"""
Python code printers
This module contains Python code printers for plain Python as well as NumPy & SciPy enabled code.
"""
from collections import defaultdict
from itertools import chain
from sympy.core import S
from sympy.core.mod import Mod
from .precedence import precedence
from .codeprinter import CodePrinter
_kw = {
'and', 'as', 'assert', 'break', 'class', 'continue', 'def', 'del', 'elif',
'else', 'except', 'finally', 'for', 'from', 'global', 'if', 'import', 'in',
'is', 'lambda', 'not', 'or', 'pass', 'raise', 'return', 'try', 'while',
'with', 'yield', 'None', 'False', 'nonlocal', 'True'
}
_known_functions = {
'Abs': 'abs',
'Min': 'min',
'Max': 'max',
}
_known_functions_math = {
'acos': 'acos',
'acosh': 'acosh',
'asin': 'asin',
'asinh': 'asinh',
'atan': 'atan',
'atan2': 'atan2',
'atanh': 'atanh',
'ceiling': 'ceil',
'cos': 'cos',
'cosh': 'cosh',
'erf': 'erf',
'erfc': 'erfc',
'exp': 'exp',
'expm1': 'expm1',
'factorial': 'factorial',
'floor': 'floor',
'gamma': 'gamma',
'hypot': 'hypot',
'loggamma': 'lgamma',
'log': 'log',
'ln': 'log',
'log10': 'log10',
'log1p': 'log1p',
'log2': 'log2',
'sin': 'sin',
'sinh': 'sinh',
'Sqrt': 'sqrt',
'tan': 'tan',
'tanh': 'tanh'
} # Not used from ``math``: [copysign isclose isfinite isinf isnan ldexp frexp pow modf
# radians trunc fmod fsum gcd degrees fabs]
_known_constants_math = {
'Exp1': 'e',
'Pi': 'pi',
'E': 'e',
'Infinity': 'inf',
'NaN': 'nan',
'ComplexInfinity': 'nan'
}
def _print_known_func(self, expr):
known = self.known_functions[expr.__class__.__name__]
return '{name}({args})'.format(name=self._module_format(known),
args=', '.join((self._print(arg) for arg in expr.args)))
def _print_known_const(self, expr):
known = self.known_constants[expr.__class__.__name__]
return self._module_format(known)
class AbstractPythonCodePrinter(CodePrinter):
printmethod = "_pythoncode"
language = "Python"
reserved_words = _kw
modules = None # initialized to a set in __init__
tab = ' '
_kf = dict(chain(
_known_functions.items(),
[(k, 'math.' + v) for k, v in _known_functions_math.items()]
))
_kc = {k: 'math.'+v for k, v in _known_constants_math.items()}
_operators = {'and': 'and', 'or': 'or', 'not': 'not'}
_default_settings = dict(
CodePrinter._default_settings,
user_functions={},
precision=17,
inline=True,
fully_qualified_modules=True,
contract=False,
standard='python3',
)
def __init__(self, settings=None):
super().__init__(settings)
# Python standard handler
std = self._settings['standard']
if std is None:
import sys
std = 'python{}'.format(sys.version_info.major)
if std != 'python3':
raise ValueError('Only Python 3 is supported.')
self.standard = std
self.module_imports = defaultdict(set)
# Known functions and constants handler
self.known_functions = dict(self._kf, **(settings or {}).get(
'user_functions', {}))
self.known_constants = dict(self._kc, **(settings or {}).get(
'user_constants', {}))
def _declare_number_const(self, name, value):
return "%s = %s" % (name, value)
def _module_format(self, fqn, register=True):
parts = fqn.split('.')
if register and len(parts) > 1:
self.module_imports['.'.join(parts[:-1])].add(parts[-1])
if self._settings['fully_qualified_modules']:
return fqn
else:
return fqn.split('(')[0].split('[')[0].split('.')[-1]
def _format_code(self, lines):
return lines
def _get_statement(self, codestring):
return "{}".format(codestring)
def _get_comment(self, text):
return " # {}".format(text)
def _expand_fold_binary_op(self, op, args):
"""
This method expands a fold on binary operations.
``functools.reduce`` is an example of a folded operation.
For example, the expression
`A + B + C + D`
is folded into
`((A + B) + C) + D`
"""
if len(args) == 1:
return self._print(args[0])
else:
return "%s(%s, %s)" % (
self._module_format(op),
self._expand_fold_binary_op(op, args[:-1]),
self._print(args[-1]),
)
def _expand_reduce_binary_op(self, op, args):
"""
This method expands a reductin on binary operations.
