/usr/share/pyshared/sympy/simplify/epathtools.py is in python-sympy 0.7.1.rc1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 | """Tools for manipulation of expressions using paths. """
from sympy.core import Basic
class EPath(object):
"""
Manipulate expressions using paths.
EPath grammar in EBNF notation::
literal ::= /[A-Za-z_][A-Za-z_0-9]*/
number ::= /-?\d+/
type ::= literal
attribute ::= literal "?"
all ::= "*"
slice ::= "[" number? (":" number? (":" number?)?)? "]"
range ::= all | slice
query ::= (type | attribute) ("|" (type | attribute))*
selector ::= range | query range?
path ::= "/" selector ("/" selector)*
See the docstring of the epath() function.
"""
__slots__ = ["_path", "_epath"]
def __new__(cls, path):
"""Construct new EPath. """
if isinstance(path, EPath):
return path
if not path:
raise ValueError("empty EPath")
_path = path
if path[0] == '/':
path = path[1:]
else:
raise NotImplementedError("non-root EPath")
epath = []
for selector in path.split('/'):
selector = selector.strip()
if not selector:
raise ValueError("empty selector")
index = 0
for c in selector:
if c.isalnum() or c == '_' or c == '|' or c == '?':
index += 1
else:
break
attrs = []
types = []
if index:
elements = selector[:index]
selector = selector[index:]
for element in elements.split('|'):
element = element.strip()
if not element:
raise ValueError("empty element")
if element.endswith('?'):
attrs.append(element[:-1])
else:
types.append(element)
span = None
if selector == '*':
pass
else:
if selector.startswith('['):
try:
i = selector.index(']')
except ValueError:
raise ValueError("expected ']', got EOL")
_span, span = selector[1:i], []
if ':' not in _span:
span = int(_span)
else:
for elt in _span.split(':', 3):
if not elt:
span.append(None)
else:
span.append(int(elt))
span = slice(*span)
selector = selector[i+1:]
if selector:
raise ValueError("trailing characters in selector")
epath.append((attrs, types, span))
obj = object.__new__(cls)
obj._path = _path
obj._epath = epath
return obj
def __repr__(self):
return "%s(%r)" % (self.__class__.__name__, self._path)
def _get_ordered_args(self, expr):
"""Sort ``expr.args`` using printing order. """
if expr.is_Add:
return expr.as_ordered_terms()
elif expr.is_Mul:
return expr.as_ordered_factors()
else:
return expr.args
def _hasattrs(self, expr, attrs):
"""Check if ``expr`` has any of ``attrs``. """
for attr in attrs:
if not hasattr(expr, attr):
return False
return True
def _hastypes(self, expr, types):
"""Check if ``expr`` is any of ``types``. """
_types = [ cls.__name__ for cls in expr.__class__.mro() ]
return bool(set(_types).intersection(types))
def _has(self, expr, attrs, types):
"""Apply ``_hasattrs`` and ``_hastypes`` to ``expr``. """
if not (attrs or types):
return True
if attrs and self._hasattrs(expr, attrs):
return True
if types and self._hastypes(expr, types):
return True
return False
def apply(self, expr, func, args=None, kwargs=None):
"""
Modify parts of an expression selected by a path.
