numpy.exp#
- numpy.exp(x,/,out=None,*,where=True,casting='same_kind',order='K',dtype=None,subok=True[,signature])=<ufunc'exp'>#
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 havea shape that the inputs broadcast to. If not provided or None,a freshly-allocated array is returned. A tuple (possible only as akeyword argument) must have length equal to the number of outputs.
- wherearray_like, optional
This condition is broadcast over the input. At locations where thecondition is True, theout array will be set to the ufunc result.Elsewhere, theout array will retain its original value.Note that if an uninitializedout array is created via the default
out=None, locations within it where the condition is False willremain uninitialized.- **kwargs
For other keyword-only arguments, see theufunc docs.
- Returns:
- outndarray or scalar
Output array, element-wise exponential ofx.This is a scalar ifx is a scalar.
See also
Notes
The irrational number
eis also known as Euler’s number. It isapproximately 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 alreadyknown (it is the real argument, described above). The second term,\(e^{ib}\), is\(\cos b + i \sin b\), a function withmagnitude 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 Functionswith 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:>>>importnumpyasnp
>>>importmatplotlib.pyplotasplt>>>importnumpyasnp
>>>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()
