Source code for pint.util


    Miscellaneous functions for pint.

    :copyright: 2016 by Pint Authors, see AUTHORS for more details.
    :license: BSD, see LICENSE for more details.

import logging
import math
import operator
import re
from import Mapping
from fractions import Fraction
from functools import lru_cache, partial
from logging import NullHandler
from numbers import Number
from token import NAME, NUMBER

from .compat import NUMERIC_TYPES, tokenizer
from .errors import DefinitionSyntaxError
from .formatting import format_unit
from .pint_eval import build_eval_tree

logger = logging.getLogger(__name__)

[docs]def matrix_to_string( matrix, row_headers=None, col_headers=None, fmtfun=lambda x: str(int(x)) ): """Takes a 2D matrix (as nested list) and returns a string. Parameters ---------- matrix : row_headers : (Default value = None) col_headers : (Default value = None) fmtfun : (Default value = lambda x: str(int(x))) Returns ------- """ ret = [] if col_headers: ret.append(("\t" if row_headers else "") + "\t".join(col_headers)) if row_headers: ret += [ rh + "\t" + "\t".join(fmtfun(f) for f in row) for rh, row in zip(row_headers, matrix) ] else: ret += ["\t".join(fmtfun(f) for f in row) for row in matrix] return "\n".join(ret)
[docs]def transpose(matrix): """Takes a 2D matrix (as nested list) and returns the transposed version. Parameters ---------- matrix : Returns ------- """ return [list(val) for val in zip(*matrix)]
[docs]def column_echelon_form(matrix, ntype=Fraction, transpose_result=False): """Calculates the column echelon form using Gaussian elimination. Parameters ---------- matrix : a 2D matrix as nested list. ntype : the numerical type to use in the calculation. (Default value = Fraction) transpose_result : indicates if the returned matrix should be transposed. (Default value = False) Returns ------- type column echelon form, transformed identity matrix, swapped rows """ lead = 0 M = transpose(matrix) _transpose = transpose if transpose_result else lambda x: x rows, cols = len(M), len(M[0]) new_M = [] for row in M: r = [] for x in row: if isinstance(x, float): x = ntype.from_float(x) else: x = ntype(x) r.append(x) new_M.append(r) M = new_M # M = [[ntype(x) for x in row] for row in M] I = [ # noqa: E741 [ntype(1) if n == nc else ntype(0) for nc in range(rows)] for n in range(rows) ] swapped = [] for r in range(rows): if lead >= cols: return _transpose(M), _transpose(I), swapped i = r while M[i][lead] == 0: i += 1 if i != rows: continue i = r lead += 1 if cols == lead: return _transpose(M), _transpose(I), swapped M[i], M[r] = M[r], M[i] I[i], I[r] = I[r], I[i] swapped.append(i) lv = M[r][lead] M[r] = [mrx / lv for mrx in M[r]] I[r] = [mrx / lv for mrx in I[r]] for i in range(rows): if i == r: continue lv = M[i][lead] M[i] = [iv - lv * rv for rv, iv in zip(M[r], M[i])] I[i] = [iv - lv * rv for rv, iv in zip(I[r], I[i])] lead += 1 return _transpose(M), _transpose(I), swapped
[docs]def pi_theorem(quantities, registry=None): """Builds dimensionless quantities using the Buckingham π theorem Parameters ---------- quantities : dict mapping between variable name and units registry : (Default value = None) Returns ------- type a list of dimensionless quantities expressed as dicts """ # Preprocess input and build the dimensionality Matrix quant = [] dimensions = set() if registry is None: getdim = lambda x: x non_int_type = float else: getdim = registry.get_dimensionality non_int_type = registry.non_int_type for name, value in quantities.items(): if isinstance(value, str): value = ParserHelper.from_string(value, non_int_type=non_int_type) if isinstance(value, dict): dims = getdim(registry.UnitsContainer(value)) elif not hasattr(value, "dimensionality"): dims = getdim(value) else: dims = value.dimensionality if not registry and any(not key.startswith("[") for key in dims): logger.warning( "A non dimension was found and a registry was not provided. " "Assuming that it is a dimension name: {}.".format(dims) ) quant.append((name, dims)) dimensions = dimensions.union(dims.keys()) dimensions = list(dimensions) # Calculate dimensionless quantities M = [ [dimensionality[dimension] for name, dimensionality in quant] for dimension in dimensions ] M, identity, pivot = column_echelon_form(M, transpose_result=False) # Collect results # Make all numbers integers and minimize the number of negative exponents. # Remove zeros results = [] for rowm, rowi in zip(M, identity): if any(el != 0 for el in rowm): continue max_den = max(f.denominator for f in rowi) neg = -1 if sum(f < 0 for f in rowi) > sum(f > 0 for f in rowi) else 1 results.append( dict( (q[0], neg * f.numerator * max_den / f.denominator) for q, f in zip(quant, rowi) if f.numerator != 0 ) ) return results
