Eigency

Eigency is a Cython interface between Numpy arrays and Matrix/Array objects from the Eigen C++ library. It is intended to simplify the process of writing C++ extensions using the Eigen library. Eigency is designed to reuse the underlying storage of the arrays when passing data back and forth, and will thus avoid making unnecessary copies whenever possible. Only in cases where copies are explicitly requested by your C++ code will they be made.

Below is a description of a range of common usage scenarios. A full working example of both setup and these different use cases is available in the test directory distributed with the this package.

Setup

To import eigency functionality, add the following to your .pyx file:

from eigency.core cimport *

In addition, in the setup.py file, the include directories must be set up to include the eigency includes. This can be done by calling the get_includes function in the eigency module:

import eigency
...
extensions = [
    Extension("module-dir-name/module-name", ["module-dir-name/module-name.pyx"],
              include_dirs = [".", "module-dir-name"] + eigency.get_includes()
              ),
]

Eigency includes a version of the Eigen library, and the get_includes function will include the path to this directory. If you have your own version of Eigen, just set the include_eigen option to False, and add your own path instead:

    include_dirs = [".", "module-dir-name", 'path-to-own-eigen'] + eigency.get_includes(include_eigen=False)

From Numpy to Eigen

Assume we are writing a Cython interface to the following C++ function:

void function_w_mat_arg(const Eigen::Map<Eigen::MatrixXd> &mat) {
    std::cout << mat << "\n";
}

Note that we use Eigen::Map to ensure that we can reuse the storage of the numpy array, thus avoiding making a copy. Assuming the C++ code is in a file called functions.h, the corresponding .pyx entry could look like this:

cdef extern from "functions.h":
     cdef void _function_w_mat_arg "function_w_mat_arg"(Map[MatrixXd] &)

# This will be exposed to Python
def function_w_mat_arg(np.ndarray array):
    return _function_w_mat_arg(Map[MatrixXd](array))

The last line contains the actual conversion. Map is an Eigency type that derives from the real Eigen map, and will take care of the conversion from the numpy array to the corresponding Eigen type.

We can now call the C++ function directly from Python:

>>> import numpy as np
>>> import eigency_tests
>>> x = np.array([[1.1, 2.2], [3.3, 4.4]])
>>> eigency_tests.function_w_mat_arg(x)
1.1 3.3
2.2 4.4

(if you are wondering about why the matrix is transposed, please see the Storage layout section below).

Types matter

The basic idea behind eigency is to share the underlying representation of a numpy array between Python and C++. This means that somewhere in the process, we need to make explicit which numerical types we are dealing with. In the function above, we specify that we expect an Eigen MatrixXd, which means that the numpy array must also contain double (i.e. float64) values. If we instead provide a numpy array of ints, we will get strange results.

>>> import numpy as np
>>> import eigency_tests
>>> x = np.array([[1, 2], [3, 4]])
>>> eigency_tests.function_w_mat_arg(x)
4.94066e-324  1.4822e-323
9.88131e-324 1.97626e-323

This is because we are explicitly asking C++ to interpret out python integer values as floats.

To avoid this type of error, you can force your cython function to accept only numpy arrays of a specific type:

cdef extern from "functions.h":
     cdef void _function_w_mat_arg "function_w_mat_arg"(Map[MatrixXd] &)

# This will be exposed to Python
def function_w_mat_arg(np.ndarray[np.float64_t, ndim=2] array):
    return _function_w_mat_arg(Map[MatrixXd](array))

(Note that when using this technique to select the type, you also need to specify the dimensions of the array (this will default to 1)). Using this new definition, users will get an error when passing arrays of the wrong type:

>>> import numpy as np
>>> import eigency_tests
>>> x = np.array([[1, 2], [3, 4]])
>>> eigency_tests.function_w_mat_arg(x)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "eigency_tests/eigency_tests.pyx", line 87, in eigency_tests.eigency_tests.function_w_mat_arg
ValueError: Buffer dtype mismatch, expected 'float64_t' but got 'long'

Since it avoids many surprises, it is strongly recommended to use this technique to specify the full types of numpy arrays in your cython code whenever possible.

Writing Eigen Map types in Cython

Since Cython does not support nested fused types, you cannot write types like Map[Matrix[double, 2, 2]]. In most cases, you won't need to, since you can just use Eigens convenience typedefs, such as Map[VectorXd]. If you need the additional flexibility of the full specification, you can use the FlattenedMap type, where all type arguments can be specified at top level, for instance FlattenedMap[Matrix, double, _2, _3] or FlattenedMap[Matrix, double, _2, Dynamic]. Note that dimensions must be prefixed with an underscore.

