Simplify init of base-class element.Element (#924)

* Simplify `Element`

and add `element.Element` to the top-level namespace

* Update _lagrange.py

* Don't use `Element.shape` in `"tetra10"` and `"triangle6"`

CHANGELOG.md

@@ -11,6 +11,7 @@ All notable changes to this project will be documented in this file. The format
 - Add `BoundaryDict` as a subclassed dict with methods to `plot()`, `screenshot()` and `imshow()`.
 - Add a new argument to apply a callable on the assembled vector/matrix of a solid body, `SolidBody(..., apply=None)`. This may be used to sum the list of sub-blocks instead of stacking them together, `SolidBody(..., block=False, apply=None)`. This is useful for mixed formulations where both the deformation gradient and the displacement values are required.
 - Add support for non-symmetric bilinear mixed forms in `IntegralForm`.
+- Add `element.Element` to the top-level package namespace.
 
 ### Changed
 - The first Piola-Kirchhoff stress tensor is evaluated if `ViewSolid(stress_type=None)`.
@@ -25,6 +26,9 @@ All notable changes to this project will be documented in this file. The format
 ### Fixed
 - Fix `Boundary(..., mode="and")` by ignoring any undefined axis.
 
+### Removed
+- Remove the unused `shape`-argument in `element.Element(shape)`. Adopt the arbitrary-lagrange element to use its own `dim`-argument. This simplifies the creation of custom finite element formulations.
+
 ## [9.1.0] - 2024-11-23
 
 ### Added

src/felupe/__init__.py

@@ -46,6 +46,7 @@
     BiQuadraticQuad,
     ConstantHexahedron,
     ConstantQuad,
+    Element,
     Hexahedron,
     Line,
     Quad,
@@ -173,6 +174,7 @@
     "BiQuadraticQuad",
     "ConstantHexahedron",
     "ConstantQuad",
+    "Element",
     "Hexahedron",
     "Line",
     "Quad",

src/felupe/element/_base.py

@@ -20,9 +20,6 @@
 
 
 class Element:
-    def __init__(self, shape):
-        self.shape = shape
-        self.dim = self.shape[1]
 
     def view(self, point_data=None, cell_data=None, cell_type=None):
         """View the element with optional given dicts of point- and cell-data items.
@@ -91,7 +88,7 @@ def plot(
         )
         if add_point_labels:
             plotter.add_point_labels(
-                points=np.pad(self.points, ((0, 0), (0, 3 - self.shape[1]))),
+                points=np.pad(self.points, ((0, 0), (0, 3 - self.points.shape[1]))),
                 labels=[f"{a}" for a in np.arange(len(self.points))],
                 font_size=font_size,
                 show_points=show_points,
@@ -108,19 +105,19 @@ def plot(
             actor.SetNormalizedShaftLength((0.9, 0.9, 0.9))
             actor.SetNormalizedTipLength((0.1, 0.1, 0.1))
 
-            if self.shape[1] == 3:
+            if self.points.shape[1] == 3:
                 actor.SetTotalLength([1.3, 1.3, 1.3])
-            elif self.shape[1] == 2:
+            elif self.points.shape[1] == 2:
                 actor.SetZAxisLabelText("")
                 actor.SetTotalLength([1.3, 1.3, 0])
-            elif self.shape[1] == 1:
+            elif self.points.shape[1] == 1:
                 actor.SetYAxisLabelText("")
                 actor.SetZAxisLabelText("")
                 actor.SetTotalLength([1.3, 0, 0])
 
             plotter.camera.zoom(0.7)
 
-        if self.shape[1] == 3:
+        if self.points.shape[1] == 3:
             plotter.camera.azimuth = -17
 
         return plotter

src/felupe/element/_hexahedron.py

@@ -69,7 +69,6 @@ def __init__(self):
         )
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "hexahedron"
-        super().__init__(shape=(1, 3))
 
     def function(self, rst):
         "Return the shape functions at given coordinates (r, s, t)."
@@ -140,7 +139,6 @@ def __init__(self):
         )
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "hexahedron"
-        super().__init__(shape=(8, 3))
 
     def function(self, rst):
         "Return the shape functions at given coordinates (r, s, t)."
@@ -263,7 +261,6 @@ def __init__(self):
         )
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "hexahedron20"
-        super().__init__(shape=(20, 3))
 
     def function(self, rst):
         "Return the shape functions at given coordinates (r, s, t)."
@@ -471,8 +468,6 @@ class TriQuadraticHexahedron(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(27, 3))
-
         self.points = np.array(
             [
                 [-1, -1, -1],

src/felupe/element/_lagrange.py

@@ -261,14 +261,14 @@ def __init__(self, order, dim, interval=(-1, 1), permute=True):
         self._nbasis = self._npoints
         self._interval = interval
 
