Merge pull request #402 from aldanor/feature/numpy-c-api

Add array methods via C API

include/pybind11/eigen.h

@@ -83,12 +83,11 @@ struct type_caster<Type, typename std::enable_if<is_eigen_dense<Type>::value &&
     static constexpr bool isVector = Type::IsVectorAtCompileTime;
 
     bool load(handle src, bool) {
-       array_t<Scalar> buffer(src, true);
-       if (!buffer.check())
+        array_t<Scalar> buf(src, true);
+        if (!buf.check())
             return false;
 
-        auto info = buffer.request();
-        if (info.ndim == 1) {
+        if (buf.ndim() == 1) {
             typedef Eigen::InnerStride<> Strides;
             if (!isVector &&
                 !(Type::RowsAtCompileTime == Eigen::Dynamic &&
@@ -96,31 +95,32 @@ struct type_caster<Type, typename std::enable_if<is_eigen_dense<Type>::value &&
                 return false;
 
             if (Type::SizeAtCompileTime != Eigen::Dynamic &&
-                info.shape[0] != (size_t) Type::SizeAtCompileTime)
+                buf.shape(0) != (size_t) Type::SizeAtCompileTime)
                 return false;
 
-            auto strides = Strides(info.strides[0] / sizeof(Scalar));
-
-            Strides::Index n_elts = (Strides::Index) info.shape[0];
+            Strides::Index n_elts = (Strides::Index) buf.shape(0);
             Strides::Index unity = 1;
 
             value = Eigen::Map<Type, 0, Strides>(
-                (Scalar *) info.ptr, rowMajor ? unity : n_elts, rowMajor ? n_elts : unity, strides);
-        } else if (info.ndim == 2) {
+                buf.mutable_data(),
+                rowMajor ? unity : n_elts,
+                rowMajor ? n_elts : unity,
+                Strides(buf.strides(0) / sizeof(Scalar))
+            );
+        } else if (buf.ndim() == 2) {
             typedef Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic> Strides;
 
-            if ((Type::RowsAtCompileTime != Eigen::Dynamic && info.shape[0] != (size_t) Type::RowsAtCompileTime) ||
-                (Type::ColsAtCompileTime != Eigen::Dynamic && info.shape[1] != (size_t) Type::ColsAtCompileTime))
+            if ((Type::RowsAtCompileTime != Eigen::Dynamic && buf.shape(0) != (size_t) Type::RowsAtCompileTime) ||
+                (Type::ColsAtCompileTime != Eigen::Dynamic && buf.shape(1) != (size_t) Type::ColsAtCompileTime))
                 return false;
 
-            auto strides = Strides(
-                info.strides[rowMajor ? 0 : 1] / sizeof(Scalar),
-                info.strides[rowMajor ? 1 : 0] / sizeof(Scalar));
-
             value = Eigen::Map<Type, 0, Strides>(
-                (Scalar *) info.ptr,
-                typename Strides::Index(info.shape[0]),
-                typename Strides::Index(info.shape[1]), strides);
+                buf.mutable_data(),
+                typename Strides::Index(buf.shape(0)),
+                typename Strides::Index(buf.shape(1)),
+                Strides(buf.strides(rowMajor ? 0 : 1) / sizeof(Scalar),
+                        buf.strides(rowMajor ? 1 : 0) / sizeof(Scalar))
+            );
         } else {
             return false;
         }
@@ -222,28 +222,18 @@ struct type_caster<Type, typename std::enable_if<is_eigen_sparse<Type>::value>::
             }
         }
 
-        auto valuesArray = array_t<Scalar>((object) obj.attr("data"));
-        auto innerIndicesArray = array_t<StorageIndex>((object) obj.attr("indices"));
-        auto outerIndicesArray = array_t<StorageIndex>((object) obj.attr("indptr"));
+        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 (!valuesArray.check() || !innerIndicesArray.check() ||
-            !outerIndicesArray.check())
+        if (!values.check() || !innerIndices.check() || !outerIndices.check())
             return false;
 
