Merge pull request #212 from eric-wieser/linear-transformation

Add transformation tools

clifford/test/test_transformations.py

@@ -0,0 +1,131 @@
+import numpy as np
+import pytest
+
+from clifford import Layout, ConformalLayout, BasisVectorIds
+from clifford import transformations
+
+
+# fixtures make the test a little faster
+
+@pytest.fixture(scope='module')
+def g2():
+    return Layout([1, 1], ids=BasisVectorIds(['u', 'v']))
+
+
+@pytest.fixture(scope='module')
+def g2c(g2):
+    return ConformalLayout([1, 1, 1, -1], ids=BasisVectorIds(['u', 'v', 'p', 'm']), layout=g2)
+
+
+@pytest.fixture(scope='module')
+def g3():
+    return Layout([1, 1, 1], ids=BasisVectorIds(['x', 'y', 'z']))
+
+
+class TestBetweenBasisVectors:
+    def test_same_layout(self, g3):
+        ex, ey, ez = g3.basis_vectors_lst
+        x = ex + 2*ey + 4*ex*ez
+
+        f = transformations.between_basis_vectors(g3, g3)
+        assert f(x) == x
+
+        f_swap = transformations.between_basis_vectors(g3, g3, {'x': 'y', 'y': 'z', 'z': 'x'})
+        assert f_swap(x) == ey + 2*ez + 4*ey*ex
+
+    def test_different_layout(self, g2, g2c, g3):
+        e1, e2 = g2.basis_vectors_lst
+        e1c, e2c, epc, emc = g2c.basis_vectors_lst
+
+        f = transformations.between_basis_vectors(g2, g2c)
+        x = 1 + 2*e1 + 3*e2 + 4*e1*e2
+        xc = 1 + 2*e1c + 3*e2c + 4*e1c*e2c
+        assert f(x) == xc
+        assert f.adjoint(xc) == x
+
+        ex, ey, ez = g3.basis_vectors_lst
+        f = transformations.between_basis_vectors(g2, g3, {'u': 'z', 'v': 'y'})
+        xs = 1 + 2*ez + 3*ey + 4*ez*ey
+        assert f(x) == xs
+        assert f.adjoint(xs) == x
+
+        # incorrect layout
+        with pytest.raises(ValueError):
+            f(xs)
+
+        # invalid basis
+        with pytest.raises(ValueError):
+            transformations.between_basis_vectors(g2, g3, {'fake': 'z', 'v': 'y'})
+        with pytest.raises(ValueError):
+            transformations.between_basis_vectors(g2, g3, {'u': 'z', 'v': 'fake'})
+
+
+class TestOutermorphismMatrix:
+    def test_invariants(self, g2):
+        e1, e2 = g2.basis_vectors_lst
+
+        matrix = np.array([[ 0, 1],
+                           [-1, 0]])
+        f = transformations.OutermorphismMatrix(matrix, g2)
+
+        # test the vector transform is as requested
+        assert f(e1) == -e2
+        assert f(e2) == e1
+        # test the generalization is correct
+        assert f(e1^e2) == f(e1)^f(e2)
+        assert f(g2.scalar) == g2.scalar
+
+        # test that distributivity is respected
+        assert f(g2.scalar + 2*e1 + 3*(e1^e2)) == f(g2.scalar) + 2*f(e1) + 3*f(e1^e2)
+
+    def test_between_layouts(self, g2, g3):
+        matrix = np.array([[1, 0],
+                           [0, 1],
+                           [0, 0]])
+        # arguments backwards
+        with pytest.raises(ValueError):
+            transformations.OutermorphismMatrix(matrix, g3, g2)
+
+        e1, e2 = g2.basis_vectors_lst
+        ex, ey, ez = g3.basis_vectors_lst
+
+        f = transformations.OutermorphismMatrix(matrix, g2, g3)
+        assert f(e1) == ex
+        assert f(e2) == ey
+
+
+class TestLinearMatrix:
+    def test_same_layout(self, g2):
+        e1, e2 = g2.basis_vectors_lst
+
+        dual_matrix = np.array([
+            [ 0,  0, 0, 1],
+            [ 0,  0, 1, 0],
+            [ 0, -1, 0, 0],
+            [-1,  0, 0, 0]
+        ])
+        f_dual = transformations.LinearMatrix(dual_matrix, g2)
+        x = 1 + 2*e2 + 3*e1*e2
+        assert f_dual(x) == x.dual()
+
+    def test_between_layouts(self, g2, g3):
+        matrix = np.array([[1, 0, 0, 0],
+                           [0, 1, 0, 0],
+                           [0, 0, 1, 0],
+                           [0, 0, 0, 0],
+                           [0, 0, 0, 0],
+                           [0, 0, 0, 0],
+                           [0, 0, 0, 0],
+                           [0, 0, 0, 1]])
+
+        # arguments backwards
+        with pytest.raises(ValueError):
+            transformations.LinearMatrix(matrix, g3, g2)
+
+        e1, e2 = g2.basis_vectors_lst
+        ex, ey, ez = g3.basis_vectors_lst
+
+        f = transformations.LinearMatrix(matrix, g2, g3)
+        assert f(e1) == ex
+        assert f(e2) == ey
+        assert f(e1^e2) == ex^ey^ez