# xarray.ufuncs.exp¶

xarray.ufuncs.exp = <xarray.ufuncs._UFuncDispatcher object>

xarray specific variant of numpy.exp. Handles xarray.Dataset, xarray.DataArray, xarray.Variable, numpy.ndarray and dask.array.Array objects with automatic dispatching.

Documentation from numpy:

exp(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

Calculate the exponential of all elements in the input array.

Parameters
xarray_like

Input values.

outndarray, 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 freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

wherearray_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 keyword-only arguments, see the ufunc docs.

Returns
outndarray or scalar

Output array, element-wise exponential of x. This is a scalar if x is a scalar.

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 $$x = \ln y = \log_e y$$, 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”, 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()