# Autowrap Module¶

The autowrap module works very well in tandem with the Indexed classes of the Tensors. Here is a simple example that shows how to setup a binary routine that calculates a matrix-vector product.

>>> from diofant.utilities.autowrap import autowrap
>>> A, x, y = map(IndexedBase, ['A', 'x', 'y'])
>>> m, n = symbols('m n', integer=True)
>>> i = Idx('i', m)
>>> j = Idx('j', n)
>>> instruction = Eq(y[i], A[i, j]*x[j]); instruction
Eq(y[i], x[j]*A[i, j])


Because the code printers treat Indexed objects with repeated indices as a summation, the above equality instance will be translated to low-level code for a matrix vector product. This is how you tell Diofant to generate the code, compile it and wrap it as a python function:

>>> matvec = autowrap(instruction)                 # doctest: +SKIP


That’s it. Now let’s test it with some numpy arrays. The default wrapper backend is f2py. The wrapper function it provides is set up to accept python lists, which it will silently convert to numpy arrays. So we can test the matrix vector product like this:

>>> M = [[0, 1],
...      [1, 0]]
>>> matvec(M, [2, 3])                              # doctest: +SKIP
[ 3.  2.]


## Implementation details¶

The autowrap module is implemented with a backend consisting of CodeWrapper objects. The base class CodeWrapper takes care of details about module name, filenames and options. It also contains the driver routine, which runs through all steps in the correct order, and also takes care of setting up and removing the temporary working directory.

The actual compilation and wrapping is done by external resources, such as the system installed f2py command. The Cython backend runs a distutils setup script in a subprocess. Subclasses of CodeWrapper takes care of these backend-dependent details.

## API Reference¶

Module for compiling codegen output, and wrap the binary for use in python.

This module provides a common interface for different external backends, such as f2py, fwrap, Cython, SWIG(?) etc. (Currently only f2py and Cython are implemented) The goal is to provide access to compiled binaries of acceptable performance with a one-button user interface, i.e.

>>> expr = ((x - y)**25).expand()
>>> binary_callable = autowrap(expr)
>>> binary_callable(1, 2)
-1.0


The callable returned from autowrap() is a binary python function, not a Diofant object. If it is desired to use the compiled function in symbolic expressions, it is better to use binary_function() which returns a Diofant Function object. The binary callable is attached as the _imp_ attribute and invoked when a numerical evaluation is requested with evalf(), or with lambdify().

>>> f = binary_function('f', expr)
>>> 2*f(x, y) + y
y + 2*f(x, y)
>>> (2*f(x, y) + y).evalf(2, subs={x: 1, y:2}, strict=False)
0.e-190


The idea is that a Diofant user will primarily be interested in working with mathematical expressions, and should not have to learn details about wrapping tools in order to evaluate expressions numerically, even if they are computationally expensive.

When is this useful?

1. For computations on large arrays, Python iterations may be too slow, and depending on the mathematical expression, it may be difficult to exploit the advanced index operations provided by NumPy.

2. For really long expressions that will be called repeatedly, the compiled binary should be significantly faster than Diofant’s .evalf()

3. If you are generating code with the codegen utility in order to use it in another project, the automatic python wrappers let you test the binaries immediately from within Diofant.

4. To create customized ufuncs for use with numpy arrays. See ufuncify.

When is this module NOT the best approach?

1. If you are really concerned about speed or memory optimizations, you will probably get better results by working directly with the wrapper tools and the low level code. However, the files generated by this utility may provide a useful starting point and reference code. Temporary files will be left intact if you supply the keyword tempdir=”path/to/files/”.

2. If the array computation can be handled easily by numpy, and you don’t need the binaries for another project.

class diofant.utilities.autowrap.CodeWrapper(generator, filepath=None, flags=[], verbose=False)[source]

Base Class for code wrappers.

class diofant.utilities.autowrap.CythonCodeWrapper(*args, **kwargs)[source]

Wrapper that uses Cython.

dump_pyx(routines, f, prefix)[source]

Write a Cython file with python wrappers

This file contains all the definitions of the routines in c code and refers to the header file.

Parameters
• routines (list) – List of Routine instances

• f (file) – File-like object to write the file to

• prefix (str) – The filename prefix, used to refer to the proper header file. Only the basename of the prefix is used.

class diofant.utilities.autowrap.DummyWrapper(generator, filepath=None, flags=[], verbose=False)[source]

Class used for testing independent of backends.

class diofant.utilities.autowrap.F2PyCodeWrapper(generator, filepath=None, flags=[], verbose=False)[source]

Wrapper that uses f2py.

class diofant.utilities.autowrap.UfuncifyCodeWrapper(generator, filepath=None, flags=[], verbose=False)[source]

Wrapper for Ufuncify.

dump_c(routines, f, prefix)[source]

Write a C file with python wrappers

This file contains all the definitions of the routines in c code.

