numpy.exp¶

numpy.
exp
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'exp'>¶ Calculate the exponential of all elements in the input array.
Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
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 freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Output array, elementwise exponential of x. This is a scalar if x 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 x = \ln y = \log_e y, then e^x = y. For real input,exp(x)
is always positive.For complex arguments,
x = a + ib
, we can write e^x = e^a e^{ib}. The first term, e^a, is already known (it is the real argument, described above). The second term, e^{ib}, is \cos b + i \sin b, a function with magnitude 1 and a periodic phase.References
[1] Wikipedia, “Exponential function”, http://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()