# xarray.ufuncs.exp

### xarray.ufuncs.exp *= <xarray.ufuncs._unary_ufunc object>*

xarray specific variant of `numpy.exp()`. Handles xarray objects by dispatching to the appropriate function for the underlying array type.

Documentation from numpy:

Calculate the exponential of all elements in the input array.

* **Parameters:**
  * **x** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like)) – Input values.
  * **out** ([`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray), [`None`](https://docs.python.org/3/builtins/constants.html#None), or [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple) of [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray) and [`None`](https://docs.python.org/3/builtins/constants.html#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 array is returned. A tuple (possible only as a
    keyword argument) must have length equal to the number of outputs.
  * **where** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like), *optional*) – This condition is broadcast over the input. At locations where the
    condition is True, the out array will be set to the ufunc result.
    Elsewhere, the out array will retain its original value.
    Note that if an uninitialized out array is created via the default
    `out=None`, locations within it where the condition is False will
    remain uninitialized.
  * **\*\*kwargs** – For other keyword-only arguments, see the
    [ufunc docs](https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs).
* **Returns:**
  **out** ([`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray) or [scalar](../user-guide/terminology.html.md#term-scalar)) – Output array, element-wise exponential of x.
  This is a scalar if x is a scalar.

#### SEE ALSO
[`expm1`](xarray.ufuncs.expm1.html.md#xarray.ufuncs.expm1)
: Calculate `exp(x) - 1` for all elements in the array.

[`exp2`](xarray.ufuncs.exp2.html.md#xarray.ufuncs.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](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,
   [https://personal.math.ubc.ca/~cbm/aands/page_69.htm](https://personal.math.ubc.ca/~cbm/aands/page_69.htm)

### Examples

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

```pycon
>>> import numpy as np
```

```pycon
>>> import matplotlib.pyplot as plt
>>> import numpy as np
```

```pycon
>>> 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)
```

```pycon
>>> 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)')
```

```pycon
>>> 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()
```

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