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# numpy.exp

`numpy.``exp`(x[, out]) = <ufunc 'exp'>

  Calculate the exponential of all elements in the input array.

  Parameters : | x : array_like Input values.
  Returns : | out : ndarray Output array, element-wise exponential of x.

  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 , then . For real input, `exp(x)` is always positive.

  For complex arguments, `x = a + ib`, we can write . The first term, , is already known (it is the real argument, described above). The second term, , is , a function with magnitude 1 and a periodic phase.

  References

  [R18] | Wikipedia, “Exponential function”, http://en.wikipedia.org/wiki/Exponential_function

  [R19] | 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])
      >>> 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])
      >>> plt.title('Phase (angle) of exp(x)')
      >>> plt.show()

  (Source code, png, pdf)