751 lines
24 KiB
Python
751 lines
24 KiB
Python
"""
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Python code printers
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This module contains Python code printers for plain Python as well as NumPy & SciPy enabled code.
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"""
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from collections import defaultdict
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from itertools import chain
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from sympy.core import S
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from sympy.core.mod import Mod
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from .precedence import precedence
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from .codeprinter import CodePrinter
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_kw = {
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'and', 'as', 'assert', 'break', 'class', 'continue', 'def', 'del', 'elif',
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'else', 'except', 'finally', 'for', 'from', 'global', 'if', 'import', 'in',
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'is', 'lambda', 'not', 'or', 'pass', 'raise', 'return', 'try', 'while',
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'with', 'yield', 'None', 'False', 'nonlocal', 'True'
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}
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_known_functions = {
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'Abs': 'abs',
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'Min': 'min',
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'Max': 'max',
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}
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_known_functions_math = {
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'acos': 'acos',
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'acosh': 'acosh',
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'asin': 'asin',
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'asinh': 'asinh',
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'atan': 'atan',
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'atan2': 'atan2',
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'atanh': 'atanh',
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'ceiling': 'ceil',
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'cos': 'cos',
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'cosh': 'cosh',
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'erf': 'erf',
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'erfc': 'erfc',
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'exp': 'exp',
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'expm1': 'expm1',
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'factorial': 'factorial',
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'floor': 'floor',
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'gamma': 'gamma',
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'hypot': 'hypot',
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'loggamma': 'lgamma',
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'log': 'log',
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'ln': 'log',
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'log10': 'log10',
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'log1p': 'log1p',
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'log2': 'log2',
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'sin': 'sin',
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'sinh': 'sinh',
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'Sqrt': 'sqrt',
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'tan': 'tan',
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'tanh': 'tanh'
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} # Not used from ``math``: [copysign isclose isfinite isinf isnan ldexp frexp pow modf
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# radians trunc fmod fsum gcd degrees fabs]
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_known_constants_math = {
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'Exp1': 'e',
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'Pi': 'pi',
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'E': 'e',
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'Infinity': 'inf',
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'NaN': 'nan',
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'ComplexInfinity': 'nan'
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}
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def _print_known_func(self, expr):
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known = self.known_functions[expr.__class__.__name__]
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return '{name}({args})'.format(name=self._module_format(known),
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args=', '.join((self._print(arg) for arg in expr.args)))
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def _print_known_const(self, expr):
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known = self.known_constants[expr.__class__.__name__]
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return self._module_format(known)
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class AbstractPythonCodePrinter(CodePrinter):
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printmethod = "_pythoncode"
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language = "Python"
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reserved_words = _kw
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modules = None # initialized to a set in __init__
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tab = ' '
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_kf = dict(chain(
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_known_functions.items(),
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[(k, 'math.' + v) for k, v in _known_functions_math.items()]
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))
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_kc = {k: 'math.'+v for k, v in _known_constants_math.items()}
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_operators = {'and': 'and', 'or': 'or', 'not': 'not'}
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_default_settings = dict(
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CodePrinter._default_settings,
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user_functions={},
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precision=17,
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inline=True,
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fully_qualified_modules=True,
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contract=False,
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standard='python3',
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)
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def __init__(self, settings=None):
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super().__init__(settings)
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# Python standard handler
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std = self._settings['standard']
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if std is None:
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import sys
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std = 'python{}'.format(sys.version_info.major)
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if std != 'python3':
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raise ValueError('Only Python 3 is supported.')
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self.standard = std
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self.module_imports = defaultdict(set)
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# Known functions and constants handler
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self.known_functions = dict(self._kf, **(settings or {}).get(
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'user_functions', {}))
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self.known_constants = dict(self._kc, **(settings or {}).get(
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'user_constants', {}))
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def _declare_number_const(self, name, value):
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return "%s = %s" % (name, value)
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def _module_format(self, fqn, register=True):
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parts = fqn.split('.')
