# NumPy

## Buffer protocol

Python supports an extremely general and convenient approach for exchanging data between plugin libraries. Types can expose a buffer view [1], which provides fast direct access to the raw internal data representation. Suppose we want to bind the following simplistic Matrix class:

    class Matrix {
    public:
        Matrix(size_t rows, size_t cols) : m_rows(rows), m_cols(cols) {
            m_data = new float[rows*cols];
        }
        float *data() { return m_data; }
        size_t rows() const { return m_rows; }
        size_t cols() const { return m_cols; }
    private:
        size_t m_rows, m_cols;
        float *m_data;
    };

The following binding code exposes the `Matrix` contents as a buffer object, making it possible to cast Matrices into NumPy arrays. It is even possible to completely avoid copy operations with Python expressions like `np.array(matrix_instance, copy = False)`.

    py::class_<Matrix>(m, "Matrix", py::buffer_protocol())
       .def_buffer([](Matrix &m) -> py::buffer_info {
            return py::buffer_info(
                m.data(),                               /* Pointer to buffer */
                sizeof(float),                          /* Size of one scalar */
                py::format_descriptor<float>::format(), /* Python struct-style format descriptor */
                2,                                      /* Number of dimensions */
                { m.rows(), m.cols() },                 /* Buffer dimensions */
                { sizeof(float) * m.cols(),             /* Strides (in bytes) for each index */
                  sizeof(float) }
            );
        });

Supporting the buffer protocol in a new type involves specifying the special `py::buffer_protocol()` tag in the `py::class_` constructor and calling the `def_buffer()` method with a lambda function that creates a `py::buffer_info` description record on demand describing a given matrix instance. The contents of `py::buffer_info` mirror the Python buffer protocol specification.

    struct buffer_info {
        void *ptr;
        py::ssize_t itemsize;
        std::string format;
        py::ssize_t ndim;
        std::vector<py::ssize_t> shape;
        std::vector<py::ssize_t> strides;
    };

To create a C++ function that can take a Python buffer object as an argument, simply use the type `py::buffer` as one of its arguments. Buffers can exist in a great variety of configurations, hence some safety checks are usually necessary in the function body. Below, you can see a basic example on how to define a custom constructor for the Eigen double precision matrix (`Eigen::MatrixXd`) type, which supports initialization from compatible buffer objects (e.g. a NumPy matrix).

    /* Bind MatrixXd (or some other Eigen type) to Python */
    typedef Eigen::MatrixXd Matrix;

    typedef Matrix::Scalar Scalar;
    constexpr bool rowMajor = Matrix::Flags & Eigen::RowMajorBit;

    py::class_<Matrix>(m, "Matrix", py::buffer_protocol())
        .def(py::init([](py::buffer b) {
            typedef Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic> Strides;

            /* Request a buffer descriptor from Python */
            py::buffer_info info = b.request();

            /* Some basic validation checks ... */
            if (info.format != py::format_descriptor<Scalar>::format())
                throw std::runtime_error("Incompatible format: expected a double array!");

            if (info.ndim != 2)
                throw std::runtime_error("Incompatible buffer dimension!");

            auto strides = Strides(
                info.strides[rowMajor ? 0 : 1] / (py::ssize_t)sizeof(Scalar),
                info.strides[rowMajor ? 1 : 0] / (py::ssize_t)sizeof(Scalar));

            auto map = Eigen::Map<Matrix, 0, Strides>(
                static_cast<Scalar *>(info.ptr), info.shape[0], info.shape[1], strides);

            return Matrix(map);
        }));

For reference, the `def_buffer()` call for this Eigen data type should look as follows:

    .def_buffer([](Matrix &m) -> py::buffer_info {
        return py::buffer_info(
            m.data(),                                /* Pointer to buffer */
            sizeof(Scalar),                          /* Size of one scalar */
            py::format_descriptor<Scalar>::format(), /* Python struct-style format descriptor */
            2,                                       /* Number of dimensions */
            { m.rows(), m.cols() },                  /* Buffer dimensions */
            { sizeof(Scalar) * (rowMajor ? m.cols() : 1),
              sizeof(Scalar) * (rowMajor ? 1 : m.rows()) }
                                                     /* Strides (in bytes) for each index */
        );
     })

For a much easier approach of binding Eigen types (although with some limitations), refer to the section on Eigen.

See also

The file `tests/test_buffers.cpp` contains a complete example that demonstrates using the buffer protocol with pybind11 in more detail.

[1]

http://docs.python.org/3/c-api/buffer.html

## Arrays

By exchanging `py::buffer` with `py::array` in the above snippet, we can restrict the function so that it only accepts NumPy arrays (rather than any type of Python object satisfying the buffer protocol).

