perf: Combat perf improvements

benchmarks/benchmarks/tools.py

@@ -44,3 +44,9 @@ def time_rank_genes_groups(self) -> None:
 
     def peakmem_rank_genes_groups(self) -> None:
         sc.tl.rank_genes_groups(self.adata, "bulk_labels", method="wilcoxon")
+
+    def time_combat(self) -> None:
+        sc.pp.combat(self.adata, key="bulk_labels")
+
+    def peakmem_combat(self) -> None:
+        sc.pp.combat(self.adata, key="bulk_labels")

src/scanpy/preprocessing/_combat.py

@@ -108,25 +108,23 @@ def _standardize_data(
     # compute pooled variance estimator
     b_hat = np.dot(np.dot(la.inv(np.dot(design.T, design)), design.T), data.T)
     grand_mean = np.dot((n_batches / n_array).T, b_hat[:n_batch, :])
-    var_pooled = (data - np.dot(design, b_hat).T) ** 2
-    var_pooled = np.dot(var_pooled, np.ones((int(n_array), 1)) / int(n_array))
+    var_pooled = (
+        (data - np.dot(design, b_hat).T).pow(2).to_numpy().mean(axis=1, keepdims=True)
+    )
 
     # Compute the means
     if np.sum(var_pooled == 0) > 0:
         print(f"Found {np.sum(var_pooled == 0)} genes with zero variance.")
-    stand_mean = np.dot(
-        grand_mean.T.reshape((len(grand_mean), 1)), np.ones((1, int(n_array)))
-    )
-    tmp = np.array(design.copy())
+    tmp = design.to_numpy(copy=True)
     tmp[:, :n_batch] = 0
-    stand_mean += np.dot(tmp, b_hat).T
+    stand_mean = grand_mean[:, np.newaxis] + np.dot(tmp, b_hat).T
 
     # need to be a bit careful with the zero variance genes
     # just set the zero variance genes to zero in the standardized data
     s_data = np.where(
         var_pooled == 0,
         0,
-        ((data - stand_mean) / np.dot(np.sqrt(var_pooled), np.ones((1, int(n_array))))),
+        (data - stand_mean) / np.sqrt(var_pooled),
     )
     s_data = pd.DataFrame(s_data, index=data.index, columns=data.columns)
 
@@ -218,7 +216,6 @@ def combat(  # noqa: PLR0915
             "within-batch variance. Filter these batches before running combat."
         )
         raise ValueError(msg)
-    n_array = float(sum(n_batches))
 
     # standardize across genes using a pooled variance estimator
     logg.info("Standardizing Data across genes.\n")
@@ -276,16 +273,13 @@ def combat(  # noqa: PLR0915
         # of multiplicative batch effect to pooled variance and add the overall gene
         # wise mean
         dsq = np.sqrt(delta_star[j, :])
-        dsq = dsq.reshape((len(dsq), 1))
-        denom = np.dot(dsq, np.ones((1, n_batches[j])))
         numer = np.array(
             bayesdata.iloc[:, batch_idxs]
             - np.dot(batch_design.iloc[batch_idxs], gamma_star).T
         )
-        bayesdata.iloc[:, batch_idxs] = numer / denom
+        bayesdata.iloc[:, batch_idxs] = numer / dsq[:, np.newaxis]
 
-    vpsq = np.sqrt(var_pooled).reshape((len(var_pooled), 1))
-    bayesdata = bayesdata * np.dot(vpsq, np.ones((1, int(n_array)))) + stand_mean
+    bayesdata = bayesdata * np.sqrt(var_pooled) + stand_mean
 
     # put back into the adata object or return
     x = bayesdata.to_numpy().transpose()
@@ -348,12 +342,7 @@ def _it_sol(
     # in the loop, gamma and delta are updated together. they depend on each other. we iterate until convergence.
     while change > conv:
         g_new = (t2 * n * g_hat + d_old * g_bar) / (t2 * n + d_old)
-        sum2 = s_data - g_new.reshape((g_new.shape[0], 1)) @ np.ones((
-            1,
-            s_data.shape[1],
-        ))
-        sum2 = sum2**2
-        sum2 = sum2.sum(axis=1)
+        sum2 = ((s_data - g_new[:, np.newaxis]) ** 2).sum(axis=1)
         d_new = (0.5 * sum2 + b) / (n / 2.0 + a - 1.0)
 
         change = max(