def test_contraction_structure_Mul_and_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
i_ji = x[i]**(y[j] * x[i])
assert get_contraction_structure(i_ji) == {None: {i_ji}}
ij_i = (x[i] * y[j])**(y[i])
assert get_contraction_structure(ij_i) == {None: {ij_i}}
j_ij_i = x[j] * (x[i] * y[j])**(y[i])
assert get_contraction_structure(j_ij_i) == {(j, ): {j_ij_i}}
j_i_ji = x[j] * x[i]**(y[j] * x[i])
assert get_contraction_structure(j_i_ji) == {(j, ): {j_i_ji}}
ij_exp_kki = x[i] * y[j] * exp(y[i] * y[k, k])
result = get_contraction_structure(ij_exp_kki)
expected = {
(i, ): {ij_exp_kki},
ij_exp_kki: [{
None: {exp(y[i] * y[k, k])},
exp(y[i] * y[k, k]): [{
None: {y[i] * y[k, k]},
y[i] * y[k, k]: [{
(k, ): {y[k, k]}
}]
}]
}]
}
assert result == expected
def test_ufunc_support():
f = Function('f')
g = Function('g')
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
a = symbols('a')
assert get_indices(f(x[i])) == ({i}, {})
assert get_indices(f(x[i], y[j])) == ({i, j}, {})
assert get_indices(f(y[i]) * g(x[i])) == (set(), {})
assert get_indices(f(a, x[i])) == ({i}, {})
assert get_indices(f(a, y[i], x[j]) * g(x[i])) == ({j}, {})
assert get_indices(g(f(x[i]))) == ({i}, {})
assert get_contraction_structure(f(x[i])) == {None: {f(x[i])}}
assert get_contraction_structure(f(y[i]) * g(x[i])) == {
(i, ): {f(y[i]) * g(x[i])}
}
assert get_contraction_structure(f(y[i]) * g(f(x[i]))) == {
(i, ): {f(y[i]) * g(f(x[i]))}
}
assert get_contraction_structure(f(x[j], y[i]) * g(x[i])) == {
(i, ): {f(x[j], y[i]) * g(x[i])}
}
def test_get_contraction_structure_complex():
x = IndexedBase('x')
y = IndexedBase('y')
A = IndexedBase('A')
i, j, k = Idx('i'), Idx('j'), Idx('k')
expr1 = y[i] + A[i, j] * x[j]
d1 = {None: {y[i]}, (j, ): {A[i, j] * x[j]}}
assert get_contraction_structure(expr1) == d1
expr2 = expr1 * A[k, i] + x[k]
d2 = {None: {x[k]}, (i, ): {expr1 * A[k, i]}, expr1 * A[k, i]: [d1]}
assert get_contraction_structure(expr2) == d2
def test_get_contraction_structure_basic():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
assert get_contraction_structure(x[i] * y[j]) == {None: {x[i] * y[j]}}
assert get_contraction_structure(x[i] + y[j]) == {None: {x[i], y[j]}}
assert get_contraction_structure(x[i] * y[i]) == {(i, ): {x[i] * y[i]}}
assert get_contraction_structure(1 + x[i] * y[i]) == {
None: {S.One},
(i, ): {x[i] * y[i]}
}
assert get_contraction_structure(x[i]**y[i]) == {None: {x[i]**y[i]}}
def test_contraction_structure_simple_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj = x[i, i]**y[j, j]
assert get_contraction_structure(ii_jj) == {
None: {ii_jj},
ii_jj: [{
(i, ): {x[i, i]}
}, {
(j, ): {y[j, j]}
}]
}
def test_get_indices_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
A = IndexedBase('A')
i, j, k = Idx('i'), Idx('j'), Idx('k')
assert get_indices(Pow(x[i], y[j])) == ({i, j}, {})
assert get_indices(Pow(x[i, k], y[j, k])) == ({i, j, k}, {})
assert get_indices(Pow(A[i, k], y[k] + A[k, j] * x[j])) == ({i, k}, {})
assert get_indices(Pow(2, x[i])) == get_indices(exp(x[i]))
# test of a design decision, this may change:
assert get_indices(Pow(x[i], 2)) == ({
i,
}, {})
def test_contraction_structure_Add_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
s_ii_jj_s = (1 + x[i, i])**(1 + y[j, j])
expected = {
None: {s_ii_jj_s},
s_ii_jj_s: [{
None: {S.One},
(i, ): {x[i, i]}
}, {
None: {S.One},
(j, ): {y[j, j]}
}]
}
result = get_contraction_structure(s_ii_jj_s)
assert result == expected
def test_get_contraction_structure_basic():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
f = Function('f')
assert get_contraction_structure(x[i] * y[j]) == {None: {x[i] * y[j]}}
assert get_contraction_structure(x[i] + y[j]) == {None: {x[i], y[j]}}
assert get_contraction_structure(x[i] * y[i]) == {(i, ): {x[i] * y[i]}}
assert get_contraction_structure(1 + x[i] * y[i]) == {
None: {1},