In many situations, we want to define a function which only accepts a NumPy array of a certain data type. This is possible via the `py::array_t<T>` template. For instance, the following function requires the argument to be a NumPy array containing double precision values.

    void f(py::array_t<double> array);

When it is invoked with a different type (e.g. an integer or a list of integers), the binding code will attempt to cast the input into a NumPy array of the requested type. This feature requires the `pybind11/numpy.h` header to be included. Note that `pybind11/numpy.h` does not depend on the NumPy headers, and thus can be used without declaring a build-time dependency on NumPy; NumPy>=1.7.0 is a runtime dependency.

Data in NumPy arrays is not guaranteed to packed in a dense manner; furthermore, entries can be separated by arbitrary column and row strides. Sometimes, it can be useful to require a function to only accept dense arrays using either the C (row-major) or Fortran (column-major) ordering. This can be accomplished via a second template argument with values `py::array::c_style` or `py::array::f_style`.

    void f(py::array_t<double, py::array::c_style | py::array::forcecast> array);

The `py::array::forcecast` argument is the default value of the second template parameter, and it ensures that non-conforming arguments are converted into an array satisfying the specified requirements instead of trying the next function overload.

There are several methods on arrays; the methods listed below under references work, as well as the following functions based on the NumPy API:

- `.dtype()` returns the type of the contained values.

- `.strides()` returns a pointer to the strides of the array (optionally pass an integer axis to get a number).

- `.flags()` returns the flag settings. `.writable()` and `.owndata()` are directly available.

- `.offset_at()` returns the offset (optionally pass indices).

- `.squeeze()` returns a view with length-1 axes removed.

- `.view(dtype)` returns a view of the array with a different dtype.

- `.reshape({i, j, ...})` returns a view of the array with a different shape. `.resize({...})` is also available.

- `.index_at(i, j, ...)` gets the count from the beginning to a given index.

There are also several methods for getting references (described below).

## Structured types

In order for `py::array_t` to work with structured (record) types, we first need to register the memory layout of the type. This can be done via `PYBIND11_NUMPY_DTYPE` macro, called in the plugin definition code, which expects the type followed by field names:

    struct A {
        int x;
        double y;
    };

    struct B {
        int z;
        A a;
    };

    // ...
    PYBIND11_MODULE(test, m) {
        // ...

        PYBIND11_NUMPY_DTYPE(A, x, y);
        PYBIND11_NUMPY_DTYPE(B, z, a);
        /* now both A and B can be used as template arguments to py::array_t */
    }

The structure should consist of fundamental arithmetic types, `std::complex`, previously registered substructures, and arrays of any of the above. Both C++ arrays and `std::array` are supported. While there is a static assertion to prevent many types of unsupported structures, it is still the user’s responsibility to use only “plain” structures that can be safely manipulated as raw memory without violating invariants.

## Vectorizing functions

Suppose we want to bind a function with the following signature to Python so that it can process arbitrary NumPy array arguments (vectors, matrices, general N-D arrays) in addition to its normal arguments:

    double my_func(int x, float y, double z);

After including the `pybind11/numpy.h` header, this is extremely simple:

    m.def("vectorized_func", py::vectorize(my_func));

Invoking the function like below causes 4 calls to be made to `my_func` with each of the array elements. The significant advantage of this compared to solutions like `numpy.vectorize()` is that the loop over the elements runs entirely on the C++ side and can be crunched down into a tight, optimized loop by the compiler. The result is returned as a NumPy array of type `numpy.dtype.float64`.

    >>> x = np.array([[1, 3], [5, 7]])
    >>> y = np.array([[2, 4], [6, 8]])
    >>> z = 3
    >>> result = vectorized_func(x, y, z)

The scalar argument `z` is transparently replicated 4 times. The input arrays `x` and `y` are automatically converted into the right types (they are of type `numpy.dtype.int64` but need to be `numpy.dtype.int32` and `numpy.dtype.float32`, respectively).

Note

Only arithmetic, complex, and POD types passed by value or by `const &` reference are vectorized; all other arguments are passed through as-is. Functions taking rvalue reference arguments cannot be vectorized.

In cases where the computation is too complicated to be reduced to `vectorize`, it will be necessary to create and access the buffer contents manually. The following snippet contains a complete example that shows how this works (the code is somewhat contrived, since it could have been done more simply using `vectorize`).

    #include <pybind11/pybind11.h>
    #include <pybind11/numpy.h>

    namespace py = pybind11;

    py::array_t<double> add_arrays(py::array_t<double> input1, py::array_t<double> input2) {
        py::buffer_info buf1 = input1.request(), buf2 = input2.request();

        if (buf1.ndim != 1 || buf2.ndim != 1)
            throw std::runtime_error("Number of dimensions must be one");

        if (buf1.size != buf2.size)
            throw std::runtime_error("Input shapes must match");

        /* No pointer is passed, so NumPy will allocate the buffer */
        auto result = py::array_t<double>(buf1.size);

        py::buffer_info buf3 = result.request();

        double *ptr1 = static_cast<double *>(buf1.ptr);
        double *ptr2 = static_cast<double *>(buf2.ptr);
        double *ptr3 = static_cast<double *>(buf3.ptr);

        for (size_t idx = 0; idx < buf1.shape[0]; idx++)
            ptr3[idx] = ptr1[idx] + ptr2[idx];

        return result;
    }

    PYBIND11_MODULE(test, m) {
        m.def("add_arrays", &add_arrays, "Add two NumPy arrays");
    }

See also

The file `tests/test_numpy_vectorize.cpp` contains a complete example that demonstrates using `vectorize()` in more detail.