-        auto outerIndices = outerIndicesArray.request();
-        auto innerIndices = innerIndicesArray.request();
-        auto values = valuesArray.request();
-
         value = Eigen::MappedSparseMatrix<Scalar, Type::Flags, StorageIndex>(
-            shape[0].cast<Index>(),
-            shape[1].cast<Index>(),
-            nnz,
-            static_cast<StorageIndex *>(outerIndices.ptr),
-            static_cast<StorageIndex *>(innerIndices.ptr),
-            static_cast<Scalar *>(values.ptr)
-        );
+            shape[0].cast<Index>(), shape[1].cast<Index>(), nnz,
+            outerIndices.mutable_data(), innerIndices.mutable_data(), values.mutable_data());
 
         return true;
     }

include/pybind11/numpy.h

@@ -19,23 +19,59 @@
 #include <sstream>
 #include <string>
 #include <initializer_list>
+#include <functional>
 
 #if defined(_MSC_VER)
 #pragma warning(push)
 #pragma warning(disable: 4127) // warning C4127: Conditional expression is constant
 #endif
 
+/* This will be true on all flat address space platforms and allows us to reduce the
+   whole npy_intp / size_t / Py_intptr_t business down to just size_t for all size
+   and dimension types (e.g. shape, strides, indexing), instead of inflicting this
+   upon the library user. */
+static_assert(sizeof(size_t) == sizeof(Py_intptr_t), "size_t != Py_intptr_t");
+
 NAMESPACE_BEGIN(pybind11)
-namespace detail {
+NAMESPACE_BEGIN(detail)
 template <typename type, typename SFINAE = void> struct npy_format_descriptor { };
 template <typename type> struct is_pod_struct;
 
+struct PyArrayDescr_Proxy {
+    PyObject_HEAD
+    PyObject *typeobj;
+    char kind;
+    char type;
+    char byteorder;
+    char flags;
+    int type_num;
+    int elsize;
+    int alignment;
+    char *subarray;
+    PyObject *fields;
+    PyObject *names;
+};
+
+struct PyArray_Proxy {
+    PyObject_HEAD
+    char *data;
+    int nd;
+    ssize_t *dimensions;
+    ssize_t *strides;
+    PyObject *base;
+    PyObject *descr;
+    int flags;
+};
+
 struct npy_api {
     enum constants {
         NPY_C_CONTIGUOUS_ = 0x0001,
         NPY_F_CONTIGUOUS_ = 0x0002,
+        NPY_ARRAY_OWNDATA_ = 0x0004,
         NPY_ARRAY_FORCECAST_ = 0x0010,
         NPY_ENSURE_ARRAY_ = 0x0040,
+        NPY_ARRAY_ALIGNED_ = 0x0100,
+        NPY_ARRAY_WRITEABLE_ = 0x0400,
         NPY_BOOL_ = 0,
         NPY_BYTE_, NPY_UBYTE_,
         NPY_SHORT_, NPY_USHORT_,
@@ -111,7 +147,14 @@ private:
         return api;
     }
 };
-}
+NAMESPACE_END(detail)
+
+#define PyArray_GET_(ptr, attr) \
+    (reinterpret_cast<::pybind11::detail::PyArray_Proxy*>(ptr)->attr)
+#define PyArrayDescr_GET_(ptr, attr) \
+    (reinterpret_cast<::pybind11::detail::PyArrayDescr_Proxy*>(ptr)->attr)
+#define PyArray_CHKFLAGS_(ptr, flag) \
+    (flag == (reinterpret_cast<::pybind11::detail::PyArray_Proxy*>(ptr)->flags & flag))
 
 class dtype : public object {
 public:
@@ -150,15 +193,15 @@ public:
     }
 
     size_t itemsize() const {
-        return attr("itemsize").cast<size_t>();
+        return (size_t) PyArrayDescr_GET_(m_ptr, elsize);
     }
 
     bool has_fields() const {
-        return attr("fields").cast<object>().ptr() != Py_None;
+        return PyArrayDescr_GET_(m_ptr, names) != nullptr;
     }
 