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if register and len(parts) > 1:
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self.module_imports['.'.join(parts[:-1])].add(parts[-1])
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if self._settings['fully_qualified_modules']:
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return fqn
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else:
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return fqn.split('(')[0].split('[')[0].split('.')[-1]
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def _format_code(self, lines):
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return lines
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def _get_statement(self, codestring):
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return "{}".format(codestring)
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def _get_comment(self, text):
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return " # {}".format(text)
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def _expand_fold_binary_op(self, op, args):
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"""
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This method expands a fold on binary operations.
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``functools.reduce`` is an example of a folded operation.
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For example, the expression
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`A + B + C + D`
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is folded into
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`((A + B) + C) + D`
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"""
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if len(args) == 1:
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return self._print(args[0])
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else:
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return "%s(%s, %s)" % (
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self._module_format(op),
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self._expand_fold_binary_op(op, args[:-1]),
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self._print(args[-1]),
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)
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def _expand_reduce_binary_op(self, op, args):
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"""
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This method expands a reductin on binary operations.
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Notice: this is NOT the same as ``functools.reduce``.
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For example, the expression
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`A + B + C + D`
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is reduced into:
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`(A + B) + (C + D)`
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"""
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if len(args) == 1:
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return self._print(args[0])
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else:
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N = len(args)
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Nhalf = N // 2
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return "%s(%s, %s)" % (
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self._module_format(op),
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self._expand_reduce_binary_op(args[:Nhalf]),
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self._expand_reduce_binary_op(args[Nhalf:]),
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)
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def _print_NaN(self, expr):
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return "float('nan')"
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def _print_Infinity(self, expr):
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return "float('inf')"
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def _print_NegativeInfinity(self, expr):
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return "float('-inf')"
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def _print_ComplexInfinity(self, expr):
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return self._print_NaN(expr)
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def _print_Mod(self, expr):
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PREC = precedence(expr)
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return ('{} % {}'.format(*(self.parenthesize(x, PREC) for x in expr.args)))
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def _print_Piecewise(self, expr):
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result = []
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i = 0
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for arg in expr.args:
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e = arg.expr
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c = arg.cond
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if i == 0:
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result.append('(')
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result.append('(')
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result.append(self._print(e))
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result.append(')')
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result.append(' if ')
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result.append(self._print(c))
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result.append(' else ')
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i += 1
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result = result[:-1]
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if result[-1] == 'True':
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result = result[:-2]
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result.append(')')
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else:
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result.append(' else None)')
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return ''.join(result)
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def _print_Relational(self, expr):
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"Relational printer for Equality and Unequality"
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op = {
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'==' :'equal',
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'!=' :'not_equal',
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'<' :'less',
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'<=' :'less_equal',
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'>' :'greater',
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'>=' :'greater_equal',
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}
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if expr.rel_op in op:
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lhs = self._print(expr.lhs)
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rhs = self._print(expr.rhs)
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return '({lhs} {op} {rhs})'.format(op=expr.rel_op, lhs=lhs, rhs=rhs)
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return super()._print_Relational(expr)
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def _print_ITE(self, expr):
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from sympy.functions.elementary.piecewise import Piecewise
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return self._print(expr.rewrite(Piecewise))
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def _print_Sum(self, expr):
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loops = (
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'for {i} in range({a}, {b}+1)'.format(
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i=self._print(i),
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a=self._print(a),
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b=self._print(b))
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for i, a, b in expr.limits)
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return '(builtins.sum({function} {loops}))'.format(
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function=self._print(expr.function),
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loops=' '.join(loops))
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def _print_ImaginaryUnit(self, expr):
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return '1j'
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def _print_KroneckerDelta(self, expr):
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a, b = expr.args
