Use in-place operations for cross-correlations

docs/source/Adaptive.py

@@ -108,6 +108,7 @@
 # [Kullback–Leibler divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence),
 # but we do not pursue this here.
 
+
 # %%
 def get_prior(num_parameters, num_ensemble, prior_std):
     """Sample prior from N(0, prior_std)."""
@@ -289,6 +290,7 @@ def g(X):
 # - The draw of prior realizations $X \sim N(0, \sigma)$.
 # - The noise (given by the `covariance` argument) that ESMDA adds to the observations.
 
+
 # %%
 def corr_true(array):
     return sp.stats.pearsonr(x_true, array).statistic

docs/source/Polynomial.py

@@ -159,7 +159,6 @@ def poly(a, b, c, x):
 )
 n_ies_iter = 7
 for i in range(n_ies_iter):
-
     step_length = steplength_exponential(i + 1)
     X_IES_ert = smoother_ies.sies_iteration(Y_IES_ert, step_length=step_length)
 

src/iterative_ensemble_smoother/experimental.py

@@ -139,33 +139,37 @@ def compute_cross_covariance_multiplier(
 
         return sp.linalg.solve(C_DD, D - Y, **solver_kwargs)  # type: ignore
 
-    def _correlation_matrix(
+    def _cov_to_corr_inplace(
         self,
         cov_XY: npt.NDArray[np.double],
-        X: npt.NDArray[np.double],
-        Y: npt.NDArray[np.double],
-    ) -> npt.NDArray[np.double]:
-        """Compute a correlation matrix given a covariance matrix."""
-        assert cov_XY.shape == (X.shape[0], Y.shape[0])
+        stds_X: npt.NDArray[np.double],
+        stds_Y: npt.NDArray[np.double],
+    ) -> None:
+        """Convert a covariance matrix to a correlation matrix in-place."""
 
-        stds_Y = np.std(Y, axis=1, ddof=1)
-        stds_X = np.std(X, axis=1, ddof=1)
-
-        # Compute the correlation matrix from the covariance matrix
-        corr_XY: npt.NDArray[np.double] = (cov_XY / stds_X[:, np.newaxis]) / stds_Y[
-            np.newaxis, :
-        ]
+        # Divide each element of cov_XY by the corresponding standard deviations
+        cov_XY /= stds_X[:, np.newaxis]
+        cov_XY /= stds_Y[np.newaxis, :]
 
-        # Perform checks. There appears to be occasional numerical issues in
-        # the equation. With 2 ensemble members, we get e.g. a max value of
-        # 1.0000000000016778. We allow some leeway and clip the results.
+        # Perform checks and clip values to [-1, 1]
         eps = 1e-8
-        if not ((corr_XY.max() <= 1 + eps) and (corr_XY.min() >= -1 - eps)):
+        if not ((cov_XY.max() <= 1 + eps) and (cov_XY.min() >= -1 - eps)):
             msg = "Cross-correlation matrix has entries not in [-1, 1]."
-            msg += f"The min and max values are: {corr_XY.min()} and {corr_XY.max()}"
+            msg += f"The min and max values are: {cov_XY.min()} and {cov_XY.max()}"
             warnings.warn(msg)
 
-        corr_XY = np.clip(corr_XY, a_min=-1, a_max=1)
+        return np.clip(cov_XY, a_min=-1, a_max=1, out=cov_XY)
+
+    def _corr_to_cov_inplace(
+        self,
+        corr_XY: npt.NDArray[np.double],
+        stds_X: npt.NDArray[np.double],
+        stds_Y: npt.NDArray[np.double],
+    ) -> None:
+        """Convert a correlation matrix to a covariance matrix in-place."""
+        # Multiply each element of corr_XY by the corresponding standard deviations
+        corr_XY *= stds_X[:, np.newaxis]
+        corr_XY *= stds_Y[np.newaxis, :]
         return corr_XY
 
     def assimilate(
@@ -174,6 +178,7 @@ def assimilate(
         X: npt.NDArray[np.double],
         Y: npt.NDArray[np.double],
         D: npt.NDArray[np.double],
+        overwrite: bool = False,
         alpha: float,
         correlation_threshold: Union[Callable[[int], float], float, None] = None,
         cov_YY: Optional[npt.NDArray[np.double]] = None,
@@ -207,6 +212,10 @@ def assimilate(
             The covariance inflation factor. The sequence of alphas should
             obey the equation sum_i (1/alpha_i) = 1. However, this is NOT
             enforced in this method. The user/caller is responsible for this.
+        overwrite: bool
+            If True, X will be overwritten and mutated.
+            If False, the method will not mutate inputs in any way.
+            Setting this to True saves memory.
         correlation_threshold : callable or float or None
             Either a callable with signature f(ensemble_size) -> float, or a
             float in the range [0, 1]. Entries in the covariance matrix that
@@ -239,6 +248,10 @@ def assimilate(
                 "`correlation_threshold` must be a callable or a float in [0, 1]"
             )
 