-    std::string kind() const {
-        return (std::string) attr("kind").cast<pybind11::str>();
+    char kind() const {
+        return PyArrayDescr_GET_(m_ptr, kind);
     }
 
 private:
@@ -171,20 +214,20 @@ private:
     dtype strip_padding() {
         // Recursively strip all void fields with empty names that are generated for
         // padding fields (as of NumPy v1.11).
-        auto fields = attr("fields").cast<object>();
-        if (fields.ptr() == Py_None)
+        if (!has_fields())
             return *this;
 
         struct field_descr { PYBIND11_STR_TYPE name; object format; pybind11::int_ offset; };
         std::vector<field_descr> field_descriptors;
 
+        auto fields = attr("fields").cast<object>();
         auto items = fields.attr("items").cast<object>();
         for (auto field : items()) {
             auto spec = object(field, true).cast<tuple>();
             auto name = spec[0].cast<pybind11::str>();
             auto format = spec[1].cast<tuple>()[0].cast<dtype>();
             auto offset = spec[1].cast<tuple>()[1].cast<pybind11::int_>();
-            if (!len(name) && format.kind() == "V")
+            if (!len(name) && format.kind() == 'V')
                 continue;
             field_descriptors.push_back({(PYBIND11_STR_TYPE) name, format.strip_padding(), offset});
         }
@@ -215,7 +258,7 @@ public:
     };
 
     array(const pybind11::dtype& dt, const std::vector<size_t>& shape,
-          const std::vector<size_t>& strides, void *ptr = nullptr) {
+          const std::vector<size_t>& strides, const void *ptr = nullptr) {
         auto& api = detail::npy_api::get();
         auto ndim = shape.size();
         if (shape.size() != strides.size())
@@ -223,7 +266,7 @@ public:
         auto descr = dt;
         object tmp(api.PyArray_NewFromDescr_(
             api.PyArray_Type_, descr.release().ptr(), (int) ndim, (Py_intptr_t *) shape.data(),
-            (Py_intptr_t *) strides.data(), ptr, 0, nullptr), false);
+            (Py_intptr_t *) strides.data(), const_cast<void *>(ptr), 0, nullptr), false);
         if (!tmp)
             pybind11_fail("NumPy: unable to create array!");
         if (ptr)
@@ -231,31 +274,139 @@ public:
         m_ptr = tmp.release().ptr();
     }
 
-    array(const pybind11::dtype& dt, const std::vector<size_t>& shape, void *ptr = nullptr)
+    array(const pybind11::dtype& dt, const std::vector<size_t>& shape, const void *ptr = nullptr)
     : array(dt, shape, default_strides(shape, dt.itemsize()), ptr) { }
 
-    array(const pybind11::dtype& dt, size_t count, void *ptr = nullptr)
+    array(const pybind11::dtype& dt, size_t count, const void *ptr = nullptr)
     : array(dt, std::vector<size_t> { count }, ptr) { }
 
     template<typename T> array(const std::vector<size_t>& shape,
-                               const std::vector<size_t>& strides, T* ptr)
+                               const std::vector<size_t>& strides, const T* ptr)
     : array(pybind11::dtype::of<T>(), shape, strides, (void *) ptr) { }
 
-    template<typename T> array(const std::vector<size_t>& shape, T* ptr)
+    template<typename T> array(const std::vector<size_t>& shape, const T* ptr)
     : array(shape, default_strides(shape, sizeof(T)), ptr) { }
 
-    template<typename T> array(size_t size, T* ptr)
-    : array(std::vector<size_t> { size }, ptr) { }
+    template<typename T> array(size_t count, const T* ptr)
+    : array(std::vector<size_t> { count }, ptr) { }
 
     array(const buffer_info &info)
     : array(pybind11::dtype(info), info.shape, info.strides, info.ptr) { }
 