## Direct access

For performance reasons, particularly when dealing with very large arrays, it is often desirable to directly access array elements without internal checking of dimensions and bounds on every access when indices are known to be already valid. To avoid such checks, the `array` class and `array_t<T>` template class offer an unchecked proxy object that can be used for this unchecked access through the `unchecked<N>` and `mutable_unchecked<N>` methods, where `N` gives the required dimensionality of the array:

    m.def("sum_3d", [](py::array_t<double> x) {
        auto r = x.unchecked<3>(); // x must have ndim = 3; can be non-writeable
        double sum = 0;
        for (py::ssize_t i = 0; i < r.shape(0); i++)
            for (py::ssize_t j = 0; j < r.shape(1); j++)
                for (py::ssize_t k = 0; k < r.shape(2); k++)
                    sum += r(i, j, k);
        return sum;
    });
    m.def("increment_3d", [](py::array_t<double> x) {
        auto r = x.mutable_unchecked<3>(); // Will throw if ndim != 3 or flags.writeable is false
        for (py::ssize_t i = 0; i < r.shape(0); i++)
            for (py::ssize_t j = 0; j < r.shape(1); j++)
                for (py::ssize_t k = 0; k < r.shape(2); k++)
                    r(i, j, k) += 1.0;
    }, py::arg().noconvert());

To obtain the proxy from an `array` object, you must specify both the data type and number of dimensions as template arguments, such as `auto r = myarray.mutable_unchecked<float, 2>()`.

If the number of dimensions is not known at compile time, you can omit the dimensions template parameter (i.e. calling `arr_t.unchecked()` or `arr.unchecked<T>()`. This will give you a proxy object that works in the same way, but results in less optimizable code and thus a small efficiency loss in tight loops.

Note that the returned proxy object directly references the array’s data, and only reads its shape, strides, and writeable flag when constructed. You must take care to ensure that the referenced array is not destroyed or reshaped for the duration of the returned object, typically by limiting the scope of the returned instance.

The returned proxy object supports some of the same methods as `py::array` so that it can be used as a drop-in replacement for some existing, index-checked uses of `py::array`:

- `.ndim()` returns the number of dimensions

- `.data(1, 2, ...)` and `r.mutable_data(1, 2, ...)`` returns a pointer to the `const T` or `T` data, respectively, at the given indices. The latter is only available to proxies obtained via `a.mutable_unchecked()`.

- `.itemsize()` returns the size of an item in bytes, i.e. `sizeof(T)`.

- `.ndim()` returns the number of dimensions.

- `.shape(n)` returns the size of dimension `n`

- `.size()` returns the total number of elements (i.e. the product of the shapes).

- `.nbytes()` returns the number of bytes used by the referenced elements (i.e. `itemsize()` times `size()`).

See also

The file `tests/test_numpy_array.cpp` contains additional examples demonstrating the use of this feature.

## Ellipsis

Python provides a convenient `...` ellipsis notation that is often used to slice multidimensional arrays. For instance, the following snippet extracts the middle dimensions of a tensor with the first and last index set to zero.

    a = ...  # a NumPy array
    b = a[0, ..., 0]

The function `py::ellipsis()` function can be used to perform the same operation on the C++ side:

    py::array a = /* A NumPy array */;
    py::array b = a[py::make_tuple(0, py::ellipsis(), 0)];

## Memory view

For a case when we simply want to provide a direct accessor to C/C++ buffer without a concrete class object, we can return a `memoryview` object. Suppose we wish to expose a `memoryview` for 2x4 uint8_t array, we can do the following:

    const uint8_t buffer[] = {
        0, 1, 2, 3,
        4, 5, 6, 7
    };
    m.def("get_memoryview2d", []() {
        return py::memoryview::from_buffer(
            buffer,                                    // buffer pointer
            { 2, 4 },                                  // shape (rows, cols)
            { sizeof(uint8_t) * 4, sizeof(uint8_t) }   // strides in bytes
        );
    });

This approach is meant for providing a `memoryview` for a C/C++ buffer not managed by Python. The user is responsible for managing the lifetime of the buffer. Using a `memoryview` created in this way after deleting the buffer in C++ side results in undefined behavior.

We can also use `memoryview::from_memory` for a simple 1D contiguous buffer:

    m.def("get_memoryview1d", []() {
        return py::memoryview::from_memory(
            buffer,               // buffer pointer
            sizeof(uint8_t) * 8   // buffer size
        );
    });

Changed in version 2.6: `memoryview::from_memory` added.