(i, ): {x[i] * y[i]}
}
assert get_contraction_structure(x[i]**y[i]) == {None: {x[i]**y[i]}}
assert (get_contraction_structure(f(x[i, i])) == {
None: {f(x[i, i])},
f(x[i, i]): [{
(i, ): {x[i, i]}
}]
})
def test_get_indices_add():
x = IndexedBase('x')
y = IndexedBase('y')
A = IndexedBase('A')
i, j, k = Idx('i'), Idx('j'), Idx('k')
assert get_indices(x[i] + 2 * y[i]) == ({
i,
}, {})
assert get_indices(y[i] + 2 * A[i, j] * x[j]) == ({
i,
}, {})
assert get_indices(y[i] + 2 * (x[i] + A[i, j] * x[j])) == ({
i,
}, {})
assert get_indices(y[i] + x[i] * (A[j, j] + 1)) == ({
i,
}, {})
assert get_indices(y[i] + x[i] * x[j] * (y[j] + A[j, k] * x[k])) == ({
i,
}, {})
def test_contraction_structure_Pow_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
z = IndexedBase('z')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj_kk = x[i, i]**y[j, j]**z[k, k]
expected = {
None: {ii_jj_kk},
ii_jj_kk: [{
(i, ): {x[i, i]}
}, {
None: {y[j, j]**z[k, k]},
y[j, j]**z[k, k]: [{
(j, ): {y[j, j]}
}, {
(k, ): {z[k, k]}
}]
}]
}
assert get_contraction_structure(ii_jj_kk) == expected
def test_scalar_broadcast():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
assert get_indices(x[i] + y[i, i]) == ({i}, {})
def test_get_indices_exceptions():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
pytest.raises(IndexConformanceException, lambda: get_indices(x[i] + y[j]))
def test_get_indices_mul():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
assert get_indices(x[j] * y[i]) == ({i, j}, {})
assert get_indices(x[i] * y[j]) == ({i, j}, {})
def test_get_indices_Indexed():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
assert get_indices(x[i, j]) == ({i, j}, {})
assert get_indices(x[j, i]) == ({j, i}, {})
def ufuncify(args,
expr,
language=None,
backend='numpy',
tempdir=None,
flags=None,
verbose=False,
helpers=None):
"""
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 (<funtion_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
----------
.. [1] http://docs.scipy.org/doc/numpy/reference/ufuncs.html
Examples
--------
>>> from diofant.utilities.autowrap import ufuncify
>>> from diofant.abc import x, y
>>> import numpy as np
>>> f = ufuncify((x, y), y + x**2)
>>> type(f) is np.ufunc
True
>>> f([1, 2, 3], 2)
array([ 3., 6., 11.])
>>> f(np.arange(5), 3)
array([ 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(numpy.array([1, 2, 3]), numpy.array([1.0, 2.0, 3.0]))
array([2., 6., 12.])
>>> f_cython = ufuncify((x, y), y + x**2, backend='Cython')
>>> f_cython(1, 2)
Traceback (most recent call last):
...
TypeError: Argument '_x' has incorrect type (expected numpy.ndarray, got int)
>>> f_cython(numpy.array([1.0]), numpy.array([2.0]))
array([ 3.])
"""
if isinstance(args, (Dummy, Symbol)):
args = (args, )
else:
args = tuple(args)
if language:
_validate_backend_language(backend, language)
else:
language = _infer_language(backend)
helpers = helpers if helpers else ()
flags = flags if flags else ()
if backend.upper() == 'NUMPY':
routine = make_routine('autofunc', expr, args)
helps = []
for name, expr, args in helpers:
helps.append(make_routine(name, expr, args))
code_wrapper = UfuncifyCodeWrapper(CCodeGen("ufuncify"), tempdir,
flags, verbose)
return code_wrapper.wrap_code(routine, helpers=helps)
else:
# Dummies are used for all added expressions to prevent name clashes
# within the original expression.
y = IndexedBase(Dummy())
m = Dummy(integer=True)
i = Idx(Dummy(integer=True), m)
f = implemented_function(Dummy().name, Lambda(args, expr))
# For each of the args create an indexed version.
indexed_args = [IndexedBase(Dummy(str(a))) for a in args]
# Order the arguments (out, args, dim)
args = [y] + indexed_args + [m]
args_with_indices = [a[i] for a in indexed_args]
return autowrap(Eq(y[i], f(*args_with_indices)), language, backend,
tempdir, tuple(args), flags, verbose, helpers)