ENH: compute CSD directly for upper-triangle channel pairs in Fourier/multitaper

doc/changes/dev/13719.newfeature.rst

@@ -0,0 +1 @@
+Improve memory usage and runtime of :func:`mne.time_frequency.csd_fourier`, :func:`mne.time_frequency.csd_multitaper`, :func:`mne.time_frequency.csd_array_fourier`, and :func:`mne.time_frequency.csd_array_multitaper` by avoiding unnecessary full-matrix CSD construction, by `Pragnya Khandelwal`_.

mne/time_frequency/csd.py

@@ -1406,22 +1406,14 @@ def _csd_fourier(X, sfreq, n_times, freq_mask, n_fft):
     x_mt, _ = _mt_spectra(X, np.hanning(n_times), sfreq, n_fft)
 
     # Hack so we can sum over axis=-2
-    weights = np.array([1.0])[:, np.newaxis, np.newaxis, np.newaxis]
+    weights = np.array([1.0])[np.newaxis, :, np.newaxis]
 
     x_mt = x_mt[:, :, freq_mask]
 
-    # Calculating CSD
-    # Tiling x_mt so that we can easily use _csd_from_mt()
-    x_mt = x_mt[:, np.newaxis, :, :]
-    x_mt = np.tile(x_mt, [1, x_mt.shape[0], 1, 1])
-    y_mt = np.transpose(x_mt, axes=[1, 0, 2, 3])
-    weights_y = np.transpose(weights, axes=[1, 0, 2, 3])
-    csds = _csd_from_mt(x_mt, y_mt, weights, weights_y)
-
-    # FIXME: don't compute full matrix in the first place
-    csds = np.array(
-        [_sym_mat_to_vector(csds[:, :, i]) for i in range(csds.shape[-1])]
-    ).T
+    # Calculate CSD for upper-triangle channel pairs directly.
+    # This avoids computing/storing the full channel x channel matrix.
+    ii, jj = np.triu_indices(x_mt.shape[0])
+    csds = _csd_from_mt(x_mt[ii], x_mt[jj], weights, weights)
 
     # Scaling by number of samples and compensating for loss of power
     # due to windowing (see section 11.5.2 in Bendat & Piersol).
@@ -1445,27 +1437,23 @@ def _csd_multitaper(
         _, weights = _psd_from_mt_adaptive(
             x_mt, eigvals, freq_mask, max_iter, return_weights=True
         )
-        # Tiling weights so that we can easily use _csd_from_mt()
-        weights = weights[:, np.newaxis, :, :]
-        weights = np.tile(weights, [1, x_mt.shape[0], 1, 1])
     else:
         # Do not use adaptive weights
-        weights = np.sqrt(eigvals)[np.newaxis, np.newaxis, :, np.newaxis]
+        weights = np.sqrt(eigvals)[np.newaxis, :, np.newaxis]
 
     x_mt = x_mt[:, :, freq_mask]
 
-    # Calculating CSD
-    # Tiling x_mt so that we can easily use _csd_from_mt()
-    x_mt = x_mt[:, np.newaxis, :, :]
-    x_mt = np.tile(x_mt, [1, x_mt.shape[0], 1, 1])
-    y_mt = np.transpose(x_mt, axes=[1, 0, 2, 3])
-    weights_y = np.transpose(weights, axes=[1, 0, 2, 3])
-    csds = _csd_from_mt(x_mt, y_mt, weights, weights_y)
-
-    # FIXME: don't compute full matrix in the first place
-    csds = np.array(
-        [_sym_mat_to_vector(csds[:, :, i]) for i in range(csds.shape[-1])]
-    ).T
+    # Calculate CSD for upper-triangle channel pairs directly.
+    # This avoids computing/storing the full channel x channel matrix.
+    ii, jj = np.triu_indices(x_mt.shape[0])
+    x_mt_i = x_mt[ii]
+    x_mt_j = x_mt[jj]
+    if adaptive:
+        weights_i = weights[ii]
+        weights_j = weights[jj]
+    else:
+        weights_i = weights_j = weights
+    csds = _csd_from_mt(x_mt_i, x_mt_j, weights_i, weights_j)
 
     # Scaling by sampling frequency for compatibility with Matlab
     csds /= sfreq