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return '(1 if {a} == {b} else 0)'.format(
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a = self._print(a),
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b = self._print(b)
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)
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def _print_MatrixBase(self, expr):
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name = expr.__class__.__name__
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func = self.known_functions.get(name, name)
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return "%s(%s)" % (func, self._print(expr.tolist()))
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_print_SparseRepMatrix = \
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_print_MutableSparseMatrix = \
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_print_ImmutableSparseMatrix = \
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_print_Matrix = \
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_print_DenseMatrix = \
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_print_MutableDenseMatrix = \
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_print_ImmutableMatrix = \
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_print_ImmutableDenseMatrix = \
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lambda self, expr: self._print_MatrixBase(expr)
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def _indent_codestring(self, codestring):
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return '\n'.join([self.tab + line for line in codestring.split('\n')])
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def _print_FunctionDefinition(self, fd):
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body = '\n'.join((self._print(arg) for arg in fd.body))
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return "def {name}({parameters}):\n{body}".format(
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name=self._print(fd.name),
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parameters=', '.join([self._print(var.symbol) for var in fd.parameters]),
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body=self._indent_codestring(body)
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)
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def _print_While(self, whl):
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body = '\n'.join((self._print(arg) for arg in whl.body))
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return "while {cond}:\n{body}".format(
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cond=self._print(whl.condition),
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body=self._indent_codestring(body)
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)
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def _print_Declaration(self, decl):
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return '%s = %s' % (
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self._print(decl.variable.symbol),
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self._print(decl.variable.value)
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)
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def _print_Return(self, ret):
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arg, = ret.args
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return 'return %s' % self._print(arg)
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def _print_Print(self, prnt):
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print_args = ', '.join((self._print(arg) for arg in prnt.print_args))
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if prnt.format_string != None: # Must be '!= None', cannot be 'is not None'
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print_args = '{} % ({})'.format(
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self._print(prnt.format_string), print_args)
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if prnt.file != None: # Must be '!= None', cannot be 'is not None'
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print_args += ', file=%s' % self._print(prnt.file)
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return 'print(%s)' % print_args
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def _print_Stream(self, strm):
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if str(strm.name) == 'stdout':
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return self._module_format('sys.stdout')
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elif str(strm.name) == 'stderr':
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return self._module_format('sys.stderr')
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else:
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return self._print(strm.name)
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def _print_NoneToken(self, arg):
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return 'None'
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def _hprint_Pow(self, expr, rational=False, sqrt='math.sqrt'):
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"""Printing helper function for ``Pow``
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Notes
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=====
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This preprocesses the ``sqrt`` as math formatter and prints division
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Examples
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========
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>>> from sympy import sqrt
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>>> from sympy.printing.pycode import PythonCodePrinter
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>>> from sympy.abc import x
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Python code printer automatically looks up ``math.sqrt``.
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>>> printer = PythonCodePrinter()
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>>> printer._hprint_Pow(sqrt(x), rational=True)
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'x**(1/2)'
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>>> printer._hprint_Pow(sqrt(x), rational=False)
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'math.sqrt(x)'
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>>> printer._hprint_Pow(1/sqrt(x), rational=True)
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'x**(-1/2)'
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>>> printer._hprint_Pow(1/sqrt(x), rational=False)
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'1/math.sqrt(x)'
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>>> printer._hprint_Pow(1/x, rational=False)
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'1/x'
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>>> printer._hprint_Pow(1/x, rational=True)
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'x**(-1)'
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Using sqrt from numpy or mpmath
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>>> printer._hprint_Pow(sqrt(x), sqrt='numpy.sqrt')
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'numpy.sqrt(x)'
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>>> printer._hprint_Pow(sqrt(x), sqrt='mpmath.sqrt')
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'mpmath.sqrt(x)'
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See Also
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========
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sympy.printing.str.StrPrinter._print_Pow
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"""
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PREC = precedence(expr)
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if expr.exp == S.Half and not rational:
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func = self._module_format(sqrt)
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arg = self._print(expr.base)
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return '{func}({arg})'.format(func=func, arg=arg)
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if expr.is_commutative and not rational:
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if -expr.exp is S.Half:
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func = self._module_format(sqrt)
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num = self._print(S.One)
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arg = self._print(expr.base)
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return f"{num}/{func}({arg})"
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if expr.exp is S.NegativeOne:
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num = self._print(S.One)
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arg = self.parenthesize(expr.base, PREC, strict=False)