+        self.dim = dim
+
         self.permute = None
         if permute:
             self.permute = [None, lagrange_line, lagrange_quad, lagrange_hexahedron][
                 dim
             ](order)
 
-        super().__init__(shape=(self._npoints, dim))
-
         # init curve-parameter matrix
         n = self._nshape
         self._AT = np.linalg.inv(
@@ -278,7 +278,7 @@ def __init__(self, order, dim, interval=(-1, 1), permute=True):
         # indices for outer product in einstein notation
         # idx = ["a", "b", "c", ...][:dim]
         # subscripts = "a,b,c -> abc"
-        self._idx = [letter for letter in alphabet][: self.dim]
+        self._idx = [letter for letter in alphabet][:dim]
         self._subscripts = ",".join(self._idx) + "->" + "".join(self._idx)
 
         # init points

src/felupe/element/_line.py

@@ -45,7 +45,6 @@ class Line(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(2, 1))
         self.points = np.array([-1, 1], dtype=float).reshape(-1, 1)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "line"

src/felupe/element/_quad.py

@@ -52,7 +52,6 @@ class ConstantQuad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(1, 2))
         self.points = np.array([[-1, -1], [1, -1], [1, 1], [-1, 1]], dtype=float)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "quad"
@@ -106,7 +105,6 @@ class Quad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(4, 2))
         self.points = np.array([[-1, -1], [1, -1], [1, 1], [-1, 1]], dtype=float)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "quad"
@@ -188,7 +186,6 @@ class QuadraticQuad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(8, 2))
         self.points = np.array(
             [
                 [-1, -1],
@@ -289,8 +286,6 @@ class BiQuadraticQuad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(9, 2))
-
         self._lagrange = ArbitraryOrderLagrange(order=2, dim=2, permute=False)
 
         self._vertices = np.array([0, 2, 8, 6])

src/felupe/element/_tetra.py

@@ -57,7 +57,6 @@ class Tetra(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(4, 3))
         self.points = np.array(
             [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float
         )
@@ -117,7 +116,6 @@ class TetraMINI(Element):
     """
 
     def __init__(self, bubble_multiplier=1.0):
-        super().__init__(shape=(5, 3))
         self.points = np.array(
             [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [1 / 3, 1 / 3, 1 / 3]],
             dtype=float,
@@ -237,8 +235,7 @@ class QuadraticTetra(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(10, 3))
-        self.points = np.zeros(self.shape)
+        self.points = np.zeros((10, 3))
         self.points[:4] = np.array(
             [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float
         )

src/felupe/element/_triangle.py

@@ -58,7 +58,6 @@ class Triangle(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(3, 2))
         self.points = np.array([[0, 0], [1, 0], [0, 1]], dtype=float)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "triangle"
@@ -115,7 +114,6 @@ class TriangleMINI(Element):
     """
 
     def __init__(self, bubble_multiplier=1.0):
-        super().__init__(shape=(4, 2))
         self.points = np.array([[0, 0], [1, 0], [0, 1], [1 / 3, 1 / 3]], dtype=float)
         self.cells = np.arange(len(self.points) - 1).reshape(1, -1)
         self.cell_type = "triangle"
@@ -198,8 +196,7 @@ class QuadraticTriangle(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(6, 2))
-        self.points = np.zeros(self.shape)
+        self.points = np.zeros((6, 2))
         self.points[:3] = np.array([[0, 0], [1, 0], [0, 1]], dtype=float)
         self.points[3] = np.mean(self.points[[0, 1]], axis=0)
         self.points[4] = np.mean(self.points[[1, 2]], axis=0)

tests/test_element.py

@@ -43,8 +43,6 @@ def test_line2():
     assert np.all(dhdr[0] == -0.5)
     assert np.all(d2hdrdr == 0.0)
 
-    assert line2.shape == dhdr.shape
-
     line2.plot(off_screen=True)
 
 
@@ -59,8 +57,6 @@ def test_line_lagrange():
     assert np.isclose(h[0], 1)
     assert np.isclose(dhdr[0, 0], -5.70833333)
 
-    assert line6.shape == dhdr.shape
-
     line6.plot(off_screen=True)
 
