backend/src/optimization_manager.py

import numpy as np
from sympy import (
    lambdify, 
    symbols, 
    sin, 
    cos, 
    tan,
    asin,
    acos,
    atan,
    exp, 
    log,
    sqrt,
    pi,
    Abs,
)

from sympy.parsing.sympy_parser import (
    standard_transformations,
    implicit_multiplication_application,
    convert_xor,
    parse_expr,
)

from optimization_logic import *


class OptimizationManager:
    def __init__(self):
        self.function_values = {"x": [], "y": []}
        self.trajectory_values = {"x": [], "y": []}
        self.settings = {}

    def handle_update_settings(self, new_settings) -> dict[str, dict] | None:
        if new_settings == self.settings:
            return None

        non_relayout_settings = (new_settings.keys() | self.settings.keys()) - {"xlim", "ylim"}
        non_relayout_settings_changed = any(
            new_settings.get(k) != self.settings.get(k)
            for k in non_relayout_settings
        )

        self.settings = new_settings

        function = new_settings.get("functionExpr", "").strip()
        mode = new_settings.get("mode", "").lower().strip()
        xlim = new_settings.get("xlim", [])
        ylim = new_settings.get("ylim", [])

        if not self._is_valid_function(function, mode, xlim, ylim):
            return {
                "trajectoryValues": {"x": [], "y": []},
                "functionValues": {"x": [], "y": []},
            }

        if non_relayout_settings_changed:
            self._reset_trajectory() 

        if not self._function_changed(function, mode):
            return {
                "trajectoryValues": self.trajectory_values,
            }

        try:
            self._compute_function_values(function, mode, xlim, ylim)
        except Exception as e:
            self.function_values = {"x": [], "y": []}
            self.trajectory_values = {"x": [], "y": []}

        return {
            "functionValues": self.function_values,
            "trajectoryValues": self.trajectory_values,
        }

    def handle_reset(self) -> dict[str, list]:
        self._reset_trajectory()
        return {
            "trajectoryValues": self.trajectory_values,
        }

    def handle_next_step(self) -> dict[str, list]:
        current_steps = len(self.trajectory_values["x"])
        self._compute_trajectory_values(self.settings, current_steps + 1)
        return {
            "trajectoryValues": self.trajectory_values,
        }

    def handle_prev_step(self) -> dict[str, list]:
        current_steps = len(self.trajectory_values["x"])
        if current_steps > 1:
            self._compute_trajectory_values(self.settings, current_steps - 1)
        return {
            "trajectoryValues": self.trajectory_values,
        }

    def handle_play(self) -> dict[str, list]:
        pass

    def handle_pause(self) -> dict[str, list]:
        pass

    def _is_valid_function(
        self, function: str, mode: str, xlim: list, ylim: list
    ) -> bool:
        # axis limit checks
        if len(xlim) != 2 or len(ylim) != 2:
            return False
        if xlim[0] >= xlim[1] or ylim[0] >= ylim[1]:
            return False

        # function expression check
        try:
            expr = self._parse_function(function)
        except Exception as e:
            return False

        if mode == "univariate" and symbols("y") in expr.free_symbols:
            return False

        return True
        
    def _function_changed(self, function: str, mode: str) -> bool:
        function = function.strip()
        previous_function = self.settings.get("function", "").strip()
        previous_mode = self.settings.get("mode", "")
        return function != previous_function or mode != previous_mode

    def _reset_trajectory(self) -> None:
        try:
            self._compute_trajectory_values(self.settings, steps=1)
        except Exception as e:
            self.trajectory_values = {"x": [], "y": []}

    def _parse_function(self, function: str) -> Expr:
        if not function.strip():
            raise ValueError("Function expression cannot be empty")

        x, y = symbols("x y")
        allowed_locals = {
            'x': x,
            'y': y,
            'sin': sin,
            'cos': cos,
            'tan': tan,
            'asin': asin,
            'acos': acos,
            'atan': atan,
            'log': log,
            'ln': log,
            'sqrt': sqrt,
            'abs': Abs,
            'exp': exp,
            'e': exp(1),
            'pi': pi,
            'π': pi,
        }

        try:
            parsed_function = parse_expr(
                function,
                local_dict=allowed_locals,
                transformations=standard_transformations + (
                    implicit_multiplication_application,
                    convert_xor,
                ),
                evaluate=True,
            )
        except Exception as e:
            raise ValueError(f"Invalid function expression: {e}")

