def test_output_arg_f():
from sympy import sin, cos, Equality
x, y, z = symbols("x,y,z")
r = Routine("foo", [Equality(y, sin(x)), cos(x)])
c = FCodeGen()
result = c.write([r], "test", header=False, empty=False)
assert result[0][0] == "test.f90"
assert result[0][1] == (
'REAL*8 function foo(x, y)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(out) :: y\n'
'y = sin(x)\n'
'foo = cos(x)\n'
'end function\n'
)
def test_cython_wrapper_outarg():
from sympy import Equality
x, y, z = symbols('x,y,z')
code_gen = CythonCodeWrapper(CCodeGen())
routine = Routine("test", Equality(z, x + y))
source = get_string(code_gen.dump_pyx, [routine])
expected = (
'cdef extern from "file.h":\n'
' void test(double x, double y, double &z)\n'
'def test_c(double x, double y):\n'
' cdef double z\n'
' test(x, y, z)\n'
' return z\n'
)
assert source == expected
def test_output_arg_c():
from sympy import sin, cos, Equality
x, y, z = symbols("x,y,z")
r = Routine("foo", [Equality(y, sin(x)), cos(x)])
c = CCodeGen()
result = c.write([r], "test", header=False, empty=False)
assert result[0][0] == "test.c"
expected = (
'#include "test.h"\n'
'#include <math.h>\n'
'double foo(double x, double &y) {\n'
' y = sin(x);\n'
' return cos(x);\n'
'}\n'
)
assert result[0][1] == expected
def test_simple_f_code():
x,y,z = symbols('x,y,z')
expr = (x+y)*z
routine = Routine("test", expr)
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = (
"REAL*8 function test(x, y, z)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(in) :: z\n"
"test = z*(x + y)\n"
"end function\n"
)
assert source == expected
def test_f_code_argument_order():
x, y, z = symbols('x,y,z')
expr = x + y
routine = Routine("test", expr, argument_sequence=[z, x, y])
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = (
"REAL*8 function test(z, x, y)\n"
"implicit none\n"
"REAL*8, intent(in) :: z\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"test = x + y\n"
"end function\n"
)
assert source == expected
def is_feasible(language, commands):
# This test should always work, otherwise the compiler is not present.
routine = Routine("test", x)
numerical_tests = [
("test", (1.0, ), 1.0, 1e-15),
("test", (-1.0, ), -1.0, 1e-15),
]
try:
run_test("is_feasible", [routine],
numerical_tests,
language,
commands,
friendly=False)
return True
except AssertionError:
return False
def test_inline_function():
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m = symbols('n m', integer=True)
A, x, y = map(IndexedBase, 'Axy')
i = Idx('i', m)
p = FCodeGen()
func = implemented_function('func', Lambda(n, n * (n + 1)))
routine = Routine('test_inline', Eq(y[i], func(x[i])))
code = get_string(p.dump_f95, [routine])
expected = ('subroutine test_inline(m, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'REAL*8, intent(in), dimension(1:m) :: x\n'
'REAL*8, intent(out), dimension(1:m) :: y\n'
'INTEGER*4 :: i\n'
'do i = 1, m\n'
' y(i) = x(i)*(1 + x(i))\n'
'end do\n'
'end subroutine\n')
assert code == expected
def test_dummy_loops_c():
from sympy.tensor import IndexedBase, Idx
# the following line could also be
# [Dummy(s, integer=True) for s in 'im']
# or [Dummy(integer=True) for s in 'im']
i, m = symbols('i m', integer=True, cls=Dummy)
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx(i, m)
expected = (
'#include "file.h"\n'
'#include <math.h>\n'
'void test_dummies(int m_%(mno)i, double *x, double *y) {\n'
' for (int i_%(ino)i=0; i_%(ino)i<m_%(mno)i; i_%(ino)i++){\n'
' y[i_%(ino)i] = x[i_%(ino)i];\n'
' }\n'
'}\n'
) % {'ino': i.label.dummy_index, 'mno': m.dummy_index}
r = Routine('test_dummies', Eq(y[i], x[i]))
c = CCodeGen()
code = get_string(c.dump_c, [r])
assert code == expected
def test_f_code_call_signature_wrap():
# Issue #7934
x = symbols('x:20')
expr = 0
for sym in x:
expr += sym
routine = Routine("test", expr)
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = """\
REAL*8 function test(x0, x1, x10, x11, x12, x13, x14, x15, x16, x17, x18, &
x19, x2, x3, x4, x5, x6, x7, x8, x9)
implicit none
REAL*8, intent(in) :: x0
REAL*8, intent(in) :: x1
REAL*8, intent(in) :: x10
