unit tests for Lanzco's method

mogu/spectral/__init__.py

@@ -1,3 +1,4 @@
 
 from .dft import slowDFT, slowInvDFT
 from .fft import FFT, invFFT
+from .lanzcos import lanzcos

test/test_lanzcos.py

@@ -1,10 +1,39 @@
 
 import unittest
 
+import numpy as np
+
+from mogu.spectral import lanzcos
+
 
 class test_lanzcos(unittest.TestCase):
-    def test_dft(self):
-        pass
+    def test_four(self):
+        tol = 1e-8
+        A = np.array(
+            [
+                [1., 1., 2., -1.],
+                [1., 2., -3., 0.],
+                [2., -3., -1., 0.],
+                [-1., 0., 0., 0.5]
+            ]
+        )
+        eigval1, eigvec1 = np.linalg.eig(A)
+        eigval2, eigvec2 = lanzcos(A, A.shape[0])
+
+        assert len(eigval2) == A.shape[0] + 1
+
+        eig1dict = {}
+        for i in range(A.shape[0]):
+            for j in range(len(eigval2)):
+                if abs(eigval1[i] - eigval2[j]) < tol:
+                    eig1dict[i] = j
+                    break
+        assert len(set(eig1dict.values())) == len(eigval1)
+
+        for i in range(A.shape[0]):
+            j = eig1dict[i]
+            assert np.abs(np.linalg.norm(eigvec2[:, j]) - 1.) < tol
+            assert np.all(np.abs(A @ eigvec2[:, j] / eigval2[j] - eigvec2[:, j]) < tol)
 
 
 if __name__ == '__main__':