xarray.ufuncs.exp#
- xarray.ufuncs.exp = <xarray.ufuncs._unary_ufunc object>#
xarray specific variant of
numpy.exp()
. Handles xarray objects by dispatching to the appropriate function for the underlying array type.Documentation from numpy:
Calculate the exponential of all elements in the input array.
- Parameters
x (array_like) – Input values.
out (
ndarray
,None
, ortuple
ofndarray
andNone
, 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 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) – 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.**kwargs – For other keyword-only arguments, see the ufunc docs.
- Returns
out (
ndarray
or scalar) – Output array, element-wise 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
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, https://personal.math.ubc.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()