REAL*8, intent(in) :: x11
REAL*8, intent(in) :: x12
REAL*8, intent(in) :: x13
REAL*8, intent(in) :: x14
REAL*8, intent(in) :: x15
REAL*8, intent(in) :: x16
REAL*8, intent(in) :: x17
REAL*8, intent(in) :: x18
REAL*8, intent(in) :: x19
REAL*8, intent(in) :: x2
REAL*8, intent(in) :: x3
REAL*8, intent(in) :: x4
REAL*8, intent(in) :: x5
REAL*8, intent(in) :: x6
REAL*8, intent(in) :: x7
REAL*8, intent(in) :: x8
REAL*8, intent(in) :: x9
test = x0 + x1 + x10 + x11 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + &
x19 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9
end function
"""
assert source == expected
def _build_routine(self, name):
expr = getattr(self, name)
out = sympy.MatrixSymbol("out", *expr.shape)
routine = Routine(
name,
[
InputArgument(self.y, dimensions=_mat_sym_dims(self.y)),
InputArgument(self.p, dimensions=_mat_sym_dims(self.p)),
InputArgument(self.e, dimensions=_mat_sym_dims(self.e)),
InputArgument(self.o, dimensions=_mat_sym_dims(self.o)),
OutputArgument(
out,
out,
expr,
datatype=default_datatypes["float"],
dimensions=_mat_sym_dims(out),
),
],
[],
[],
[],
)
return routine
def test_no_results_f():
raises(ValueError, lambda: Routine("test", []))
def autowrap(expr,
language='F95',
backend='f2py',
tempdir=None,
args=None,
flags=[],
verbose=False,
helpers=[]):
"""Generates python callable binaries based on the math expression.
expr
The SymPy expression that should be wrapped as a binary routine
:Optional arguments:
language
The programming language to use, currently 'C' or 'F95'
backend
The wrapper backend to use, currently f2py or Cython
tempdir
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
Sequence of the formal parameters of the generated code, if ommited the
function signature is determined by the code generator.
flags
Additional option flags that will be passed to the backend
verbose
If True, autowrap will not mute the command line backends. This can be
helpful for debugging.
helpers
Used to define auxillary expressions needed for the main expr. If the
main expression need to do call a specialized function it should be put
in the ``helpers`` list. Autowrap will then make sure that the compiled
main expression can link to the helper routine. Items should be tuples
with (<funtion_name>, <sympy_expression>, <arguments>). It is
mandatory to supply an argument sequence to helper routines.
>>> from sympy.abc import x, y, z
>>> from sympy.utilities.autowrap import autowrap
>>> expr = ((x - y + z)**(13)).expand()
>>> binary_func = autowrap(expr) # doctest: +SKIP
>>> binary_func(1, 4, 2) # doctest: +SKIP
-1.0
"""
code_generator = get_code_generator(language, "autowrap")
CodeWrapperClass = _get_code_wrapper_class(backend)
code_wrapper = CodeWrapperClass(code_generator, tempdir, flags, verbose)
try:
routine = Routine('autofunc', expr, args)
except CodeGenArgumentListError, e:
# if all missing arguments are for pure output, we simply attach them
# at the end and try again, because the wrappers will silently convert
# them to return values anyway.
new_args = []
for missing in e.missing_args:
if not isinstance(missing, OutputArgument):
raise
new_args.append(missing.name)
routine = Routine('autofunc', expr, args + new_args)
try:
routine = Routine('autofunc', expr, args)
except CodeGenArgumentListError, e:
# if all missing arguments are for pure output, we simply attach them
# at the end and try again, because the wrappers will silently convert
# them to return values anyway.
new_args = []
for missing in e.missing_args:
if not isinstance(missing, OutputArgument):
raise
new_args.append(missing.name)
routine = Routine('autofunc', expr, args + new_args)
helps = []
for name, expr, args in helpers:
helps.append(Routine(name, expr, args))
return code_wrapper.wrap_code(routine, helpers=helps)
def binary_function(symfunc, expr, **kwargs):
"""Returns a sympy function with expr as binary implementation
This is a convenience function that automates the steps needed to
autowrap the SymPy expression and attaching it to a Function object
with implemented_function().
