typename props::Scalar);
215    array a;
216    if (props::vector)
217        a = array({ src.size() }, { elem_size * src.innerStride() }, src.data(), base);
218    else
219        a = array({ src.rows(), src.cols() }, { elem_size * src.rowStride(), elem_size * src.colStride() },
220                  src.data(), base);
221
222    if (!writeable)
223        array_proxy(a.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;
224
225    return a.release();
226}
227
228// Takes an lvalue ref to some Eigen type and a (python) base object, creating a numpy array that
229// reference the Eigen object's data with `base` as the python-registered base class (if omitted,
230// the base will be set to None, and lifetime management is up to the caller).  The numpy array is
231// non-writeable if the given type is const.
232template <typename props, typename Type>
233handle eigen_ref_array(Type &src, handle parent = none()) {
234    // none here is to get past array's should-we-copy detection, which currently always
235    // copies when there is no base.  Setting the base to None should be harmless.
236    return eigen_array_cast<props>(src, parent, !std::is_const<Type>::value);
237}
238
239// Takes a pointer to some dense, plain Eigen type, builds a capsule around it, then returns a numpy
240// array that references the encapsulated data with a python-side reference to the capsule to tie
241// its destruction to that of any dependent python objects.  Const-ness is determined by whether or
242// not the Type of the pointer given is const.
243template <typename props, typename Type, typename = enable_if_t<is_eigen_dense_plain<Type>::value>>
244handle eigen_encapsulate(Type *src) {
245    capsule base(src, [](void *o) { delete static_cast<Type *>(o); });
246    return eigen_ref_array<props>(*src, base);
247}
248
249// Type caster for regular, dense matrix types (e.g. MatrixXd), but not maps/refs/etc. of dense
250// types.
251template<typename Type>
252struct type_caster<Type, enable_if_t<is_eigen_dense_plain<Type>::value>> {
253    using Scalar = typename Type::Scalar;
254    using props = EigenProps<Type>;
255
256    bool load(handle src, bool convert) {
257        // If we're in no-convert mode, only load if given an array of the correct type
258        if (!convert && !isinstance<array_t<Scalar>>(src))
259            return false;
260
261        // Coerce into an array, but don't do type conversion yet; the copy below handles it.
262        auto buf = array::ensure(src);
263
264        if (!buf)
265            return false;
266
267        auto dims = buf.ndim();
268        if (dims < 1 || dims > 2)
269            return false;
270
271        auto fits = props::conformable(buf);
272        if (!fits)
273            return false;
274
275        // Allocate the new type, then build a numpy reference into it
276        value = Type(fits.rows, fits.cols);
277        auto ref = reinterpret_steal<array>(eigen_ref_array<props>(value));
278        if (dims == 1) ref = ref.squeeze();
279        else if (ref.ndim() == 1) buf = buf.squeeze();
280
281        int result = detail::npy_api::get().PyArray_CopyInto_(ref.ptr(), buf.ptr());
282
283        if (result < 0) { // Copy failed!
284            PyErr_Clear();
285            return false;
286        }
287
288        return true;
289    }
290
291private:
292
293    // Cast implementation
294    template <typename CType>
295    static handle cast_impl(CType *src, return_value_policy policy, handle parent) {
296        switch (policy) {
297            case return_value_policy::take_ownership:
298            case return_value_policy::automatic:
299                return eigen_encapsulate<props>(src);
300            case return_value_policy::move:
301                return eigen_encapsulate<props>(new CType(std::move(*src)));
302            case return_value_policy::copy:
303                return eigen_array_cast<props>(*src);
304            case return_value_policy::reference:
305            case return_value_policy::automatic_reference:
306                return eigen_ref_array<props>(*src);
307            case return_value_policy::reference_internal:
308                return eigen_ref_array<props>(*src, parent);
309            default:
310                throw cast_error("unhandled return_value_policy: should not happen!");
311        };
312    }
313
314public:
315
316    // Normal returned non-reference, non-const value:
317    static handle cast(Type &&src, return_value_policy /* policy */, handle parent) {
318        return cast_impl(&src, return_value_policy::move, parent);
319    }
320    // If you return a non-reference const, we mark the numpy array readonly:
321    static handle cast(const Type &&src, return_value_policy /* policy */, handle parent) {
322        return cast_impl(&src, return_value_policy::move, parent);
323    }
324    // lvalue reference return; default (automatic) becomes copy
325    static handle cast(Type &src, return_value_policy policy, handle parent) {
326        if (policy == return_value_policy::automatic || policy == return_value_policy::automatic_reference)
327            policy = return_value_policy::copy;
328        return cast_impl(&src, policy, parent);
329    }
330    // const lvalue reference return; default (automatic) becomes copy
331    static handle cast(const Type &src, return_value_policy policy, handle parent) {
332        if (policy == return_value_policy::automatic || policy == return_value_policy::automatic_reference)
333            policy = return_value_policy::copy;
334        return cast(&src, policy, parent);
335    }
336    // non-const pointer return
337    static handle cast(Type *src, return_value_policy policy, handle parent) {
338        return cast_impl(src, policy, parent);
339    }
340    // const pointer return
341    static handle cast(const Type *src, return_value_policy policy, handle parent) {
342        return cast_impl(src, policy, parent);
343    }
344
345    static constexpr auto name = props::descriptor;
346
347    operator Type*() { return &value; }
348    operator Type&() { return value; }
349    operator Type&&() && { return std::move(value); }
350    template <typename T> using cast_op_type = movable_cast_op_type<T>;
351
352private:
353    Type value;
354};
355
356// Base class for casting reference/map/block/etc. objects back to python.
