Add smoothness metric

nigsp/objects.py

@@ -43,6 +43,7 @@ def __init__(
         surr_split=None,
         sdi=None,
         gsdi=None,
+        smoothness=None,
         fc=None,
         fc_split=None,
     ):
@@ -82,6 +83,7 @@ def __init__(
         self.surr_split = deepcopy(surr_split)
         self.sdi = deepcopy(sdi)
         self.gsdi = deepcopy(gsdi)
+        self.smoothness = deepcopy(smoothness)
         self.fc = deepcopy(fc)
         self.fc_split = deepcopy(fc_split)
 
@@ -168,6 +170,11 @@ def compute_gsdi(self, mean=False, keys=None):  # pragma: no cover
         self.gsdi = operations.gsdi(self.ts_split, mean, keys)
         return self
 
+    def compute_smoothness(self, signal):  # pragma: no cover
+        """Implement metrics.smoothness as class method."""
+        self.smoothness = operations.smoothness(self.lapl_mtx, signal)
+        return self
+
     def create_surrogates(self, sc_type="informed", n_surr=1000, seed=None):
         """Implement surrogates.sc_informed and sc_uninformed as class method."""
         sc_args = {"timeseries": self.timeseries, "n_surr": n_surr}

nigsp/operations/__init__.py

@@ -15,7 +15,7 @@
 # Import all operations.
 from .graph import nodestrength, zerocross
 from .laplacian import decomposition, symmetric_normalised_laplacian
-from .metrics import functional_connectivity, gsdi, sdi
+from .metrics import functional_connectivity, gsdi, sdi, smoothness
 from .nifti import apply_atlas, apply_mask, mat_to_vol, unfold_atlas, unmask, vol_to_mat
 from .surrogates import random_sign, sc_informed, sc_uninformed, test_significance
 from .timeseries import (

nigsp/operations/metrics.py

@@ -246,6 +246,25 @@ def _fc(timeseries, mean=False):
     return fc
 
 
+def smoothness(laplacian, signal):
+    """Compute the smoothness of a signal over the graph corresponding to given laplacian.
+
+    Parameters
+    ----------
+    node_signal : numpy.ndarray
+        any signal defined with one value per node.
+    laplacian : numpy.ndarray
+        graph laplacian to use.
+
+    Returns
+    -------
+    smoothness : float
+        the smoothness of the signal.
+    """
+    LGR.info("Compute signal smoothness.")
+    return np.dot(signal.T, np.dot(laplacian, signal))
+
+
 """
 Copyright 2022, Stefano Moia.
 

nigsp/tests/test_metrics.py

@@ -72,6 +72,16 @@ def test_gsdi():
     assert (gsdi_out["beta_over_alpha"] == gsdi_in).all()
 
 
+def test_smoothness():
+    signal = rand(10, 1)
+    laplacian = rand(10, 10)
+
+    expected_smoothness = np.dot(signal.T, np.dot(laplacian, signal))
+    computed_smoothness = metrics.smoothness(laplacian, signal)
+
+    assert np.isclose(expected_smoothness, computed_smoothness, rtol=1e-10)
+
+
 # ### Break tests
 def test_break_sdi():
     ts1 = np.arange(1, 3)[..., np.newaxis]