        unknown_symbols = parsed_function.free_symbols - {x, y}
        if unknown_symbols:
            unknown_names = ", ".join(sorted(str(s) for s in unknown_symbols))
            raise ValueError(f"Unknown variable(s): {unknown_names}. Allowed: x, y")
        
        return parsed_function

    def _compute_function_values(self, function: str, mode: str, xlim: list, ylim: list) -> None:
        expr = self._parse_function(function)

        if mode == "univariate":
            x = np.linspace(xlim[0], xlim[1], 100)
            f = lambdify('x', expr, modules=['numpy'])
            y = f(x)

            if not isinstance(y, np.ndarray):
                y = np.full_like(x, y)

            self.function_values = {
                "x": x.tolist(),
                "y": y.tolist(),
            }

        elif mode == "bivariate":
            x = np.linspace(xlim[0], xlim[1], 100)
            y = np.linspace(ylim[0], ylim[1], 100)
            X, Y = np.meshgrid(x, y)
            f = lambdify(('x', 'y'), expr, modules=['numpy'])
            Z = f(X, Y)

            if not isinstance(Z, np.ndarray):
                Z = np.full_like(X, Z)

            self.function_values = {
                "x": x.tolist(),
                "y": y.tolist(),
                "z": Z.tolist(),
            }

        else:
            raise ValueError("Unsupported mode")

    def _compute_trajectory_values(self, settings: dict, steps: int) -> None:
        mode = settings.get("mode", "").lower().strip()
        algorithm = settings.get("algorithm", "").lower().strip().replace(" ", "_")
        function = self._parse_function(settings.get("functionExpr", "").strip())

        if mode == "univariate":
            if algorithm == "gradient_descent":
                self.trajectory_values = gd_univariate(
                    function,
                    float(settings["x0"]),
                    float(settings["learningRate"]),
                    float(settings["momentum"]),
                    steps,
                )
            elif algorithm == "nesterov":
                self.trajectory_values = nesterov_univariate(
                    function,
                    float(settings["x0"]),
                    float(settings["learningRate"]),
                    float(settings["momentum"]),
                    steps,
                )
            elif algorithm == "adam":
                self.trajectory_values = adam_univariate(
                    function,
                    float(settings["x0"]),
                    float(settings["learningRate"]),
                    float(settings["beta1"]),
                    float(settings["beta2"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "adagrad":
                self.trajectory_values = adagrad_univariate(
                    function,
                    float(settings["x0"]),
                    float(settings["learningRate"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "rmsprop":
                self.trajectory_values = rmsprop_univariate(
                    function,
                    float(settings["x0"]),
                    float(settings["learningRate"]),
                    float(settings["beta"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "adadelta":
                self.trajectory_values = adadelta_univariate(
                    function,
                    float(settings["x0"]),
                    float(settings["beta"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "newton":
                self.trajectory_values = newton_univariate(
                    function,
                    float(settings["x0"]),
                    steps,
                )
            else:
                raise ValueError("Unsupported algorithm for univariate mode")

        elif mode == "bivariate":
            if algorithm == "gradient_descent":
                self.trajectory_values = gd_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    float(settings["learningRate"]),
                    float(settings["momentum"]),
                    steps,
                )
            elif algorithm == "nesterov":
                self.trajectory_values = nesterov_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    float(settings["learningRate"]),
                    float(settings["momentum"]),
                    steps,
                )
            elif algorithm == "adam":
                self.trajectory_values = adam_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    float(settings["learningRate"]),
                    float(settings["beta1"]),
                    float(settings["beta2"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "adagrad":
                self.trajectory_values = adagrad_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    float(settings["learningRate"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "rmsprop":
                self.trajectory_values = rmsprop_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    float(settings["learningRate"]),
                    float(settings["beta"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "adadelta":
                self.trajectory_values = adadelta_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    float(settings["beta"]),
                    float(settings["epsilon"]),
                    steps,
                )
            elif algorithm == "newton":
                self.trajectory_values = newton_bivariate(
                    function,
                    float(settings["x0"]),
                    float(settings["y0"]),
                    steps,
                )
            else:
                raise ValueError("Unsupported algorithm for bivariate mode")