import copy
import logging
import math
import operator
import re
import numpy
import numbers
import scipy.constants
from pyparsing import Word, alphas, nums, oneOf, Literal
from pyparsing import ZeroOrMore, OneOrMore, StringStart
from pyparsing import StringEnd, Optional, Forward
from pyparsing import CaselessLiteral, Group, StringEnd
from pyparsing import NoMatch, stringEnd, alphanums
default_functions = {'sin' : numpy.sin,
'cos' : numpy.cos,
'tan' : numpy.tan,
'sqrt': numpy.sqrt,
'log10':numpy.log10,
'log2':numpy.log2,
'ln': numpy.log,
'arccos':numpy.arccos,
'arcsin':numpy.arcsin,
'arctan':numpy.arctan,
'abs':numpy.abs
}
default_variables = {'j':numpy.complex(0,1),
'e':numpy.e,
'pi':numpy.pi,
'k':scipy.constants.k,
'c':scipy.constants.c,
'T':298.15,
'q':scipy.constants.e
}
log = logging.getLogger("mitx.courseware.capa")
class UndefinedVariable(Exception):
def raiseself(self):
''' Helper so we can use inside of a lambda '''
raise self
general_whitespace = re.compile('[^\w]+')
def check_variables(string, variables):
''' Confirm the only variables in string are defined.
Pyparsing uses a left-to-right parser, which makes the more
elegant approach pretty hopeless.
achar = reduce(lambda a,b:a|b ,map(Literal,alphas)) # Any alphabetic character
undefined_variable = achar + Word(alphanums)
undefined_variable.setParseAction(lambda x:UndefinedVariable("".join(x)).raiseself())
varnames = varnames | undefined_variable'''
possible_variables = re.split(general_whitespace, string) # List of all alnums in string
bad_variables = list()
for v in possible_variables:
if len(v) == 0:
continue
if v[0] <= '9' and '0' <= 'v': # Skip things that begin with numbers
continue
if v not in variables:
bad_variables.append(v)
if len(bad_variables)>0:
raise UndefinedVariable(' '.join(bad_variables))
def evaluator(variables, functions, string, cs=False):
''' Evaluate an expression. Variables are passed as a dictionary
from string to value. Unary functions are passed as a dictionary
from string to function. Variables must be floats.
cs: Case sensitive
TODO: Fix it so we can pass integers and complex numbers in variables dict
'''
# log.debug("variables: {0}".format(variables))
# log.debug("functions: {0}".format(functions))
# log.debug("string: {0}".format(string))
def lower_dict(d):
return dict([(k.lower(), d[k]) for k in d])
all_variables = copy.copy(default_variables)
all_functions = copy.copy(default_functions)
if not cs:
all_variables = lower_dict(all_variables)
all_functions = lower_dict(all_functions)
all_variables.update(variables)
all_functions.update(functions)
if not cs:
string_cs = string.lower()
all_functions = lower_dict(all_functions)
all_variables = lower_dict(all_variables)
CasedLiteral = CaselessLiteral
else:
string_cs = string
CasedLiteral = Literal
check_variables(string_cs, set(all_variables.keys()+all_functions.keys()))
if string.strip() == "":
return float('nan')