Notice: this is NOT the same as ``functools.reduce``.
For example, the expression
`A + B + C + D`
is reduced into:
`(A + B) + (C + D)`
"""
if len(args) == 1:
return self._print(args[0])
else:
N = len(args)
Nhalf = N // 2
return "%s(%s, %s)" % (
self._module_format(op),
self._expand_reduce_binary_op(args[:Nhalf]),
self._expand_reduce_binary_op(args[Nhalf:]),
)
def _print_NaN(self, expr):
return "float('nan')"
def _print_Infinity(self, expr):
return "float('inf')"
def _print_NegativeInfinity(self, expr):
return "float('-inf')"
def _print_ComplexInfinity(self, expr):
return self._print_NaN(expr)
def _print_Mod(self, expr):
PREC = precedence(expr)
return ('{} % {}'.format(*(self.parenthesize(x, PREC) for x in expr.args)))
def _print_Piecewise(self, expr):
result = []
i = 0
for arg in expr.args:
e = arg.expr
c = arg.cond
if i == 0:
result.append('(')
result.append('(')
result.append(self._print(e))
result.append(')')
result.append(' if ')
result.append(self._print(c))
result.append(' else ')
i += 1
result = result[:-1]
if result[-1] == 'True':
result = result[:-2]
result.append(')')
else:
result.append(' else None)')
return ''.join(result)
def _print_Relational(self, expr):
"Relational printer for Equality and Unequality"
op = {
'==' :'equal',
'!=' :'not_equal',
'<' :'less',
'<=' :'less_equal',
'>' :'greater',
'>=' :'greater_equal',
}
if expr.rel_op in op:
lhs = self._print(expr.lhs)
rhs = self._print(expr.rhs)
return '({lhs} {op} {rhs})'.format(op=expr.rel_op, lhs=lhs, rhs=rhs)
return super()._print_Relational(expr)
def _print_ITE(self, expr):
from sympy.functions.elementary.piecewise import Piecewise
return self._print(expr.rewrite(Piecewise))
def _print_Sum(self, expr):
loops = (
'for {i} in range({a}, {b}+1)'.format(
i=self._print(i),
a=self._print(a),
b=self._print(b))
for i, a, b in expr.limits)
return '(builtins.sum({function} {loops}))'.format(
function=self._print(expr.function),
loops=' '.join(loops))
def _print_ImaginaryUnit(self, expr):
return '1j'
def _print_KroneckerDelta(self, expr):
a, b = expr.args
return '(1 if {a} == {b} else 0)'.format(
a = self._print(a),
b = self._print(b)
)
def _print_MatrixBase(self, expr):
name = expr.__class__.__name__
func = self.known_functions.get(name, name)
return "%s(%s)" % (func, self._print(expr.tolist()))
_print_SparseRepMatrix = \
_print_MutableSparseMatrix = \
_print_ImmutableSparseMatrix = \
_print_Matrix = \
_print_DenseMatrix = \
_print_MutableDenseMatrix = \
_print_ImmutableMatrix = \
_print_ImmutableDenseMatrix = \
lambda self, expr: self._print_MatrixBase(expr)
def _indent_codestring(self, codestring):
return '\n'.join([self.tab + line for line in codestring.split('\n')])
def _print_FunctionDefinition(self, fd):
body = '\n'.join((self._print(arg) for arg in fd.body))
return "def {name}({parameters}):\n{body}".format(
name=self._print(fd.name),
parameters=', '.join([self._print(var.symbol) for var in fd.parameters]),
body=self._indent_codestring(body)
)
def _print_While(self, whl):
body = '\n'.join((self._print(arg) for arg in whl.body))
return "while {cond}:\n{body}".format(
cond=self._print(whl.condition),
body=self._indent_codestring(body)
)
def _print_Declaration(self, decl):
return '%s = %s' % (
self._print(decl.variable.symbol),
self._print(decl.variable.value)
)
def _print_Return(self, ret):
arg, = ret.args
return 'return %s' % self._print(arg)
def _print_Print(self, prnt):
print_args = ', '.join((self._print(arg) for arg in prnt.print_args))
if prnt.format_string != None: # Must be '!= None', cannot be 'is not None'
print_args = '{} % ({})'.format(
self._print(prnt.format_string), print_args)
if prnt.file != None: # Must be '!= None', cannot be 'is not None'
print_args += ', file=%s' % self._print(prnt.file)
return 'print(%s)' % print_args
def _print_Stream(self, strm):
if str(strm.name) == 'stdout':
return self._module_format('sys.stdout')
elif str(strm.name) == 'stderr':
return self._module_format('sys.stderr')
else:
return self._print(strm.name)
def _print_NoneToken(self, arg):
return 'None'
def _hprint_Pow(self, expr, rational=False, sqrt='math.sqrt'):
"""Printing helper function for ``Pow``
Notes
=====
This preprocesses the ``sqrt`` as math formatter and prints division
Examples
========
>>> from sympy import sqrt
>>> from sympy.printing.pycode import PythonCodePrinter
>>> from sympy.abc import x
Python code printer automatically looks up ``math.sqrt``.