 
@@ -77,8 +73,6 @@ def test_quad0():
     assert np.all(dhdr[0] == 0)
     assert np.all(d2hdrdr == 0.0)
 
-    assert quad0.shape == dhdr.shape
-
 
 def test_quad4():
     quad4 = fem.element.Quad()
@@ -93,8 +87,6 @@ def test_quad4():
     assert np.all(dhdr[0] == -0.5)
     assert d2hdrdr.shape == (4, 2, 2)
 
-    assert quad4.shape == dhdr.shape
-
     quad4.plot(off_screen=True)
 
 
@@ -111,8 +103,6 @@ def test_quad8():
     assert np.all(dhdr[0] == -1.5)
     assert d2hdrdr.shape == (8, 2, 2)
 
-    assert quad8.shape == dhdr.shape
-
 
 def test_quad9():
     quad9 = fem.element.BiQuadraticQuad()
@@ -125,8 +115,6 @@ def test_quad9():
     assert h[0] == 1
     assert np.all(dhdr[0] == -1.5)
 
-    assert quad9.shape == dhdr.shape
-
 
 def test_hex0():
     hex0 = fem.element.ConstantHexahedron()
@@ -141,8 +129,6 @@ def test_hex0():
     assert np.all(dhdr[0] == 0)
     assert np.all(d2hdrdr == 0)
 
-    assert hex0.shape == dhdr.shape
-
 
 def test_hex8():
     hex8 = fem.element.Hexahedron()
@@ -157,8 +143,6 @@ def test_hex8():
     assert np.all(dhdr[0] == -0.5)
     assert d2hdrdr.shape == (8, 3, 3)
 
-    assert hex8.shape == dhdr.shape
-
 
 def test_hex20():
     hex20 = fem.element.QuadraticHexahedron()
@@ -171,8 +155,6 @@ def test_hex20():
     assert h[0] == 1
     assert np.all(dhdr[0] == -1.5)
 
-    assert hex20.shape == dhdr.shape
-
     hex20.plot(off_screen=True)
 
 
@@ -187,8 +169,6 @@ def test_hex27():
     assert h[0] == 1
     assert np.all(dhdr[0] == -1.5)
 
-    assert hex27.shape == dhdr.shape
-
     hex27.plot(off_screen=True)
 
 
@@ -205,9 +185,6 @@ def test_tri3():
     assert np.all(dhdr[0] == -1)
     assert np.all(d2hdrdr == 0)
 
-    assert tri3.shape == dhdr.shape
-
-
 def test_tri6():
     tri6 = fem.element.QuadraticTriangle()
 
@@ -219,8 +196,6 @@ def test_tri6():
     assert h[0] == 1
     assert np.all(dhdr[0] == -3)
 
-    assert tri6.shape == dhdr.shape
-
 
 def test_tri_mini():
     trim = fem.element.TriangleMINI()
@@ -236,8 +211,6 @@ def test_tri_mini():
     assert np.all(dhdr[0] == -1)
     assert d2hdrdr.shape == (4, 2, 2)
 
-    assert trim.shape == dhdr.shape
-
 
 def test_tet4():
     tet4 = fem.element.Tetra()
@@ -252,8 +225,6 @@ def test_tet4():
     assert np.all(dhdr[0] == -1)
     assert np.all(d2hdrdr == 0)
 
-    assert tet4.shape == dhdr.shape
-
 
 def test_tet10():
     tet10 = fem.element.QuadraticTetra()
@@ -266,8 +237,6 @@ def test_tet10():
     assert h[0] == 1
     assert np.all(dhdr[0] == -3)
 
-    assert tet10.shape == dhdr.shape
-
 
 def test_tet_mini():
     tetm = fem.element.TetraMINI()
@@ -283,8 +252,6 @@ def test_tet_mini():
     assert np.all(dhdr[0] == -1)
     assert d2hdrdr.shape == (5, 3, 3)
 
-    assert tetm.shape == dhdr.shape
-
 
 def test_aol():
     aol32 = fem.element.ArbitraryOrderLagrange(order=3, dim=2)
@@ -296,15 +263,13 @@ def test_aol():
     dhdr = aol32.gradient(r)
 
     assert h[0] == 1
-    assert aol32.shape == dhdr.shape
 
     r = [-1, -1, -1]
 
     h = aol23.function(r)
     dhdr = aol23.gradient(r)
 
     assert h[0] == 1
-    assert aol23.shape == dhdr.shape
 
 
 if __name__ == "__main__":