-    pybind11::dtype dtype() {
-        return attr("dtype").cast<pybind11::dtype>();
+    /// Array descriptor (dtype)
+    pybind11::dtype dtype() const {
+        return object(PyArray_GET_(m_ptr, descr), true);
+    }
+
+    /// Total number of elements
+    size_t size() const {
+        return std::accumulate(shape(), shape() + ndim(), (size_t) 1, std::multiplies<size_t>());
+    }
+
+    /// Byte size of a single element
+    size_t itemsize() const {
+        return (size_t) PyArrayDescr_GET_(PyArray_GET_(m_ptr, descr), elsize);
+    }
+
+    /// Total number of bytes
+    size_t nbytes() const {
+        return size() * itemsize();
+    }
+
+    /// Number of dimensions
+    size_t ndim() const {
+        return (size_t) PyArray_GET_(m_ptr, nd);
+    }
+
+    /// Dimensions of the array
+    const size_t* shape() const {
+        return reinterpret_cast<const size_t *>(PyArray_GET_(m_ptr, dimensions));
+    }
+
+    /// Dimension along a given axis
+    size_t shape(size_t dim) const {
+        if (dim >= ndim())
+            fail_dim_check(dim, "invalid axis");
+        return shape()[dim];
+    }
+
+    /// Strides of the array
+    const size_t* strides() const {
+        return reinterpret_cast<const size_t *>(PyArray_GET_(m_ptr, strides));
+    }
+
+    /// Stride along a given axis
+    size_t strides(size_t dim) const {
+        if (dim >= ndim())
+            fail_dim_check(dim, "invalid axis");
+        return strides()[dim];
+    }
+
+    /// If set, the array is writeable (otherwise the buffer is read-only)
+    bool writeable() const {
+        return PyArray_CHKFLAGS_(m_ptr, detail::npy_api::NPY_ARRAY_WRITEABLE_);
+    }
+
+    /// If set, the array owns the data (will be freed when the array is deleted)
+    bool owndata() const {
+        return PyArray_CHKFLAGS_(m_ptr, detail::npy_api::NPY_ARRAY_OWNDATA_);
+    }
+
+    /// Pointer to the contained data. If index is not provided, points to the
+    /// beginning of the buffer. May throw if the index would lead to out of bounds access.
+    template<typename... Ix> const void* data(Ix&&... index) const {
+        return static_cast<const void *>(PyArray_GET_(m_ptr, data) + offset_at(index...));
+    }
+
+    /// Mutable pointer to the contained data. If index is not provided, points to the
+    /// beginning of the buffer. May throw if the index would lead to out of bounds access.
+    /// May throw if the array is not writeable.
+    template<typename... Ix> void* mutable_data(Ix&&... index) {
+        check_writeable();
+        return static_cast<void *>(PyArray_GET_(m_ptr, data) + offset_at(index...));
+    }
+
+    /// Byte offset from beginning of the array to a given index (full or partial).
+    /// May throw if the index would lead to out of bounds access.
+    template<typename... Ix> size_t offset_at(Ix&&... index) const {
+        if (sizeof...(index) > ndim())
+            fail_dim_check(sizeof...(index), "too many indices for an array");
+        return get_byte_offset(index...);
+    }
+
+    size_t offset_at() const { return 0; }
+
+    /// Item count from beginning of the array to a given index (full or partial).
+    /// May throw if the index would lead to out of bounds access.
+    template<typename... Ix> size_t index_at(Ix&&... index) const {
+        return offset_at(index...) / itemsize();
     }
 
 protected:
-    template <typename T, typename SFINAE> friend struct detail::npy_format_descriptor;
+    template<typename, typename> friend struct detail::npy_format_descriptor;
+
+    void fail_dim_check(size_t dim, const std::string& msg) const {
+        throw index_error(msg + ": " + std::to_string(dim) +
+                          " (ndim = " + std::to_string(ndim()) + ")");
+    }
+
+    template<typename... Ix> size_t get_byte_offset(Ix&&... index) const {
+        const size_t idx[] = { (size_t) index... };
+        if (!std::equal(idx + 0, idx + sizeof...(index), shape(), std::less<size_t>{})) {
+            auto mismatch = std::mismatch(idx + 0, idx + sizeof...(index), shape(), std::less<size_t>{});
+            throw index_error(std::string("index ") + std::to_string(*mismatch.first) +
+                              " is out of bounds for axis " + std::to_string(mismatch.first - idx) +
+                              " with size " + std::to_string(*mismatch.second));
+        }
+        return std::inner_product(idx + 0, idx + sizeof...(index), strides(), (size_t) 0);
+    }
+
+    size_t get_byte_offset() const { return 0; }
+
+    void check_writeable() const {
+        if (!writeable())
+            throw std::runtime_error("array is not writeable");
+    }
 