>>> printer = PythonCodePrinter()
>>> printer._hprint_Pow(sqrt(x), rational=True)
'x**(1/2)'
>>> printer._hprint_Pow(sqrt(x), rational=False)
'math.sqrt(x)'
>>> printer._hprint_Pow(1/sqrt(x), rational=True)
'x**(-1/2)'
>>> printer._hprint_Pow(1/sqrt(x), rational=False)
'1/math.sqrt(x)'
>>> printer._hprint_Pow(1/x, rational=False)
'1/x'
>>> printer._hprint_Pow(1/x, rational=True)
'x**(-1)'
Using sqrt from numpy or mpmath
>>> printer._hprint_Pow(sqrt(x), sqrt='numpy.sqrt')
'numpy.sqrt(x)'
>>> printer._hprint_Pow(sqrt(x), sqrt='mpmath.sqrt')
'mpmath.sqrt(x)'
See Also
========
sympy.printing.str.StrPrinter._print_Pow
"""
PREC = precedence(expr)
if expr.exp == S.Half and not rational:
func = self._module_format(sqrt)
arg = self._print(expr.base)
return '{func}({arg})'.format(func=func, arg=arg)
if expr.is_commutative and not rational:
if -expr.exp is S.Half:
func = self._module_format(sqrt)
num = self._print(S.One)
arg = self._print(expr.base)
return f"{num}/{func}({arg})"
if expr.exp is S.NegativeOne:
num = self._print(S.One)
arg = self.parenthesize(expr.base, PREC, strict=False)
return f"{num}/{arg}"
base_str = self.parenthesize(expr.base, PREC, strict=False)
exp_str = self.parenthesize(expr.exp, PREC, strict=False)
return "{}**{}".format(base_str, exp_str)
class ArrayPrinter:
def _arrayify(self, indexed):
from sympy.tensor.array.expressions.from_indexed_to_array import convert_indexed_to_array
try:
return convert_indexed_to_array(indexed)
except Exception:
return indexed
def _get_einsum_string(self, subranks, contraction_indices):
letters = self._get_letter_generator_for_einsum()
contraction_string = ""
counter = 0
d = {j: min(i) for i in contraction_indices for j in i}
indices = []
for rank_arg in subranks:
lindices = []
for i in range(rank_arg):
if counter in d:
lindices.append(d[counter])
else:
lindices.append(counter)
counter += 1
indices.append(lindices)
mapping = {}
letters_free = []
letters_dum = []
for i in indices:
for j in i:
if j not in mapping:
l = next(letters)
mapping[j] = l
else:
l = mapping[j]
contraction_string += l
if j in d:
if l not in letters_dum:
letters_dum.append(l)
else:
letters_free.append(l)
contraction_string += ","
contraction_string = contraction_string[:-1]
return contraction_string, letters_free, letters_dum
def _get_letter_generator_for_einsum(self):
for i in range(97, 123):
yield chr(i)
for i in range(65, 91):
yield chr(i)
raise ValueError("out of letters")
def _print_ArrayTensorProduct(self, expr):
letters = self._get_letter_generator_for_einsum()
contraction_string = ",".join(["".join([next(letters) for j in range(i)]) for i in expr.subranks])
return '%s("%s", %s)' % (
self._module_format(self._module + "." + self._einsum),
contraction_string,
", ".join([self._print(arg) for arg in expr.args])
)
def _print_ArrayContraction(self, expr):
from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
base = expr.expr
contraction_indices = expr.contraction_indices
if isinstance(base, ArrayTensorProduct):
elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
ranks = base.subranks
else:
elems = self._print(base)
ranks = [len(base.shape)]
contraction_string, letters_free, letters_dum = self._get_einsum_string(ranks, contraction_indices)
if not contraction_indices:
return self._print(base)
if isinstance(base, ArrayTensorProduct):
elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
else:
elems = self._print(base)
return "%s(\"%s\", %s)" % (
self._module_format(self._module + "." + self._einsum),
"{}->{}".format(contraction_string, "".join(sorted(letters_free))),
