# Testing#

On each update, SimPEG is tested using the continuous integration service Azure pipelines. We use Codecov to check and provide stats on how much of the code base is covered by tests. This tells which lines of code have been run in the test suite. It does not tell you about the quality of the tests run! In order to assess that, have a look at the tests we are running - they tell you the assumptions that we do not want to break within the code base.

Within the repository, the tests are located in the top-level **tests**
directory. Tests are organized similar to the structure of the repository.
There are several types of tests we employ, this is not an exhaustive list,
but meant to provide a few places to look when you are developing and would
like to check that the code you wrote satisfies the assumptions you think it
should.

Testing is performed with `pytest`

which is available through PyPI.
Checkout the docs on pytest.

## Compare with known values#

In a simple case, you might know the exact value of what the output should be
and you can `assert`

that this is in fact the case. For example,
we setup a 3D `BaseRectangularMesh`

and assert that it has 3 dimensions.

```
from discretize.base import BaseRectangularMesh
import numpy as np
mesh = BaseRectangularMesh([6, 2, 3])
def test_mesh_dimensions():
assert mesh.dim == 3
```

All functions with the naming convention `test_XXX`

are run. Here we check that the dimensions are correct for the 3D mesh.

If the value is not an integer, you can be subject to floating point errors,
so `assert ==`

might be too harsh. In this case, you will want to use
the `numpy.testing`

module to check for approximate equals. For instance,

```
import numpy as np
import discretize
from SimPEG import maps
def test_map_multiplication(self):
mesh = discretize.TensorMesh([2,3])
exp_map = maps.ExpMap(mesh)
vert_map = maps.SurjectVertical1D(mesh)
combo = exp_map*vert_map
m = np.arange(3.0)
t_true = np.exp(np.r_[0,0,1,1,2,2.])
np.testing.assert_allclose(combo * m, t_true)
```

These are rather simple examples, more advanced tests might include solving an
electromagnetic problem numerically and comparing it to an analytical solution
, or performing an adjoint test
to test `Jvec`

and `Jtvec`

.

## Order and Derivative Tests#

Order tests can be used when you are testing differential operators (we are using a second-order, staggered grid discretization for our operators). For example, testing a 2D curl operator in test_operators.py

```
import numpy as np
import unittest
from discretize.tests import OrderTest
class TestCurl2D(OrderTest):
name = "Cell Grad 2D - Dirichlet"
meshTypes = ['uniformTensorMesh']
meshDimension = 2
meshSizes = [8, 16, 32, 64]
def getError(self):
# Test function
ex = lambda x, y: np.cos(y)
ey = lambda x, y: np.cos(x)
sol = lambda x, y: -np.sin(x)+np.sin(y)
sol_curl2d = call2(sol, self.M.gridCC)
Ec = cartE2(self.M, ex, ey)
sol_ana = self.M.edge_curl*self.M.project_face_vector(Ec)
err = np.linalg.norm((sol_curl2d-sol_ana), np.inf)
return err
def test_order(self):
self.orderTest()
```

Derivative tests are a particular type of Order and Derivative Tests, and since they
are used so extensively, discretize includes a `check_derivative`

method.

In the case of testing a derivative, we consider a Taylor expansion of a function about \(x\). For a small perturbation \(\Delta x\),

As \(\Delta x\) decreases, we expect \(\|f(x) - f(x + \Delta x)\|\) to have first order convergence (e.g. the improvement in the approximation is directly related to how small \(\Delta x\) is, while if we include the first derivative in our approximation, we expect that \(\|f(x) + J(x)\Delta x - f(x + \Delta x)\|\) to converge at a second-order rate. For example, all maps have an associated derivative test . An example from test_FDEM_derivs.py

```
def deriv_test(fdemType, comp):
# setup simulation, survey
def fun(x):
return survey.dpred(x), lambda x: sim.Jvec(x0, x)
return tests.check_derivative(fun, x0, num=2, plotIt=False, eps=FLR)
```