# Compute Gradients of a Field#

Estimate the gradient of a scalar or vector field in a data set.

The ordering for the output gradient tuple will be {du/dx, du/dy, du/dz, dv/dx, dv/dy, dv/dz, dw/dx, dw/dy, dw/dz} for an input array {u, v, w}.

Showing the `pyvista.DataSetFilters.compute_derivative()` filter.

```import numpy as np

import pyvista as pv
from pyvista import examples

# A vtkStructuredGrid - but could be any mesh type
mesh
```
UniformGridInformation
N Cells158400
N Points167580
X Bounds1.000e+02, 1.750e+02
Y Bounds8.000e+01, 1.280e+02
Z Bounds1.000e+00, 4.500e+01
Dimensions76, 49, 45
Spacing1.000e+00, 1.000e+00, 1.000e+00
N Arrays2
NameFieldTypeN CompMinMax
scalarsPointsfloat3210.000e+005.800e+02
vectorsPointsfloat323-2.263e+011.662e+01

Now compute the gradients of the `vectors` vector field in the point data of that mesh. This is as simple as calling `pyvista.DataSetFilters.compute_derivative()`.

```mesh_g = mesh.compute_derivative(scalars="vectors")
```

Out:

```array([[ 7.2189998e-03,  7.6569999e-03,  3.8799997e-03, ...,
-7.3850001e-03,  1.0060001e-03, -2.1000043e-05],
[ 4.2885002e-03,  9.3000010e-04, -6.5520001e-03, ...,
-6.1399997e-03,  3.6770001e-03,  1.1730000e-02],
[ 5.4014996e-03,  1.2539998e-03, -4.6510003e-03, ...,
3.4900010e-04,  8.0140000e-03,  8.1439996e-03],
...,
[-6.3999998e-04, -2.6340000e-03,  6.1740000e-03, ...,
-4.3205000e-03, -1.2229999e-03, -1.8960000e-03],
[-1.5900000e-03, -3.4460002e-03,  4.1279998e-03, ...,
-2.9000000e-03, -5.9960000e-03, -5.8140000e-03],
[-9.1199996e-04, -4.0670000e-03, -1.5819999e-03, ...,
-2.4759998e-03, -8.5290000e-03, -5.3939996e-03]], dtype=float32)
```

Note

You can also use `pyvista.DataSetFilters.compute_derivative()` for computing other derivative based quantities, such as divergence, vorticity, and Q-criterion. See function documentation for options.

`mesh_g["gradient"]` is an `N` by 9 NumPy array of the gradients, so we could make a dictionary of NumPy arrays of the gradients like:

```def gradients_to_dict(arr):
"""A helper method to label the gradients into a dictionary."""
keys = np.array(
["du/dx", "du/dy", "du/dz", "dv/dx", "dv/dy", "dv/dz", "dw/dx", "dw/dy", "dw/dz"]
)
keys = keys.reshape((3, 3))[:, : arr.shape[1]].ravel()

```

Out:

```{'du/dx': array([ 0.007219 ,  0.0042885,  0.0054015, ..., -0.00064  , -0.00159  ,
-0.000912 ], dtype=float32), 'du/dy': array([ 0.007657,  0.00093 ,  0.001254, ..., -0.002634, -0.003446,
-0.004067], dtype=float32), 'du/dz': array([ 0.00388 , -0.006552, -0.004651, ...,  0.006174,  0.004128,
-0.001582], dtype=float32), 'dv/dx': array([-7.5999997e-04, -1.0585000e-03, -2.9600000e-03, ...,
-1.9554999e-03,  9.9999888e-06,  2.6600000e-03], dtype=float32), 'dv/dy': array([ 0.000226, -0.00503 , -0.003388, ..., -0.0059  , -0.008274,
-0.000512], dtype=float32), 'dv/dz': array([-0.006821, -0.000382,  0.006909, ..., -0.001991, -0.003061,
-0.00189 ], dtype=float32), 'dw/dx': array([-0.007385 , -0.00614  ,  0.000349 , ..., -0.0043205, -0.0029   ,
-0.002476 ], dtype=float32), 'dw/dy': array([ 0.001006,  0.003677,  0.008014, ..., -0.001223, -0.005996,
-0.008529], dtype=float32), 'dw/dz': array([-2.1000043e-05,  1.1730000e-02,  8.1439996e-03, ...,
-1.8960000e-03, -5.8140000e-03, -5.3939996e-03], dtype=float32)}
```

And we can add all of those components as individual arrays back to the mesh by:

```mesh_g.point_data.update(gradients)
mesh_g
```
UniformGridInformation
N Cells158400
N Points167580
X Bounds1.000e+02, 1.750e+02
Y Bounds8.000e+01, 1.280e+02
Z Bounds1.000e+00, 4.500e+01
Dimensions76, 49, 45
Spacing1.000e+00, 1.000e+00, 1.000e+00
N Arrays12
NameFieldTypeN CompMinMax
scalarsPointsfloat3210.000e+005.800e+02
vectorsPointsfloat323-2.263e+011.662e+01
du/dxPointsfloat321-8.293e+008.336e+00
du/dyPointsfloat321-1.084e+018.334e+00
du/dzPointsfloat321-8.300e+008.317e+00
dv/dxPointsfloat321-1.133e+011.536e+01
dv/dyPointsfloat321-1.585e+011.170e+01
dv/dzPointsfloat321-1.131e+017.459e+00
dw/dxPointsfloat321-8.738e+001.212e+01
dw/dyPointsfloat321-8.734e+008.740e+00
dw/dzPointsfloat321-1.124e+018.728e+00

```keys = np.array(list(gradients.keys())).reshape(3, 3)

p = pv.Plotter(shape=keys.shape)
for i in range(keys.shape[0]):
for j in range(keys.shape[1]):
name = keys[i, j]
p.subplot(i, j)
p.view_isometric()
p.show()
```

And there you have it, the gradients for a vector field! We could also do this for a scalar field like for the `scalars` field in the given dataset.

```mesh_g = mesh.compute_derivative(scalars="scalars")

```

Out:

```{'du/dx': array([-7. , -7. , -4. , ..., -0.5, -1.5, -2. ], dtype=float32), 'du/dy': array([ 0.,  5., 12., ..., -3., -1., -3.], dtype=float32), 'du/dz': array([-13.,  -8.,  -3., ...,   4.,   4.,   1.], dtype=float32)}
```
```mesh_g.point_data.update(gradients)

p = pv.Plotter(shape=keys.shape)

for i in range(keys.shape[0]):
for j in range(keys.shape[1]):
name = keys[i, j]
p.subplot(i, j)