     static std::vector<size_t> default_strides(const std::vector<size_t>& shape, size_t itemsize) {
         auto ndim = shape.size();
@@ -278,14 +429,46 @@ public:
 
     array_t(const buffer_info& info) : array(info) { }
 
-    array_t(const std::vector<size_t>& shape, const std::vector<size_t>& strides, T* ptr = nullptr)
+    array_t(const std::vector<size_t>& shape, const std::vector<size_t>& strides, const T* ptr = nullptr)
     : array(shape, strides, ptr) { }
 
-    array_t(const std::vector<size_t>& shape, T* ptr = nullptr)
+    array_t(const std::vector<size_t>& shape, const T* ptr = nullptr)
     : array(shape, ptr) { }
 
-    array_t(size_t size, T* ptr = nullptr)
-    : array(size, ptr) { }
+    array_t(size_t count, const T* ptr = nullptr)
+    : array(count, ptr) { }
+
+    constexpr size_t itemsize() const {
+        return sizeof(T);
+    }
+
+    template<typename... Ix> size_t index_at(Ix&... index) const {
+        return offset_at(index...) / itemsize();
+    }
+
+    template<typename... Ix> const T* data(Ix&&... index) const {
+        return static_cast<const T*>(array::data(index...));
+    }
+
+    template<typename... Ix> T* mutable_data(Ix&&... index) {
+        return static_cast<T*>(array::mutable_data(index...));
+    }
+
+    // Reference to element at a given index
+    template<typename... Ix> const T& at(Ix&&... index) const {
+        if (sizeof...(index) != ndim())
+            fail_dim_check(sizeof...(index), "index dimension mismatch");
+        // not using offset_at() / index_at() here so as to avoid another dimension check
+        return *(static_cast<const T*>(array::data()) + get_byte_offset(index...) / itemsize());
+    }
+
+    // Mutable reference to element at a given index
+    template<typename... Ix> T& mutable_at(Ix&&... index) {
+        if (sizeof...(index) != ndim())
+            fail_dim_check(sizeof...(index), "index dimension mismatch");
+        // not using offset_at() / index_at() here so as to avoid another dimension check
+        return *(static_cast<T*>(array::mutable_data()) + get_byte_offset(index...) / itemsize());
+    }
 
     static bool is_non_null(PyObject *ptr) { return ptr != nullptr; }
 
@@ -678,16 +861,13 @@ struct vectorize_helper {
         if (size == 1)
             return cast(f(*((Args *) buffers[Index].ptr)...));
 
-        array result(buffer_info(nullptr, sizeof(Return),
-            format_descriptor<Return>::format(),
-            ndim, shape, strides));
-
-        buffer_info buf = result.request();
-        Return *output = (Return *) buf.ptr;
+        array_t<Return> result(shape, strides);
+        auto buf = result.request();
+        auto output = (Return *) buf.ptr;
 
         if (trivial_broadcast) {
             /* Call the function */
-            for (size_t i=0; i<size; ++i) {
+            for (size_t i = 0; i < size; ++i) {
                 output[i] = f((buffers[Index].size == 1
                                ? *((Args *) buffers[Index].ptr)
                                : ((Args *) buffers[Index].ptr)[i])...);

tests/CMakeLists.txt

@@ -19,6 +19,7 @@ set(PYBIND11_TEST_FILES
   test_kwargs_and_defaults.cpp
   test_methods_and_attributes.cpp
   test_modules.cpp
+  test_numpy_array.cpp
   test_numpy_dtypes.cpp
   test_numpy_vectorize.cpp
   test_opaque_types.cpp

