def add_module(self, module):
for fname, f in module.__dict__.items():
if fname[0] == '_': continue
if isinstance(f, collections.Callable):
self.add_function(f)
elif math2.is_number(f):
self.add_constant(f, fname)
def add(self, expr):
''' add expr
:return: bool True if it has been added
'''
if expr is None:
return False
try:
k = expr() # the key is the numeric value of expr
except (TypeError, ValueError):
return False
if not math2.is_number(k):
return False
if type(k) is complex:
return False
if self.int:
# limit to integers... but maybe we're extremely close
k = math2.int_or_float(k)
if not isinstance(k, int): return False
if k < 0:
return self.add(-expr)
if self.max is not None and k > self.max:
return False
if k in self:
if self.improve and expr.complexity() >= self[k].complexity():
return False
self[k] = expr
return True
def isconstant(self):
''':return: True if Expr evaluates to a constant number or bool'''
res = self()
if math2.is_number(res):
return True
if isinstance(res, bool):
return True
return False
def eval(self, node):
'''safe eval of ast node : only functions and _operators listed above can be used
:param node: ast.AST to evaluate
:param ctx: dict of varname : value to substitute in node
:return: number or expression string
'''
if isinstance(node, ast.Num): # <number>
return node.n
elif isinstance(node, ast.Name):
return self.variables.get(node.id, node.id) # return value or var
elif isinstance(node, ast.Attribute):
return getattr(self.variables, [node.value.id], node.attr)
elif isinstance(node, ast.Tuple):
return tuple(self.eval(e) for e in node.elts)
elif isinstance(node, ast.Call):
params = [self.eval(arg) for arg in node.args]
if node.func.id not in self.functions:
raise NameError('%s function not allowed' % node.func.id)
f = self.functions[node.func.id][0]
res = f(*params)
# try to correct small error
return math2.int_or_float(res, 0, 1e-12)
elif isinstance(node, ast.BinOp): # <left> <operator> <right>
op = self.operators[type(node.op)]
left = self.eval(node.left)
right = self.eval(node.right)
if math2.is_number(left) and math2.is_number(right):
res = op[0](left, right)
# no correction here !
return res
else:
return "%s%s%s" % (left, op[_dialect_python], right)
elif isinstance(node, ast.UnaryOp): # <operator> <operand> e.g., -1
right = self.eval(node.operand)
return self.operators[type(node.op)][0](right)
elif isinstance(node, ast.Compare):
left = self.eval(node.left)
for op, right in zip(node.ops, node.comparators):
# TODO: find what to do when multiple items in list
return self.operators[type(op)][0](left, self.eval(right))
elif isinstance(node, ast.NameConstant):
return node.value
else:
logging.warning(ast.dump(node, False, False))
return self.eval(node.body) # last chance
def add_module(self, module):
for fname, f in module.__dict__.items():
if fname[0] == '_':
continue
if isinstance(f, collections.Callable):
self.add_function(f)
elif math2.is_number(f):
self.add_constant(f, fname)
def eval(self, node):
'''safe eval of ast node : only functions and _operators listed above can be used
:param node: ast.AST to evaluate
:param ctx: dict of varname : value to substitute in node
:return: number or expression string
'''
if isinstance(node, ast.Num): # <number>
return node.n
elif isinstance(node, ast.Name):
return self.variables.get(node.id, node.id) # return value or var
elif isinstance(node, ast.Attribute):
return getattr(self[node.value.id], node.attr)
elif isinstance(node, ast.Tuple):
return tuple(self.eval(e) for e in node.elts)
elif isinstance(node, ast.Call):
params = [self.eval(arg) for arg in node.args]
if not node.func.id in self.functions:
raise NameError('%s function not allowed' % node.func.id)
f = self.functions[node.func.id][0]
res = f(*params)
return math2.int_or_float(res, 0, 1e-12) # try to correct small error
elif isinstance(node, ast.BinOp): # <left> <operator> <right>
op = self.operators[type(node.op)]
left = self.eval(node.left)
right = self.eval(node.right)
if math2.is_number(left) and math2.is_number(right):
res = op[0](left, right)