Using full specifications of the Eigen types, the previous example would look like this:

cdef extern from "functions.h":
     cdef void _function_w_mat_arg "function_w_mat_arg" (FlattenedMap[Matrix, double, Dynamic, Dynamic] &)

# This will be exposed to Python
def function_w_mat_arg(np.ndarray[np.float64_t, ndim=2] array):
    return _function_w_mat_arg(FlattenedMap[Matrix, double, Dynamic, Dynamic](array))

FlattenedType takes four template parameters: arraytype, scalartype, rows and cols. Eigen supports a few other template arguments for setting the storage layout and Map strides. Since cython does not support default template arguments for fused types, we have instead defined separate types for this purpose. These are called FlattenedMapWithOrder and FlattenedMapWithStride with five and eight template arguments, respectively. For details on their use, see the section about storage layout below.

From Numpy to Eigen (insisting on a copy)

Eigency will not complain if the C++ function you interface with does not take a Eigen Map object, but instead a regular Eigen Matrix or Array. However, in such cases, a copy will be made. Actually, the procedure is exactly the same as above. In the .pyx file, you still define everything exactly the same way as for the Map case described above.

For instance, given the following C++ function:

void function_w_vec_arg_no_map(const Eigen::VectorXd &vec);

The Cython definitions would still look like this:

cdef extern from "functions.h":
     cdef void _function_w_vec_arg_no_map "function_w_vec_arg_no_map"(Map[VectorXd] &)

# This will be exposed to Python
def function_w_vec_arg_no_map(np.ndarray[np.float64_t] array):
    return _function_w_vec_arg_no_map(Map[VectorXd](array))

Cython will not mind the fact that the argument type in the extern declaration (a Map type) differs from the actual one in the .h file, as long as one can be assigned to the other. Since Map objects can be assigned to their corresponding Matrix/Array types this works seemlessly. But keep in mind that this assignment will make a copy of the underlying data.

Eigen to Numpy

C++ functions returning a reference to an Eigen Matrix/Array can also be transferred to numpy arrays without copying their content. Assume we have a class with a single getter function that returns an Eigen matrix member:

class MyClass {
public:
    MyClass():
        matrix(Eigen::Matrix3d::Constant(3.)) {
    }
    Eigen::MatrixXd &get_matrix() {
        return this->matrix;
    }
private:
    Eigen::Matrix3d matrix;
};

The Cython C++ class interface is specified as usual:

     cdef cppclass _MyClass "MyClass":
         _MyClass "MyClass"() except +
         Matrix3d &get_matrix()

And the corresponding Python wrapper:

cdef class MyClass:
    cdef _MyClass *thisptr;

    def __cinit__(self):
        self.thisptr = new _MyClass()

    def __dealloc__(self):
        del self.thisptr

    def get_matrix(self):
        return ndarray(self.thisptr.get_matrix())

This last line contains the actual conversion. Again, eigency has its own version of ndarray, that will take care of the conversion for you.

Due to limitations in Cython, Eigency cannot deal with full Matrix/Array template specifications as return types (e.g. Matrix[double, 4, 2]). However, as a workaround, you can use PlainObjectBase as a return type in such cases (or in all cases if you prefer):

         PlainObjectBase &get_matrix()

Overriding default behavior

The ndarray conversion type specifier will attempt do guess whether you want a copy or a view, depending on the return type. Most of the time, this is probably what you want. However, there might be cases where you want to override this behavior. For instance, functions returning const references will result in a copy of the array, since the const-ness cannot be enforced in Python. However, you can always override the default behavior by using the ndarray_copy or ndarray_view functions.

Expanding the MyClass example from before:

class MyClass {
public:
    ...
    const Eigen::MatrixXd &get_const_matrix() {
        return this->matrix;
    }
    ...
};

With the corresponding cython interface specification The Cython C++ class interface is specified as usual:

     cdef cppclass _MyClass "MyClass":
         ...
         const Matrix3d &get_const_matrix()

The following would return a copy

cdef class MyClass:
    ...
    def get_const_matrix(self):
        return ndarray(self.thisptr.get_const_matrix())

while the following would force it to return a view

cdef class MyClass:
    ...
    def get_const_matrix(self):
        return ndarray_view(self.thisptr.get_const_matrix())

Eigen to Numpy (non-reference return values)

Functions returning an Eigen object (not a reference), are specified in a similar way. For instance, given the following C++ function:

Eigen::Matrix3d function_w_mat_retval();

The Cython code could be written as:

cdef extern from "functions.h":
     cdef Matrix3d _function_w_mat_retval "function_w_mat_retval" ()

# This will be exposed to Python
def function_w_mat_retval():
    return ndarray_copy(_function_w_mat_retval())

As mentioned above, you can replace Matrix3d (or any other Eigen return type) with PlainObjectBase, which is especially relevant when working with Eigen object that do not have an associated convenience typedef.

Note that we use ndarray_copy instead of ndarray to explicitly state that a copy should be made. In c++11 compliant compilers, it will detect the rvalue reference and automatically make a copy even if you just use ndarray (see next section), but to ensure that it works also with older compilers it is recommended to always use ndarray_copy when returning newly constructed eigen values.

