wrightomega.py
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import numpy as np
try:
import mpmath # type: ignore[import]
except ImportError:
pass
def mpmath_wrightomega(x):
return mpmath.lambertw(mpmath.exp(x), mpmath.mpf('-0.5'))
def wrightomega_series_error(x):
series = x
desired = mpmath_wrightomega(x)
return abs(series - desired) / desired
def wrightomega_exp_error(x):
exponential_approx = mpmath.exp(x)
desired = mpmath_wrightomega(x)
return abs(exponential_approx - desired) / desired
def main():
desired_error = 2 * np.finfo(float).eps
print('Series Error')
for x in [1e5, 1e10, 1e15, 1e20]:
with mpmath.workdps(100):
error = wrightomega_series_error(x)
print(x, error, error < desired_error)
print('Exp error')
for x in [-10, -25, -50, -100, -200, -400, -700, -740]:
with mpmath.workdps(100):
error = wrightomega_exp_error(x)
print(x, error, error < desired_error)
if __name__ == '__main__':
main()