def test_newtons_method_function__ccode():
x = sp.Symbol("x", real=True)
expr = sp.cos(x) - x**3
func = newtons_method_function(expr, x)
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std="c99")
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[
(
"newton.c",
("#include <math.h>\n"
"#include <stdio.h>\n") + ccode(func),
),
(
"_newton.pyx",
("#cython: language_level={}\n".format("3") +
"cdef extern double newton(double)\n"
"def py_newton(x):\n"
" return newton(x)\n"),
),
],
build_dir=folder,
compile_kwargs=compile_kw,
)
assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
def test_newtons_method_function__ccode_parameters():
args = x, A, k, p = sp.symbols("x A k p")
expr = A * sp.cos(k * x) - p * x**3
raises(ValueError, lambda: newtons_method_function(expr, x))
use_wurlitzer = wurlitzer
func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
if not has_c():
skip("No C compiler found.")
if not cython:
skip("cython not installed.")
compile_kw = dict(std="c99")
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[
(
"newton_par.c",
("#include <math.h>\n"
"#include <stdio.h>\n") + ccode(func),
),
(
"_newton_par.pyx",
("#cython: language_level={}\n".format("3") +
"cdef extern double newton(double, double, double, double)\n"
"def py_newton(x, A=1, k=1, p=1):\n"
" return newton(x, A, k, p)\n"),
),
],
compile_kwargs=compile_kw,
build_dir=folder,
)
if use_wurlitzer:
with wurlitzer.pipes() as (out, err):
result = mod.py_newton(0.5)
else:
result = mod.py_newton(0.5)
assert abs(result - 0.865474033102) < 1e-12
if not use_wurlitzer:
skip(
"C-level output only tested when package 'wurlitzer' is available."
)
out, err = out.read(), err.read()
assert err == ""
assert (out == """\
x= 0.5 d_x= 0.61214
x= 1.1121 d_x= -0.20247
x= 0.90967 d_x= -0.042409
x= 0.86726 d_x= -0.0017867
x= 0.86548 d_x= -3.1022e-06
x= 0.86547 d_x= -9.3421e-12
x= 0.86547 d_x= 3.6902e-17
""") # try to run tests with LC_ALL=C if this assertion fails
def test_compiled_ccode_with_rewriting():
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
x = Symbol('x')
about_two = 2**(58 / S(117)) * 3**(97 / S(117)) * 5**(4 / S(39)) * 7**(
92 / S(117)) / S(30) * pi
# about_two: 1.999999999999581826
unchanged = 2 * exp(x) - about_two
xval = S(10)**-11
ref = unchanged.subs(x, xval).n(19) # 2.0418173913673213e-11
rewritten = optimize(2 * exp(x) - about_two, [expm1_opt])
# Unfortunately, we need to call ``.n()`` on our expressions before we hand them
# to ``ccode``, and we need to request a large number of significant digits.
# In this test, results converged for double precision when the following number
# of significant digits were chosen:
NUMBER_OF_DIGITS = 25 # TODO: this should ideally be automatically handled.
func_c = '''
#include <math.h>
double func_unchanged(double x) {
return %(unchanged)s;
}
double func_rewritten(double x) {
return %(rewritten)s;
}
''' % dict(unchanged=ccode(unchanged.n(NUMBER_OF_DIGITS)),
rewritten=ccode(rewritten.n(NUMBER_OF_DIGITS)))
func_pyx = '''
#cython: language_level=3
cdef extern double func_unchanged(double)
cdef extern double func_rewritten(double)
def py_unchanged(x):
return func_unchanged(x)
def py_rewritten(x):
return func_rewritten(x)
'''
with tempfile.TemporaryDirectory() as folder:
mod, info = compile_link_import_strings([('func.c', func_c),
('_func.pyx', func_pyx)],
build_dir=folder,
compile_kwargs=dict(std='c99'))
err_rewritten = abs(mod.py_rewritten(1e-11) - ref)
err_unchanged = abs(mod.py_unchanged(1e-11) - ref)
assert 1e-27 < err_rewritten < 1e-25 # highly accurate.
assert 1e-19 < err_unchanged < 1e-16 # quite poor.
def test_copying_function():
if not np:
skip("numpy not installed.")
if not has_c():
skip("No C compiler found.")
if not cython:
skip("Cython not found.")
info = None
with TemporaryDirectory() as folder:
mod, info = _render_compile_import(_mk_func1(), build_dir=folder)
inp = np.arange(10.0)
out = np.empty_like(inp)
mod._our_test_function(inp, out)
assert np.allclose(inp, out)
def test_copying_function():
if not np:
skip("numpy not installed.")
if not has_c():
skip("No C compiler found.")
if not cython:
skip("Cython not found.")
