Created
May 5, 2021 21:21
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| import numpy as np | |
| # (x-4)^3(x-16)(x-21) | |
| p = np.poly1d([1, -49, 828, -5872, 18496, -21504]) | |
| print(p) | |
| # roots = np.array([4] * 2019 + [16, 21], dtype=object) | |
| # p = np.poly1d(roots, True) | |
| bounds = [1, 2021] | |
| crit_points = [ | |
| x for x in p.deriv().r if x.imag == 0 and bounds[0] < x.real < bounds[1] | |
| ] | |
| print(f'Границы: {bounds}') | |
| print() | |
| y = [p(point) for point in crit_points] | |
| index_of_min = y.index(min(y)) | |
| print('min:') | |
| print(f' x: {crit_points[index_of_min]} y: {y[index_of_min]}') | |
| index_of_max = y.index(max(y)) | |
| print('min:') | |
| print(f' x: {crit_points[index_of_max]} y: {y[index_of_max]}') |
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| # (x-4)^3(x-16)(x-21) | |
| poly = [ | |
| [4, 3], | |
| [16, 1], | |
| [21, 1] | |
| ] | |
| epsilon = 0.001 | |
| less_epsilon = 0.00001 | |
| def evaluate_poly(poly, x): | |
| result = 1 | |
| for root in poly: | |
| result = result * (x - root[0]) ** root[1] | |
| return result | |
| def dichotomy_min(a, b, epsilon, poly): | |
| while b - a > 0.001: | |
| p = (b + a) / 2 - 0.00001 | |
| q = (b + a) / 2 + 0.00001 | |
| if evaluate_poly(poly, p) < evaluate_poly(poly, q): | |
| b = q | |
| else: | |
| a = p | |
| return (b + a) / 2 | |
| def dichotomy_max(a, b, epsilon, poly): | |
| while b - a > 0.001: | |
| p = (b + a) / 2 - 0.00001 | |
| q = (b + a) / 2 + 0.00001 | |
| if evaluate_poly(poly, p) > evaluate_poly(poly, q): | |
| b = q | |
| else: | |
| a = p | |
| return (b + a) / 2 | |
| x = [] | |
| for i in range(len(poly) - 1): | |
| x.append( | |
| dichotomy_min(poly[i][0], poly[i + 1][0], less_epsilon, poly) | |
| ) | |
| y = [evaluate_poly(poly, _) for _ in x] | |
| index_of_min = y.index(min(y)) | |
| print('min:') | |
| print(f' x: {x[index_of_min]} y: {y[index_of_min]}') | |
| x = [] | |
| for i in range(len(poly) - 1): | |
| x.append( | |
| dichotomy_max(poly[i][0], poly[i + 1][0], less_epsilon, poly) | |
| ) | |
| y = [evaluate_poly(poly, _) for _ in x] | |
| index_of_max = y.index(max(y)) | |
| print('max:') | |
| print(f' x: {x[index_of_max]} y: {y[index_of_max]}') |
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