357template <typename MapType> struct eigen_map_caster {
358private:
359    using props = EigenProps<MapType>;
360
361public:
362
363    // Directly referencing a ref/map's data is a bit dangerous (whatever the map/ref points to has
364    // to stay around), but we'll allow it under the assumption that you know what you're doing (and
365    // have an appropriate keep_alive in place).  We return a numpy array pointing directly at the
366    // ref's data (The numpy array ends up read-only if the ref was to a const matrix type.) Note
367    // that this means you need to ensure you don't destroy the object in some other way (e.g. with
368    // an appropriate keep_alive, or with a reference to a statically allocated matrix).
369    static handle cast(const MapType &src, return_value_policy policy, handle parent) {
370        switch (policy) {
371            case return_value_policy::copy:
372                return eigen_array_cast<props>(src);
373            case return_value_policy::reference_internal:
374                return eigen_array_cast<props>(src, parent, is_eigen_mutable_map<MapType>::value);
375            case return_value_policy::reference:
376            case return_value_policy::automatic:
377            case return_value_policy::automatic_reference:
378                return eigen_array_cast<props>(src, none(), is_eigen_mutable_map<MapType>::value);
379            default:
380                // move, take_ownership don't make any sense for a ref/map:
381                pybind11_fail("Invalid return_value_policy for Eigen Map/Ref/Block type");
382        }
383    }
384
385    static constexpr auto name = props::descriptor;
386
387    // Explicitly delete these: support python -> C++ conversion on these (i.e. these can be return
388    // types but not bound arguments).  We still provide them (with an explicitly delete) so that
389    // you end up here if you try anyway.
390    bool load(handle, bool) = delete;
391    operator MapType() = delete;
392    template <typename> using cast_op_type = MapType;
393};
394
395// We can return any map-like object (but can only load Refs, specialized next):
396template <typename Type> struct type_caster<Type, enable_if_t<is_eigen_dense_map<Type>::value>>
397    : eigen_map_caster<Type> {};
398
399// Loader for Ref<...> arguments.  See the documentation for info on how to make this work without
400// copying (it requires some extra effort in many cases).
401template <typename PlainObjectType, typename StrideType>
402struct type_caster<
403    Eigen::Ref<PlainObjectType, 0, StrideType>,
404    enable_if_t<is_eigen_dense_map<Eigen::Ref<PlainObjectType, 0, StrideType>>::value>
405> : public eigen_map_caster<Eigen::Ref<PlainObjectType, 0, StrideType>> {
406private:
407    using Type = Eigen::Ref<PlainObjectType, 0, StrideType>;
408    using props = EigenProps<Type>;
409    using Scalar = typename props::Scalar;
410    using MapType = Eigen::Map<PlainObjectType, 0, StrideType>;
411    using Array = array_t<Scalar, array::forcecast |
412                ((props::row_major ? props::inner_stride : props::outer_stride) == 1 ? array::c_style :
413                 (props::row_major ? props::outer_stride : props::inner_stride) == 1 ? array::f_style : 0)>;
414    static constexpr bool need_writeable = is_eigen_mutable_map<Type>::value;
415    // Delay construction (these have no default constructor)
416    std::unique_ptr<MapType> map;
417    std::unique_ptr<Type> ref;
418    // Our array.  When possible, this is just a numpy array pointing to the source data, but
419    // sometimes we can't avoid copying (e.g. input is not a numpy array at all, has an incompatible
420    // layout, or is an array of a type that needs to be converted).  Using a numpy temporary
421    // (rather than an Eigen temporary) saves an extra copy when we need both type conversion and
422    // storage order conversion.  (Note that we refuse to use this temporary copy when loading an
423    // argument for a Ref<M> with M non-const, i.e. a read-write reference).