[docs]def solve_dependencies(dependencies): """Solve a dependency graph. Parameters ---------- dependencies : dependency dictionary. For each key, the value is an iterable indicating its dependencies. Returns ------- type iterator of sets, each containing keys of independents tasks dependent only of the previous tasks in the list. """ while dependencies: # values not in keys (items without dep) t = {i for v in dependencies.values() for i in v} - dependencies.keys() # and keys without value (items without dep) t.update(k for k, v in dependencies.items() if not v) # can be done right away if not t: raise ValueError( "Cyclic dependencies exist among these items: {}".format( ", ".join(repr(x) for x in dependencies.items()) ) ) # and cleaned up dependencies = {k: v - t for k, v in dependencies.items() if v} yield t
def find_shortest_path(graph, start, end, path=None): path = (path or []) + [start] if start == end: return path if start not in graph: return None shortest = None for node in graph[start]: if node not in path: newpath = find_shortest_path(graph, node, end, path) if newpath: if not shortest or len(newpath) < len(shortest): shortest = newpath return shortest def find_connected_nodes(graph, start, visited=None): if start not in graph: return None visited = visited or set() visited.add(start) for node in graph[start]: if node not in visited: find_connected_nodes(graph, node, visited) return visited
[docs]class udict(dict): """Custom dict implementing __missing__.""" def __missing__(self, key): return 0
[docs] def copy(self): return udict(self)
[docs]class UnitsContainer(Mapping): """The UnitsContainer stores the product of units and their respective exponent and implements the corresponding operations. UnitsContainer is a read-only mapping. All operations (even in place ones) Parameters ---------- Returns ------- type """ __slots__ = ("_d", "_hash", "_one", "_non_int_type") def __init__(self, *args, **kwargs): if args and isinstance(args[0], UnitsContainer): default_non_int_type = args[0]._non_int_type else: default_non_int_type = float self._non_int_type = kwargs.pop("non_int_type", default_non_int_type) if self._non_int_type is float: self._one = 1 else: self._one = self._non_int_type("1") d = udict(*args, **kwargs) self._d = d for key, value in d.items(): if not isinstance(key, str): raise TypeError("key must be a str, not {}".format(type(key))) if not isinstance(value, Number): raise TypeError("value must be a number, not {}".format(type(value))) if not isinstance(value, int) and not isinstance(value, self._non_int_type): d[key] = self._non_int_type(value) self._hash = None def copy(self): return self.__copy__() def add(self, key, value): newval = self._d[key] + value new = self.copy() if newval: new._d[key] = newval else: new._d.pop(key) new._hash = None return new
[docs] def remove(self, keys): """Create a new UnitsContainer purged from given keys. Parameters ---------- keys : Returns ------- """ new = self.copy() for k in keys: new._d.pop(k) new._hash = None return new
[docs] def rename(self, oldkey, newkey): """Create a new UnitsContainer in which an entry has been renamed. Parameters ---------- oldkey : newkey : Returns ------- """ new = self.copy() new._d[newkey] = new._d.pop(oldkey) new._hash = None return new
def __iter__(self): return iter(self._d) def __len__(self): return len(self._d) def __getitem__(self, key): return self._d[key] def __contains__(self, key): return key in self._d def __hash__(self): if self._hash is None: self._hash = hash(frozenset(self._d.items())) return self._hash # Only needed by pickle protocol 0 and 1 (used by pytables) def __getstate__(self): return self._d, self._hash, self._one, self._non_int_type def __setstate__(self, state): self._d, self._hash, self._one, self._non_int_type = state def __eq__(self, other): if isinstance(other, UnitsContainer): # UnitsContainer.__hash__(self) is not the same as hash(self); see # ParserHelper.__hash__ and __eq__. # Different hashes guarantee that the actual contents are different, but # identical hashes give no guarantee of equality. # e.g. in CPython, hash(-1) == hash(-2) if UnitsContainer.__hash__(self) != UnitsContainer.__hash__(other): return False other = other._d elif isinstance(other, str): other = ParserHelper.from_string(other, self._non_int_type) other = other._d return dict.