improve Field norm() method

nifty5/data_objects/distributed_do.py

@@ -32,7 +32,7 @@ __all__ = ["ntask", "rank", "master", "local_shape", "data_object", "full",
            "local_data", "ibegin", "ibegin_from_shape", "np_allreduce_sum",
            "np_allreduce_min", "np_allreduce_max",
            "distaxis", "from_local_data", "from_global_data", "to_global_data",
-           "redistribute", "default_distaxis", "is_numpy",
+           "redistribute", "default_distaxis", "is_numpy", "absmax", "norm",
            "lock", "locked", "uniform_full", "transpose", "to_global_data_rw",
            "ensure_not_distributed", "ensure_default_distributed"]
 
@@ -553,3 +553,22 @@ def ensure_default_distributed(arr):
     if arr._distaxis != 0:
         arr = redistribute(arr, dist=0)
     return arr
+
+
+def absmax(arr):
+    if arr._data.size == 0:
+        tmp = np.array(0, dtype=arr._data.dtype)
+    else:
+        tmp = np.linalg.norm(arr._data, ord=np.inf)
+    res = np.empty_like(tmp)
+    _comm.Allreduce(tmp, res, MPI.MAX)
+    return res[()]
+
+
+def norm(arr, ord=2):
+    if ord == np.inf:
+        return absmax(arr)
+    tmp = np.linalg.norm(np.atleast_1d(arr._data), ord=ord) ** ord
+    res = np.empty_like(tmp)
+    _comm.Allreduce(tmp, res, MPI.SUM)
+    return res[()] ** (1./ord)

nifty5/data_objects/numpy_do.py

@@ -31,7 +31,7 @@ __all__ = ["ntask", "rank", "master", "local_shape", "data_object", "full",
            "local_data", "ibegin", "ibegin_from_shape", "np_allreduce_sum",
            "np_allreduce_min", "np_allreduce_max",
            "distaxis", "from_local_data", "from_global_data", "to_global_data",
-           "redistribute", "default_distaxis", "is_numpy",
+           "redistribute", "default_distaxis", "is_numpy", "absmax", "norm",
            "lock", "locked", "uniform_full", "to_global_data_rw",
            "ensure_not_distributed", "ensure_default_distributed"]
 
@@ -141,3 +141,11 @@ def ensure_not_distributed(arr, axes):
 
 def ensure_default_distributed(arr):
     return arr
+
+
+def absmax(arr):
+    return np.linalg.norm(arr, ord=np.inf)
+
+
+def norm(arr, ord=2):
+    return np.linalg.norm(np.atleast_1d(arr), ord=ord)

nifty5/field.py

@@ -360,25 +360,20 @@ class Field(object):
         # For the moment, do this the explicit, non-optimized way
         return (self.conjugate()*x).sum(spaces=spaces)
 
-    def norm(self):
+    def norm(self, ord=2):
         """ Computes the L2-norm of the field values.
 
-        Returns
-        -------
-        float
-            The L2-norm of the field values.
-        """
-        return np.sqrt(abs(self.vdot(x=self)))
-
-    def squared_norm(self):
-        """ Computes the square of the L2-norm of the field values.
+        Parameters
+        ----------
+        ord : int, default=2
+            accepted values: 1, 2, ..., np.inf
 
         Returns
         -------
         float
-            The square of the L2-norm of the field values.
+            The L2-norm of the field values.
         """
-        return abs(self.vdot(x=self))
+        return dobj.norm(self._val, ord)
 
     def conjugate(self):
         """ Returns the complex conjugate of the field.

nifty5/multi_field.py

@@ -137,15 +137,24 @@ class MultiField(object):
             domain, tuple(Field.from_global_data(domain[key], arr[key], sum_up)
                           for key in domain.keys()))
 
-    def norm(self):
-        """ Computes the L2-norm of the field values.
+    def norm(self, ord=2):
+        """ Computes the norm of the field values.
+
+        Parameters
+        ----------
+        ord : int, default=2
+            accepted values: 1, 2, ..., np.inf
 
         Returns
         -------
         norm : float
-            The L2-norm of the field values.
+            The norm of the field values.
         """
-        return np.sqrt(np.abs(self.vdot(x=self)))
+        nrm = np.asarray([f.norm(ord) for f in self._val])
+        if ord == np.inf:
+            return nrm.max()
+        return (nrm ** ord).sum() ** (1./ord)
+#        return np.sqrt(np.abs(self.vdot(x=self)))
 
     def sum(self):
         """ Computes the sum all field values.
@@ -168,16 +177,6 @@ class MultiField(object):
         """
         return utilities.my_sum(map(lambda d: d.size, self._domain.domains()))
 
-    def squared_norm(self):
-        """ Computes the square of the L2-norm of the field values.
-
-        Returns
-        -------
-        float
-            The square of the L2-norm of the field values.
-        """
-        return abs(self.vdot(x=self))
-
     def __neg__(self):
         return self._transform(lambda x: -x)
 

test/test_field.py

@@ -110,6 +110,16 @@ class Test_Functionality(unittest.TestCase):
         assert_allclose(sc1.mean.local_data, fp1.local_data, rtol=0.2)
         assert_allclose(sc2.mean.local_data, fp2.local_data, rtol=0.2)
 
+    def test_norm(self):
+        s = ift.RGSpace((10,))
+        f = ift.Field.from_random("normal", domain=s, dtype=np.complex128)
+        gd = f.to_global_data()
+        assert_allclose(f.norm(), np.linalg.norm(gd))
+        assert_allclose(f.norm(1), np.linalg.norm(gd, ord=1))
+        assert_allclose(f.norm(2), np.linalg.norm(gd, ord=2))
+        assert_allclose(f.norm(3), np.linalg.norm(gd, ord=3))
+        assert_allclose(f.norm(np.inf), np.linalg.norm(gd, ord=np.inf))
+
     def test_vdot(self):
         s = ift.RGSpace((10,))
         f1 = ift.Field.from_random("normal", domain=s, dtype=np.complex128)