# no correction here !
return res
else:
return "%s%s%s" % (left, op[_dialect_python], right)
elif isinstance(node, ast.UnaryOp): # <operator> <operand> e.g., -1
right = self.eval(node.operand)
return self.operators[type(node.op)][0](right)
elif isinstance(node, ast.Compare):
left = self.eval(node.left)
for op, right in zip(node.ops, node.comparators):
# TODO: find what to do when multiple items in list
return self.operators[type(op)][0](left, self.eval(right))
elif isinstance(node, ast.NameConstant):
return node.value
else:
logging.warning(ast.dump(node, False, False))
return self.eval(node.body) # last chance
def __eq__(self, other):
if math2.is_number(other):
try:
return self() == other
except:
return False
if not isinstance(other, Expr):
other = Expr(other, self.context)
return str(self()) == str(other())
def __lt__(self, other):
if math2.is_number(other):
try:
return self() < other
except:
return False
if not isinstance(other, Expr):
other = Expr(other, self.context)
return float(self()) < float(other())
def __eq__(self, other):
if math2.is_number(other):
try:
return self() == other
except:
return False
if not isinstance(other, Expr):
other = Expr(other, self.context)
return str(self()) == str(other())
def __lt__(self, other):
if math2.is_number(other):
try:
return self() < other
except:
return False
if not isinstance(other, Expr):
other = Expr(other, self.context)
return float(self()) < float(other())
def __mul__(self, other):
if math2.is_number(other):
mean = self.mean
var = other * self.variance
else: # it's a Stat
mean = self.mean * other.mean
# https://fr.wikipedia.org/wiki/Variance_(statistiques_et_probabilit%C3%A9s)#Produit
var = self.variance * other.variance + \
self.variance * other.mean ** 2 + other.variance * self.mean ** 2
return Stats(mean=mean, var=var)
def __add__(self, other):
if math2.is_number(other):
other = Stats([other])
# https://fr.wikipedia.org/wiki/Variance_(statistiques_et_probabilit%C3%A9s)#Produit
try:
cov = covariance(self, other)
except:
cov = 0
mean = (self.mean + other.mean) / 2 # TODO : improve
var = self.variance + other.variance + 2 * cov
return Stats(mean=mean, var=var)
def strftimedelta(t,fmt='%H:%M:%S'):
"""
:param t: float seconds or timedelta
"""
if not math2.is_number(t):
t=t.total_seconds()
hours, remainder = divmod(t, 3600)
minutes, seconds = divmod(remainder, 60)
res=fmt.replace('%H','%d'%hours)
res=res.replace('%h','%d'%hours if hours else '')
res=res.replace('%M','%02d'%minutes)
res=res.replace('%m','%d'%minutes if minutes else '')
res=res.replace('%S','%02d'%seconds)
return res
def __mul__(self,other):
if isinstance(other,six.string_types):
return self.colorize('black',other)
if math2.is_number(other):
return self.compose(None,other)
if other.nchannels>self.nchannels:
return other*self
if other.nchannels==1:
if self.nchannels==1:
return self.compose(None,other.array)
rgba=list(self.split('RGBA'))
rgba[-1]=rgba[-1]*other
return Image(rgba,'RGBA')
raise NotImplemented('%s * %s'%(self,other))
def strftimedelta(t, fmt='%H:%M:%S'):
"""
:param t: float seconds or timedelta
"""
if not math2.is_number(t):
t = t.total_seconds()
hours, remainder = divmod(t, 3600)
minutes, seconds = divmod(remainder, 60)
res = fmt.replace('%H', '%d' % hours)
res = res.replace('%h', '%d' % hours if hours else '')
res = res.replace('%M', '%02d' % minutes)
res = res.replace('%m', '%d' % minutes if minutes else '')
res = res.replace('%S', '%02d' % seconds)
return res
def __mul__(self, other):
if isinstance(other, str):
return self.colorize('black', other)
if math2.is_number(other):
return self.compose(None, other)
if other.nchannels > self.nchannels:
return other * self
if other.nchannels == 1:
if self.nchannels == 1:
return self.compose(None, other.array)
rgba = list(self.split('RGBA'))
rgba[-1] = rgba[-1] * other
return Image(rgba, 'RGBA')
raise NotImplementedError('%s * %s' % (self, other))
def __call__(self, x=None, **kwargs):
'''evaluate the Expr at x OR compose self(x())'''
if isinstance(x, Expr): # composition
return self.applx(x)
if itertools2.isiterable(x):
return [self(x) for x in x] # return a displayable list
if x is not None:
kwargs['x'] = x
kwargs['self'] = self # allows to call methods such as in Stats
self.context.variables = kwargs
try:
e = self.context.eval(self.body)
except TypeError: # some params remain symbolic
return self
except Exception as error: # ZeroDivisionError, OverflowError
return None
if math2.is_number(e):
return e
return Expr(e, self.context)
def __call__(self, x=None, **kwargs):
'''evaluate the Expr at x OR compose self(x())'''
if isinstance(x, Expr): # composition
return self.applx(x)
if itertools2.isiterable(x):
return [self(x) for x in x] # return a displayable list
if x is not None:
kwargs['x'] = x
kwargs['self'] = self # allows to call methods such as in Stats
self.context.variables = kwargs
try:
e = self.context.eval(self.body)
except TypeError: # some params remain symbolic
return self
except Exception as error: # ZeroDivisionError, OverflowError
return None
if math2.is_number(e):
return e
return Expr(e, self.context)
def __init__(self, init=[], default=0, period=(-math2.inf, +math2.inf)):
# Note : started by deriving a list of (point,value), but this leads to a problem:
# the value is taken into account in sort order by bisect
# so instead of defining one more class with a __cmp__ method, I split both lists
if math2.is_number(period):
period = (0, period)
try: # copy constructor ?