+        # Do not overwrite input arguments
+        if not overwrite:
+            X = np.copy(X)
+
         # Create `correlation_threshold` if the argument is a float
         if is_float:
             corr_threshold: float = correlation_threshold  # type: ignore
@@ -261,25 +274,27 @@ def correlation_threshold(ensemble_size: int) -> float:
         # X by parameter group (rows), the storage requirement decreases
         cov_XY = empirical_cross_covariance(X, Y)
         assert cov_XY.shape == (X.shape[0], Y.shape[0])
-        corr_XY = self._correlation_matrix(cov_XY, X, Y)
-        assert corr_XY.shape == cov_XY.shape
+
+        stds_X = np.std(X, axis=1, ddof=1)
+        stds_Y = np.std(Y, axis=1, ddof=1)
+
+        corr_XY = self._cov_to_corr_inplace(cov_XY, stds_X, stds_Y)
 
         # Determine which elements in the cross covariance matrix that will
         # be set to zero
         threshold = correlation_threshold(X.shape[1])
         significant_corr_XY = np.abs(corr_XY) > threshold
 
+        cov_XY = self._corr_to_cov_inplace(corr_XY, stds_X, stds_Y)
+
         # Pre-compute the covariance cov(Y, Y) here, and index on it later
         if cov_YY is None:
             cov_YY = empirical_cross_covariance(Y, Y)
         else:
             assert cov_YY.ndim == 2, "'cov_YY' must be a 2D array"
             assert cov_YY.shape == (Y.shape[0], Y.shape[0])
 
-        # TODO: memory could be saved by overwriting the input X
-        X_out: npt.NDArray[np.double] = np.copy(X)
-        for (unique_row, indices_of_row) in groupby_indices(significant_corr_XY):
-
+        for unique_row, indices_of_row in groupby_indices(significant_corr_XY):
             if verbose:
                 print(
                     f"    Assimilating {len(indices_of_row)} parameters"
@@ -294,8 +309,6 @@ def correlation_threshold(ensemble_size: int) -> float:
             if np.all(~unique_row):
                 continue
 
-            # Get the parameters (X) that have identical significant responses (Y)
-            X_subset = X[indices_of_row, :]
             Y_subset = Y[unique_row, :]
 
             # Compute the masked arrays for these variables
@@ -320,9 +333,9 @@ def correlation_threshold(ensemble_size: int) -> float:
                 Y=Y_subset,
                 cov_YY=cov_YY_subset,  # Passing cov(Y, Y) avoids re-computation
             )
-            X_out[indices_of_row, :] = X_subset + cov_XY_subset @ T
+            X[indices_of_row, :] += cov_XY_subset @ T
 
-        return X_out
+        return X
 
 
 class RowScaling:

tests/test_experimental.py

@@ -19,7 +19,6 @@
 
 @pytest.mark.parametrize("seed", range(25))
 def test_groupby_indices(seed):
-
     rng = np.random.default_rng(seed)
     rows = rng.integers(10, 100)
     columns = rng.integers(2, 9)
@@ -39,8 +38,7 @@ def test_groupby_indices(seed):
     assert intersection_idx == set()
 
     # Verify each entry in the groups
-    for (unique_row, indices_of_row) in groups:
-
+    for unique_row, indices_of_row in groups:
         # Repeat this unique row the number of times it occurs in X
         repeated = np.repeat(
             unique_row[np.newaxis, :], repeats=len(indices_of_row), axis=0
@@ -50,7 +48,6 @@ def test_groupby_indices(seed):
 
 @pytest.fixture()
 def linear_problem(request):
-
     # Seed the problem using indirect parametrization:
     # https://docs.pytest.org/en/latest/example/parametrize.html#indirect-parametrization
     rng = np.random.default_rng(request.param)
@@ -86,7 +83,6 @@ class TestAdaptiveESMDA:
     def test_that_adaptive_localization_with_cutoff_1_equals_ensemble_prior(
         self, linear_problem
     ):
-
         # Create a problem with g(x) = A @ x
         X, g, observations, covariance, _ = linear_problem
 
@@ -98,7 +94,6 @@ def test_that_adaptive_localization_with_cutoff_1_equals_ensemble_prior(
         X_i = np.copy(X)
         alpha = normalize_alpha(np.ones(5))
         for alpha_i in alpha:
-
             # Run forward model
             Y_i = g(X_i)
 
