This is documentation for an old release of NumPy (version 1.3.). Read this page in the documentation of the latest stable release (version > 1.17).
Calculate the exponential of the elements in the input array.
Parameters: | x : array_like
|
---|---|
Returns: | out : ndarray
|
Notes
The irrational number e is also known as Euler’s number. It is
approximately 2.718281, and is the base of the natural logarithm,
ln (this means that, if ,
then
. For real input, exp(x) is always positive.
For complex arguments, x = a + ib, we can write
. The first term,
, is already
known (it is the real argument, described above). The second term,
, is
, a function with magnitude
1 and a periodic phase.
References
[28] | Wikipedia, “Exponential function”, http://en.wikipedia.org/wiki/Exponential_function |
[29] | M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” Dover, 1964, p. 69, http://www.math.sfu.ca/~cbm/aands/page_69.htm |
Examples
Plot the magnitude and phase of exp(x) in the complex plane:
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-2*np.pi, 2*np.pi, 100)
>>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane
>>> out = np.exp(xx)
>>> plt.subplot(121)
>>> plt.imshow(np.abs(out),
... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi])
>>> plt.title('Magnitude of exp(x)')
>>> plt.subplot(122)
>>> plt.imshow(np.angle(out),
... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi])
>>> plt.title('Phase (angle) of exp(x)')
>>> plt.show()