Adding the ND basis

high_order_layers_torch/Basis.py

@@ -397,6 +397,7 @@ def interpolate(self, x: Tensor, w: Tensor) -> Tensor:
         """
 
         basis = []
+        # TODO: get rid of this loop!
         for j in range(self.n):
             basis_j = self.basis(x, j)
             basis.append(basis_j)
@@ -406,6 +407,37 @@ def interpolate(self, x: Tensor, w: Tensor) -> Tensor:
         return out_sum
 
 
+class BasisFlatND:
+    """
+    Single N dimensional element.
+    """
+
+    def __init__(
+        self, n: int, basis: Callable[[Tensor, list[int]], float], dimensions: int
+    ):
+        self.n = n
+        self.basis = basis
+        self.dimensions = dimensions
+        a = torch.arange(n)
+        self.indexes = torch.stack(torch.meshgrid([a]*dimensions)).reshape(dimensions, -1).T
+
+    def interpolate(self, x: Tensor, w: Tensor) -> Tensor:
+        """
+        :param x: size[batch, input, dimension]
+        :param w: size[input, output, basis]
+        :returns: size[batch, output]
+        """
+
+        basis = []
+        for index in range(self.indexes):
+            basis_j = self.basis(x, index=index)
+            basis.append(basis_j)
+        basis = torch.stack(basis)
+        out_sum = torch.einsum("ijk,lki->jl", basis, w)
+
+        return out_sum
+
+
 class BasisFlatProd:
     """
     Single segment.

tests/test_layers.py

@@ -1,7 +1,7 @@
 import os
 
 import pytest
-
+import math
 from high_order_layers_torch.FunctionalConvolution import *
 from high_order_layers_torch.LagrangePolynomial import *
 from high_order_layers_torch.LagrangePolynomial import LagrangePoly, LagrangeBasisND
@@ -20,6 +20,7 @@
 from high_order_layers_torch.networks import *
 from high_order_layers_torch.PolynomialLayers import *
 import torch
+from high_order_layers_torch.Basis import BasisFlatND
 
 torch.set_default_device(device="cpu")
 
@@ -38,6 +39,15 @@ def test_variable_dimension_input(n, in_features, out_features, segments):
     layer(a)
 """
 
+def test_basis_nd() :
+    dimensions = 3
+    n=5
+    lb = LagrangeBasisND(n=n, dimensions=dimensions)
+    basis = BasisFlatND(n=n, dimensions=dimensions, basis=lb)
+
+    # The indexes should be unique so we cover all indices
+    assert len(set(basis.indexes)) == math.pow(5, dimensions)
+
 
 @pytest.mark.parametrize("dimensions", [1, 2, 3, 4])
 def test_lagrange_basis(dimensions):