performance optimize _generate_fourier_series_np

CHANGELOG.rst

@@ -147,11 +147,12 @@ Harmonic model
 - de-duplicate the expression of months in their harmonic form (`#415 <https://github.com/MESMER-group/mesmer/pull/415>`_)
   move creation of the month array to the deepest level (`#487 <https://github.com/MESMER-group/mesmer/pull/487>`_).
 - fix indexing of harmonic model coefficients (`#415 <https://github.com/MESMER-group/mesmer/pull/415>`_)
--  Refactor variable names, small code improvements, fixes and clean docstring
+-  Refactor variable names, small code improvements, optimization, fixes and clean docstring
    (`#415 <https://github.com/MESMER-group/mesmer/pull/415>`_,
    `#424 <https://github.com/MESMER-group/mesmer/pull/424>`_,
-   `#433 <https://github.com/MESMER-group/mesmer/pull/433>`_, and
-   `#512 <https://github.com/MESMER-group/mesmer/pull/512>`_)
+   `#433 <https://github.com/MESMER-group/mesmer/pull/433>`_,
+   `#512 <https://github.com/MESMER-group/mesmer/pull/512>`_, and
+   `#512 <https://github.com/MESMER-group/mesmer/pull/512>`_).
 - add tests (
   `#431 <https://github.com/MESMER-group/mesmer/pull/431>`_, and
   `#458 <https://github.com/MESMER-group/mesmer/pull/458>`_)

mesmer/stats/_harmonic_model.py

@@ -35,22 +35,33 @@ def _generate_fourier_series_np(yearly_predictor, coeffs):
         Fourier Series of order n calculated over yearly_predictor and months with coeffs.
 
     """
-    order = int(coeffs.size / 4)
-    n_years = yearly_predictor.size // 12
-    # NOTE: months from 0..11 for consistency with standard fourier series and fft
-    months = np.tile(np.arange(12), n_years)
-
-    seasonal_cycle = np.nansum(
-        [
-            (coeffs[idx * 4] * yearly_predictor + coeffs[idx * 4 + 1])
-            * np.cos(2 * np.pi * i * months / 12)
-            + (coeffs[idx * 4 + 2] * yearly_predictor + coeffs[idx * 4 + 3])
-            * np.sin(2 * np.pi * i * months / 12)
-            for idx, i in enumerate(range(1, order + 1))
-        ],
-        axis=0,
-    )
-    return seasonal_cycle
+
+    # NOTE: performance-optimized fourier series generation
+
+    coeffs = coeffs[~np.isnan(coeffs)]
+    order = coeffs.size // 4
+
+    # create 2D array of angles with shape (months, order)
+    # as 2 * np.pi * k * np.arange(12).reshape(-1, 1) / 12 but faster
+
+    factor = 2 * np.pi / 12
+    k = np.arange(1.0, order + 1)
+    alpha = np.arange(12 * factor, step=factor).reshape(-1, 1) * k
+
+    # combine cosine and sine into one array
+    cos_sin = np.empty((12, order * 2))
+    cos_sin[:, :order] = np.cos(alpha)
+    cos_sin[:, order:] = np.sin(alpha)
+
+    # sum coefficients - equivalent to np.sum(cos_sin * coeffs[0::2], axis=1)
+    coeff_a = cos_sin @ coeffs[0::2]
+    coeff_b = cos_sin @ coeffs[1::2]
+
+    # reshape yearly_predictor so the coeffs are correctly broadcast
+    yearly_predictor = yearly_predictor.reshape(-1, 12)
+    seasonal_cycle = coeff_a * yearly_predictor + coeff_b
+
+    return seasonal_cycle.flatten()
 
 
 def predict_harmonic_model(yearly_predictor, coeffs, time, time_dim="time"):
@@ -171,6 +182,10 @@ def _calculate_bic(n_samples, order, mse):
     """
 
     n_params = order * 4
+
+    # assume mse smaller eps is 'perfect' - only relevant for noiseless test data
+    mse = mse if mse > np.finfo(float).eps else 0.0
+
     return n_samples * np.log(mse) + n_params * np.log(n_samples)
 
 

tests/unit/test_harmonic_model.py

@@ -30,7 +30,7 @@ def test_generate_fourier_series_np():
 
     result = _generate_fourier_series_np(yearly_predictor, coeffs)
 
-    np.testing.assert_equal(result, expected)
+    np.testing.assert_allclose(result, expected, rtol=1e-13)
 
     coeffs = np.array([1, -2, 3.14, -1])
     result = _generate_fourier_series_np(yearly_predictor, coeffs)