Features/98 moments - skew and kurtosis

CHANGELOG.md

@@ -7,15 +7,17 @@
 - [#577](https://github.com/helmholtz-analytics/heat/pull/577) Add `ndim` property in dndarray
 - [#578](https://github.com/helmholtz-analytics/heat/pull/578) Bugfix: Bad variable in reshape
 - [#580](https://github.com/helmholtz-analytics/heat/pull/580) New feature: `fliplr()`
-- [#581](https://github.com/helmholtz-analytics/heat/pull/581) New Feature: `DNDarray.tolist()`
+- [#581](https://github.com/helmholtz-analytics/heat/pull/581) New feature: `DNDarray.tolist()`
 - [#583](https://github.com/helmholtz-analytics/heat/pull/583) New feature: `rot90()`
-- [#593](https://github.com/helmholtz-analytics/heat/pull/593) New feature `arctan2()`
+- [#593](https://github.com/helmholtz-analytics/heat/pull/593) New feature: `arctan2()`
 - [#594](https://github.com/helmholtz-analytics/heat/pull/594) New feature: Advanced indexing
-- [#594](https://github.com/helmholtz-analytics/heat/pull/594) Bugfix: getitem and setitem memory consumption heavily reduced
+- [#594](https://github.com/helmholtz-analytics/heat/pull/594) Bugfix: `__getitem__` and `__setitem__` memory consumption heavily reduced
 - [#596](https://github.com/helmholtz-analytics/heat/pull/596) New feature: `outer()`
 - [#598](https://github.com/helmholtz-analytics/heat/pull/598) Type casting changed to PyTorch style casting (i.e. intuitive casting) instead of safe casting
 - [#600](https://github.com/helmholtz-analytics/heat/pull/600) New feature: `shape()`
 - [#614](https://github.com/helmholtz-analytics/heat/pull/614) New feature: printing of DNDarrays and ``__repr__`` and ``__str__`` functions
+- [#615](https://github.com/helmholtz-analytics/heat/pull/615) New feature: `skew()`
+- [#615](https://github.com/helmholtz-analytics/heat/pull/615) New feature: `kurtosis()`
 - [#618](https://github.com/helmholtz-analytics/heat/pull/618) Printing of unbalnced DNDarrays added
 
 # v0.4.0

heat/cluster/spectral.py

@@ -107,7 +107,13 @@ def _spectral_embedding(self, X):
         """
         L = self._laplacian.construct(X)
         # 3. Eigenvalue and -vector calculation via Lanczos Algorithm
-        v0 = ht.ones((L.shape[0],), dtype=L.dtype, split=0, device=L.device) / math.sqrt(L.shape[0])
+        v0 = ht.full(
+            (L.shape[0],),
+            fill_value=1.0 / math.sqrt(L.shape[0]),
+            dtype=L.dtype,
+            split=0,
+            device=L.device,
+        )
         V, T = ht.lanczos(L, self.n_lanczos, v0)
 
         # 4. Calculate and Sort Eigenvalues and Eigenvectors of tridiagonal matrix T

heat/core/dndarray.py

@@ -4,7 +4,7 @@
 import math
 import torch
 import warnings
-from typing import List
+from typing import List, Union
 
 from . import arithmetics
 from . import devices
@@ -147,10 +147,7 @@ def size(self):
         size : int
             number of total elements of the tensor
         """
-        try:
-            return np.prod(self.__gshape)
-        except TypeError:
-            return 1
+        return torch.prod(torch.tensor(self.gshape, device=self.device.torch_device)).item()
 
     @property
     def gnumel(self):
@@ -1703,6 +1700,35 @@ def item(self):
         """
         return self.__array.item()
 
+    def kurtosis(self, axis=None, unbiased=True, Fischer=True):
+        """
+        Compute the kurtosis (Fisher or Pearson) of a dataset.
+        TODO: add return type annotation (DNDarray) and x annotation (DNDarray)
+
+        Kurtosis is the fourth central moment divided by the square of the variance.
+        If Fisher’s definition is used, then 3.0 is subtracted from the result to give 0.0 for a normal distribution.
+
+        If unbiased is True (defualt) then the kurtosis is calculated using k statistics to
+        eliminate bias coming from biased moment estimators
+
+        Parameters
+        ----------
+        x : ht.DNDarray
+            Input array
+        axis : NoneType or Int
+            Axis along which skewness is calculated, Default is to compute over the whole array `x`
+        unbiased : Bool
+            if True (default) the calculations are corrected for bias
+        Fischer : bool
+            Whether use Fischer's definition or not. If true 3. is subtracted from the result.
+
+        Warnings
+        --------
+        UserWarning: Dependent on the axis given and the split configuration a UserWarning may be thrown during this
+            function as data is transferred between processes
+        """
+        return statistics.kurtosis(self, axis, unbiased, Fischer)
+
     def __le__(self, other):
         """
         Element-wise rich comparison of relation "less than or equal" with values from second operand (scalar or tensor)
@@ -3227,6 +3253,26 @@ def sinh(self, out=None):
         """
         return trigonometrics.sinh(self, out)
 
+    def skew(self, axis=None, unbiased=True):
+        """
+        Compute the sample skewness of a data set.
+
+        Parameters
+        ----------
+        x : ht.DNDarray
+            Input array
+        axis : NoneType or Int
+            Axis along which skewness is calculated, Default is to compute over the whole array `x`
+        unbiased : Bool
+            if True (default) the calculations are corrected for bias
+
+        Warnings
+        --------
+        UserWarning: Dependent on the axis given and the split configuration a UserWarning may be thrown during this
+            function as data is transferred between processes
+        """
+        return statistics.skew(self, axis, unbiased)
+
     def sqrt(self, out=None):
         """
         Return the non-negative square-root of the tensor element-wise.

heat/core/linalg/solver.py

@@ -155,13 +155,13 @@ def lanczos(A, m, v0=None, V_out=None, T_out=None):
                 b = torch.dot(vi_loc, vi_loc)
                 A.comm.Allreduce(ht.communication.MPI.IN_PLACE, a, ht.communication.MPI.SUM)
                 A.comm.Allreduce(ht.communication.MPI.IN_PLACE, b, ht.communication.MPI.SUM)
-                vr._DNDarray__array = vr._DNDarray__array - a / b * vi_loc
+                vr._DNDarray__array -= a / b * vi_loc
 
             vi = vr / ht.norm(vr)
 
         w = ht.matmul(A, vi)
         alpha = ht.dot(w, vi)
-        w = w - alpha * vi - beta * V[:, i - 1]
+        w -= alpha * vi - beta * V[:, i - 1]
 
         T[i - 1, i] = beta
         T[i, i - 1] = beta