# How to create an GWCS from quantities and times#

This example shows how to create a GWCS from astropy quantities.

```import numpy as np
from matplotlib import pyplot as plt

import astropy.units as u
from astropy.time import Time

from ndcube import NDCube
from ndcube.extra_coords import QuantityTableCoordinate, TimeTableCoordinate
```

We aim to create coordinates that are focused around time and energies using astropy quantities.

```energy = np.arange(10) * u.keV
time = Time('2020-01-01 00:00:00') + np.arange(9)*u.s
```

Then, we need to turn these into lookup tables using `QuantityTableCoordinate` and `TimeTableCoordinate` to create table coordinates.

```energy_coord = QuantityTableCoordinate(energy, names='energy', physical_types='em.energy')
print(energy_coord)

time_coord = TimeTableCoordinate(time, names='time', physical_types='time')
print(time_coord)
```
```QuantityTableCoordinate ['energy'] ['em.energy']:
<Quantity [0., 1., 2., 3., 4., 5., 6., 7., 8., 9.] keV>
TimeTableCoordinate ['time'] ['time']:
['2020-01-01 00:00:00.000' '2020-01-01 00:00:01.000'
'2020-01-01 00:00:02.000' '2020-01-01 00:00:03.000'
'2020-01-01 00:00:04.000' '2020-01-01 00:00:05.000'
'2020-01-01 00:00:06.000' '2020-01-01 00:00:07.000'
'2020-01-01 00:00:08.000']
```

Now we need to combine table coordinates created above and extract the `.wcs` from the result.

```wcs = (time_coord & energy_coord).wcs
print(wcs)
```
```     From        Transform
-------------- -------------
PixelFrame CompoundModel
CompositeFrame          None
```

Now, we have all the pieces required to construct a `NDCube` with this data and the GWCS we just created.

```data = np.random.rand(len(time), len(energy))
cube = NDCube(data=data, wcs=wcs)
print(cube)
```
```NDCube
------
Shape: (9, 10)
Physical Types of Axes: [('em.energy',), ('time',)]
Unit: None
Data Type: float64
```

Finally, we will plot the cube.

```cube.plot()

plt.show()
```

Total running time of the script: (0 minutes 0.375 seconds)

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