Merge pull request #66 from Cornell-QCA/model

added functions for F inverse and FinvRF

python/anyon_braiding_simulator/Model.py

@@ -121,3 +121,63 @@ def getFMatrix(self, a: str, b: str, c: str, d: str) -> np.ndarray:
                 raise ValueError('invalid anyon name')
 
         return self._f_mtx[anyondict[a]][anyondict[b]][anyondict[c]][anyondict[d]]
+
+    def getFInv(self, a: str, b: str, c: str, d: str) -> np.ndarray:
+        """
+        Parameters
+        ----------
+        a : str
+            name of anyon corresponding to first lower index
+        b : str
+            name of anyon corresponding to second lower index
+        c : str
+            name of anyon corresponding to third lower index
+        d : str
+            name of anyon corresponding to upper index
+
+        Only the following strings are accepted as parameters:
+        vacuum, sigma, psi
+
+        Requires that all anyons used as parameters are contained with the
+        given model
+
+        For details on notation, c.f.r. On classification of modular tensor
+        categories by Rowell, Stong, and Wang
+        https://www.arxiv.org/abs/0712.1377
+
+        Returns
+        -------
+        the Inverse F-matrix corresponding to the set of indices in the model
+        """
+
+        return np.linalg.inv(self.getFMatrix(a,b,c,d))
+
+    def getFInvRF(self, a: str, b: str, c: str, d: str) -> np.ndarray:
+        """
+        Parameters
+        ----------
+        a : str
+            name of anyon corresponding to first lower index
+        b : str
+            name of anyon corresponding to second lower index
+        c : str
+            name of anyon corresponding to third lower index
+        d : str
+            name of anyon corresponding to upper index
+
+        Only the following strings are accepted as parameters:
+        vacuum, sigma, psi
+
+        Requires that all anyons used as parameters are contained with the
+        given model
+
+        For details on notation, c.f.r. On classification of modular tensor
+        categories by Rowell, Stong, and Wang
+        https://www.arxiv.org/abs/0712.1377
+
+        Returns
+        -------
+        the matrix product of (F^-1)RF corresponding to the set of indices in the model
+        """
+
+        return self.getFInv(a,b,c,d) @ self._r_mtx @ self.getFMatrix(a,b,c,d)

python/tests/test_model.py

@@ -38,3 +38,35 @@ def test_f_matrix(initialize_ising):
     assert np.equal(ising.getFMatrix('psi', 'psi', 'psi', 'vacuum'), np.identity(2)).all()
     assert np.equal(ising.getFMatrix('psi', 'vacuum', 'psi', 'psi'), np.identity(2)).all()
     assert np.equal(ising.getFMatrix('psi', 'psi', 'psi', 'psi'), np.identity(2)).all()
+
+@pytest.mark.model
+def test_f_inverse(initialize_ising):
+    ising = initialize_ising
+
+    # check F with all sigma subscripts cancels with inverse
+    assert np.isclose(ising.getFMatrix('sigma', 'sigma', 'sigma', 'sigma') @ ising.getFInv('sigma', 'sigma', 'sigma', 'sigma'), np.identity(2)).all()
+    assert np.isclose(ising.getFInv('sigma', 'sigma', 'sigma', 'sigma') @ ising.getFMatrix('sigma', 'sigma', 'sigma', 'sigma'), np.identity(2)).all()
+
+    # check other non identity matrices
+    assert np.isclose(ising.getFMatrix('psi', 'sigma', 'sigma', 'vacuum') @ ising.getFInv('psi', 'sigma', 'sigma', 'vacuum'), np.identity(2)).all()
+    assert np.isclose(ising.getFInv('psi', 'sigma', 'sigma', 'vacuum') @ ising.getFMatrix('psi', 'sigma', 'sigma', 'vacuum'), np.identity(2)).all()
+
+    assert np.isclose(ising.getFMatrix('sigma', 'sigma', 'psi', 'psi') @ ising.getFInv('sigma', 'sigma', 'psi', 'psi'), np.identity(2)).all()
+    assert np.isclose(ising.getFInv('sigma', 'sigma', 'psi', 'psi') @ ising.getFMatrix('sigma', 'sigma', 'psi', 'psi'), np.identity(2)).all()
+
+    # check identity matrices
+    assert np.isclose(ising.getFMatrix('psi', 'psi', 'psi', 'vacuum') @ ising.getFInv('psi', 'psi', 'psi', 'vacuum'), np.identity(2)).all()
+    assert np.isclose(ising.getFInv('psi', 'psi', 'psi', 'vacuum') @ ising.getFMatrix('psi', 'psi', 'psi', 'vacuum'), np.identity(2)).all()
+
+@pytest.mark.model
+def test_FinvRF(initialize_ising):
+    ising = initialize_ising
+
+    # check F with all sigma subscripts
+    assert np.isclose(ising.getFInvRF('sigma', 'sigma', 'sigma', 'sigma'), np.linalg.inv(ising.getFMatrix('sigma', 'sigma', 'sigma', 'sigma')) @ ising._r_mtx @ ising.getFMatrix('sigma', 'sigma', 'sigma', 'sigma')).all()
+
+    # check other non identity matrices
+    assert np.isclose(ising.getFInvRF('psi', 'sigma', 'sigma', 'vacuum'), np.linalg.inv(ising.getFMatrix('psi', 'sigma', 'sigma', 'vacuum')) @ ising._r_mtx @ ising.getFMatrix('psi', 'sigma', 'sigma', 'vacuum')).all()
+
+    # check identity matrices
+    assert np.isclose(ising.getFInvRF('psi', 'psi', 'psi', 'vacuum'), np.linalg.inv(ising.getFMatrix('psi', 'psi', 'psi', 'vacuum')) @ ising._r_mtx @ ising.getFMatrix('psi', 'psi', 'psi', 'vacuum')).all()