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 \(\Delta x\),

\[f(x + \Delta x) \simeq f(x) + J(x) \Delta x + \mathcal{O}(h^2)\]

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)