Yet Another Solver

solver.py

import matplotlib.pyplot as plt
import numpy as np


class Solution:
    def __init__(
        self,
        a: float,
        b: list[float],
        c: list[float],
        d: float,
    ) -> None:
        self.a: float = a
        self.b: list[float] = b.copy()
        self.c: list[float] = c.copy()
        self.d: float = d
        # breakpoints
        self.bps: list[float] = [-ci / bi for bi, ci in zip(self.b, self.c)]

    def f(self, x: float):
        return (
            self.a / 2 * x * x
            + self.d * x
            + sum(bi * x + ci for bi, ci in zip(self.b, self.c) if bi * x + ci >= 0)
        )

    def fp(self, x: float):
        return (
            self.a * x
            + self.d
            + sum(bi for bi, ci in zip(self.b, self.c) if bi * x + ci >= 0)
        )

    def fp_zero(self, x: float):
        z = (
            -(self.d + sum(bi for bi, ci in zip(self.b, self.c) if bi * x + ci >= 0))
            / self.a
        )
        plt.plot(z, 0, "o", color="#9b59b6", markersize=3)

    def plt_fp(self, f=False, fp=True):
        xs = np.linspace(min(self.bps) - 1, max(self.bps) + 1, 10000)
        bps = [bp + 1e-4 for bp in self.bps]

        # axis X
        plt.xlabel("x")
        plt.axhline(color="grey", linestyle="--")
        # axis Y
        plt.ylabel("y")
        plt.axvline(color="grey", linestyle="--")

        if f:
            f_xs = np.array([self.f(x) for x in xs])
            f_bps = np.array([self.f(x) for x in bps])
            plt.plot(xs, f_xs, color="#16a085")

        if fp:
            fp_xs = np.array([self.fp(x) for x in xs])
            fp_bps = np.array([self.fp(x) for x in bps])
            plt.plot(xs, fp_xs)
            plt.plot(bps, fp_bps, "o", color="#2980b9", markersize=3)
            for bp, fp_bp in zip(bps, fp_bps):
                plt.axline(
                    (bp, fp_bp), slope=a, color="grey", linestyle=":", linewidth=0.5
                )
            for bp in bps:
                self.fp_zero(bp)

        plt.show()


m = 3
a = 1.5
d = 1
b = [1, 1.2, -0.9]
c = [0.1, -1.4, -1.2]
# m = 10
# a = abs(np.random.normal(0, 1))
# d = np.random.normal(0, 1)
# b = list(np.random.normal(0, 1, m))
# c = list(np.random.normal(0, 1, m))
Solution(a, b, c, d).plt_fp()