tests/test_numpy_array.cpp

+/*
+    tests/test_numpy_array.cpp -- test core array functionality
+
+    Copyright (c) 2016 Ivan Smirnov <i.s.smirnov@gmail.com>
+
+    All rights reserved. Use of this source code is governed by a
+    BSD-style license that can be found in the LICENSE file.
+*/
+
+#include "pybind11_tests.h"
+
+#include <pybind11/numpy.h>
+#include <pybind11/stl.h>
+
+#include <cstdint>
+#include <vector>
+
+using arr = py::array;
+using arr_t = py::array_t<uint16_t, 0>;
+
+template<typename... Ix> arr data(const arr& a, Ix&&... index) {
+    return arr(a.nbytes() - a.offset_at(index...), (const uint8_t *) a.data(index...));
+}
+
+template<typename... Ix> arr data_t(const arr_t& a, Ix&&... index) {
+    return arr(a.size() - a.index_at(index...), a.data(index...));
+}
+
+arr& mutate_data(arr& a) {
+    auto ptr = (uint8_t *) a.mutable_data();
+    for (size_t i = 0; i < a.nbytes(); i++)
+        ptr[i] = (uint8_t) (ptr[i] * 2);
+    return a;
+}
+
+arr_t& mutate_data_t(arr_t& a) {
+    auto ptr = a.mutable_data();
+    for (size_t i = 0; i < a.size(); i++)
+        ptr[i]++;
+    return a;
+}
+
+template<typename... Ix> arr& mutate_data(arr& a, Ix&&... index) {
+    auto ptr = (uint8_t *) a.mutable_data(index...);
+    for (size_t i = 0; i < a.nbytes() - a.offset_at(index...); i++)
+        ptr[i] = (uint8_t) (ptr[i] * 2);
+    return a;
+}
+
+template<typename... Ix> arr_t& mutate_data_t(arr_t& a, Ix&&... index) {
+    auto ptr = a.mutable_data(index...);
+    for (size_t i = 0; i < a.size() - a.index_at(index...); i++)
+        ptr[i]++;
+    return a;
+}
+
+template<typename... Ix> size_t index_at(const arr& a, Ix&&... idx) { return a.index_at(idx...); }
+template<typename... Ix> size_t index_at_t(const arr_t& a, Ix&&... idx) { return a.index_at(idx...); }
+template<typename... Ix> size_t offset_at(const arr& a, Ix&&... idx) { return a.offset_at(idx...); }
+template<typename... Ix> size_t offset_at_t(const arr_t& a, Ix&&... idx) { return a.offset_at(idx...); }
+template<typename... Ix> size_t at_t(const arr_t& a, Ix&&... idx) { return a.at(idx...); }
+template<typename... Ix> arr_t& mutate_at_t(arr_t& a, Ix&&... idx) { a.mutable_at(idx...)++; return a; }
+
+#define def_index_fn(name, type) \
+    sm.def(#name, [](type a) { return name(a); }); \
+    sm.def(#name, [](type a, int i) { return name(a, i); }); \
+    sm.def(#name, [](type a, int i, int j) { return name(a, i, j); }); \
+    sm.def(#name, [](type a, int i, int j, int k) { return name(a, i, j, k); });
+
+test_initializer numpy_array([](py::module &m) {
+    auto sm = m.def_submodule("array");
+
+    sm.def("ndim", [](const arr& a) { return a.ndim(); });
+    sm.def("shape", [](const arr& a) { return arr(a.ndim(), a.shape()); });
+    sm.def("shape", [](const arr& a, size_t dim) { return a.shape(dim); });
+    sm.def("strides", [](const arr& a) { return arr(a.ndim(), a.strides()); });
+    sm.def("strides", [](const arr& a, size_t dim) { return a.strides(dim); });
+    sm.def("writeable", [](const arr& a) { return a.writeable(); });
+    sm.def("size", [](const arr& a) { return a.size(); });
+    sm.def("itemsize", [](const arr& a) { return a.itemsize(); });
+    sm.def("nbytes", [](const arr& a) { return a.nbytes(); });
+    sm.def("owndata", [](const arr& a) { return a.owndata(); });
+
+    def_index_fn(data, const arr&);
+    def_index_fn(data_t, const arr_t&);
+    def_index_fn(index_at, const arr&);
+    def_index_fn(index_at_t, const arr_t&);
+    def_index_fn(offset_at, const arr&);
+    def_index_fn(offset_at_t, const arr_t&);
+    def_index_fn(mutate_data, arr&);
+    def_index_fn(mutate_data_t, arr_t&);
+    def_index_fn(at_t, const arr_t&);
+    def_index_fn(mutate_at_t, arr_t&);
+});

