maxframe.tensor.exp

maxframe.tensor.exp(x, out=None, where=None, **kwargs)

Calculate the exponential of all elements in the input tensor.

Parameters:

• 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.

Returns:

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

Return type:

Tensor

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”, http://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 maxframe.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)')
>>> plt.show()