info = None
with TemporaryDirectory() as folder:
mod, info = _render_compile_import(_mk_func1(), build_dir=folder)
inp = np.arange(10.0)
out = np.empty_like(inp)
mod._our_test_function(inp, out)
assert np.allclose(inp, out)
def test_newtons_method_function__ccode_parameters():
args = x, A, k, p = sp.symbols('x A k p')
expr = A * sp.cos(k * x) - p * x**3
raises(ValueError, lambda: newtons_method_function(expr, x))
use_wurlitzer = wurlitzer
func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
if not has_c():
skip("No C compiler found.")
if not cython:
skip("cython not installed.")
compile_kw = dict(std='c99')
with tempfile.TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[('newton_par.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton_par.pyx',
("#cython: language_level={}\n".format("3") +
"cdef extern double newton(double, double, double, double)\n"
"def py_newton(x, A=1, k=1, p=1):\n"
" return newton(x, A, k, p)\n"))],
compile_kwargs=compile_kw,
build_dir=folder)
if use_wurlitzer:
with wurlitzer.pipes() as (out, err):
result = mod.py_newton(0.5)
else:
result = mod.py_newton(0.5)
assert abs(result - 0.865474033102) < 1e-12
if not use_wurlitzer:
skip(
"C-level output only tested when package 'wurlitzer' is available."
)
out, err = out.read(), err.read()
assert err == ''
assert out == """\
def test_newtons_method_function__ccode():
x = sp.Symbol('x', real=True)
expr = sp.cos(x) - x**3
func = newtons_method_function(expr, x)
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std='c99')
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings([
('newton.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton.pyx', ("cdef extern double newton(double)\n"
"def py_newton(x):\n"
" return newton(x)\n"))
], build_dir=folder, compile_kwargs=compile_kw)
assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
def test_compile_link_import_strings():
if not numpy:
skip("numpy not installed.")
if not cython:
skip("cython not installed.")
from sympy.utilities._compilation import has_c
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std='c99', include_dirs=[numpy.get_include()])
info = None
try:
mod, info = compile_link_import_strings(_sources1, compile_kwargs=compile_kw)
data = numpy.random.random(1024*1024*8) # 64 MB of RAM needed..
res_mod = mod.sigmoid(data)
res_npy = npy(data)
assert numpy.allclose(res_mod, res_npy)
finally:
if info and info['build_dir']:
shutil.rmtree(info['build_dir'])
def test_newtons_method_function__ccode():
x = sp.Symbol('x', real=True)
expr = sp.cos(x) - x**3
func = newtons_method_function(expr, x)
if not cython:
skip("cython not installed.")
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std='c99')
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings(
[('newton.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton.pyx', ("cdef extern double newton(double)\n"
"def py_newton(x):\n"
" return newton(x)\n"))],
build_dir=folder,
compile_kwargs=compile_kw)
assert abs(mod.py_newton(0.5) - 0.865474033102) < 1e-12
def test_compile_link_import_strings():
if not numpy:
skip("numpy not installed.")
if not cython:
skip("cython not installed.")
from sympy.utilities._compilation import has_c
if not has_c():
skip("No C compiler found.")
compile_kw = dict(std='c99', include_dirs=[numpy.get_include()])
info = None
try:
mod, info = compile_link_import_strings(_sources1, compile_kwargs=compile_kw)
data = numpy.random.random(1024*1024*8) # 64 MB of RAM needed..
res_mod = mod.sigmoid(data)
res_npy = npy(data)
assert numpy.allclose(res_mod, res_npy)
finally:
if info and info['build_dir']:
shutil.rmtree(info['build_dir'])
def test_newtons_method_function__ccode_parameters():
args = x, A, k, p = sp.symbols('x A k p')
expr = A*sp.cos(k*x) - p*x**3
raises(ValueError, lambda: newtons_method_function(expr, x))
use_wurlitzer = wurlitzer
func = newtons_method_function(expr, x, args, debug=use_wurlitzer)
if not has_c():
skip("No C compiler found.")
if not cython:
skip("cython not installed.")
compile_kw = dict(std='c99')
with TemporaryDirectory() as folder:
mod, info = compile_link_import_strings([
('newton_par.c', ('#include <math.h>\n'
'#include <stdio.h>\n') + ccode(func)),
('_newton_par.pyx', ("cdef extern double newton(double, double, double, double)\n"
"def py_newton(x, A=1, k=1, p=1):\n"
" return newton(x, A, k, p)\n"))
], compile_kwargs=compile_kw, build_dir=folder)
if use_wurlitzer:
with wurlitzer.pipes() as (out, err):
result = mod.py_newton(0.5)
else:
result = mod.py_newton(0.5)
assert abs(result - 0.865474033102) < 1e-12
if not use_wurlitzer:
skip("C-level output only tested when package 'wurlitzer' is available.")
out, err = out.read(), err.read()
assert err == ''
assert out == """\