tests/test_numpy_array.py

+import pytest
+
+with pytest.suppress(ImportError):
+    import numpy as np
+
+
+@pytest.fixture(scope='function')
+def arr():
+    return np.array([[1, 2, 3], [4, 5, 6]], '<u2')
+
+
+@pytest.requires_numpy
+def test_array_attributes():
+    from pybind11_tests.array import (
+        ndim, shape, strides, writeable, size, itemsize, nbytes, owndata
+    )
+
+    a = np.array(0, 'f8')
+    assert ndim(a) == 0
+    assert all(shape(a) == [])
+    assert all(strides(a) == [])
+    with pytest.raises(IndexError) as excinfo:
+        shape(a, 0)
+    assert str(excinfo.value) == 'invalid axis: 0 (ndim = 0)'
+    with pytest.raises(IndexError) as excinfo:
+        strides(a, 0)
+    assert str(excinfo.value) == 'invalid axis: 0 (ndim = 0)'
+    assert writeable(a)
+    assert size(a) == 1
+    assert itemsize(a) == 8
+    assert nbytes(a) == 8
+    assert owndata(a)
+
+    a = np.array([[1, 2, 3], [4, 5, 6]], 'u2').view()
+    a.flags.writeable = False
+    assert ndim(a) == 2
+    assert all(shape(a) == [2, 3])
+    assert shape(a, 0) == 2
+    assert shape(a, 1) == 3
+    assert all(strides(a) == [6, 2])
+    assert strides(a, 0) == 6
+    assert strides(a, 1) == 2
+    with pytest.raises(IndexError) as excinfo:
+        shape(a, 2)
+    assert str(excinfo.value) == 'invalid axis: 2 (ndim = 2)'
+    with pytest.raises(IndexError) as excinfo:
+        strides(a, 2)
+    assert str(excinfo.value) == 'invalid axis: 2 (ndim = 2)'
+    assert not writeable(a)
+    assert size(a) == 6
+    assert itemsize(a) == 2
+    assert nbytes(a) == 12
+    assert not owndata(a)
+
+
+@pytest.requires_numpy
+@pytest.mark.parametrize('args, ret', [([], 0), ([0], 0), ([1], 3), ([0, 1], 1), ([1, 2], 5)])
+def test_index_offset(arr, args, ret):
+    from pybind11_tests.array import index_at, index_at_t, offset_at, offset_at_t
+    assert index_at(arr, *args) == ret
+    assert index_at_t(arr, *args) == ret
+    assert offset_at(arr, *args) == ret * arr.dtype.itemsize
+    assert offset_at_t(arr, *args) == ret * arr.dtype.itemsize
+
+
+@pytest.requires_numpy
+def test_dim_check_fail(arr):
+    from pybind11_tests.array import (index_at, index_at_t, offset_at, offset_at_t, data, data_t,
+                                      mutate_data, mutate_data_t)
+    for func in (index_at, index_at_t, offset_at, offset_at_t, data, data_t,
+                 mutate_data, mutate_data_t):
+        with pytest.raises(IndexError) as excinfo:
+            func(arr, 1, 2, 3)
+        assert str(excinfo.value) == 'too many indices for an array: 3 (ndim = 2)'
+
+
+@pytest.requires_numpy
+@pytest.mark.parametrize('args, ret',
+                         [([], [1, 2, 3, 4, 5, 6]),
+                          ([1], [4, 5, 6]),
+                          ([0, 1], [2, 3, 4, 5, 6]),
+                          ([1, 2], [6])])
