Cython interface between the numpy arrays and the Matrix/Array classes of the Eigen C++ library

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 (see example below)

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) { ... }

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.

## 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 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 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 inteface 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 inteface 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 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 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 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.

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