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November 16, 2022 08:05
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argparse.py
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| #!/usr/bin/env python3 | |
| import argparse | |
| from math import sin | |
| from scipy.misc import derivative | |
| def parse_args(): | |
| parser = argparse.ArgumentParser(description='Newthon\\'s method for finding roots') | |
| parser.add_argument('f', type=str, help='The function whose root we are trying to find') | |
| parser.add_argument('--x0', default=1, type=float, help='The initial guess') | |
| parser.add_argument('--tolerance', default=1e-7, type=float, help='How many digits of accuracy is desired') | |
| parser.add_argument('--epsilon', default=1e-14, type=float, help='Do not divide by a number smaller than this') | |
| parser.add_argument('--max_iterations', default=50, type=int, help='Max number of iterations') | |
| return parser.parse_args() | |
| if __name__ == '__main__': | |
| solution_found = False | |
| args = parse_args() | |
| print(args) | |
| x0 = args.x0 | |
| def f(x): | |
| return eval(args.f) | |
| def fprime(x): | |
| return derivative(f, x) | |
| for i in range(args.max_iterations): | |
| y = f(x0) | |
| yprime = fprime(x0) | |
| # Stop if the denominator is too small | |
| if abs(yprime) < args.epsilon: | |
| break | |
| # Do Newton's computation | |
| x1 = x0 - y/yprime | |
| # Stop when the result is within the desired tolerance | |
| if abs(x1 - x0) <= args.tolerance: | |
| solution_found = True | |
| break | |
| # Update x0 to start the process again | |
| x0 = x1 | |
| if solution_found: | |
| # x1 is a solution within tolerance and maximum number of iterations | |
| print("Solution: ", x1) | |
| exit(0) | |
| else: | |
| # Newton's method did not converge | |
| print("Did not converge") | |
| exit(1) |
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