scipy.special.airye#
- scipy.special.airye(z, out=None) = <ufunc 'airye'>#
- Exponentially scaled Airy functions and their derivatives. - Scaling: - eAi = Ai * exp(2.0/3.0*z*sqrt(z)) eAip = Aip * exp(2.0/3.0*z*sqrt(z)) eBi = Bi * exp(-abs(2.0/3.0*(z*sqrt(z)).real)) eBip = Bip * exp(-abs(2.0/3.0*(z*sqrt(z)).real)) - Parameters:
- zarray_like
- Real or complex argument. 
- outtuple of ndarray, optional
- Optional output arrays for the function values 
 
- Returns:
- eAi, eAip, eBi, eBip4-tuple of scalar or ndarray
- Exponentially scaled Airy functions eAi and eBi, and their derivatives eAip and eBip 
 
 - See also - Notes - Wrapper for the AMOS [1] routines zairy and zbiry. - References [1]- Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/ - Examples - We can compute exponentially scaled Airy functions and their derivatives: - >>> import numpy as np >>> from scipy.special import airye >>> import matplotlib.pyplot as plt >>> z = np.linspace(0, 50, 500) >>> eAi, eAip, eBi, eBip = airye(z) >>> f, ax = plt.subplots(2, 1, sharex=True) >>> for ind, data in enumerate([[eAi, eAip, ["eAi", "eAip"]], ... [eBi, eBip, ["eBi", "eBip"]]]): ... ax[ind].plot(z, data[0], "-r", z, data[1], "-b") ... ax[ind].legend(data[2]) ... ax[ind].grid(True) >>> plt.show()   - We can compute these using usual non-scaled Airy functions by: - >>> from scipy.special import airy >>> Ai, Aip, Bi, Bip = airy(z) >>> np.allclose(eAi, Ai * np.exp(2.0 / 3.0 * z * np.sqrt(z))) True >>> np.allclose(eAip, Aip * np.exp(2.0 / 3.0 * z * np.sqrt(z))) True >>> np.allclose(eBi, Bi * np.exp(-abs(np.real(2.0 / 3.0 * z * np.sqrt(z))))) True >>> np.allclose(eBip, Bip * np.exp(-abs(np.real(2.0 / 3.0 * z * np.sqrt(z))))) True - Comparing non-scaled and exponentially scaled ones, the usual non-scaled function quickly underflows for large values, whereas the exponentially scaled function does not. - >>> airy(200) (0.0, 0.0, nan, nan) >>> airye(200) (0.07501041684381093, -1.0609012305109042, 0.15003188417418148, 2.1215836725571093)