Source code for symengine.utilities

from .lib.symengine_wrapper import Symbol, Basic
from itertools import combinations, permutations, product, product as cartes
import re as _re
import string
import sys


_range = _re.compile('([0-9]*:[0-9]+|[a-zA-Z]?:[a-zA-Z])')


[docs]def symbols(names, **args): """ Transform strings into instances of :class:`Symbol` class. :func:`symbols` function returns a sequence of symbols with names taken from ``names`` argument, which can be a comma or whitespace delimited string, or a sequence of strings:: >>> from symengine import symbols >>> x, y, z = symbols('x,y,z') >>> a, b, c = symbols('a b c') The type of output is dependent on the properties of input arguments:: >>> symbols('x') x >>> symbols('x,') (x,) >>> symbols('x,y') (x, y) >>> symbols(('a', 'b', 'c')) (a, b, c) >>> symbols(['a', 'b', 'c']) [a, b, c] >>> symbols(set(['a', 'b', 'c'])) set([a, b, c]) If an iterable container is needed for a single symbol, set the ``seq`` argument to ``True`` or terminate the symbol name with a comma:: >>> symbols('x', seq=True) (x,) To reduce typing, range syntax is supported to create indexed symbols. Ranges are indicated by a colon and the type of range is determined by the character to the right of the colon. If the character is a digit then all contiguous digits to the left are taken as the nonnegative starting value (or 0 if there is no digit left of the colon) and all contiguous digits to the right are taken as 1 greater than the ending value:: >>> symbols('x:10') (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) >>> symbols('x5:10') (x5, x6, x7, x8, x9) >>> symbols('x5(:2)') (x50, x51) >>> symbols('x5:10,y:5') (x5, x6, x7, x8, x9, y0, y1, y2, y3, y4) >>> symbols(('x5:10', 'y:5')) ((x5, x6, x7, x8, x9), (y0, y1, y2, y3, y4)) If the character to the right of the colon is a letter, then the single letter to the left (or 'a' if there is none) is taken as the start and all characters in the lexicographic range *through* the letter to the right are used as the range:: >>> symbols('x:z') (x, y, z) >>> symbols('x:c') # null range () >>> symbols('x(:c)') (xa, xb, xc) >>> symbols(':c') (a, b, c) >>> symbols('a:d, x:z') (a, b, c, d, x, y, z) >>> symbols(('a:d', 'x:z')) ((a, b, c, d), (x, y, z)) Multiple ranges are supported; contiguous numerical ranges should be separated by parentheses to disambiguate the ending number of one range from the starting number of the next:: >>> symbols('x:2(1:3)') (x01, x02, x11, x12) >>> symbols(':3:2') # parsing is from left to right (00, 01, 10, 11, 20, 21) Only one pair of parentheses surrounding ranges are removed, so to include parentheses around ranges, double them. And to include spaces, commas, or colons, escape them with a backslash:: >>> symbols('x((a:b))') (x(a), x(b)) >>> symbols('x(:1\,:2)') # or 'x((:1)\,(:2))' (x(0,0), x(0,1)) """ result = [] if isinstance(names, str): marker = 0 literals = ['\,', '\:', '\ '] for i in range(len(literals)): lit = literals.pop(0) if lit in names: while chr(marker) in names: marker += 1 lit_char = chr(marker) marker += 1 names = names.replace(lit, lit_char) literals.append((lit_char, lit[1:])) def literal(s): if literals: for c, l in literals: s = s.replace(c, l) return s names = names.strip() as_seq = names.endswith(',') if as_seq: names = names[:-1].rstrip() if not names: raise ValueError('no symbols given') # split on commas names = [n.strip() for n in names.split(',')] if not all(n for n in names): raise ValueError('missing symbol between commas') # split on spaces for i in range(len(names) - 1, -1, -1): names[i: i + 1] = names[i].split() cls = args.pop('cls', Symbol) seq = args.pop('seq', as_seq) for name in names: if not name: raise ValueError('missing symbol') if ':' not in name: symbol = cls(literal(name), **args) result.append(symbol) continue split = _range.split(name) # remove 1 layer of bounding parentheses around ranges for i in range(len(split) - 1): if i and ':' in split[i] and split[i] != ':' and \ split[i - 1].endswith('(') and \ split[i + 1].startswith(')'): split[i - 1] = split[i - 1][:-1] split[i + 1] = split[i + 1][1:] for i, s in enumerate(split): if ':' in s: if s[-1].endswith(':'): raise ValueError('missing end range') a, b = s.split(':') if b[-1] in string.digits: a = 0 if not a else int(a) b = int(b) split[i] = [str(c) for c in range(a, b)] else: a = a or 'a' split[i] = [string.ascii_letters[c] for c in range( string.ascii_letters.index(a), string.ascii_letters.index(b) + 1)] # inclusive if not split[i]: break else: split[i] = [s] else: seq = True if len(split) == 1: names = split[0] else: names = [''.join(s) for s in cartes(*split)] if literals: result.extend([cls(literal(s), **args) for s in names]) else: result.extend([cls(s, **args) for s in names]) if not seq and len(result) <= 1: if not result: return () return result[0] return tuple(result) else: for name in names: result.append(symbols(name, **args)) return type(names)(result)
