feat: add BigO analysis (#90)

* feat: add BigO analysis

* docs: add analysis to api reference

* fix: add warnings for BigO

* fix: improve warnings for BigO

docs/reference.md

@@ -2,6 +2,8 @@
 
 ::: bartiq
 
+::: bartiq.analysis
+
 ::: bartiq.precompilation
 
 ::: bartiq.symbolics

src/bartiq/analysis.py

@@ -0,0 +1,119 @@
+# Copyright 2024 PsiQuantum, Corp.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import warnings
+from typing import Optional
+
+from sympy import Expr, Function, Poly, Symbol, prod
+
+
+class BigO:
+    def __init__(self, expr: Expr, variable: Optional[Symbol] = None):
+        """Class for representing expressions in Big O notation.
+
+        It analyzes given expression and returns all the Big O terms in it.
+        If variable is provided, it analyses scaling in this particular variable,
+        otherwise it assumes all the symbols are variables.
+
+        Note:
+            It's an experimental tool and is meant to facilitate the analysis, but
+            it might not produce correct results, especially for more complicated
+            expressions. In case of any problems please create an issue on project's GitHub,
+            we'd love to hear your feedback on this!
+
+        Args:
+            expr: sympy expression we want to analyze
+            variable: variable for which we want to performa analysis.
+        """
+        if variable is None:
+            gens = []
+        else:
+            gens = [variable]
+        self.expr = _convert_to_big_O(expr, gens)
+
+    def __add__(self, other):
+        if isinstance(other, self.__class__):
+            return BigO(_remove_big_O_function(self.expr) + _remove_big_O_function(other.expr))
+        else:
+            return BigO(_remove_big_O_function(self.expr) + _remove_big_O_function(other))
+
+    def __eq__(self, other):
+        return self.expr == other.expr
+
+    def __mul__(self, other):
+        if isinstance(other, self.__class__):
+            return BigO(_remove_big_O_function(self.expr) * _remove_big_O_function(other.expr))
+        else:
+            return BigO(_remove_big_O_function(self.expr) * _remove_big_O_function(other))
+
+    def __repr__(self) -> str:
+        return f"{self.expr}"
+
+
+def _remove_big_O_function(expr: Expr) -> Expr:
+    args = expr.args
+    new_args = []
+    for arg in args:
+        if isinstance(arg, Function("O")):
+            assert len(arg.args) == 1
+            new_args.append(arg.args[0])
+        else:
+            new_args.append(arg)
+    return sum(new_args)
+
+
+def _add_big_o_function(expr: Expr) -> Expr:
+    if isinstance(expr, Function("O")):
+        return expr
+    return Function("O")(expr)
+
+
+def _convert_to_big_O(expr: Expr, gens: Optional[list[Expr]] = None) -> Expr:
+    gens = gens or []
+    if len(expr.free_symbols) == 0:
+        return _add_big_o_function(1)
+    if len(expr.free_symbols) > 1 and len(gens) == 0:
+        warnings.warn(
+            "Results for using BigO with multiple variables might be unreliable. "
+            "For better results please select a variable of interest."
+        )
+    poly = Poly(expr, *gens)
+    leading_terms = _get_leading_terms(poly)
+    return sum(map(_add_big_o_function, leading_terms))
+
+
+def _get_leading_terms(poly):
+    terms, _ = zip(*poly.terms())
+    leading_terms = []
+    for term in terms:
+        if not _term_less_than_or_equal_to_all_others(term, leading_terms):
+            leading_terms.append(term)
+
+    return [_make_term_expression(poly.gens, leading_term) for leading_term in leading_terms]
+
+
+def _term_less_than_or_equal_to_all_others(candidate, other_terms):
+    if not other_terms:
+        return False
+
+    return all(_less_than(candidate, term) for term in other_terms)
+
+
+def _less_than(term_1, term_2):
+    return all(a <= b for a, b in zip(term_1, term_2))
+
+
+def _make_term_expression(gens, term):
+    powers = [gen**order for gen, order in zip(gens, term)]
+    return prod(powers)

tests/test_analysis.py

@@ -0,0 +1,92 @@
+# Copyright 2024 PsiQuantum, Corp.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import pytest
+import sympy
+from sympy.abc import x, y
+
+from bartiq.analysis import BigO
+
+
+@pytest.mark.parametrize(
+    "expr,variable,expected",
+    [
+        (
+            x**y + y**x + x * y + x**2 * y + 3 + x * y**2 + x + y + 1,
+            None,
+            BigO(x**y) + BigO(y**x) + BigO(x * y**2) + BigO(x**2 * y),
+        ),
+        (
+            x * y + x**2 * y + 3 + x * y**3 + x + y + 1,
+            x,
+            BigO(x**2),
+        ),
+        (
+            x * y + x**2 * y + 3 + x * y**3 + x + y + 1,
+            y,
+            BigO(y**3),
+        ),
+        (
+            sympy.sympify("f(x) + y"),
+            y,
+            BigO(y),
+        ),
+        (
+            sympy.sympify("log(x) + y**2 + y"),
+            None,
+            BigO(sympy.sympify("log(x)")) + BigO(y**2),
+        ),
+    ],
+)
+def test_BigO(expr, variable, expected):
+    assert BigO(expr, variable) == expected
+
+
+def test_BigO_throws_warning_for_multiple_variables():
+    with pytest.warns(
+        match="Results for using BigO with multiple variables might be unreliable. "
+        "For better results please select a variable of interest."
+    ):
+        BigO(x**y + y**x + x * y + x**2 * y + 3 + x * y**2 + x + y + 1)
+
+
+def test_adding_BigO_expressions():
+    assert BigO(x) + BigO(x) == BigO(x)
+    assert BigO(x) * BigO(x) == BigO(x**2)
+    assert BigO(2 * y + 17) + BigO(x - 1) == BigO(x) + BigO(y)
+    assert BigO(x, variable=y) + BigO(y, variable=x) == BigO(sympy.sympify(1))
+
+
+@pytest.mark.parametrize(
+    "expr,gens,expected",
+    [
+        (
+            x**0.5,
+            x,
+            BigO(x**0.5),
+        ),
+        (
+            sympy.log(x) + sympy.log(x) * x,
+            x,
+            BigO(sympy.log(x) * x),
+        ),
+        (
+            sympy.log(x) + sympy.log(x) * x,
+            x,
+            BigO(sympy.log(x) * x),
+        ),
+    ],
+)
+def test_failing_big_O_cases(expr, gens, expected):
+    pytest.xfail()