Add support computing entropy on tensors

docs/source/api/api_core.rst

@@ -41,6 +41,7 @@ Gaussian-Copula mutual-information supporting univariate / multivariate multi-di
 
    copnorm_nd
    copnorm_cat_nd
+   ent_nd_g
    mi_nd_gg
    mi_model_nd_gd
    cmi_nd_ggg

frites/core/__init__.py

@@ -12,4 +12,4 @@
                       cmi_1d_ggg, gccmi_1d_ccc, gccmi_1d_ccd, cmi_1d_ggd)
 from .gcmi_nd import (mi_nd_gg, mi_model_nd_gd, cmi_nd_ggg, gcmi_nd_cc,  # noqa
                       gcmi_model_nd_cd, gccmi_nd_ccnd, gccmi_model_nd_cdnd,
-                      gccmi_nd_ccc, cmi_nd_ggd)
+                      gccmi_nd_ccc, cmi_nd_ggd, ent_nd_g)

frites/core/gcmi_nd.py

@@ -61,6 +61,63 @@ def nd_shape_checking(x, y, mvaxis, traxis):
     assert all([x.shape[k] == y.shape[k] for k in dims])
 
 
+###############################################################################
+###############################################################################
+#                                  ENTROPY
+###############################################################################
+###############################################################################
+
+
+def ent_nd_g(x, mvaxis=None, traxis=-1, biascorrect=True, shape_checking=True):
+    """Entropy of a continuous variable.
+
+    Parameters
+    ----------
+    x : array_like
+        Array to consider for computing the entropy.
+    mvaxis : int | None
+        Spatial location of the axis to consider if multi-variate analysis
+        is needed
+    traxis : int | -1
+        Spatial location of the trial axis. By default the last axis is
+        considered
+    biascorrect : bool | True
+        Specifies whether bias correction should be applied to the estimated MI
+    shape_checking : bool | True
+        Perform a reshape and check that x and y shapes are consistents. For
+        high performances and to avoid extensive memory usage, it's better to
+        already have x and y with a shape of (..., mvaxis, traxis) and to set
+        this parameter to False
+
+    Returns
+    -------
+    mi : array_like
+        The mutual information with the same shape as x and y, without the
+        mvaxis and traxis
+    """
+    if shape_checking:
+        x = nd_reshape(x, mvaxis=mvaxis, traxis=traxis)
+    nvarx, ntrl = x.shape[-2], x.shape[-1]
+
+    # covariance
+    c = np.einsum('...ij, ...kj->...ik', x, x)
+    c /= float(ntrl - 1.)
+    chc = np.linalg.cholesky(c)
+
+    # entropy in nats
+    hx = np.log(np.einsum('...ii->...i', chc)).sum(-1) + 0.5 * nvarx * (
+        np.log(2 * np.pi) + 1.0)
+
+    ln2 = np.log(2)
+    if biascorrect:
+        psiterms = psi((ntrl - np.arange(1, nvarx + 1).astype(
+            float)) / 2.) / 2.
+        dterm = (ln2 - np.log(ntrl - 1.)) / 2.
+        hx = hx - nvarx * dterm - psiterms.sum()
+
+    return hx
+
+
 ###############################################################################
 ###############################################################################
 #                          MUTUAL INFORMATION

frites/core/tests/test_gcmi_nd.py

@@ -3,11 +3,17 @@
 
 from frites.core.gcmi_nd import (mi_nd_gg, mi_model_nd_gd, cmi_nd_ggg,
                                  gcmi_nd_cc, gcmi_model_nd_cd, gccmi_nd_ccnd,
-                                 gccmi_model_nd_cdnd, gccmi_nd_ccc)
+                                 gccmi_model_nd_cdnd, gccmi_nd_ccc, ent_nd_g)
 
 
 class TestGcmiNd(object):  # noqa
 
+    def ent_nd_g(self):
+        """Test function ent_nd_g."""
+        x_g = np.random.normal(size=(10, 1000, 20))
+        assert ent_nd_g(x_g, traxis=1).shape == (10, 20)
+        assert ent_nd_g(x_g, traxis=1, mvaxis=0).shape == (20,)
+
     def test_mi_nd_gg(self):
         """Test function mi_nd_gg."""
         x_g = np.random.normal(size=(10, 1000, 20))
@@ -68,3 +74,6 @@ def test_gccmi_nd_ccc(self):
         z_c = np.random.uniform(0, 50, size=(10, 1000, 20))
         assert gccmi_nd_ccc(x_c, y_c, z_c, traxis=1).shape == (10, 20)
         assert gccmi_nd_ccc(x_c, y_c, z_c, traxis=1, mvaxis=0).shape == (20,)
+
+if __name__ == "__main__":
+    TestGcmiNd().ent_nd_g()