__eq__(self._d, other) def __str__(self): return self.__format__("") def __repr__(self): tmp = "{%s}" % ", ".join( ["'{}': {}".format(key, value) for key, value in sorted(self._d.items())] ) return "<UnitsContainer({})>".format(tmp) def __format__(self, spec): return format_unit(self, spec) def format_babel(self, spec, **kwspec): return format_unit(self, spec, **kwspec) def __copy__(self): # Skip expensive health checks performed by __init__ out = object.__new__(self.__class__) out._d = self._d.copy() out._hash = self._hash out._non_int_type = self._non_int_type out._one = self._one return out def __mul__(self, other): if not isinstance(other, self.__class__): err = "Cannot multiply UnitsContainer by {}" raise TypeError(err.format(type(other))) new = self.copy() for key, value in other.items(): new._d[key] += value if new._d[key] == 0: del new._d[key] new._hash = None return new __rmul__ = __mul__ def __pow__(self, other): if not isinstance(other, NUMERIC_TYPES): err = "Cannot power UnitsContainer by {}" raise TypeError(err.format(type(other))) new = self.copy() for key, value in new._d.items(): new._d[key] *= other new._hash = None return new def __truediv__(self, other): if not isinstance(other, self.__class__): err = "Cannot divide UnitsContainer by {}" raise TypeError(err.format(type(other))) new = self.copy() for key, value in other.items(): new._d[key] -= value if new._d[key] == 0: del new._d[key] new._hash = None return new def __rtruediv__(self, other): if not isinstance(other, self.__class__) and other != 1: err = "Cannot divide {} by UnitsContainer" raise TypeError(err.format(type(other))) return self ** -1
[docs]class ParserHelper(UnitsContainer): """The ParserHelper stores in place the product of variables and their respective exponent and implements the corresponding operations. ParserHelper is a read-only mapping. All operations (even in place ones) Parameters ---------- Returns ------- type WARNING : The hash value used does not take into account the scale attribute so be careful if you use it as a dict key and then two unequal object can have the same hash. """ __slots__ = ("scale",) def __init__(self, scale=1, *args, **kwargs): super().__init__(*args, **kwargs) self.scale = scale
[docs] @classmethod def from_word(cls, input_word, non_int_type=float): """Creates a ParserHelper object with a single variable with exponent one. Equivalent to: ParserHelper({'word': 1}) Parameters ---------- input_word : Returns ------- """ if non_int_type is float: return cls(1, [(input_word, 1)], non_int_type=non_int_type) else: ONE = non_int_type("1.0") return cls(ONE, [(input_word, ONE)], non_int_type=non_int_type)
@classmethod def eval_token(cls, token, use_decimal=False, non_int_type=float): # TODO: remove this code when use_decimal is deprecated if use_decimal: raise DeprecationWarning( "`use_decimal` is deprecated, use `non_int_type` keyword argument when instantiating the registry.\n" ">>> from decimal import Decimal\n" ">>> ureg = UnitRegistry(non_int_type=Decimal)" ) token_type = token.type token_text = token.string if token_type == NUMBER: if non_int_type is float: try: return int(token_text) except ValueError: return float(token_text) else: return non_int_type(token_text) elif token_type == NAME: return ParserHelper.from_word(token_text, non_int_type=non_int_type) else: raise Exception("unknown token type")
[docs] @classmethod @lru_cache() def from_string(cls, input_string, non_int_type=float): """Parse linear expression mathematical units and return a quantity object. Parameters ---------- input_string : Returns ------- """ if not input_string: return cls(non_int_type=non_int_type) input_string = string_preprocessor(input_string) if "[" in input_string: input_string = input_string.replace("[", "__obra__").replace( "]", "__cbra__" ) reps = True else: reps = False gen = tokenizer(input_string) ret = build_eval_tree(gen).evaluate( partial(cls.eval_token, non_int_type=non_int_type) ) if isinstance(ret, Number): return ParserHelper(ret, non_int_type=non_int_type) if reps: ret = ParserHelper( ret.scale, { key.replace("__obra__", "[").replace("__cbra__", "]"): value for key, value in ret.items() }, non_int_type=non_int_type, ) for k in list(ret): if k.lower() == "nan": del ret._d[k] ret.scale = math.nan return ret
