numpy.
exp
Calculate the exponential of all elements in the input array.
Input values.
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.
This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.
out=None
For other keyword-only arguments, see the ufunc docs.
Output array, element-wise exponential of x. This is a scalar if x is a scalar.
See also
expm1
Calculate exp(x) - 1 for all elements in the array.
exp(x) - 1
exp2
Calculate 2**x for all elements in the array.
2**x
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
e
ln
System Message: WARNING/2 (x = \ln y = \log_e y)
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System Message: WARNING/2 (e^x = y)
exp(x)
For complex arguments, x = a + ib, we can write
x = a + ib
System Message: WARNING/2 (e^x = e^a e^{ib})
System Message: WARNING/2 (e^a)
System Message: WARNING/2 (e^{ib})
System Message: WARNING/2 (\cos b + i \sin b)
References
Wikipedia, “Exponential function”, https://en.wikipedia.org/wiki/Exponential_function
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()