elems,
)
def _print_ArrayDiagonal(self, expr):
from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
diagonal_indices = list(expr.diagonal_indices)
if isinstance(expr.expr, ArrayTensorProduct):
subranks = expr.expr.subranks
elems = expr.expr.args
else:
subranks = expr.subranks
elems = [expr.expr]
diagonal_string, letters_free, letters_dum = self._get_einsum_string(subranks, diagonal_indices)
elems = [self._print(i) for i in elems]
return '%s("%s", %s)' % (
self._module_format(self._module + "." + self._einsum),
"{}->{}".format(diagonal_string, "".join(letters_free+letters_dum)),
", ".join(elems)
)
def _print_PermuteDims(self, expr):
return "%s(%s, %s)" % (
self._module_format(self._module + "." + self._transpose),
self._print(expr.expr),
self._print(expr.permutation.array_form),
)
def _print_ArrayAdd(self, expr):
return self._expand_fold_binary_op(self._module + "." + self._add, expr.args)
def _print_OneArray(self, expr):
return "%s((%s,))" % (
self._module_format(self._module+ "." + self._ones),
','.join(map(self._print,expr.args))
)
def _print_ZeroArray(self, expr):
return "%s((%s,))" % (
self._module_format(self._module+ "." + self._zeros),
','.join(map(self._print,expr.args))
)
def _print_Assignment(self, expr):
#XXX: maybe this needs to happen at a higher level e.g. at _print or
#doprint?
lhs = self._print(self._arrayify(expr.lhs))
rhs = self._print(self._arrayify(expr.rhs))
return "%s = %s" % ( lhs, rhs )
def _print_IndexedBase(self, expr):
return self._print_ArraySymbol(expr)
class PythonCodePrinter(AbstractPythonCodePrinter):
def _print_sign(self, e):
return '(0.0 if {e} == 0 else {f}(1, {e}))'.format(
f=self._module_format('math.copysign'), e=self._print(e.args[0]))
def _print_Not(self, expr):
PREC = precedence(expr)
return self._operators['not'] + self.parenthesize(expr.args[0], PREC)
def _print_Indexed(self, expr):
base = expr.args[0]
index = expr.args[1:]
return "{}[{}]".format(str(base), ", ".join([self._print(ind) for ind in index]))
def _print_Pow(self, expr, rational=False):
return self._hprint_Pow(expr, rational=rational)
def _print_Rational(self, expr):
return '{}/{}'.format(expr.p, expr.q)
def _print_Half(self, expr):
return self._print_Rational(expr)
def _print_frac(self, expr):
return self._print_Mod(Mod(expr.args[0], 1))
def _print_Symbol(self, expr):
name = super()._print_Symbol(expr)
if name in self.reserved_words:
if self._settings['error_on_reserved']:
msg = ('This expression includes the symbol "{}" which is a '
'reserved keyword in this language.')
raise ValueError(msg.format(name))
return name + self._settings['reserved_word_suffix']
elif '{' in name: # Remove curly braces from subscripted variables
return name.replace('{', '').replace('}', '')
else:
return name
_print_lowergamma = CodePrinter._print_not_supported
_print_uppergamma = CodePrinter._print_not_supported
_print_fresnelc = CodePrinter._print_not_supported
_print_fresnels = CodePrinter._print_not_supported
for k in PythonCodePrinter._kf:
setattr(PythonCodePrinter, '_print_%s' % k, _print_known_func)
for k in _known_constants_math:
setattr(PythonCodePrinter, '_print_%s' % k, _print_known_const)
def pycode(expr, **settings):
""" Converts an expr to a string of Python code
Parameters
==========
expr : Expr
A SymPy expression.
fully_qualified_modules : bool
Whether or not to write out full module names of functions
(``math.sin`` vs. ``sin``). default: ``True``.
standard : str or None, optional
Only 'python3' (default) is supported.
This parameter may be removed in the future.
