generating tridiagonal matrix

mogu/spectral/lanzcos.py

@@ -1,3 +1,29 @@
 
 # implementing Lanzco's algorithm
 
+import numpy as np
+
+
+def lanzcos(M, k):
+    assert M.shape[0] == M.shape[1]
+    assert (M == M.T).all()
+    d = M.shape[1]
+    assert k <= d
+
+    a = np.zeros(k+1)
+    b = np.zeros(k)
+
+    v0 = np.random.uniform(size=d)
+    v0 /= np.linalg.norm(v0)
+
+    a[0] = v0.T @ M @ v0
+    v1 = M @ v0 - a[0]*v0
+    v1 /= np.linalg.norm(v1)
+
+    for i in range(1, k+1):
+        a[i] = v1.T @ M @ v1
+        b[i-1] = v0.T @ M @ v1
+        v2 = M @ v1 - a[i]*v1 - b[i-1]*v0
+        v2 /= np.linalg.norm(v2)
+
+        v0, v1 = v1, v2

requirements.txt

@@ -1,6 +1,6 @@
 Cython>=0.29.0
-numpy>=1.18.0
-scipy>=1.6.0
+numpy>=1.22.0
+scipy>=1.9.0
 numba>=0.53.0
 networkx>=2.0
 graphflow>=0.1.1

test/test_lanzcos.py

@@ -0,0 +1,11 @@
+
+import unittest
+
+
+class test_lanzcos(unittest.TestCase):
+    def test_dft(self):
+        pass
+
+
+if __name__ == '__main__':
+    unittest.main()