[docs]def var(names, **args): """ Create symbols and inject them into the global namespace. INPUT: - s -- a string, either a single variable name, or - a space separated list of variable names, or - a list of variable names. This calls :func:`symbols` with the same arguments and puts the results into the *global* namespace. It's recommended not to use :func:`var` in library code, where :func:`symbols` has to be used:: Examples ======== >>> from symengine import var >>> var('x') x >>> x x >>> var('a,ab,abc') (a, ab, abc) >>> abc abc See :func:`symbols` documentation for more details on what kinds of arguments can be passed to :func:`var`. """ def traverse(symbols, frame): """Recursively inject symbols to the global namespace. """ for symbol in symbols: if isinstance(symbol, Basic): frame.f_globals[symbol.__str__()] = symbol # Once we hace an undefined function class # implemented, put a check for function here else: traverse(symbol, frame) from inspect import currentframe frame = currentframe().f_back try: syms = symbols(names, **args) if syms is not None: if isinstance(syms, Basic): frame.f_globals[syms.__str__()] = syms # Once we hace an undefined function class # implemented, put a check for function here else: traverse(syms, frame) finally: del frame # break cyclic dependencies as stated in inspect docs return syms
try: import py from py.test import skip, raises USE_PYTEST = getattr(sys, '_running_pytest', False) except ImportError: USE_PYTEST = False if not USE_PYTEST: def raises(expectedException, code=None): """ Tests that ``code`` raises the exception ``expectedException``. ``code`` may be a callable, such as a lambda expression or function name. If ``code`` is not given or None, ``raises`` will return a context manager for use in ``with`` statements; the code to execute then comes from the scope of the ``with``. ``raises()`` does nothing if the callable raises the expected exception, otherwise it raises an AssertionError. Examples ======== >>> from symengine.pytest import raises >>> raises(ZeroDivisionError, lambda: 1/0) >>> raises(ZeroDivisionError, lambda: 1/2) Traceback (most recent call last): ... AssertionError: DID NOT RAISE >>> with raises(ZeroDivisionError): ... n = 1/0 >>> with raises(ZeroDivisionError): ... n = 1/2 Traceback (most recent call last): ... AssertionError: DID NOT RAISE Note that you cannot test multiple statements via ``with raises``: >>> with raises(ZeroDivisionError): ... n = 1/0 # will execute and raise, aborting the ``with`` ... n = 9999/0 # never executed This is just what ``with`` is supposed to do: abort the contained statement sequence at the first exception and let the context manager deal with the exception. To test multiple statements, you'll need a separate ``with`` for each: >>> with raises(ZeroDivisionError): ... n = 1/0 # will execute and raise >>> with raises(ZeroDivisionError): ... n = 9999/0 # will also execute and raise """ if code is None: return RaisesContext(expectedException) elif callable(code): try: code() except expectedException: return raise AssertionError("DID NOT RAISE") elif isinstance(code, str): raise TypeError( '\'raises(xxx, "code")\' has been phased out; ' 'change \'raises(xxx, "expression")\' ' 'to \'raises(xxx, lambda: expression)\', ' '\'raises(xxx, "statement")\' ' 'to \'with raises(xxx): statement\'') else: raise TypeError( 'raises() expects a callable for the 2nd argument.') class RaisesContext(object): def __init__(self, expectedException): self.expectedException = expectedException def __enter__(self): return None def __exit__(self, exc_type, exc_value, traceback): if exc_type is None: raise AssertionError("DID NOT RAISE") return issubclass(exc_type, self.expectedException) class NotIterable: """ Use this as mixin when creating a class which is not supposed to return true when iterable() is called on its instances. I.e. avoid infinite loop when calling e.g. list() on the instance """ pass def iterable(i, exclude=(str, dict, NotIterable)): """ Return a boolean indicating whether ``i`` is SymPy iterable. True also indicates that the iterator is finite, i.e. you e.g. call list(...) on the instance. When SymPy is working with iterables, it is almost always assuming that the iterable is not a string or a mapping, so those are excluded by default. If you want a pure Python definition, make exclude=None. To exclude multiple items, pass them as a tuple. """ try: iter(i) except TypeError: return False if exclude: return not isinstance(i, exclude) return True def is_sequence(i): """ Return a boolean indicating whether ``i`` is a sequence in the SymPy sense. If anything that fails the test below should be included as being a sequence for your application, set 'include' to that object's type; multiple types should be passed as a tuple of types. """ return hasattr(i, '__getitem__') and iterable(i)