expand harmonic model xarray test (MESMER-group#458)

* add more sophisticated xarray test

* delete Shrutis test file

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Mathias Hauser <mathause@users.noreply.github.com>

tests/unit/test_harmonic_model.py

@@ -172,23 +172,51 @@ def test_fit_to_bic_numerical_stability():
     np.testing.assert_allclose(predictions, expected_predictions)
 
 
-@pytest.mark.parametrize(
-    "coefficients",
-    [
-        np.array([0, -1, 0, -2]),
-        np.array([1, 2, 3, 4, 5, 6, 7, 8]),
-        np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),
-    ],
-)
-def test_fit_to_bic_xr(coefficients):
-    yearly_predictor = trend_data_2D(n_timesteps=10, n_lat=3, n_lon=2)
+def get_2D_coefficients(order_per_cell, n_lat=3, n_lon=2):
+    n_cells = n_lat * n_lon
+    max_order = 6
+
+    # generate coefficients that resemble real ones
+    # generate rapidly decreasing coefficients for increasing orders
+    trend = np.repeat(np.linspace(1.2, 0.2, max_order) ** 2, 4)
+    # the first coefficients are rather small  (scaling of seasonal variability with temperature change)
+    # while the second ones are large (constant distance of each month from the yearly mean)
+    scale = np.tile([0.01, 5.0], (n_cells, max_order * 2))
+    # generate some variability so not all coefficients are exactly the same
+    rng = np.random.default_rng(0)
+    variability = rng.normal(loc=0, scale=0.1, size=(n_cells, max_order * 4))
+    # put it together
+    coeffs = trend * scale + variability
+    coeffs = np.round(coeffs, 1)
+
+    # replace superfluous orders with nans
+    for cell, order in enumerate(order_per_cell):
+        coeffs[cell, order * 4 :] = np.nan
+
+    LON, LAT = np.meshgrid(np.arange(n_lon), np.arange(n_lat))
+
+    coords = {
+        "lon": ("cells", LON.flatten()),
+        "lat": ("cells", LAT.flatten()),
+    }
+
+    return xr.DataArray(coeffs, dims=("cells", "coeff"), coords=coords)
+
+
+def test_fit_to_bic_xr():
+    n_ts = 10
+    orders = [1, 2, 3, 4, 5, 6]
+
+    coefficients = get_2D_coefficients(order_per_cell=orders, n_lat=3, n_lon=2)
+
+    yearly_predictor = trend_data_2D(n_timesteps=n_ts, n_lat=3, n_lon=2)
 
     freq = "AS" if Version(pd.__version__) < Version("2.2") else "YS"
     yearly_predictor["time"] = xr.cftime_range(
-        start="2000-01-01", periods=10, freq=freq
+        start="2000-01-01", periods=n_ts, freq=freq
     )
 
-    time = xr.cftime_range(start="2000-01-01", periods=10 * 12, freq="MS")
+    time = xr.cftime_range(start="2000-01-01", periods=n_ts * 12, freq="MS")
     monthly_time = xr.DataArray(
         time,
         dims=["time"],
@@ -200,17 +228,27 @@ def test_fit_to_bic_xr(coefficients):
     monthly_target = xr.apply_ufunc(
         generate_fourier_series_np,
         upsampled_yearly_predictor,
-        input_core_dims=[["time"]],
+        coefficients,
+        input_core_dims=[["time"], ["coeff"]],
         output_core_dims=[["time"]],
         vectorize=True,
         output_dtypes=[float],
-        kwargs={"coeffs": coefficients, "months": months},
+        kwargs={"months": months},
     )
 
+    # test if the model can recover the monthly target from perfect fourier series
     result = fit_to_bic_xr(yearly_predictor, monthly_target)
-
+    np.testing.assert_equal(result.n_sel.values, orders)
     xr.testing.assert_allclose(result["predictions"], monthly_target, atol=0.1)
 
+    # test if the model can recover the underlying cycle with noise on top of monthly target
+    rng = np.random.default_rng(0)
+    noisy_monthly_target = monthly_target + rng.normal(
+        loc=0, scale=0.1, size=monthly_target.values.shape
+    )
+    result = fit_to_bic_xr(yearly_predictor, noisy_monthly_target)
+    xr.testing.assert_allclose(result["predictions"], monthly_target, atol=0.2)
+
 
 def test_fit_to_bix_xr_instance_checks():
     yearly_predictor = trend_data_2D(n_timesteps=10, n_lat=3, n_lon=2)