Mapytex/pymath/calculus/str2tokens.py

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#!/usr/bin/env python
# encoding: utf-8
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from .generic import Stack, isOperator, isNumber, isPolynom
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from .operator import op
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from decimal import Decimal
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def str2tokens(exp):
""" Parse the string into tokens then turn it into postfix form
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>>> str2tokens('2+3*4')
[2, 3, 4, '*', '+']
>>> str2tokens('2*3+4')
[2, 3, '*', 4, '+']
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>>> str2tokens('2x+4')
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[2, < <class 'pymath.calculus.polynom.Polynom'> [0, 1]>, '*', 4, '+']
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"""
in_tokens = str2in_tokens(exp)
post_tokens = in2post_fix(in_tokens)
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return post_tokens
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def str2in_tokens(exp):
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""" Parse the expression, ie tranform a string into a list of tokens
/!\ float are not availiable yet!
:param exp: The expression (a string)
:returns: list of token
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>>> str2in_tokens('2+3*4')
[2, '+', 3, '*', 4]
>>> str2in_tokens('2*3+4')
[2, '*', 3, '+', 4]
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"""
tokens = ['']
for character in exp:
if character.isdigit():
# for "big" numbers (like 2345)
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if isinstance(tokens[-1], int):
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if tokens[-1] > 0:
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tokens[-1] = tokens[-1] * 10 + int(character)
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else:
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tokens[-1] = tokens[-1] * 10 - int(character)
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elif isinstance(tokens[-1], Decimal):
after_coma += 1
if tokens[-1] >= 0:
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tokens[-1] = tokens[-1] + int(character) * Decimal('0.1') ** after_coma
else:
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tokens[-1] = tokens[-1]- int(character) * Decimal('0.1') ** after_coma
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# Special case for "-" at the begining of an expression or before
# "("
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elif tokens[-1] == "-" and \
str(tokens[-2]) in " (+-*/:":
tokens[-1] = - int(character)
else:
tokens.append(int(character))
elif character in "+-*/:^":
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tokens.append(character)
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elif character == ")":
tokens.append(character)
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elif character == "(":
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# If "3(", ")(", "x("
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if isNumber(tokens[-1]) \
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or tokens[-1] == ")" \
or isPolynom(tokens[-1]):
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tokens.append("*")
tokens.append(character)
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elif character.isalpha():
# If "3x", ")x", "xy"
if isNumber(tokens[-1]) \
or tokens[-1] == ")" \
or isPolynom(tokens[-1]):
tokens.append("*")
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from pymath.calculus.polynom import Polynom
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tokens.append(Polynom([0, 1], letter=character))
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elif character == ".":
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if isinstance(tokens[-1], Decimal):
raise ValueError("A number has 2 points...!")
else:
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tokens[-1] = Decimal(tokens[-1])
after_coma = 0
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elif character != " ":
raise ValueError("{} is an unvalid character".format(character))
return tokens[1:]
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def in2post_fix(infix_tokens):
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""" From the infix_tokens list compute the corresponding postfix_tokens list
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@param infix_tokens: the infix list of tokens to transform into postfix form.
@return: the corresponding postfix list of tokens.
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>>> in2post_fix(['(', 2, '+', 5, '-', 1, ')', '/', '(', 3, '*', 4, ')'])
[2, 5, 1, '-', '+', 3, 4, '*', '/']
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>>> in2post_fix(['-', '(', '-', 2, ')'])
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[2, '-', '-']
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>>> in2post_fix(['-', '(', '-', 2, '+', 3, '*', 4, ')'])
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[2, '-', 3, 4, '*', '+', '-']
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"""
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# Stack where operator will be stocked
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opStack = Stack()
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# final postfix list of tokens
postfix_tokens = []
# stack with the nbr of tokens still to compute in postfix_tokens
arity_Stack = Stack()
arity_Stack.push(0)
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for (pos_token, token) in enumerate(infix_tokens):
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# Pour voir ce qu'il se passe dans cette procédure
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#print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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if token == ")":
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next_op = opStack.pop()
while next_op != "(":
postfix_tokens.append(next_op)
next_op = opStack.pop()
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# Go back to old arity
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arity_Stack.pop()
# Raise the arity
arity = arity_Stack.pop()
arity_Stack.push(arity + 1)
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elif op.can_be_operator(token):
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if token == "(":
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opStack.push(op.get_op(token))
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# Set next arity counter
arity_Stack.push(0)
else:
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arity = arity_Stack.pop()
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token_op = op.get_op(token, arity + 1)
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# Reset arity to 0 in case there is other operators (the real
# operation would be "-op.arity + 1")
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arity_Stack.push(0)
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while (not opStack.isEmpty()) and opStack.peek(
).priority >= token_op.priority:
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next_op = opStack.pop()
postfix_tokens.append(next_op)
opStack.push(token_op)
#print("--", token, " -> ", str(arity + 1))
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else:
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postfix_tokens.append(token)
arity = arity_Stack.pop()
arity_Stack.push(arity + 1)
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# Pour voir ce qu'il se passe dans cette procédure
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#print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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while not opStack.isEmpty():
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next_op = opStack.pop()
postfix_tokens.append(next_op)
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# Pour voir ce qu'il se passe dans cette procédure
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#print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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if arity_Stack.peek() != 1:
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raise ValueError(
"Unvalid expression. The arity Stack is ",
str(arity_Stack))
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return postfix_tokens
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if __name__ == '__main__':
#a, s, m, d, p = Operator("+"), Operator("-"), Operator("*"), Operator("/"), Operator("^")
#in_tokens = str2in_tokens("2+3*4")
#print("\t in_tokens :" + str(in_tokens))
#
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# print(in2post_fix(in_tokens))
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#print(in2post_fix([op.par, 2, op.add, 5, op.sub, 1, ')', op.div, op.par, 3, op.mul, 4, ')']))
#print(in2post_fix([op.sub1, op.par, op.sub1, 2, ')']))
#print(in2post_fix([op.sub1, op.par, op.sub1, 2, op.add, 3, op.mul, 4, ')']))
print(str2tokens('2*3+4'))
print("\n------")
print(str2tokens('2x+4'))
print("\n------")
print(str2tokens('xx+4'))
print("\n------")
print(str2tokens('x(2+1)+4'))
print("\n------")
#import doctest
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# doctest.testmod()
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# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del