move python scripts

maxwell/misc/eigenvalues.py

@@ -0,0 +1,40 @@
+#! /usr/bin/env python3
+import numpy as np
+
+A = np.array([[0, 0, 0], [0, 0, -1], [0, -1, 0]])
+B = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])
+
+
+def similarity_transform(matrix):
+    L, S = np.linalg.eig(matrix)
+    L = np.diag(L)
+    S = S.transpose()
+    assert np.allclose(np.matmul(S.transpose(), np.matmul(L, S)), matrix)
+    return L, S
+
+
+def plusminus(matrix):
+    L, S = similarity_transform(matrix)
+
+    def signed(op):
+        return 0.5 * np.matmul(S.transpose(), np.matmul(op(L, np.abs(L)), S))
+
+    plus = signed(np.add)
+    minus = signed(np.subtract)
+
+    assert np.allclose(matrix, plus + minus)
+    return plus, minus
+
+
+Aplus, Aminus = plusminus(A)
+Bplus, Bminus = plusminus(B)
+
+print("A+")
+print(Aplus)
+print("A-")
+print(Aminus)
+print()
+print("B+")
+print(Bplus)
+print("B-")
+print(Bminus)