+def test_data(arr, args, ret):
+    from pybind11_tests.array import data, data_t
+    assert all(data_t(arr, *args) == ret)
+    assert all(data(arr, *args)[::2] == ret)
+    assert all(data(arr, *args)[1::2] == 0)
+
+
+@pytest.requires_numpy
+def test_mutate_readonly(arr):
+    from pybind11_tests.array import mutate_data, mutate_data_t, mutate_at_t
+    arr.flags.writeable = False
+    for func, args in (mutate_data, ()), (mutate_data_t, ()), (mutate_at_t, (0, 0)):
+        with pytest.raises(RuntimeError) as excinfo:
+            func(arr, *args)
+        assert str(excinfo.value) == 'array is not writeable'
+
+
+@pytest.requires_numpy
+@pytest.mark.parametrize('dim', [0, 1, 3])
+def test_at_fail(arr, dim):
+    from pybind11_tests.array import at_t, mutate_at_t
+    for func in at_t, mutate_at_t:
+        with pytest.raises(IndexError) as excinfo:
+            func(arr, *([0] * dim))
+        assert str(excinfo.value) == 'index dimension mismatch: {} (ndim = 2)'.format(dim)
+
+
+@pytest.requires_numpy
+def test_at(arr):
+    from pybind11_tests.array import at_t, mutate_at_t
+
+    assert at_t(arr, 0, 2) == 3
+    assert at_t(arr, 1, 0) == 4
+
+    assert all(mutate_at_t(arr, 0, 2).ravel() == [1, 2, 4, 4, 5, 6])
+    assert all(mutate_at_t(arr, 1, 0).ravel() == [1, 2, 4, 5, 5, 6])
+
+
+@pytest.requires_numpy
+def test_mutate_data(arr):
+    from pybind11_tests.array import mutate_data, mutate_data_t
+
+    assert all(mutate_data(arr).ravel() == [2, 4, 6, 8, 10, 12])
+    assert all(mutate_data(arr).ravel() == [4, 8, 12, 16, 20, 24])
+    assert all(mutate_data(arr, 1).ravel() == [4, 8, 12, 32, 40, 48])
+    assert all(mutate_data(arr, 0, 1).ravel() == [4, 16, 24, 64, 80, 96])
+    assert all(mutate_data(arr, 1, 2).ravel() == [4, 16, 24, 64, 80, 192])
+
+    assert all(mutate_data_t(arr).ravel() == [5, 17, 25, 65, 81, 193])
+    assert all(mutate_data_t(arr).ravel() == [6, 18, 26, 66, 82, 194])
+    assert all(mutate_data_t(arr, 1).ravel() == [6, 18, 26, 67, 83, 195])
+    assert all(mutate_data_t(arr, 0, 1).ravel() == [6, 19, 27, 68, 84, 196])
+    assert all(mutate_data_t(arr, 1, 2).ravel() == [6, 19, 27, 68, 84, 197])
+
+
+@pytest.requires_numpy
+def test_bounds_check(arr):
+    from pybind11_tests.array import (index_at, index_at_t, data, data_t,
+                                      mutate_data, mutate_data_t, at_t, mutate_at_t)
+    funcs = (index_at, index_at_t, data, data_t,
+             mutate_data, mutate_data_t, at_t, mutate_at_t)
+    for func in funcs:
+        with pytest.raises(IndexError) as excinfo:
+            index_at(arr, 2, 0)
+        assert str(excinfo.value) == 'index 2 is out of bounds for axis 0 with size 2'
+        with pytest.raises(IndexError) as excinfo:
+            index_at(arr, 0, 4)
+        assert str(excinfo.value) == 'index 4 is out of bounds for axis 1 with size 3'