>>> from sympy.abc import x, y, z
>>> from sympy.utilities.autowrap import binary_function
>>> expr = ((x - y)**(25)).expand()
>>> f = binary_function('f', expr) # doctest: +SKIP
def test_ufuncify_source():
from sympy import Equality
x, y, z = symbols('x,y,z')
code_wrapper = UfuncifyCodeWrapper(CCodeGen("ufuncify"))
CodeWrapper._module_counter = 0
routine = Routine("test", x + y + z)
source = get_string(code_wrapper.dump_c, [routine])
expected = """\
#include "Python.h"
#include "math.h"
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/halffloat.h"
#include "file.h"
static PyMethodDef wrapper_module_0Methods[] = {
{NULL, NULL, 0, NULL}
};
static void test_ufunc(char **args, npy_intp *dimensions, npy_intp* steps, void* data)
{
npy_intp i;
npy_intp n = dimensions[0];
char *in0 = args[0];
char *in1 = args[1];
char *in2 = args[2];
char *out1 = args[3];
npy_intp in0_step = steps[0];
npy_intp in1_step = steps[1];
npy_intp in2_step = steps[2];
npy_intp out1_step = steps[3];
for (i = 0; i < n; i++) {
*((double *)out1) = test(*(double *)in0, *(double *)in1, *(double *)in2);
in0 += in0_step;
in1 += in1_step;
in2 += in2_step;
out1 += out1_step;
}
}
PyUFuncGenericFunction test_funcs[1] = {&test_ufunc};
static char test_types[4] = {NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE};
static void *test_data[1] = {NULL};
#if PY_VERSION_HEX >= 0x03000000
static struct PyModuleDef moduledef = {
PyModuleDef_HEAD_INIT,
"wrapper_module_0",
NULL,
-1,
wrapper_module_0Methods,
NULL,
NULL,
NULL,
NULL
};
PyMODINIT_FUNC PyInit_wrapper_module_0(void)
{
PyObject *m, *d;
PyObject *ufunc0;
m = PyModule_Create(&moduledef);
if (!m) {
return NULL;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
ufunc0 = PyUFunc_FromFuncAndData(test_funcs, test_data, test_types, 1, 3, 1,
PyUFunc_None, "wrapper_module_0", "Created in SymPy with Ufuncify", 0);
PyDict_SetItemString(d, "test", ufunc0);
Py_DECREF(ufunc0);
return m;
}
#else
PyMODINIT_FUNC initwrapper_module_0(void)
{
PyObject *m, *d;
PyObject *ufunc0;
m = Py_InitModule("wrapper_module_0", wrapper_module_0Methods);
if (m == NULL) {
return;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
ufunc0 = PyUFunc_FromFuncAndData(test_funcs, test_data, test_types, 1, 3, 1,
PyUFunc_None, "wrapper_module_0", "Created in SymPy with Ufuncify", 0);
PyDict_SetItemString(d, "test", ufunc0);
Py_DECREF(ufunc0);
}
#endif"""
assert source == expected
def routine(self, name, expr, argument_sequence, global_vars):
"""Creates an Routine object that is appropriate for this language.
This implementation is appropriate for at least C/Fortran. Subclasses
can override this if necessary.
Here, we assume at most one return value (the l-value) which must be
scalar. Additional outputs are OutputArguments (e.g., pointers on
right-hand-side or pass-by-reference). Matrices are always returned
via OutputArguments. If ``argument_sequence`` is None, arguments will
be ordered alphabetically, but with all InputArguments first, and then
OutputArgument and InOutArguments.
This implementation is almost the same as the CodeGen class, but
expensive calls to Basic.atoms() have been replaced with
cheaper equivalents.
"""
if is_sequence(expr) and not isinstance(expr, (MatrixBase, MatrixExpr)):
if not expr:
raise ValueError("No expression given")
expressions = Tuple(*expr)
else:
expressions = Tuple(expr)
expr_free_symbols = expressions.free_symbols
# local variables
local_vars = {i.label for i in expr_free_symbols if isinstance(i, Idx)}
# global variables
global_vars = set() if global_vars is None else set(global_vars)
# symbols that should be arguments
symbols = expr_free_symbols - local_vars - global_vars
new_symbols = set([])
new_symbols.update(symbols)
for symbol in symbols:
if isinstance(symbol, Idx):
new_symbols.remove(symbol)
new_symbols.update(symbol.args[1].free_symbols)
if isinstance(symbol, Indexed):
new_symbols.remove(symbol)
symbols = new_symbols
# Decide whether to use output argument or return value
return_val = []
output_args = []
for expr in expressions:
if isinstance(expr, Equality):
out_arg = expr.lhs
expr = expr.rhs
if isinstance(out_arg, Indexed):
dims = tuple([ (S.Zero, dim - 1) for dim in out_arg.shape])
symbol = out_arg.base.label
elif isinstance(out_arg, Symbol):
dims = []
symbol = out_arg
elif isinstance(out_arg, MatrixSymbol):
dims = tuple([ (S.Zero, dim - 1) for dim in out_arg.shape])
symbol = out_arg
else:
raise CodeGenError("Only Indexed, Symbol, or MatrixSymbol "
"can define output arguments.")
