# jax.numpy.exp¶

jax.numpy.exp(x)

Calculate the exponential of all elements in the input array.

LAX-backend implementation of exp(). Original docstring below.

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

Parameters

x (array_like) – Input values.

Returns

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

Return type

ndarray or scalar

See also

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()