ops = { "^" : operator.pow,
"*" : operator.mul,
"/" : operator.truediv,
"+" : operator.add,
"-" : operator.sub,
}
# We eliminated extreme ones, since they're rarely used, and potentially
# confusing. They may also conflict with variables if we ever allow e.g.
# 5R instead of 5*R
suffixes={'%':0.01,'k':1e3,'M':1e6,'G':1e9,
'T':1e12,#'P':1e15,'E':1e18,'Z':1e21,'Y':1e24,
'c':1e-2,'m':1e-3,'u':1e-6,
'n':1e-9,'p':1e-12}#,'f':1e-15,'a':1e-18,'z':1e-21,'y':1e-24}
def super_float(text):
''' Like float, but with si extensions. 1k goes to 1000'''
if text[-1] in suffixes:
return float(text[:-1])*suffixes[text[-1]]
else:
return float(text)
def number_parse_action(x): # [ '7' ] -> [ 7 ]
return [super_float("".join(x))]
def exp_parse_action(x): # [ 2 ^ 3 ^ 2 ] -> 512
x = [e for e in x if isinstance(e, numbers.Number)] # Ignore ^
x.reverse()
x=reduce(lambda a,b:b**a, x)
return x
def parallel(x): # Parallel resistors [ 1 2 ] => 2/3
if len(x) == 1:
return x[0]
if 0 in x:
return float('nan')
x = [1./e for e in x if isinstance(e, numbers.Number)] # Ignore ||
return 1./sum(x)
def sum_parse_action(x): # [ 1 + 2 - 3 ] -> 0
total = 0.0
op = ops['+']
for e in x:
if e in set('+-'):
op = ops[e]
else:
total=op(total, e)
return total
def prod_parse_action(x): # [ 1 * 2 / 3 ] => 0.66
prod = 1.0
op = ops['*']
for e in x:
if e in set('*/'):
op = ops[e]
else:
prod=op(prod, e)
return prod
def func_parse_action(x):
return [all_functions[x[0]](x[1])]
number_suffix=reduce(lambda a,b:a|b, map(Literal,suffixes.keys()), NoMatch()) # SI suffixes and percent
(dot,minus,plus,times,div,lpar,rpar,exp)=map(Literal,".-+*/()^")
number_part=Word(nums)
inner_number = ( number_part+Optional("."+number_part) ) | ("."+number_part) # 0.33 or 7 or .34
number=Optional(minus | plus)+ inner_number + \
Optional(CaselessLiteral("E")+Optional("-")+number_part)+ \
Optional(number_suffix) # 0.33k or -17
number=number.setParseAction( number_parse_action ) # Convert to number
# Predefine recursive variables
expr = Forward()
factor = Forward()
def sreduce(f, l):
''' Same as reduce, but handle len 1 and len 0 lists sensibly '''
if len(l)==0:
return NoMatch()
if len(l)==1:
return l[0]
return reduce(f, l)
# Handle variables passed in. E.g. if we have {'R':0.5}, we make the substitution.
# Special case for no variables because of how we understand PyParsing is put together
if len(all_variables)>0:
# We sort the list so that var names (like "e2") match before
# mathematical constants (like "e"). This is kind of a hack.
all_variables_keys = sorted(all_variables.keys(), key=len, reverse=True)
varnames = sreduce(lambda x,y:x|y, map(lambda x: CasedLiteral(x), all_variables_keys))
varnames.setParseAction(lambda x:map(lambda y:all_variables[y], x))
else:
varnames=NoMatch()
# Same thing for functions.
if len(all_functions)>0:
funcnames = sreduce(lambda x,y:x|y, map(lambda x: CasedLiteral(x), all_functions.keys()))
function = funcnames+lpar.suppress()+expr+rpar.suppress()
function.setParseAction(func_parse_action)
else:
function = NoMatch()
atom = number | function | varnames | lpar+expr+rpar
factor << (atom + ZeroOrMore(exp+atom)).setParseAction(exp_parse_action) # 7^6
paritem = factor + ZeroOrMore(Literal('||')+factor) # 5k || 4k
paritem=paritem.setParseAction(parallel)
term = paritem + ZeroOrMore((times|div)+paritem) # 7 * 5 / 4 - 3
term = term.setParseAction(prod_parse_action)
expr << Optional((plus|minus)) + term + ZeroOrMore((plus|minus)+term) # -5 + 4 - 3
expr=expr.setParseAction(sum_parse_action)
return (expr+stringEnd).parseString(string)[0]
if __name__=='__main__':
variables={'R1':2.0, 'R3':4.0}
functions={'sin':numpy.sin, 'cos':numpy.cos}
print "X",evaluator(variables, functions, "10000||sin(7+5)-6k")
print "X",evaluator(variables, functions, "13")
print evaluator({'R1': 2.0, 'R3':4.0}, {}, "13")
print evaluator({'e1':1,'e2':1.0,'R3':7,'V0':5,'R5':15,'I1':1,'R4':6}, {},"e2")
print evaluator({'a': 2.2997471478310274, 'k': 9, 'm': 8, 'x': 0.66009498411213041}, {}, "5")
print evaluator({},{}, "-1")
print evaluator({},{}, "-(7+5)")
print evaluator({},{}, "-0.33")
print evaluator({},{}, "-.33")
print evaluator({},{}, "5+1*j")
print evaluator({},{}, "j||1")
print evaluator({},{}, "e^(j*pi)")
print evaluator({},{}, "5+7 QWSEKO")