if expr.has(symbol):
output_args.append(
InOutArgument(symbol, out_arg, expr, dimensions=dims))
else:
output_args.append(
OutputArgument(symbol, out_arg, expr, dimensions=dims))
# avoid duplicate arguments
symbols.remove(symbol)
elif isinstance(expr, (ImmutableMatrix, MatrixSlice)):
# Create a "dummy" MatrixSymbol to use as the Output arg
out_arg = MatrixSymbol('out_%s' % abs(hash(expr)), *expr.shape)
dims = tuple([(S.Zero, dim - 1) for dim in out_arg.shape])
output_args.append(
OutputArgument(out_arg, out_arg, expr, dimensions=dims))
else:
return_val.append(Result(expr))
arg_list = []
# setup input argument list
array_symbols = {}
for array in [i for i in expr_free_symbols if isinstance(i, Indexed)]:
array_symbols[array.base.label] = array
for array in [i for i in expr_free_symbols if isinstance(i, MatrixSymbol)]:
array_symbols[array] = array
for symbol in sorted(symbols, key=str):
if symbol in array_symbols:
dims = []
array = array_symbols[symbol]
for dim in array.shape:
dims.append((S.Zero, dim - 1))
metadata = {'dimensions': dims}
else:
metadata = {}
arg_list.append(InputArgument(symbol, **metadata))
output_args.sort(key=lambda x: str(x.name))
arg_list.extend(output_args)
if argument_sequence is not None:
# if the user has supplied IndexedBase instances, we'll accept that
new_sequence = []
for arg in argument_sequence:
if isinstance(arg, IndexedBase):
new_sequence.append(arg.label)
else:
new_sequence.append(arg)
argument_sequence = new_sequence
missing = [x for x in arg_list if x.name not in argument_sequence]
if missing:
msg = "Argument list didn't specify: {0} "
msg = msg.format(", ".join([str(m.name) for m in missing]))
raise CodeGenArgumentListError(msg, missing)
# create redundant arguments to produce the requested sequence
name_arg_dict = {x.name: x for x in arg_list}
new_args = []
for symbol in argument_sequence:
try:
new_args.append(name_arg_dict[symbol])
except KeyError:
new_args.append(InputArgument(symbol))
arg_list = new_args
return Routine(name, arg_list, return_val, local_vars, global_vars)
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 SymPy 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>, <sympy_expression>, <arguments>). It
is mandatory to supply an argument sequence to helper routines.
Note
----
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 sympy.utilities.autowrap import ufuncify
>>> from sympy.abc import x, y
>>> import numpy as np
>>> f = ufuncify((x, y), y + x**2)
>>> type(f)
numpy.ufunc
>>> 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):
File "<stdin>", line 1, in <module>
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, 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 = Routine('autofunc', expr, args)
helps = []
for name, expr, args in helpers:
helps.append(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, args, flags, verbose, helpers)
def autowrap(expr,
language=None,
backend='f2py',
tempdir=None,
args=None,
flags=None,
verbose=False,
helpers=None):
"""Generates python callable binaries based on the math expression.
Parameters
----------
expr
The SymPy 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 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 (<funtion_name>, <sympy_expression>, <arguments>). It
is mandatory to supply an argument sequence to helper routines.
>>> from sympy.abc import x, y, z
>>> from sympy.utilities.autowrap import autowrap
>>> expr = ((x - y + z)**(13)).expand()
>>> binary_func = autowrap(expr)
>>> binary_func(1, 4, 2)
-1.0
"""
if language:
_validate_backend_language(backend, language)
else:
language = _infer_language(backend)
helpers = helpers if helpers else ()
flags = flags if flags else ()
code_generator = get_code_generator(language, "autowrap")
CodeWrapperClass = _get_code_wrapper_class(backend)
code_wrapper = CodeWrapperClass(code_generator, tempdir, flags, verbose)
try:
routine = Routine('autofunc', expr, args)
except CodeGenArgumentListError as e:
# if all missing arguments are for pure output, we simply attach them
# at the end and try again, because the wrappers will silently convert
# them to return values anyway.
new_args = []
for missing in e.missing_args:
if not isinstance(missing, OutputArgument):
raise
new_args.append(missing.name)
routine = Routine('autofunc', expr, args + new_args)
helps = []
for name, expr, args in helpers:
helps.append(Routine(name, expr, args))
return code_wrapper.wrap_code(routine, helpers=helps)