def __copy__(self): new = super().__copy__() new.scale = self.scale return new def copy(self): return self.__copy__() def __hash__(self): if self.scale != 1: mess = "Only scale 1 ParserHelper instance should be considered hashable" raise ValueError(mess) return super().__hash__() # Only needed by pickle protocol 0 and 1 (used by pytables) def __getstate__(self): return super().__getstate__() + (self.scale,) def __setstate__(self, state): super().__setstate__(state[:-1]) self.scale = state[-1] def __eq__(self, other): if isinstance(other, ParserHelper): return self.scale == other.scale and super().__eq__(other) elif isinstance(other, str): return self == ParserHelper.from_string(other, self._non_int_type) elif isinstance(other, Number): return self.scale == other and not len(self._d) else: return self.scale == 1 and super().__eq__(other) def operate(self, items, op=operator.iadd, cleanup=True): d = udict(self._d) for key, value in items: d[key] = op(d[key], value) if cleanup: keys = [key for key, value in d.items() if value == 0] for key in keys: del d[key] return self.__class__(self.scale, d, non_int_type=self._non_int_type) def __str__(self): tmp = "{%s}" % ", ".join( ["'{}': {}".format(key, value) for key, value in sorted(self._d.items())] ) return "{} {}".format(self.scale, tmp) def __repr__(self): tmp = "{%s}" % ", ".join( ["'{}': {}".format(key, value) for key, value in sorted(self._d.items())] ) return "<ParserHelper({}, {})>".format(self.scale, tmp) def __mul__(self, other): if isinstance(other, str): new = self.add(other, self._one) elif isinstance(other, Number): new = self.copy() new.scale *= other elif isinstance(other, self.__class__): new = self.operate(other.items()) new.scale *= other.scale else: new = self.operate(other.items()) return new __rmul__ = __mul__ def __pow__(self, other): d = self._d.copy() for key in self._d: d[key] *= other return self.__class__(self.scale ** other, d, non_int_type=self._non_int_type) def __truediv__(self, other): if isinstance(other, str): new = self.add(other, -1) elif isinstance(other, Number): new = self.copy() new.scale /= other elif isinstance(other, self.__class__): new = self.operate(other.items(), operator.sub) new.scale /= other.scale else: new = self.operate(other.items(), operator.sub) return new __floordiv__ = __truediv__ def __rtruediv__(self, other): new = self.__pow__(-1) if isinstance(other, str): new = new.add(other, self._one) elif isinstance(other, Number): new.scale *= other elif isinstance(other, self.__class__): new = self.operate(other.items(), operator.add) new.scale *= other.scale else: new = new.operate(other.items(), operator.add) return new
#: List of regex substitution pairs. _subs_re = [ ("\N{DEGREE SIGN}", " degree"), (r"([\w\.\-\+\*\\\^])\s+", r"\1 "), # merge multiple spaces (r"({}) squared", r"\1**2"), # Handle square and cube (r"({}) cubed", r"\1**3"), (r"cubic ({})", r"\1**3"), (r"square ({})", r"\1**2"), (r"sq ({})", r"\1**2"), ( r"\b([0-9]+\.?[0-9]*)(?=[e|E][a-zA-Z]|[a-df-zA-DF-Z])", r"\1*", ), # Handle numberLetter for multiplication (r"([\w\.\-])\s+(?=\w)", r"\1*"), # Handle space for multiplication ] #: Compiles the regex and replace {} by a regex that matches an identifier. _subs_re = [(re.compile(a.format(r"[_a-zA-Z][_a-zA-Z0-9]*")), b) for a, b in _subs_re] _pretty_table = str.maketrans("⁰¹²³⁴⁵⁶⁷⁸⁹·⁻", "0123456789*-") _pretty_exp_re = re.compile(r"⁻?[⁰¹²³⁴⁵⁶⁷⁸⁹]+(?:\.[⁰¹²³⁴⁵⁶⁷⁸⁹]*)?") def string_preprocessor(input_string): input_string = input_string.replace(",", "") input_string = input_string.replace(" per ", "/") for a, b in _subs_re: input_string = a.sub(b, input_string) # Replace pretty format characters for pretty_exp in _pretty_exp_re.findall(input_string): exp = "**" + pretty_exp.translate(_pretty_table) input_string = input_string.replace(pretty_exp, exp) input_string = input_string.translate(_pretty_table) # Handle caret exponentiation input_string = input_string.replace("^", "**") return input_string def _is_dim(name): return name[0] == "[" and name[-1] == "]"
[docs]class SharedRegistryObject: """Base class for object keeping a reference to the registree. Such object are for now Quantity and Unit, in a number of places it is that an object from this class has a '_units' attribute. Parameters ---------- Returns ------- """ def __new__(cls, *args, **kwargs): inst = object.__new__(cls) if not hasattr(cls, "_REGISTRY"): # Base class, not subclasses dynamically by # UnitRegistry._init_dynamic_classes from . import _APP_REGISTRY inst._REGISTRY = _APP_REGISTRY return inst def _check(self, other): """Check if the other object use a registry and if so that it is the same registry. Parameters ---------- other : Returns ------- type other don't use a registry and raise ValueError if other don't use the same unit registry. """ if self._REGISTRY is getattr(other, "_REGISTRY", None): return True elif isinstance(other, SharedRegistryObject): mess = "Cannot operate with {} and {} of different registries." raise ValueError( mess.format(self.__class__.__name__, other.__class__.__name__) ) else: return False