@@ -127,7 +122,6 @@ def test_that_adaptive_localization_with_cutoff_1_equals_ensemble_prior(
     def test_that_adaptive_localization_with_cutoff_0_equals_standard_ESMDA_update(
         self, linear_problem
     ):
-
         # Create a problem with g(x) = A @ x
         X, g, observations, covariance, rng = linear_problem
 
@@ -141,8 +135,7 @@ def test_that_adaptive_localization_with_cutoff_0_equals_standard_ESMDA_update(
         )
 
         X_i = np.copy(X)
-        for i, alpha_i in enumerate(alpha, 1):
-
+        for _, alpha_i in enumerate(alpha, 1):
             # Run forward model
             Y_i = g(X_i)
 
@@ -152,12 +145,13 @@ def test_that_adaptive_localization_with_cutoff_0_equals_standard_ESMDA_update(
             )
 
             # Update the relevant parameters and write to X
-            X_i = smoother.assimilate(
+            smoother.assimilate(
                 X=X_i,
                 Y=Y_i,
                 D=D_i,
+                overwrite=True,
                 alpha=alpha_i,
-                correlation_threshold=lambda ensemble_size: 0,
+                correlation_threshold=0,
             )
 
         # =============================================================================
@@ -171,7 +165,7 @@ def test_that_adaptive_localization_with_cutoff_0_equals_standard_ESMDA_update(
         )
 
         X_i2 = np.copy(X)
-        for i in range(smoother.num_assimilations()):
+        for _ in range(smoother.num_assimilations()):
             X_i2 = smoother.assimilate(X_i2, g(X_i2))
 
         assert np.allclose(X_i, X_i2)
@@ -194,7 +188,7 @@ def test_that_posterior_generalized_variance_increases_in_cutoff(
         members decrease, this test starts to fail more often."""
 
         # Create a problem with g(x) = A @ x
-        X, g, observations, covariance, rng = linear_problem
+        X, g, observations, covariance, _ = linear_problem
         if full_covariance:
             covariance = np.diag(covariance)
 
@@ -208,8 +202,7 @@ def test_that_posterior_generalized_variance_increases_in_cutoff(
         )
 
         X_i = np.copy(X)
-        for i, alpha_i in enumerate(alpha, 1):
-
+        for _, alpha_i in enumerate(alpha, 1):
             # Run forward model
             Y_i = g(X_i)
 
@@ -226,14 +219,14 @@ def test_that_posterior_generalized_variance_increases_in_cutoff(
                 Y=Y_i,
                 D=D_i,
                 alpha=alpha_i,
-                correlation_threshold=lambda ensemble_size: cutoff_low,
+                correlation_threshold=cutoff_low,
             )
             X_i_high_cutoff = smoother.assimilate(
                 X=X_i,
                 Y=Y_i,
                 D=D_i,
                 alpha=alpha_i,
-                correlation_threshold=lambda ensemble_size: cutoff_high,
+                correlation_threshold=cutoff_high,
             )
 
             # Compute covariances
@@ -410,8 +403,8 @@ def test_that_cov_YY_can_be_computed_outside_of_assimilate(
         """
 
         # Create a problem with g(x) = A @ x
-        X, g, observations, covariance, rng = linear_problem
-        num_parameters, ensemble_size = X.shape
+        X, g, observations, covariance, _ = linear_problem
+        _, ensemble_size = X.shape
 
         alpha = normalize_alpha(np.array([5, 4, 3, 2, 1]))  # Vector of inflation values
         smoother = AdaptiveESMDA(
@@ -535,7 +528,7 @@ def multiply(self, X, K):
         row_groups = [tuple(range(17)), tuple(range(17, 100))]
         # When alpha=1 in row scaling, we perform a full update
         X_with_row_scaling = [
-            (X[idx, :], RowScaling(alpha=1)) for i, idx in enumerate(row_groups)
+            (X[idx, :], RowScaling(alpha=1)) for _, idx in enumerate(row_groups)
         ]
 
         # Perform an update using row scaling
@@ -556,7 +549,7 @@ def multiply(self, X, K):
             inversion=inversion,
             seed=1,
         )
-        for iteration in range(smoother.num_assimilations()):
+        for _ in range(smoother.num_assimilations()):
             X_posterior = smoother.assimilate(X, Y)
 
         # The result should be the same
@@ -566,7 +559,6 @@ def multiply(self, X, K):
 
 
 if __name__ == "__main__":
-
     pytest.main(
         args=[
             __file__,