424    Array copy_or_ref;
425public:
426    bool load(handle src, bool convert) {
427        // First check whether what we have is already an array of the right type.  If not, we can't
428        // avoid a copy (because the copy is also going to do type conversion).
429        bool need_copy = !isinstance<Array>(src);
430
431        EigenConformable<props::row_major> fits;
432        if (!need_copy) {
433            // We don't need a converting copy, but we also need to check whether the strides are
434            // compatible with the Ref's stride requirements
435            Array aref = reinterpret_borrow<Array>(src);
436
437            if (aref && (!need_writeable || aref.writeable())) {
438                fits = props::conformable(aref);
439                if (!fits) return false; // Incompatible dimensions
440                if (!fits.template stride_compatible<props>())
441                    need_copy = true;
442                else
443                    copy_or_ref = std::move(aref);
444            }
445            else {
446                need_copy = true;
447            }
448        }
449
450        if (need_copy) {
451            // We need to copy: If we need a mutable reference, or we're not supposed to convert
452            // (either because we're in the no-convert overload pass, or because we're explicitly
453            // instructed not to copy (via `py::arg().noconvert()`) we have to fail loading.
454            if (!convert || need_writeable) return false;
455
456            Array copy = Array::ensure(src);
457            if (!copy) return false;
458            fits = props::conformable(copy);
459            if (!fits || !fits.template stride_compatible<props>())
460                return false;
461            copy_or_ref = std::move(copy);
462            loader_life_support::add_patient(copy_or_ref);
463        }
464
465        ref.reset();
466        map.reset(new MapType(data(copy_or_ref), fits.rows, fits.cols, make_stride(fits.stride.outer(), fits.stride.inner())));
467        ref.reset(new Type(*map));
468
469        return true;
470    }
471
472    operator Type*() { return ref.get(); }
473    operator Type&() { return *ref; }
474    template <typename _T> using cast_op_type = pybind11::detail::cast_op_type<_T>;
475
476private:
477    template <typename T = Type, enable_if_t<is_eigen_mutable_map<T>::value, int> = 0>
478    Scalar *data(Array &a) { return a.mutable_data(); }
479
480    template <typename T = Type, enable_if_t<!is_eigen_mutable_map<T>::value, int> = 0>
481    const Scalar *data(Array &a) { return a.data(); }
482
483    // Attempt to figure out a constructor of `Stride` that will work.
484    // If both strides are fixed, use a default constructor:
485    template <typename S> using stride_ctor_default = bool_constant<
486        S::InnerStrideAtCompileTime != Eigen::Dynamic && S::OuterStrideAtCompileTime != Eigen::Dynamic &&
487        std::is_default_constructible<S>::value>;
488    // Otherwise, if there is a two-index constructor, assume it is (outer,inner) like
489    // Eigen::Stride, and use it:
490    template <typename S> using stride_ctor_dual = bool_constant<
491        !stride_ctor_default<S>::value && std::is_constructible<S, EigenIndex, EigenIndex>::value>;
492    // Otherwise, if there is a one-index constructor, and just one of the strides is dynamic, use
493    // it (passing whichever stride is dynamic).
494    template <typename S> using stride_ctor_outer = bool_constant<
495        !any_of<stride_ctor_default<S>, stride_ctor_dual<S>>::value &&
496        S::OuterStrideAtCompileTime == Eigen::Dynamic && S::InnerStrideAtCompileTime != Eigen::Dynamic &&
497        std::is_constructible<S, EigenIndex>::value>;
498    template <typename S> using stride_ctor_inner = bool_constant<
499        !any_of<stride_ctor_default<S>, stride_ctor_dual<S>>::value &&
500        S::InnerStrideAtCompileTime == Eigen::Dynamic && S::OuterStrideAtCompileTime != Eigen::Dynamic &&
501        std::is_constructible<S, EigenIndex>::value>;
502
503    template <typename S = StrideType, enable_if_t<stride_ctor_default<S>::value, int> = 0>
504    static S make_stride(EigenIndex, EigenIndex) { return S(); }
505    template <typename S = StrideType, enable_if_t<stride_ctor_dual<S>::value, int> = 0>
506    static S make_stride(EigenIndex outer, EigenIndex inner) { return S(outer, inner); }
507    template <typename S = StrideType, enable_if_t<stride_ctor_outer<S>::value, int> = 0>
508    static S make_stride(EigenIndex outer, EigenIndex) { return S(outer); }
509    template <typename S = StrideType, enable_if_t<stride_ctor_inner<S>::value, int> = 0>
510    static S make_stride(EigenIndex, EigenIndex inner) { return S(inner); }
511
512};
513
514// type_caster for special matrix types (e.g. DiagonalMatrix), which are EigenBase, but not
515// EigenDense (i.e. they don't have a data(), at least not with the usual matrix layout).
