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# Vectorfield#

```import hvplot.xarray  # noqa
```

`vectorfield` accepts 2d arrays of magnitude and angle on a grid and produces an array of vectors. x and y can be 2d or 1d coordinates.

```import numpy as np
import xarray as xr
import cartopy.crs as ccrs
```
```def sample_data(shape=(20, 30)):
"""
Return ``(x, y, u, v, crs)`` of some vector data
computed mathematically. The returned crs will be a rotated
pole CRS, meaning that the vectors will be unevenly spaced in
regular PlateCarree space.

"""
crs = ccrs.RotatedPole(pole_longitude=177.5, pole_latitude=37.5)

x = np.linspace(311.9, 391.1, shape[1])
y = np.linspace(-23.6, 24.8, shape[0])

x2d, y2d = np.meshgrid(x, y)
u = 10 * (2 * np.cos(2 * np.deg2rad(x2d) + 3 * np.deg2rad(y2d + 30)) ** 2)
v = 20 * np.cos(6 * np.deg2rad(x2d))

return x, y, u, v, crs

xs, ys, U, V, crs = sample_data()

mag = np.sqrt(U**2 + V**2)
angle = (np.pi/2.) - np.arctan2(U/mag, V/mag)

ds = xr.Dataset({'mag': xr.DataArray(mag, dims=('y', 'x'), coords={'y': ys, 'x': xs}),
'angle': xr.DataArray(angle, dims=('y', 'x'), coords={'y': ys, 'x': xs})},
attrs={'crs': crs})
ds
```
```<xarray.Dataset> Size: 10kB
Dimensions:  (y: 20, x: 30)
Coordinates:
* y        (y) float64 160B -23.6 -21.05 -18.51 -15.96 ... 19.71 22.25 24.8
* x        (x) float64 240B 311.9 314.6 317.4 320.1 ... 385.6 388.4 391.1
Data variables:
mag      (y, x) float64 5kB 6.459 2.149 5.899 11.25 ... 22.28 22.74 22.0
angle    (y, x) float64 5kB 1.413 0.3677 -0.9793 ... -0.9368 -1.049 -1.127
Attributes:
crs:      +proj=ob_tran +ellps=WGS84 +a=6378137.0 +o_proj=latlon +o_lon_p...```
```ds.hvplot.vectorfield(x='x', y='y', angle='angle', mag='mag', hover=False).opts(magnitude='mag')
```

## Geographic Data#

If a dataset has an attr called `crs` which is a cartopy object or a proj4 string, then just by setting the option `geo=True` will use the correct crs.

```ds.hvplot.vectorfield(x='x', y='y', angle='angle', mag='mag',
hover=False, geo=True, tiles="CartoLight")
```

If you set `coastline` or `features` it will keep the original crs and transform the features to the data crs.

```ds.hvplot.vectorfield(x='x', y='y', angle='angle', mag='mag',
hover=False, geo=True, coastline=True)
```