mirror of
https://github.com/rodneyosodo/numerical-analysis.git
synced 2026-06-23 04:10:09 +00:00
0x6f736f646f
98 lines
3.8 KiB
Python
98 lines
3.8 KiB
Python
import math
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import cmath
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import numpy as np
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from matplotlib import pyplot as plt
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class SOLVECCH:
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def __init__(self):
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self.a = None
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self.b = None
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self.c = None
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self.y_o = None
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self.y_prime = None
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self.X = np.linspace(-1 * np.pi, np.pi, 100)
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def get_inputs(self):
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"""
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Gets the user inputs for the coefficients and initial conditions
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a: The coefficient a
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b: The coefficient b
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c: The coefficient c
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y_o: Initial condition when y(0) is equal to a value
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y_prime: Initial condition when y'(0) is equal to a value
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"""
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self.a = float(input("Enter the value of a: "))
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self.b = float(input("Enter the value of b: "))
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self.c = float(input("Enter the value of c: "))
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self.y_o = float(input("Enter the value of y(0): "))
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self.y_prime = float(input("Enter the value of y`(0): "))
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def plot_solution(self, eq: np.array) -> None:
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"""
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Plots the equation in the solution
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:param eq: The characteristic equation
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"""
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fig = plt.figure(figsize=(14, 8))
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plt.plot(self.X, eq, 'b', label='Data points')
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plt.legend()
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plt.grid(True, linestyle=':')
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plt.xlim([-6, 6])
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plt.ylim([-4, 4])
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plt.title('CCH')
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plt.xlabel('x-axis')
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plt.ylabel('y-axis')
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plt.show()
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def solve_cch(self) -> bool:
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"""
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This function solve the quadratic equations the produces the output equation
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:rtype: bool
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:return: The status of the function
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"""
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discriminant = self.b ** 2 - 4 * self.a * self.c
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if discriminant > 0:
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print("The roots are real")
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r1 = (-self.b + math.sqrt((self.b * self.b) - (4 * self.a * self.c))) / (2 * self.a)
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r2 = (-self.b - math.sqrt((self.b * self.b) - (4 * self.a * self.c))) / (2 * self.a)
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A = np.array([[1, 1], [r1, r2]])
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B = np.array([self.y_o, self.y_prime])
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C = np.linalg.solve(A, B)
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eq = round(C[0], 4) * np.exp(r1 * self.X) + round(C[1], 4) * np.exp(r2 * self.X)
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print("Equation is: y = {}e^{}t + {}e^{}t".format(round(C[0], 4), r1, round(C[1], 4), r2))
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self.plot_solution(eq=eq)
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elif discriminant == 0:
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print("The roots are repeated")
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r1 = (-self.b + math.sqrt((self.b * self.b) - (4 * self.a * self.c))) / (2 * self.a)
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eq = round(self.y_o, 4) * np.exp(r1 * self.X) + round((self.y_prime - r1 * self.y_o), 4) * self.X * np.exp(
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r1 * self.X)
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print("Equation is: y = {}e^{}t + {}te^{}t".format(round(self.y_o, 4), r1,
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round((self.y_prime - r1 * self.y_o), 4), r1))
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self.plot_solution(eq=eq)
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elif discriminant < 0:
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print("The roots are imaginary")
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r1 = (-self.b + cmath.sqrt((self.b * self.b) - (4 * self.a * self.c))) / (2 * self.a)
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r2 = (-self.b - cmath.sqrt((self.b * self.b) - (4 * self.a * self.c))) / (2 * self.a)
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A = np.array([[1, 0], [r1.real, r1.imag]])
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B = np.array([self.y_o, self.y_prime])
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C = np.linalg.solve(A, B)
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eq = np.exp(r1.real * self.X) * (
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round(C[0], 4) * np.cos(r1.imag * self.X) + round(C[1], 4) * np.sin(-1 * r2.imag * self.X))
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print("Equation is: y = e^{}t ({} cos({}t) + {} sin({}t))".format(r1.real, round(C[0], 4), r1.imag,
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round(C[1], 4), -1 * r2.imag))
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self.plot_solution(eq=eq)
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return True
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def main(self):
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self.get_inputs()
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self.solve_cch()
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if __name__ == "__main__":
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my_solve = SOLVECCH()
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my_solve.main()
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