Added math expressions parser

This commit is contained in:
Dmitriy Shishkov 2023-10-09 07:03:54 +03:00
parent 2b260b0762
commit 5763c996c4
Signed by: dm1sh
GPG Key ID: 027994B0AA357688
13 changed files with 922 additions and 0 deletions

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parser/.gitignore vendored Normal file
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*.pyc

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parser/README.md Normal file
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# Math expression parser
Math expression evaluation library. It supports most of useful math operations and functions. Expressions can contain variables which can be substituted with `int`s, `float`s or `numpy.ndarray`s.
## Example usage
```python
from parser import Parser
parser = Parser("(-b + sqrt(b^2-4a c))/(2a)")
parser.variables_names # {'c', 'a', 'b'}
parser.evaluate({"a": 1, "b": -3, "c": 2}) # 1.0
parser.evaluate({"a": [1, 1, 1], "b": [-5, -6, -9], "c": [6, 9, 20]}) # [2. 3. 4.]
```
## Expression syntax
Expression can contain numbers or variable names with functions applyed to them, separated with operators or united with braces.
Theese are supported:
Functions:
|name| math |
|--|--|
| `abs` | $\|x\|$ |
| `acos` | $\cos^{-1}(x)$ |
| `acosh` | $\cosh^{-1}(x)$ |
| `acot` | $\cot^{-1}(x)$ |
| `asin` | $\sin^{-1}(x)$ |
| `asinh` | $\sinh^{-1}(x)$ |
| `atan` | $\tan^{-1}(x)$ |
| `avg` | $\overline x$ |
| `cos` | $\cos(x)$ |
| `cosh` | $\cosh(x)$ |
| `cot` | $\cot(x)$ |
| `exp` | $\exp(x)$ |
| `lg` | $\lg(x)$ |
| `ln` | $\ln(x)$ |
| `log10` | $\log_{10}(x)$ |
| `log2` | $\log_2(x)$ |
| `prod` | $\displaystyle \prod_{i=0}^n x_i$ |
| `sgn` | $sgn(x)$ |
| `sin` | $\sin(x)$ |
| `sinh` | $\sinh(x)$ |
| `sqrt` | $\sqrt{x}$ |
| `sum` | $\displaystyle\sum_{i=0}^n x_i$ |
| `tan` | $\tan(x)$ |
| `tanh` | $\tanh(x)$ |
Operators: `+`, `-`, `*`, `/`, `^`, `%`
Braces: `()`, `[]`, `{}`
Floating points: `.`, `,`
Functions have only one argument, provided in braces. Operators must have two operands except minus (if it is the first character of equation or braced expression).
`sum` and `prod` sums and multiplies all elements in variable if it is `numpy.ndarray` and produces a `float`.
**! There is no error handling yet !**

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parser/parser/__init__.py Normal file
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from .parser import (
BinaryExpression,
Expression,
Operation,
Parser,
Token,
Tokenizer,
UnaryExpression,
ValueExpression,
)
__all__ = (
"BinaryExpression",
"Expression",
"Operation",
"Parser",
"Token",
"Tokenizer",
"UnaryExpression",
"ValueExpression",
)

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parser/parser/__main__.py Normal file
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from parser import Parser
expression = input("Input math expression: ")
parser = Parser(expression)
print("Variables in your expression: " + ", ".join(parser.variables_names))
variables = {}
for key in parser.variables_names:
variables[key] = float(input(f"Input '{key}' variable value: "))
res = parser.evaluate(variables)
print(f"Evaluation result is: {res}")

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import abc
from collections.abc import Callable, Mapping
from .types import FunctionType, OperatorType, ValueType
class Expression(abc.ABC):
_evaluator: Callable[[Mapping[str, ValueType]], ValueType]
def evaluate(self, variables: Mapping[str, ValueType]):
return self._evaluator(variables)
class ValueExpression(Expression):
def __init__(self, a: str | ValueType):
self.__debug_a = a
if isinstance(a, str):
self._evaluator = lambda vars: vars[a]
else:
self._evaluator = lambda _: a
def __repr__(self):
return f"<{self.__debug_a}>"
class UnaryExpression(Expression):
def __init__(self, function: FunctionType, a: Expression):
self.__debug_f = function.__name__
self.__debug_a = repr(a)
self._evaluator = lambda vars: function(a.evaluate(vars))
def __repr__(self):
return f"<{self.__debug_f}({self.__debug_a})>"
class BinaryExpression(Expression):
def __init__(
self,
function: OperatorType,
a: Expression,
b: Expression,
):
self.__debug_f = function.__name__
self.__debug_a = repr(a)
self.__debug_b = repr(b)
self._evaluator = lambda vars: function(a.evaluate(vars), b.evaluate(vars))
def __repr__(self):
return f"<{self.__debug_a} {self.__debug_f} {self.__debug_b}>"

