Calculate the exponential of all elements in the input array.
Parameters: | x : array_like
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Returns: | out : ndarray
Output array, element-wise exponential of x.
|
See also
- expm1
- Calculate exp(x) - 1 for all elements in the array.
- exp2
- Calculate 2**x for all elements in the array.
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
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,
then
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. For real input, exp(x) is always positive.
For complex arguments, x = a + ib, we can write
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. The first term,
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, is already
known (it is the real argument, described above). The second term,
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, is
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, a function with magnitude
1 and a periodic phase.
References
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()
(Source code, png, pdf)