self.x = list(init.x)
self.y = list(init.y)
self.period = period or init.period # allow to force periodicity
except AttributeError:
self.x = []
self.y = []
self.period = period
self.append(period[0], default)
self.extend(init)
# to initialize context and such stuff
super(Piecewise, self).__init__(0)
self.body = '?' # should not happen
def __init__(self, f, context=default_context):
'''
:param f: function or operator, Expr to copy construct, or formula string
'''
self.context = context
if isinstance(f, Expr): # copy constructor
self.body = f.body
return
elif isinstance(f, ast.AST):
self.body = f
return
elif inspect.isfunction(f):
try:
f = get_function_source(f)
except ValueError:
f = '%s(x)' % f.__name__
elif isinstance(f, collections.Callable): # builtin function
f = '%s(x)' % f.__name__
elif f in ('True', 'False'):
f = bool(f == 'True')
if type(f) is bool:
self.body = ast.Num(f)
return
if type(f) is float: # try to beautify it
if math2.is_integer(f):
f = math2.rint(f)
else:
f = plouffe(f)
if math2.is_number(f): # store it with full precision
self.body = ast.Num(f)
return
# accept ^ as power operator rather than xor ...
f = str(f).replace('^', '**')
self.body = compile(f, 'Expr', 'eval', ast.PyCF_ONLY_AST).body
def __init__(self, f, context=default_context):
'''
:param f: function or operator, Expr to copy construct, or formula string
'''
self.context = context
if isinstance(f, Expr): # copy constructor
self.body = f.body
return
elif isinstance(f, ast.AST):
self.body = f
return
elif inspect.isfunction(f):
try:
f = get_function_source(f)
except ValueError:
f = '%s(x)' % f.__name__
elif isinstance(f, collections.Callable): # builtin function
f = '%s(x)' % f.__name__
elif f in ('True', 'False'):
f = bool(f == 'True')
if type(f) is bool:
self.body = ast.Num(f)
return
if type(f) is float: # try to beautify it
if math2.is_integer(f):
f = math2.rint(f)
else:
f = plouffe(f)
if math2.is_number(f): # store it with full precision
self.body = ast.Num(f)
return
f = str(f).replace('^', '**') # accept ^ as power operator rather than xor ...
self.body = compile(f, 'Expr', 'eval', ast.PyCF_ONLY_AST).body
def add(self, expr):
''' add expr
:return: bool True if it has been added
'''
if expr is None:
return False
try:
k = expr() # the key is the numeric value of expr
except (TypeError, ValueError):
return False
if not math2.is_number(k):
return False
if type(k) is complex:
return False
if self.int:
# limit to integers... but maybe we're extremely close
k = math2.int_or_float(k)
if not isinstance(k, int):
return False
if k < 0:
return self.add(-expr)
if self.max is not None and k > self.max:
return False
if k in self:
if self.improve and expr.complexity() >= self[k].complexity():
return False
self[k] = expr
return True
def isconstant(self):
''':return: True if Expr evaluates to a constant number or bool'''
res = self()
if math2.is_number(res): return True
if isinstance(res, bool): return True
return False