notes: 2025-06-22 21:49:40 from w11

1 files changed, 28 insertions, 26 deletions

diff --git a/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb b/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb
index c62c0b1..c9682db 100644
--- a/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb
+++ b/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb
@@ -9,7 +9,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -73,7 +73,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -83,7 +83,7 @@
        "       [1, 1]])"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -147,28 +147,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [],
    "source": [
     "def fibo(n):\n",
     "    F = np.array([[0,1],[1,1]], dtype=int)\n",
     "    D, P = lin.eig(F)\n",
-    "    return (P @ lin.matrix_power(np.diag(D),n) @ lin.inv(P))[0]"
+    "    return (P @ lin.matrix_power(np.diag(D),n) @ lin.inv(P))[1,0]"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([5., 8.])"
+       "np.float64(8.0)"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -187,15 +187,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "84.8 μs ± 7.75 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n",
-      "109 μs ± 6.71 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
+      "128 μs ± 71 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n",
+      "102 μs ± 6.96 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
      ]
     }
    ],
@@ -224,7 +224,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -237,10 +237,10 @@
        "       [1, 1, 1, 0, 0, 0, 0, 0],\n",
        "       [0, 0, 1, 1, 1, 0, 1, 0],\n",
        "       [1, 1, 0, 1, 0, 1, 0, 1],\n",
-       "       [1, 0, 0, 0, 0, 0, 0, 0]])"
+       "       [1, 0, 0, 0, 0, 0, 0, 0]], dtype=int32)"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -281,21 +281,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[0.774 0.387 1.419 1.419 1.032 1.29  1.548 0.129]]\n",
-      "[[0.542 0.5   1.25  1.583 0.833 1.75  1.292 0.25 ]]\n",
-      "[[0.742 0.426 1.127 1.608 0.756 1.636 1.526 0.179]]\n",
-      "[[0.672 0.497 1.183 1.527 0.748 1.635 1.496 0.242]]\n",
-      "[[0.694 0.487 1.19  1.542 0.766 1.613 1.489 0.219]]\n",
-      "[[0.683 0.484 1.189 1.545 0.771 1.622 1.481 0.226]]\n",
-      "[[0.686 0.482 1.187 1.546 0.767 1.624 1.485 0.222]]\n",
-      "[[0.686 0.484 1.186 1.546 0.767 1.624 1.485 0.223]]\n",
+      "[[0.615 0.308 1.538 1.538 0.923 1.231 1.538 0.308]]\n",
+      "[[0.513 0.513 1.231 1.538 0.821 1.846 1.333 0.205]]\n",
+      "[[0.776 0.439 1.114 1.62  0.743 1.62  1.519 0.169]]\n",
+      "[[0.668 0.493 1.184 1.523 0.756 1.622 1.501 0.252]]\n",
+      "[[0.689 0.489 1.196 1.539 0.764 1.618 1.486 0.218]]\n",
+      "[[0.685 0.483 1.186 1.547 0.772 1.621 1.481 0.224]]\n",
+      "[[0.685 0.482 1.187 1.546 0.767 1.624 1.485 0.223]]\n",
+      "[[0.686 0.484 1.186 1.545 0.767 1.624 1.485 0.223]]\n",
       "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n",
       "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n",
       "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n",
@@ -311,8 +311,8 @@
     "\n",
     "while (np.absolute(np.max(vprime - v)) > 1e-5): # which norm is used here?\n",
     "    v = vprime\n",
-    "    vprime = \n",
-    "    vprime *= \n",
+    "    vprime = A @ v\n",
+    "    vprime *= N / vprime.sum()\n",
     "    print(vprime.T)\n"
    ]
   },
@@ -333,7 +333,9 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "val"
+   ]
   },
   {
    "cell_type": "code",