Parameters
• routines (list) – List of Routine instances

• f (file) – File-like object to write the file to

• prefix (str) – The filename prefix, used to name the imported module.

diofant.utilities.autowrap.autowrap(expr, language=None, backend='f2py', tempdir=None, args=None, flags=None, verbose=False, helpers=None)[source]

Generates python callable binaries based on the math expression.

Parameters
• expr – The Diofant expression that should be wrapped as a binary routine.

• language (string, optional) – If supplied, (options: ‘C’ or ‘F95’), specifies the language of the generated code. If None [default], the language is inferred based upon the specified backend.

• backend (string, optional) – Backend used to wrap the generated code. Either ‘f2py’ [default], or ‘cython’.

• tempdir (string, optional) – Path to directory for temporary files. If this argument is supplied, the generated code and the wrapper input files are left intact in the specified path.

• args (iterable, optional) – An ordered iterable of symbols. Specifies the argument sequence for the function.

• flags (iterable, optional) – Additional option flags that will be passed to the backend.

• verbose (bool, optional) – If True, autowrap will not mute the command line backends. This can be helpful for debugging.

• helpers (iterable, optional) – Used to define auxillary expressions needed for the main expr. If the main expression needs to call a specialized function it should be put in the helpers iterable. Autowrap will then make sure that the compiled main expression can link to the helper routine. Items should be tuples with (<function_name>, <diofant_expression>, <arguments>). It is mandatory to supply an argument sequence to helper routines.

Examples

>>> expr = ((x - y + z)**13).expand()
>>> binary_func = autowrap(expr)
>>> binary_func(1, 4, 2)
-1.0

diofant.utilities.autowrap.binary_function(symfunc, expr, **kwargs)[source]

Returns a diofant function with expr as binary implementation

This is a convenience function that automates the steps needed to autowrap the Diofant expression and attaching it to a Function object with implemented_function().

>>> expr = ((x - y)**25).expand()
>>> f = binary_function('f', expr)
>>> type(f)
<class 'diofant.core.function.UndefinedFunction'>
>>> 2*f(x, y)
2*f(x, y)
>>> f(x, y).evalf(2, subs={x: 1, y: 2})
-1.0

diofant.utilities.autowrap.ufuncify(args, expr, language=None, backend='numpy', tempdir=None, flags=None, verbose=False, helpers=None)[source]

Generates a binary function that supports broadcasting on numpy arrays.

Parameters
• args (iterable) – Either a Symbol or an iterable of symbols. Specifies the argument sequence for the function.

• expr – A Diofant expression that defines the element wise operation.

• language (string, optional) – If supplied, (options: ‘C’ or ‘F95’), specifies the language of the generated code. If None [default], the language is inferred based upon the specified backend.

• backend (string, optional) – Backend used to wrap the generated code. Either ‘numpy’ [default], ‘cython’, or ‘f2py’.

• tempdir (string, optional) – Path to directory for temporary files. If this argument is supplied, the generated code and the wrapper input files are left intact in the specified path.

• flags (iterable, optional) – Additional option flags that will be passed to the backend

• verbose (bool, optional) – If True, autowrap will not mute the command line backends. This can be helpful for debugging.

• helpers (iterable, optional) – Used to define auxillary expressions needed for the main expr. If the main expression needs to call a specialized function it should be put in the helpers iterable. Autowrap will then make sure that the compiled main expression can link to the helper routine. Items should be tuples with (<function_name>, <diofant_expression>, <arguments>). It is mandatory to supply an argument sequence to helper routines.

Notes

The default backend (‘numpy’) will create actual instances of numpy.ufunc. These support ndimensional broadcasting, and implicit type conversion. Use of the other backends will result in a “ufunc-like” function, which requires equal length 1-dimensional arrays for all arguments, and will not perform any type conversions.

References

Examples

>>> import numpy as np
>>> f = ufuncify((x, y), y + x**2)
>>> type(f) is np.ufunc
True
>>> f([1, 2, 3], 2)
[  3.   6.  11.]
>>> f(np.arange(5), 3)
[  3.   4.   7.  12.  19.]


For the F2Py and Cython backends, inputs are required to be equal length 1-dimensional arrays. The F2Py backend will perform type conversion, but the Cython backend will error if the inputs are not of the expected type.

>>> f_fortran = ufuncify((x, y), y + x**2, backend='F2Py')
>>> f_fortran(1, 2)
[ 3.]
>>> f_fortran(np.array([1, 2, 3]), np.array([1.0, 2.0, 3.0]))
[  2.   6.  12.]