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return f"{num}/{arg}"
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base_str = self.parenthesize(expr.base, PREC, strict=False)
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exp_str = self.parenthesize(expr.exp, PREC, strict=False)
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return "{}**{}".format(base_str, exp_str)
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class ArrayPrinter:
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def _arrayify(self, indexed):
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from sympy.tensor.array.expressions.from_indexed_to_array import convert_indexed_to_array
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try:
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return convert_indexed_to_array(indexed)
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except Exception:
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return indexed
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def _get_einsum_string(self, subranks, contraction_indices):
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letters = self._get_letter_generator_for_einsum()
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contraction_string = ""
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counter = 0
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d = {j: min(i) for i in contraction_indices for j in i}
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indices = []
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for rank_arg in subranks:
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lindices = []
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for i in range(rank_arg):
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if counter in d:
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lindices.append(d[counter])
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else:
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lindices.append(counter)
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counter += 1
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indices.append(lindices)
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mapping = {}
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letters_free = []
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letters_dum = []
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for i in indices:
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for j in i:
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if j not in mapping:
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l = next(letters)
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mapping[j] = l
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else:
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l = mapping[j]
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contraction_string += l
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if j in d:
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if l not in letters_dum:
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letters_dum.append(l)
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else:
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letters_free.append(l)
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contraction_string += ","
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contraction_string = contraction_string[:-1]
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return contraction_string, letters_free, letters_dum
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def _get_letter_generator_for_einsum(self):
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for i in range(97, 123):
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yield chr(i)
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for i in range(65, 91):
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yield chr(i)
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raise ValueError("out of letters")
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def _print_ArrayTensorProduct(self, expr):
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letters = self._get_letter_generator_for_einsum()
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contraction_string = ",".join(["".join([next(letters) for j in range(i)]) for i in expr.subranks])
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return '%s("%s", %s)' % (
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self._module_format(self._module + "." + self._einsum),
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contraction_string,
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", ".join([self._print(arg) for arg in expr.args])
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)
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def _print_ArrayContraction(self, expr):
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from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
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base = expr.expr
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contraction_indices = expr.contraction_indices
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if isinstance(base, ArrayTensorProduct):
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elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
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ranks = base.subranks
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else:
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elems = self._print(base)
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ranks = [len(base.shape)]
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contraction_string, letters_free, letters_dum = self._get_einsum_string(ranks, contraction_indices)
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if not contraction_indices:
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return self._print(base)
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if isinstance(base, ArrayTensorProduct):
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elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
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else:
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elems = self._print(base)
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return "%s(\"%s\", %s)" % (
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self._module_format(self._module + "." + self._einsum),
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"{}->{}".format(contraction_string, "".join(sorted(letters_free))),
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elems,
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)
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def _print_ArrayDiagonal(self, expr):
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from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
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diagonal_indices = list(expr.diagonal_indices)
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if isinstance(expr.expr, ArrayTensorProduct):
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subranks = expr.expr.subranks
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elems = expr.expr.args
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else:
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subranks = expr.subranks
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elems = [expr.expr]
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diagonal_string, letters_free, letters_dum = self._get_einsum_string(subranks, diagonal_indices)
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elems = [self._print(i) for i in elems]
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return '%s("%s", %s)' % (
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self._module_format(self._module + "." + self._einsum),
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"{}->{}".format(diagonal_string, "".join(letters_free+letters_dum)),
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", ".join(elems)
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)
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def _print_PermuteDims(self, expr):
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return "%s(%s, %s)" % (
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self._module_format(self._module + "." + self._transpose),
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self._print(expr.expr),
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self._print(expr.permutation.array_form),
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)
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def _print_ArrayAdd(self, expr):
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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')
|