now arnoldi works, index problems. It still does not return the correct output required bythe paper

data/results/algo1/different_tau.csv

@@ -1,6 +1,6 @@
 alpha,products m-v,tau,time
-"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",19,1e-05,13.51
+"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",19,1e-05,14.4
-"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",56,1e-06,34.74
+"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",56,1e-06,33.8
-"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",113,1e-07,90.85
+"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",113,1e-07,84.19
-"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",275,1e-08,157.45
+"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",275,1e-08,136.66
-"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",454,1e-09,221.05
+"[0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99]",454,1e-09,193.94

src/algo2_testing.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -29,41 +29,37 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 86,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def Arnoldi(A, v, m): #  defined ad algorithm 2 in the paper\n",
+    "def Arnoldi(A, v, m): \n",
     "    beta = norm(v)\n",
-    "    print(\"A\")\n",
+    "    v = v/beta \n",
-    "    v = v/beta\n",
+    "    h = sp.sparse.lil_matrix((m,m)) \n",
-    "    print(\"B\")\n",
-    "    h = sp.sparse.lil_matrix((m,m))\n",
-    "    print(\"C\")\n",
     "\n",
     "    for j in range(m):\n",
-    "        w = A.dot(v)\n",
+    "        w = A @ v  \n",
-    "        print(\"D\")\n",
     "        for i in range(j):\n",
-    "            h[i,j] = v.T.dot(w)\n",
+    "            tmp = v.T @ w  \n",
-    "            print(\"E\")\n",
+    "            h[i,j] = tmp[0,0]\n",
-    "            w = w - h[i,j]*v[i]\n",
+    "            w = w - h[i,j]*v \n",
-    "            print(\"F\")\n",
+    "        h[j,j-1] = norm(w) \n",
     "\n",
-    "        h[j+1,j] = norm(w)\n",
+    "        if h[j,j-1] == 0: \n",
-    "        print(\"G\")\n",
+    "            print(\"Arnoldi breakdown\")\n",
-    "\n",
-    "        if h[j+1,j] == 0:\n",
-    "            print(\"The algorithm didn't converge\")\n",
     "            m = j\n",
-    "            v[m+1] = 0\n",
+    "            v = 0\n",
     "            break\n",
     "        else:\n",
-    "            print(\"H\")\n",
+    "            v = w/h[j,j-1] \n",
-    "            v[j+1] = w**h[j+1,j] # THIS IS WRONG, I DON'T KNOW HOW TO FIX IT. ERROR \" matrix is not square\"\n",
+    "        \n",
-    "            print(\"I\")\n",
+    "    print(\"Arnoldi finished\\n\")\n",
-    "\n",
+    "    print(\"h is \", h.shape)\n",
-    "    return v, h, m, beta, j"
+    "    print(\"v is \", v.shape)\n",
+    "    print(\"m is \", m)\n",
+    "    print(\"beta is \", beta)\n",
+    "    return v, h, m, beta, j # this is not the output required in the paper, I should return the matrix V and the matrix H\n"
    ]
   },
   {
@@ -75,20 +71,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 82,
    "metadata": {},
    "outputs": [],
    "source": [
-    "A = sp.sparse.rand(100,100, density=0.5, format='lil')\n",
+    "m = 100\n",
-    "v = sp.sparse.rand(100,1, density=0.5, format='lil')\n",
+    "A = sp.sparse.rand(m,m, density=0.5, format='lil')\n",
-    "m = 100"
+    "v = sp.sparse.rand(m,1, density=0.5, format='lil')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 87,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Arnoldi finished\n",
+      "\n",
+      "h is  (100, 100)\n",
+      "v is  (100, 1)\n",
+      "m is  100\n",
+      "beta is  1.0\n"
+     ]
+    }
+   ],
    "source": [
     "v, h, m, beta, j = Arnoldi(A, v, m)"
    ]

src/main.py

@@ -113,7 +113,7 @@ class Utilities:
 
     def transition_matrix(P, v, d):
         print("Creating the transition matrix...")
-        Pt = P + v.dot(d.T)
+        Pt = P + v @ (d.T)
         print("Transition matrix created\n")
         return Pt
 
@@ -154,7 +154,7 @@ class Algorithms:
         start_time = time.time()
 
         print("STARTING ALGORITHM 1...")
-        u = Pt.dot(v) - v
+        u = Pt @ v - v
         mv = 1 # number of matrix-vector multiplications
         r = sp.sparse.lil_matrix((n,1))
         Res = sp.sparse.lil_matrix((len(a),1))
@@ -169,7 +169,7 @@ class Algorithms:
                 x = r + v
 
         while max(Res) > tau and mv < max_mv:
-            u = Pt*u
+            u = Pt @ u
             mv += 1
 
             for i in range(len(a)):
@@ -193,26 +193,28 @@ class Algorithms:
         return mv, x, r, total_time
 
     # Refers to Algorithm 2 in the paper, it's needed to implement the algorithm 4. It doesn't work yet. Refer to the file testing.ipynb for more details. This function down here is just a place holder for now
-    def Arnoldi(A, v, m):
+def Arnoldi(A, v, m):
     beta = norm(v)
     v = v/beta
     h = sp.sparse.lil_matrix((m,m))
 
-        for j in range(1,m):
+    for j in range(m):
-            w = A.dot(v)
+        w = A @ v
-            for i in range(1,j):
+        for i in range(j):
-                h[i,j] = v.T.dot(w)
+            tmp = v.T @ w
+            h[i,j] = tmp[0,0]
             w = w - h[i,j]*v
+        h[j,j-1] = norm(w)
 
-            h[j+i,j] = norm(w)
+        if h[j,j-1] == 0:
-
+            print("Arnoldi breakdown")
-            if h[j+1,j] == 0:
             m = j
-                v[m+1] = 0
+            v = 0
             break
         else:
-                v[j+1] = w/h[j+1,j]
+            v = w/h[j,j-1]
-        return v, h, m, beta, j
+    return v, h, m, beta, j # this is not the output required in the paper, I should return the matrix V and the matrix H
+
 
 # pandas dataframe to store the results
 df = pd.DataFrame(columns=['alpha', 'products m-v', 'tau', 'time'])