**Examples**
>>> from sympy.simplify.epathtools import EPath
>>> from sympy import sin, cos, E
>>> from sympy.abc import x, y, z, t
>>> path = EPath("/*/[0]/Symbol")
>>> expr = [((x, 1), 2), ((3, y), z)]
>>> path.apply(expr, lambda expr: expr**2)
[((x**2, 1), 2), ((3, y**2), z)]
>>> path = EPath("/*/*/Symbol")
>>> expr = t + sin(x + 1) + cos(x + y + E)
>>> path.apply(expr, lambda expr: 2*expr)
t + sin(2*x + 1) + cos(2*x + 2*y + E)
"""
def _apply(path, expr, func):
if not path:
return func(expr)
else:
selector, path = path[0], path[1:]
attrs, types, span = selector
if isinstance(expr, Basic):
if not expr.is_Atom:
args, basic = self._get_ordered_args(expr), True
else:
return expr
elif hasattr(expr, '__iter__'):
args, basic = expr, False
else:
return expr
args = list(args)
if span is not None:
if type(span) == slice:
indices = range(*span.indices(len(args)))
else:
indices = [span]
else:
indices = xrange(len(args))
for i in indices:
try:
arg = args[i]
except IndexError:
continue
if self._has(arg, attrs, types):
args[i] = _apply(path, arg, func)
if basic:
return expr.func(*args)
else:
return expr.__class__(args)
_args, _kwargs = args or (), kwargs or {}
_func = lambda expr: func(expr, *_args, **_kwargs)
return _apply(self._epath, expr, _func)
def select(self, expr):
"""
Retrieve parts of an expression selected by a path.
**Examples**
>>> from sympy.simplify.epathtools import EPath
>>> from sympy import sin, cos, E
>>> from sympy.abc import x, y, z, t
>>> path = EPath("/*/[0]/Symbol")
>>> expr = [((x, 1), 2), ((3, y), z)]
>>> path.select(expr)
[x, y]
>>> path = EPath("/*/*/Symbol")
>>> expr = t + sin(x + 1) + cos(x + y + E)
>>> path.select(expr)
[x, x, y]
"""
result = []
def _select(path, expr):
if not path:
result.append(expr)
else:
selector, path = path[0], path[1:]
attrs, types, span = selector
if isinstance(expr, Basic):
args = self._get_ordered_args(expr)
elif hasattr(expr, '__iter__'):
args = expr
else:
return
if span is not None:
if type(span) == slice:
args = args[span]
else:
try:
args = [args[span]]
except IndexError:
return
for arg in args:
if self._has(arg, attrs, types):
_select(path, arg)
_select(self._epath, expr)
return result
def epath(path, expr=None, func=None, args=None, kwargs=None):
"""
Manipulate parts of an expression selected by a path.
This function allows to manipulate large nested expressions in single
line of code, utilizing techniques to those applied in XML processing
standards (e.g. XPath).
If ``func`` is ``None``, :func:`epath` retrieves elements selected by
the ``path``. Otherwise it applies ``func`` to each matching element.
Note that it is more efficient to create an EPath object and use the select
and apply methods of that object, since this will compile the path string
only once. This function should only be used as a convenient shortcut for
interactive use.
**Syntax**
select all : "/*"
Equivalent of ``for arg in args:``.
select slice : "/[0]" | "/[1:5]" | "/[1:5:2]"
Supports standard Python's slice syntax.
select by type : "/list" | "/list|tuple"
Emulates :func:`isinstance`.
select by attribute : "/__iter__?"
Emulates :func:`hasattr`.
**Parameters**
path : str | EPath
A path as a string or a compiled EPath.
expr : Basic | iterable
An expression or a container of expressions.
func : callable (optional)
A callable that will be applied to matching parts.
args : tuple (optional)
Additional positional arguments to ``func``.
kwargs : dict (optional)
Additional keyword arguments to ``func``.
**Examples**
>>> from sympy.simplify.epathtools import epath
>>> from sympy import sin, cos, E
>>> from sympy.abc import x, y, z, t
>>> path = "/*/[0]/Symbol"
>>> expr = [((x, 1), 2), ((3, y), z)]
>>> epath(path, expr)
[x, y]
>>> epath(path, expr, lambda expr: expr**2)
[((x**2, 1), 2), ((3, y**2), z)]
>>> path = "/*/*/Symbol"
>>> expr = t + sin(x + 1) + cos(x + y + E)
>>> epath(path, expr)
[x, x, y]
>>> epath(path, expr, lambda expr: 2*expr)
t + sin(2*x + 1) + cos(2*x + 2*y + E)
"""
_epath = EPath(path)
if expr is None:
return _epath
if func is None:
return _epath.select(expr)
else:
return _epath.apply(expr, func, args, kwargs)
|