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from dataclasses import dataclass
import numpy as np
from .types import FunctionType, OperatorType, ValueType
def acot(x: ValueType):
return np.arctan(1 / x)
def cot(x: ValueType):
return 1 / np.tan(x)
functions: dict[str, FunctionType] = {
"abs": np.abs,
"acos": np.arccos,
"acosh": np.arccosh,
"acot": acot,
"asin": np.arcsin,
"asinh": np.arcsinh,
"atan": np.arctan,
"avg": np.average,
"cos": np.cos,
"cosh": np.cosh,
"cot": cot,
"exp": np.exp,
"lg": np.log10,
"ln": np.log,
"log10": np.log10,
"log2": np.log2,
"prod": np.prod,
"sgn": np.sign,
"sin": np.sin,
"sinh": np.sinh,
"sqrt": np.sqrt,
"sum": np.sum,
"tan": np.tan,
"tah": np.tanh,
}
operators: dict[str, OperatorType] = {
"+": np.add,
"-": np.subtract,
"*": np.multiply,
"/": np.divide,
"%": np.mod,
"^": np.float_power,
}
priorities: dict[str, int] = {
"(": 0,
"+": 1,
"-": 1,
"*": 2,
"/": 2,
"%": 2,
"^": 3,
"f": 4, # function
")": 5,
}
@dataclass
class Operation:
evaluator: (FunctionType | OperatorType | str)
priority: int
size: int
class FunctionOperation(Operation):
def __init__(self, name: str):
super().__init__(functions[name], priorities["f"], 1)
class BraceOperation(Operation):
def __init__(self, name: str):
super().__init__(name, priorities[name], 0)
class OperatorOperation(Operation):
def __init__(self, name: str):
super().__init__(operators[name], priorities[name], 2)

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from collections.abc import Mapping
from .expression import BinaryExpression, Expression, UnaryExpression, ValueExpression
from .operation import (
BraceOperation,
FunctionOperation,
Operation,
OperatorOperation,
priorities,
)
from .tokenizer import Token, Tokenizer
from .types import ValueType
class Parser:
def __init__(self, input_expr: str):
self.input_expr = input_expr
self.variables_names: set[str] = set()
self.tokenize()
self.parse()
def tokenize(self):
self.tokens = Tokenizer(self.input_expr)
def parse(self):
self.val_stack: list[Expression] = []
self.op_stack: list[Operation] = []
for t_val, t_type in self.tokens:
if t_type in (Token.Number, Token.Variable):
self.val_stack.append(ValueExpression(t_val))
if t_type == Token.Variable:
self.variables_names.add(t_val)
elif t_type == Token.Function:
self.op_stack.append(FunctionOperation(t_val))
elif t_type == Token.LBrace:
self.op_stack.append(BraceOperation("("))
elif t_type == Token.RBrace:
while len(self.op_stack) > 0 and not (
self.op_stack[-1].size == 0 and self.op_stack[-1].priority == 0
): # until next in stack is lbrace
self.do_one()
self.op_stack.pop() # pop lbrace
elif t_type == Token.Operator:
t_priority = priorities[t_val]
while (
len(self.op_stack) > 0 and self.op_stack[-1].priority > t_priority
):
self.do_one()
self.op_stack.append(OperatorOperation(t_val))
while len(self.op_stack) > 0:
self.do_one()
self._evaluator = self.val_stack[0].evaluate
self.__debug_expr = repr(self.val_stack)
def evaluate(self, variables: Mapping[str, ValueType]):
return self._evaluator(variables)
def do_one(self):
op = self.op_stack.pop()
if op.size == 1:
a = self.val_stack.pop()
self.val_stack.append(UnaryExpression(op.evaluator, a))
elif op.size == 2:
b, a = self.val_stack.pop(), self.val_stack.pop() # inversed pop order
self.val_stack.append(BinaryExpression(op.evaluator, a, b))
def __repr__(self):
return self.__debug_expr