[docs]class PrettyIPython: """Mixin to add pretty-printers for IPython""" def _repr_html_(self): if "~" in self.default_format: return "{:~H}".format(self) else: return "{:H}".format(self) def _repr_latex_(self): if "~" in self.default_format: return "${:~L}$".format(self) else: return "${:L}$".format(self) def _repr_pretty_(self, p, cycle): if "~" in self.default_format: p.text("{:~P}".format(self)) else: p.text("{:P}".format(self))
[docs]def to_units_container(unit_like, registry=None): """Convert a unit compatible type to a UnitsContainer. Parameters ---------- unit_like : registry : (Default value = None) Returns ------- """ mro = type(unit_like).mro() if UnitsContainer in mro: return unit_like elif SharedRegistryObject in mro: return unit_like._units elif str in mro: if registry: return registry._parse_units(unit_like) else: return ParserHelper.from_string(unit_like) elif dict in mro: if registry: return registry.UnitsContainer(unit_like) else: return UnitsContainer(unit_like)
[docs]def infer_base_unit(q): """ Parameters ---------- q : Returns ------- type """ d = udict() for unit_name, power in q._units.items(): candidates = q._REGISTRY.parse_unit_name(unit_name) assert len(candidates) == 1 _, base_unit, _ = candidates[0] d[base_unit] += power # remove values that resulted in a power of 0 return UnitsContainer({k: v for k, v in d.items() if v != 0})
[docs]def getattr_maybe_raise(self, item): """Helper function invoked at start of all overridden ``__getattr__``. Raise AttributeError if the user tries to ask for a _ or __ attribute, *unless* it is immediately followed by a number, to enable units encompassing constants, such as ``L / _100km``. Parameters ---------- item : string Item to be found. Returns ------- """ # Double-underscore attributes are tricky to detect because they are # automatically prefixed with the class name - which may be a subclass of self if ( item.endswith("__") or len(item.lstrip("_")) == 0 or (item.startswith("_") and not item.lstrip("_")[0].isdigit()) ): raise AttributeError("%r object has no attribute %r" % (self, item))
[docs]class SourceIterator: """Iterator to facilitate reading the definition files. Accepts any sequence (like a list of lines, a file or another SourceIterator) The iterator yields the line number and line (skipping comments and empty lines) and stripping white spaces. for lineno, line in SourceIterator(sequence): # do something here """ def __new__(cls, sequence): if isinstance(sequence, SourceIterator): return sequence obj = object.__new__(cls) if sequence is not None: obj.internal = enumerate(sequence, 1) obj.last = (None, None) return obj def __iter__(self): return self def __next__(self): line = "" while not line or line.startswith("#"): lineno, line = next(self.internal) line = line.split("#", 1)[0].strip() self.last = lineno, line return lineno, line next = __next__
[docs] def block_iter(self): """Iterate block including header.""" return BlockIterator(self)
[docs]class BlockIterator(SourceIterator): """Like SourceIterator but stops when it finds '@end' It also raises an error if another '@' directive is found inside. """ def __new__(cls, line_iterator): obj = SourceIterator.__new__(cls, None) obj.internal = line_iterator.internal obj.last = line_iterator.last obj.done_last = False return obj def __next__(self): if not self.done_last: self.done_last = True return self.last lineno, line = SourceIterator.__next__(self) if line.startswith("@end"): raise StopIteration elif line.startswith("@"): raise DefinitionSyntaxError("cannot nest @ directives", lineno=lineno) return lineno, line next = __next__
[docs]def iterable(y): """Check whether or not an object can be iterated over. Vendored from numpy under the terms of the BSD 3-Clause License. (Copyright (c) 2005-2019, NumPy Developers.) Parameters ---------- value : Input object. type : object y : """ try: iter(y) except TypeError: return False return True
[docs]def sized(y): """Check whether or not an object has a defined length. Parameters ---------- value : Input object. type : object y : """ try: len(y) except TypeError: return False return True