mars.tensor.exp(x, out=None, where=None, **kwargs)[source]

Calculate the exponential of all elements in the input tensor.

  • x (array_like) – Input values.

  • out (Tensor, None, or tuple of Tensor 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 tensor 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 keyword-only arguments, see the ufunc docs.


out – Output tensor, element-wise exponential of x.

Return type


See also


Calculate exp(x) - 1 for all elements in the array.


Calculate 2**x for all elements in the array.


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.



Wikipedia, “Exponential function”,


M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” Dover, 1964, p. 69,


Plot the magnitude and phase of exp(x) in the complex plane:

>>> import mars.tensor as mt
>>> import matplotlib.pyplot as plt
>>> x = mt.linspace(-2*mt.pi, 2*mt.pi, 100)
>>> xx = x + 1j * x[:, mt.newaxis] # a + ib over complex plane
>>> out = mt.exp(xx)
>>> plt.subplot(121)
>>> plt.imshow(mt.abs(out).execute(),
...            extent=[-2*mt.pi, 2*mt.pi, -2*mt.pi, 2*mt.pi], cmap='gray')
>>> plt.title('Magnitude of exp(x)')
>>> plt.subplot(122)
>>> plt.imshow(mt.angle(out).execute(),
...            extent=[-2*mt.pi, 2*mt.pi, -2*mt.pi, 2*mt.pi], cmap='hsv')
>>> plt.title('Phase (angle) of exp(x)')