Examples
========
>>> from sympy import pycode, tan, Symbol
>>> pycode(tan(Symbol('x')) + 1)
'math.tan(x) + 1'
"""
return PythonCodePrinter(settings).doprint(expr)
_not_in_mpmath = 'log1p log2'.split()
_in_mpmath = [(k, v) for k, v in _known_functions_math.items() if k not in _not_in_mpmath]
_known_functions_mpmath = dict(_in_mpmath, **{
'beta': 'beta',
'frac': 'frac',
'fresnelc': 'fresnelc',
'fresnels': 'fresnels',
'sign': 'sign',
'loggamma': 'loggamma',
'hyper': 'hyper',
'meijerg': 'meijerg',
'besselj': 'besselj',
'bessely': 'bessely',
'besseli': 'besseli',
'besselk': 'besselk',
})
_known_constants_mpmath = {
'Exp1': 'e',
'Pi': 'pi',
'GoldenRatio': 'phi',
'EulerGamma': 'euler',
'Catalan': 'catalan',
'NaN': 'nan',
'Infinity': 'inf',
'NegativeInfinity': 'ninf'
}
def _unpack_integral_limits(integral_expr):
""" helper function for _print_Integral that
- accepts an Integral expression
- returns a tuple of
- a list variables of integration
- a list of tuples of the upper and lower limits of integration
"""
integration_vars = []
limits = []
for integration_range in integral_expr.limits:
if len(integration_range) == 3:
integration_var, lower_limit, upper_limit = integration_range
else:
raise NotImplementedError("Only definite integrals are supported")
integration_vars.append(integration_var)
limits.append((lower_limit, upper_limit))
return integration_vars, limits
class MpmathPrinter(PythonCodePrinter):
"""
Lambda printer for mpmath which maintains precision for floats
"""
printmethod = "_mpmathcode"
language = "Python with mpmath"
_kf = dict(chain(
_known_functions.items(),
[(k, 'mpmath.' + v) for k, v in _known_functions_mpmath.items()]
))
_kc = {k: 'mpmath.'+v for k, v in _known_constants_mpmath.items()}
def _print_Float(self, e):
# XXX: This does not handle setting mpmath.mp.dps. It is assumed that
# the caller of the lambdified function will have set it to sufficient
# precision to match the Floats in the expression.
# Remove 'mpz' if gmpy is installed.
args = str(tuple(map(int, e._mpf_)))
return '{func}({args})'.format(func=self._module_format('mpmath.mpf'), args=args)
def _print_Rational(self, e):
return "{func}({p})/{func}({q})".format(
func=self._module_format('mpmath.mpf'),
q=self._print(e.q),
p=self._print(e.p)
)
def _print_Half(self, e):
return self._print_Rational(e)
def _print_uppergamma(self, e):
return "{}({}, {}, {})".format(
self._module_format('mpmath.gammainc'),
self._print(e.args[0]),
self._print(e.args[1]),
self._module_format('mpmath.inf'))
def _print_lowergamma(self, e):
return "{}({}, 0, {})".format(
self._module_format('mpmath.gammainc'),
self._print(e.args[0]),
self._print(e.args[1]))
def _print_log2(self, e):
return '{0}({1})/{0}(2)'.format(
self._module_format('mpmath.log'), self._print(e.args[0]))
def _print_log1p(self, e):
return '{}({})'.format(
self._module_format('mpmath.log1p'), self._print(e.args[0]))
def _print_Pow(self, expr, rational=False):
return self._hprint_Pow(expr, rational=rational, sqrt='mpmath.sqrt')
def _print_Integral(self, e):
integration_vars, limits = _unpack_integral_limits(e)
return "{}(lambda {}: {}, {})".format(
self._module_format("mpmath.quad"),
", ".join(map(self._print, integration_vars)),
self._print(e.args[0]),
", ".join("(%s, %s)" % tuple(map(self._print, l)) for l in limits))
for k in MpmathPrinter._kf:
setattr(MpmathPrinter, '_print_%s' % k, _print_known_func)
for k in _known_constants_mpmath:
setattr(MpmathPrinter, '_print_%s' % k, _print_known_const)
class SymPyPrinter(AbstractPythonCodePrinter):
language = "Python with SymPy"
def _print_Function(self, expr):
mod = expr.func.__module__ or ''
return '%s(%s)' % (self._module_format(mod + ('.' if mod else '') + expr.func.__name__),
', '.join((self._print(arg) for arg in expr.args)))
def _print_Pow(self, expr, rational=False):
return self._hprint_Pow(expr, rational=rational, sqrt='sympy.sqrt')