Corrupt data when returning non-map types

The tendency of Eigency to avoid copies whenever possible can lead to corrupted data when returning non-map Eigen arrays. For instance, in the function_w_mat_retval from the previous section, a temporary value will be returned from C++, and we have to take care to make a copy of this data instead of letting the resulting numpy array refer directly to this memory. In C++11, this situation can be detected directly using rvalue references, and it will therefore automatically make a copy:

def function_w_mat_retval():
    # This works in C++11, because it detects the rvalue reference
    return ndarray(_function_w_mat_retval()) 

However, to make sure it works with older compilers, it is recommended to use the ndarray_copy conversion:

def function_w_mat_retval():
    # Explicit request for copy - this always works
    return ndarray_copy(_function_w_mat_retval()) 

Storage layout - why arrays are sometimes transposed

The default storage layout used in numpy and Eigen differ. Numpy uses a row-major layout (C-style) per default while Eigen uses a column-major layout (Fortran style) by default. In Eigency, we prioritize to avoid copying of data whenever possible, which can have unexpected consequences in some cases: There is no problem when passing values from C++ to Python - we just adjust the storage layout of the returned numpy array to match that of Eigen. However, since the storage layout is encoded into the type of the Eigen array (or the type of the Map), we cannot automatically change the layout in the Python to C++ direction. In Eigency, we have therefore opted to return the transposed array/matrix in such cases. This provides the user with the flexibility to deal with the problem either in Python (use order="F" when constructing your numpy array), or on the C++ side: (1) explicitly define your argument to have the row-major storage layout, 2) manually set the Map stride, or 3) just call .transpose() on the received array/matrix).

As an example, consider the case of a C++ function that both receives and returns a Eigen Map type, thus acting as a filter:

Eigen::Map<Eigen::ArrayXXd> function_filter(Eigen::Map<Eigen::ArrayXXd> &mat) {
    return mat;
}

The Cython code could be:

cdef extern from "functions.h":
    ...
    cdef Map[ArrayXXd] &_function_filter1 "function_filter1" (Map[ArrayXXd] &)

def function_filter1(np.ndarray[np.float64_t, ndim=2] array):
    return ndarray(_function_filter1(Map[ArrayXXd](array)))

If we call this function from Python in the standard way, we will see that the array is transposed on the way from Python to C++, and remains that way when it is again returned to Python:

>>> x = np.array([[1., 2., 3., 4.], [5., 6., 7., 8.]])
>>> y = function_filter1(x)
>>> print x
[[ 1.  2.  3.  4.]
 [ 5.  6.  7.  8.]]
>>> print y
[[ 1.  5.]
 [ 2.  6.]
 [ 3.  7.]
 [ 4.  8.]]

The simplest way to avoid this is to tell numpy to use a column-major array layout instead of the default row-major layout. This can be done using the order='F' option:

>>> x = np.array([[1., 2., 3., 4.], [5., 6., 7., 8.]], order='F')
>>> y = function_filter1(x)
>>> print x
[[ 1.  2.  3.  4.]
 [ 5.  6.  7.  8.]]
>>> print y
[[ 1.  2.  3.  4.]
 [ 5.  6.  7.  8.]]

The other alternative is to tell Eigen to use RowMajor layout. This requires changing the C++ function definition:

typedef Eigen::Map<Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> > RowMajorArrayMap;

RowMajorArrayMap &function_filter2(RowMajorArrayMap &mat) {
    return mat;
}

To write the corresponding Cython definition, we need the expanded version of FlattenedMap called FlattenedMapWithOrder, which allows us to specify the storage order:

cdef extern from "functions.h":
    ...
    cdef PlainObjectBase _function_filter2 "function_filter2" (FlattenedMapWithOrder[Array, double, Dynamic, Dynamic, RowMajor])

def function_filter2(np.ndarray[np.float64_t, ndim=2] array):
    return ndarray(_function_filter2(FlattenedMapWithOrder[Array, double, Dynamic, Dynamic, RowMajor](array)))

Another alternative is to keep the array itself in RowMajor format, but use different stride values for the Map type:

typedef Eigen::Map<Eigen::ArrayXXd, Eigen::Unaligned, Eigen::Stride<1, Eigen::Dynamic> > CustomStrideMap;

CustomStrideMap &function_filter3(CustomStrideMap &);

In this case, in Cython, we need to use the even more extended FlattenedMap type called FlattenedMapWithStride, taking eight arguments:

cdef extern from "functions.h":
    ...
    cdef PlainObjectBase _function_filter3 "function_filter3" (FlattenedMapWithStride[Array, double, Dynamic, Dynamic, ColMajor, Unaligned, _1, Dynamic])

def function_filter3(np.ndarray[np.float64_t, ndim=2] array):
    return ndarray(_function_filter3(FlattenedMapWithStride[Array, double, Dynamic, Dynamic, ColMajor, Unaligned, _1, Dynamic](array)))

In all three cases, the returned array will now be of the same shape as the original.