516// load() is not supported, but we can cast them into the python domain by first copying to a
517// regular Eigen::Matrix, then casting that.
518template <typename Type>
519struct type_caster<Type, enable_if_t<is_eigen_other<Type>::value>> {
520protected:
521    using Matrix = Eigen::Matrix<typename Type::Scalar, Type::RowsAtCompileTime, Type::ColsAtCompileTime>;
522    using props = EigenProps<Matrix>;
523public:
524    static handle cast(const Type &src, return_value_policy /* policy */, handle /* parent */) {
525        handle h = eigen_encapsulate<props>(new Matrix(src));
526        return h;
527    }
528    static handle cast(const Type *src, return_value_policy policy, handle parent) { return cast(*src, policy, parent); }
529
530    static constexpr auto name = props::descriptor;
531
532    // Explicitly delete these: support python -> C++ conversion on these (i.e. these can be return
533    // types but not bound arguments).  We still provide them (with an explicitly delete) so that
534    // you end up here if you try anyway.
535    bool load(handle, bool) = delete;
536    operator Type() = delete;
537    template <typename> using cast_op_type = Type;
538};
539
540template<typename Type>
541struct type_caster<Type, enable_if_t<is_eigen_sparse<Type>::value>> {
542    typedef typename Type::Scalar Scalar;
543    typedef remove_reference_t<decltype(*std::declval<Type>().outerIndexPtr())> StorageIndex;
544    typedef typename Type::Index Index;
545    static constexpr bool rowMajor = Type::IsRowMajor;
546
547    bool load(handle src, bool) {
548        if (!src)
549            return false;
550
551        auto obj = reinterpret_borrow<object>(src);
552        object sparse_module = module::import("scipy.sparse");
553        object matrix_type = sparse_module.attr(
554            rowMajor ? "csr_matrix" : "csc_matrix");
555
556        if (!obj.get_type().is(matrix_type)) {
557            try {
558                obj = matrix_type(obj);
559            } catch (const error_already_set &) {
560                return false;
561            }
562        }
563
564        auto values = array_t<Scalar>((object) obj.attr("data"));
565        auto innerIndices = array_t<StorageIndex>((object) obj.attr("indices"));
566        auto outerIndices = array_t<StorageIndex>((object) obj.attr("indptr"));
567        auto shape = pybind11::tuple((pybind11::object) obj.attr("shape"));
568        auto nnz = obj.attr("nnz").cast<Index>();
569
570        if (!values || !innerIndices || !outerIndices)
571            return false;
572
573        value = Eigen::MappedSparseMatrix<Scalar, Type::Flags, StorageIndex>(
574            shape[0].cast<Index>(), shape[1].cast<Index>(), nnz,
575            outerIndices.mutable_data(), innerIndices.mutable_data(), values.mutable_data());
576
577        return true;
578    }
579
580    static handle cast(const Type &src, return_value_policy /* policy */, handle /* parent */) {
581        const_cast<Type&>(src).makeCompressed();
582
583        object matrix_type = module::import("scipy.sparse").attr(
584            rowMajor ? "csr_matrix" : "csc_matrix");
585
586        array data(src.nonZeros(), src.valuePtr());
587        array outerIndices((rowMajor ? src.rows() : src.cols()) + 1, src.outerIndexPtr());
588        array innerIndices(src.nonZeros(), src.innerIndexPtr());
589
590        return matrix_type(
591            std::make_tuple(data, innerIndices, outerIndices),
592            std::make_pair(src.rows(), src.cols())
593        ).release();
594    }
595
596    PYBIND11_TYPE_CASTER(Type, _<(Type::IsRowMajor) != 0>("scipy.sparse.csr_matrix[", "scipy.sparse.csc_matrix[")
597            + npy_format_descriptor<Scalar>::name + _("]"));
598};
599
600NAMESPACE_END(detail)
601NAMESPACE_END(PYBIND11_NAMESPACE)
602
603#if defined(__GNUG__) || defined(__clang__)
604#  pragma GCC diagnostic pop
605#elif defined(_MSC_VER)
606#  pragma warning(pop)
607#endif
608