31 lines
1.2 KiB
Python
31 lines
1.2 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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def question_4():
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# x = 1.920 -> 2.080 (included) step = 0.001
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x = np.arange(1.920, 2.081, 0.001)
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# p = [1, -18, 144, -672, 2016, -4032, 5376, -4608, 2304, -512]
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# from x^9 to x^0
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coeffs = [1, -18, 144, -672, 2016, -4032, 5376, -4608, 2304, -512]
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p_coeff = np.polyval(coeffs, x)
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# p(x) = (x-2)^9
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p_fact = (x - 2.0) ** 9
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plt.plot(x, p_coeff, label='Coefficient Form', lw=2)
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plt.plot(x, p_fact, label='Factored Form', lw=2, ls='--')
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plt.yscale('symlog', linthresh=1e-10)
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plt.xlabel('x', fontsize=14)
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plt.ylabel('p(x)', fontsize=14)
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plt.title('Comparison of Polynomial Forms', fontsize=16)
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# save the figure
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plt.legend(fontsize=12)
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plt.grid(True, which='both', ls='--', lw=0.5)
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plt.savefig('question4.png')
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plt.show()
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abs_diff = np.abs(p_coeff - p_fact)
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rel_diff = abs_diff / (np.abs(p_fact) + 1e-30)
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print("Maximum Absolute Difference:", np.max(abs_diff))
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print("Maximum Relative Difference:", (abs_diff[np.argmax(np.abs(p_fact))] /
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(np.abs(p_fact).max() + 1e-30)))
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if __name__ == "__main__":
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question_4() |