README.md

@@ -4,7 +4,7 @@ Project description
 
 ---
 
-## Quick Start
+## 🚀 Quick Start
 
 ### Setup
 
@@ -19,13 +19,3 @@ Project description
 - **Test**: `uv run pytest`
 - **Format**: `uv run ruff format .`
 - **Lint**: `uv run ruff check . --fix`
-
-## References
-
-[1] Susnjara et al., Accelerated filtering on graphs using Lanczos method.
-
-[2] https://epfl-lts2.github.io/gspbox-html/
-
-## Online guides
-
-https://every-algorithm.github.io/2024/05/23/lanczos_algorithm.html

src/afgl/lanczos.py

@@ -1,12 +1,6 @@
 import numpy as np
-import numpy.linalg as LA
 
 """
-Arguments
-L Real valued NxN symmetric matrix
-s vector of size N
-M natural number indicating basis size
-
 Returns
 -------
 V : ndarray
@@ -19,22 +13,16 @@ beta : ndarray
 
 
 def lanczos(L, s, M):
-    N = len(s)
     alp = np.zeros(M)
-    beta = np.zeros(M - 1)
-    V = np.zeros((N, M))
-    V[:, 0] = s / LA.norm(s)
-
-    for j in range(M):
-        w = L @ V[:, j]
-        alp[j] = np.dot(V[:, j], w)
-
-        v_tilde = w - V[:, j] * alp[j]
-        if j > 0:
-            v_tilde = v_tilde - V[:, j - 1] * beta[j - 1]
-
-        if j < M - 1:
-            beta[j] = LA.norm(v_tilde)
-            V[:, j + 1] = v_tilde / beta[j]
-
-    return [V, alp, beta]
+    beta = np.zeros(M)
+    V = np.zeros(M)
+    V[0] = s / np.norm(s)
+
+    for j in range(0, M):
+        w = L * V
+        alp[j] = V[j] @ w
+        Vtmp = w - V[j] * alp[j]
+        if j > 1:
+            Vtmp = Vtmp - V[j - 1] * beta[j - 1]
+        beta[j] = np.norm(Vtmp)
+        V[j + 1] = Vtmp / beta[j]

tests/test_main.py

@@ -1,29 +0,0 @@
-import numpy as np
-import numpy.linalg as LA
-from afgl.lanczos import lanczos
-
-"""
-Todo: better test case
-"""
-
-
-def test_lanczos_return_correct_solution():
-    N = 1000
-    M = 999
-
-    eigvals = np.random.uniform(10000, 100000, N)
-    Q, _ = LA.qr(np.random.randn(N, N))
-    L = Q @ np.diag(eigvals) @ Q.T
-
-    s = np.random.randint(1, 10, N)
-    [V, alp, beta] = lanczos(L, s, M)
-
-    T = np.diag(alp) + np.diag(beta, -1) + np.diag(beta, 1)
-
-    x = LA.solve(L, s)
-    e_1 = np.zeros(M)
-    e_1[0] = 1
-    y = (LA.inv(T) @ e_1) * LA.norm(s)
-    x_lanczos = V @ y
-
-    assert LA.norm(x - x_lanczos) < 1e-10