numpy.exp
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numpy.exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'exp'>
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Calculate the exponential of all elements in the input array.
Parameters: -
x : array_like
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Input values.
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out : ndarray, None, or tuple of ndarray and None, optional
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A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or
None
, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. -
where : array_like, optional
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Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
- **kwargs
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For other keyword-only arguments, see the ufunc docs.
Returns: -
out : ndarray or scalar
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Output array, element-wise exponential of
x
. This is a scalar ifx
is a scalar.
See also
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
[1] Wikipedia, “Exponential function”, https://en.wikipedia.org/wiki/Exponential_function [2] 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], cmap='gray') >>> 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], cmap='hsv') >>> plt.title('Phase (angle) of exp(x)') >>> plt.show()
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Licensed under the 3-clause BSD License.
https://docs.scipy.org/doc/numpy-1.16.1/reference/generated/numpy.exp.html