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from collections.abc import Generator
from dataclasses import dataclass
from typing import Optional
from .operation import functions, operators
from .types import Token, TokenType
@dataclass
class Tokenizer:
expression: str
def __iter__(self) -> Generator[TokenType, None, None]:
accumulator = ""
prev = None
for ch in self.expression:
if (breaker_type := self.is_breaker(ch)) is not None:
if len(accumulator) > 0:
# ch is `(` after function name
if breaker_type == Token.LBrace and self.is_function(accumulator):
yield accumulator, Token.Function
prev = Token.Function
accumulator = ""
else:
value, token_type = self.detect_number(accumulator)
yield value, token_type
prev = token_type
accumulator = ""
# `(` after variable or number
if breaker_type == Token.LBrace:
yield "*", Token.Operator
prev = Token.Operator
# Unary minus case
if ch == "-" and (prev == Token.LBrace or prev is None):
yield 0, Token.Number
prev = Token.Number
# `(expr)(expr)` case
if breaker_type == Token.LBrace and prev == Token.RBrace:
yield "*", Token.Operator
prev = Token.Operator
if breaker_type != Token.Space:
yield ch, breaker_type
prev = breaker_type
else:
# Variable or function name after braced expr or variable and space
if prev == Token.RBrace or prev == Token.Variable:
yield "*", Token.Operator
prev = Token.Operator
# Floating point number
if ch in ",.":
accumulator += "."
continue
# Variable or function name after number
if (
not ch.isdecimal()
and (num := Tokenizer.is_number(accumulator)) is not None
):
yield num, Token.Number
yield "*", Token.Operator
prev = Token.Operator
accumulator = ""
accumulator += ch
if len(accumulator) > 0:
yield self.detect_number(accumulator)
@staticmethod
def is_breaker(character) -> Optional[Token]:
if character in operators:
return Token.Operator
if character in "([{":
return Token.LBrace
if character in ")]}":
return Token.RBrace
if character == " ":
return Token.Space
return None
@staticmethod
def is_number(string) -> Optional[float]:
try:
return float(string)
except ValueError:
return None
@staticmethod
def detect_number(string) -> TokenType:
if (num := Tokenizer.is_number(string)) is not None:
return num, Token.Number
else:
return string, Token.Variable
@staticmethod
def is_function(lexeme: str) -> bool:
if lexeme in functions:
return True
return False

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from collections.abc import Callable
from enum import Enum, auto
import numpy as np
ValueType = int | float | np.ndarray
FunctionType = Callable[[ValueType], ValueType]
OperatorType = Callable[[ValueType, ValueType], ValueType]
class Token(Enum):
Variable = auto()
Number = auto()
Function = auto()
Operator = auto()
LBrace = auto()
RBrace = auto()
Space = auto()
TokenType = tuple[str | float, Token]

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[[package]]
name = "typeguard"
version = "3.0.2"
description = "Run-time type checker for Python"
category = "dev"
optional = false
python-versions = ">=3.7.4"
files = [
{file = "typeguard-3.0.2-py3-none-any.whl", hash = "sha256:bbe993854385284ab42fd5bd3bee6f6556577ce8b50696d6cb956d704f286c8e"},
{file = "typeguard-3.0.2.tar.gz", hash = "sha256:fee5297fdb28f8e9efcb8142b5ee219e02375509cd77ea9d270b5af826358d5a"},
]
[package.extras]
doc = ["packaging", "sphinx-autodoc-typehints (>=1.2.0)", "sphinx-rtd-theme"]
test = ["mypy (>=0.991)", "pytest (>=7)"]
[[package]]
name = "typing-extensions"
version = "4.8.0"
description = "Backported and Experimental Type Hints for Python 3.8+"
category = "dev"
optional = false
python-versions = ">=3.8"
files = [
{file = "typing_extensions-4.8.0-py3-none-any.whl", hash = "sha256:8f92fc8806f9a6b641eaa5318da32b44d401efaac0f6678c9bc448ba3605faa0"},
{file = "typing_extensions-4.8.0.tar.gz", hash = "sha256:df8e4339e9cb77357558cbdbceca33c303714cf861d1eef15e1070055ae8b7ef"},
]
[metadata]
lock-version = "2.0"
python-versions = ">=3.11,<3.13"
content-hash = "3180680d07071b1bed28aa242a0feb41baa73446b6edfefab15e2252da5dfdbf"

25
parser/pyproject.toml Normal file
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@ -0,0 +1,25 @@
[tool.poetry]
name = "parser"
version = "0.1.0"
description = ""
authors = ["dm1sh <me@dmitriy.icu>"]
readme = "README.md"
[tool.poetry.dependencies]
python = ">=3.11,<3.13"
numpy = "^1.26.0"
[tool.poetry.group.dev.dependencies]
black = "^23.9.1"
mypy = "^1.5.1"
ruff = "^0.0.292"
jedi-language-server = "^0.41.1"
isort = "^5.12.0"
[build-system]
requires = ["poetry-core"]
build-backend = "poetry.core.masonry.api"
[tool.isort]
profile = "black"

0
parser/tests/__init__.py Normal file
View File

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@ -0,0 +1,14 @@
from parser import Parser
def test_Parser():
parser = Parser("(-b + sqrt(b^2-4a c))/(2a)")
assert parser.variables_names == {"c", "a", "b"}
assert parser.evaluate({"a": 1, "b": -3, "c": 2}) == 1.0
assert all(
parser.evaluate({"a": [1, 1, 1], "b": [-5, -6, -9], "c": [6, 9, 20]})
== [2.0, 3.0, 4.0]
)