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zCC--;jf+7kUk}<#TnbIW=0Y{ZPppfur@GGR1uKfq=7)h(HU?HO3J zAcl>hVTH>@qYBF@)?mHP_!6wCYoQyBhWLsLOf! eps: + return x_abs_diff/(x_abs_sum + f1_abs + f2_abs) + else: + return x_abs_diff + f1_abs + f2_abs + +def scan_root_ranges(LF, x1, x2, step=0.1): + x = x1 + while x < x2: + if np.sign(LF(x)) != np.sign(LF(x+step)): + yield (x, x+step) + x += step + +def grubus_R(LF_terms): + return 1 + max(abs(ai) for ai in LF_terms[:-1]) / LF_terms[-1] + +def mul_every_by(numbers: list[float], scalar: float): + return list(map(lambda a: scalar*a, numbers)) + +def filter_negative(numbers: list[float]): + return list(filter(lambda a: a < 0, numbers)) + +def tikslesnis_R_range(LF_terms: list[float]): + LF_terms = LF_terms.copy() + if LF_terms[-1] < 0: + # f(x) => -f(x) + LF_terms = mul_every_by(LF_terms, -1) + + + k = len(LF_terms) - max(i for i, a in enumerate(LF_terms[:-1]) if a < 0) - 1 + B = max(abs(a) for a in LF_terms[:-1] if a < 0) + R_teig = 1 + (B / LF_terms[-1]) ** (1/k) + + # f(x) => f(-x) + for i in range(1, len(LF_terms), 2): + LF_terms[i] *= -1 + + if len(LF_terms) % 2 == 0: + # f(x) => -f(x) + LF_terms = mul_every_by(LF_terms, -1) + + if any(True for a in LF_terms[:-1] if a < 0) > 0: + B = max(abs(a) for a in LF_terms[:-1] if a < 0) + k = len(LF_terms) - max(i for i, a in enumerate(LF_terms[:-1]) if a < 0) - 1 + R_neig = 1 + (B / LF_terms[-1]) ** (1/k) + else: + R_neig = 0 + + return (R_neig, R_teig) + +def roots_range(LF_terms: list[float]): + R = grubus_R(LF_terms) + R_neig, R_teig = tikslesnis_R_range(LF_terms) + return (-min(R, R_neig), min(R, R_teig)) + +def get_coeffs(func): + x_symbol = sympy.symbols("x") + a: sympy.Poly = sympy.Poly(func(x_symbol), x_symbol) + coeffs = list(map(float, a.coeffs())) + coeffs.reverse() + return coeffs + +def solve_stygos(F, min_x, max_x, view_x, max_iterations=30, epsilon=1e-6, animation_delay=0.05): + numpy_F = lambda x: F(NumpyMathLibrary, x) + + textbox = create_scroll_textbox(140, 20) + textbox_append_line(textbox, "-------- Stygu metodas -------------") + + my_plot = MyPlot(animation_delay) + my_plot.plot_function(view_x[0], view_x[1], numpy_F) + my_plot.add_zero_line(view_x[0], view_x[1]) + + textbox_append_line(textbox, "Saknies reiksmes tikslinimas Stygu metodu:") + + results = [] + + for x1, x2 in scan_root_ranges(numpy_F, min_x, max_x): + start_x1 = x1 + start_x2 = x2 + my_plot.subplot.plot([x1, x2], [0, 0], 'mo--') + plt.draw() + + f1 = numpy_F(x1) + f2 = numpy_F(x2) + my_plot.update_edge_points(x1, f1, x2, f2) + + for i in range(1, max_iterations + 1): + if f2 == 0: + f2 += epsilon/2 + k = np.abs(f1 / f2) + x_middle = (x1 + k * x2) / (1 + k) # stygos nulio taskas + middle_value = numpy_F(x_middle) + + my_plot.clear_connecting_line() + my_plot.update_middle_point(x_middle, middle_value) + + if np.sign(f1) != np.sign(middle_value): + x2 = x_middle + f2 = middle_value + else: + x1 = x_middle + f1 = middle_value + + my_plot.clear_middle_point() + my_plot.update_edge_points(x1, f1, x2, f2) + + tksl = get_guess_accuracy(x1, x2, f1, f2, epsilon) + textbox_append_line(textbox, f"{i:2d}. x1={x1:-20g}, x2={x2:-20g}, f1={f1:-20g}, f2={f2:-20g}, tikslumas={tksl:-20g}") + + if tksl < epsilon: + break + + tksl = get_guess_accuracy(x1, x2, f1, f2, epsilon) + if tksl < epsilon: + print(f"Isspresta: x={x1:g}, f={f1:g}, tikslumas={tksl:g}") + else: + print("Tikslumas nepasiektas") + + results.append([start_x1, start_x2, x1, tksl, i]) + + return results + +def solve_liestiniu(F, min_x, max_x, view_x, epsilon=1e-8, animation_delay=0.5): + sympy_F = lambda x: F(SympyMathLibrary, x) + numpy_F = lambda x: F(NumpyMathLibrary, x) + + x_symbol = sympy.symbols("x") + DF_symbolical = sympy_F(x_symbol).diff(x_symbol) + DF = sympy.lambdify((x_symbol), DF_symbolical) + + x=np.arange(view_x[0], view_x[1], 0.05); y=numpy_F(x) + + plt.xlabel("x"); plt.ylabel("y"); plt.plot(x, y, 'b'); plt.grid() + + results = [] + + for x1, x2 in scan_root_ranges(numpy_F, min_x, max_x): + start_x = (x1+x2)/2 + + xi = start_x + iterations = 0 + while np.abs(numpy_F(xi)) > epsilon: + xi_bef = xi + xi = xi - (1 / DF(xi)) * numpy_F(xi) + iterations += 1 + + plt.plot([xi_bef], numpy_F(xi_bef), 'ob') + plt.plot([xi], [0], 'or') + plt.plot([xi_bef, xi], [numpy_F(xi_bef), 0], 'r-') + plt.plot([xi, xi], [0, numpy_F(xi)], 'g--') + plt.draw() + plt.pause(animation_delay) + + results.append((x1, x2, xi, np.abs(numpy_F(xi)), iterations)) + + return results + +def prefix_results(prefix, results): + return map(lambda line: [*prefix, *line], results) + +def main_1(F, G, G_range, F_view_x): + results = [] + + LF_terms = get_coeffs(lambda x: F(StandardMathLibrary, x)) + F_min_x, F_max_x = roots_range(LF_terms) + print("f(x) intervalas: nuo", F_min_x, "iki", F_max_x) + results.extend(prefix_results(["f(x)", "Stygų" ], solve_stygos(F, F_min_x, F_max_x, F_view_x))) + results.extend(prefix_results(["f(x)", "Liestinių"], solve_liestiniu(F, F_min_x, F_max_x, F_view_x))) + + results.extend(prefix_results(["g(x)", "Stygų" ], solve_stygos(G, G_range[0], G_range[1], G_range))) + results.extend(prefix_results(["g(x)", "Liestinių"], solve_liestiniu(G, G_range[0], G_range[1], G_range))) + + headers = ["Funkcija", "Metodas", "Skenavimo min", "Skenavimo max", "Kirtimo taškas","Tikslumas", "Iteracijos"] + print(tabulate(results, headers, tablefmt="grid")) + +def print_coeffs_desmos(coeffs): + coeffs_strs = [] + for i, coeff in enumerate(coeffs): + x_power = len(coeffs)-i-1 + x_power_str = "^".join(c for c in str(x_power)) + coeffs_strs.append(f"({coeff} * x^{x_power_str})") + print(" + ".join(coeffs_strs)) + +def main_2(H, H_range, epsilon=1e-4, animation_delay=0.05): + standard_H = lambda x: H(StandardMathLibrary, x) + numpy_H = lambda x: H(NumpyMathLibrary, x) + sympy_H = lambda x: H(SympyMathLibrary, x) + + my_plot = MyPlot(animation_delay) + my_plot.plot_function(H_range[0], H_range[1], numpy_H) + plt.pause(animation_delay) + + x,f,fp,df=sympy.symbols(('x','f','fp','df')) + + f=sympy_H(x) + x0=(H_range[0]+H_range[1])/2 + + fp=f.subs(x,x0) + N = 1 + + #print(f"{N}, {abs(sympy.Poly(fp,x)(foo) - standard_H(foo)):f}") + + while True: + f=f.diff(x) + fp=fp+f.subs(x,x0)/math.factorial(N)*(x-x0)**N; + N += 1 + + a=sympy.Poly(fp,x) + #print(f"{N}, {abs(a(foo) - standard_H(foo)):f}") + if abs(a(H_range[0]) - standard_H(H_range[0])) < epsilon and abs(a(H_range[1]) - standard_H(H_range[1])) < epsilon: + break + + if N % 5 == 0: + my_plot.plot_function(H_range[0], H_range[1], sympy.lambdify(x, fp, 'numpy'), 'r--') + plt.pause(animation_delay) + + + print("N =",N) + print_coeffs_desmos(sympy.Poly(fp,x).all_coeffs()) + my_plot.plot_function(H_range[0], H_range[1], sympy.lambdify(x, fp, 'numpy'), 'r--') + plt.pause(animation_delay) + +# Variantas: 20 +main_1( + F=(lambda m, x: 1.34 * (x**4) - 16.35 * (x**3) + 65.13 * (x**2) - 83.45 * (x**1) - 3.27), + G=(lambda m, x: m.sin(x) - m.log(x)/2 + 0.1), + G_range=(0.1, 10), + F_view_x=(-0.5, 5) +) + +main_2( + H=(lambda m, x: -8*m.sin(x) + 32*m.sin(10*x) - 10), + H_range=(0, 1) +) + +input("Baigti darba! Wooo! Press 'ENTER'") \ No newline at end of file