From 84c966d1ab14af414491db1f74b395979030b751 Mon Sep 17 00:00:00 2001
From: raj_mathe <raj.dahya@math.uni-leipzig.de>
Date: Sat, 8 Oct 2022 10:25:42 +0200
Subject: [PATCH] main > main: nb - added seed for repeatability, corrected
 spectral bound

---
 docs/examples_dilations.ipynb | 56 +++++++++++++++++------------------
 1 file changed, 28 insertions(+), 28 deletions(-)

diff --git a/docs/examples_dilations.ipynb b/docs/examples_dilations.ipynb
index 1a0df70..984fa8e 100644
--- a/docs/examples_dilations.ipynb
+++ b/docs/examples_dilations.ipynb
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -37,12 +37,13 @@
     "os.chdir(os.path.dirname(_dh[0]));\n",
     "sys.path.insert(0, os.getcwd());\n",
     "\n",
-    "from src.examples_dilations import *;"
+    "from src.examples_dilations import *;\n",
+    "np.random.seed(7098123); # for repeatability"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -63,7 +64,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -75,10 +76,10 @@
       "\n",
       " i    spec bound of A_i    A_i dissipative (<==> T_i contractive)?\n",
       "---  -------------------  -----------------------------------------\n",
-      " 1        -0.465478                         True\n",
-      " 2        -0.465478                         True\n",
-      " 3        -0.465478                         True\n",
-      " 4        -0.465478                         True\n"
+      " 1        -1.000000                         True\n",
+      " 2        -1.000000                         True\n",
+      " 3        -1.000000                         True\n",
+      " 4        -1.000000                         True\n"
      ]
     }
    ],
@@ -98,7 +99,7 @@
     "for i, A_i in enumerate(A):\n",
     "    omega_Re = spec_bounds((1/2)*(A_i + A_i.T.conj()));\n",
     "    omega = spec_bounds(A_i);\n",
-    "    data.append((i+1, omega_Re, True if (omega_Re <= 0) else False));\n",
+    "    data.append((i+1, omega, True if (omega_Re <= 0) else False));\n",
     "\n",
     "repr = tabulate(\n",
     "    tabular_data = data,\n",
@@ -113,7 +114,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -130,17 +131,17 @@
       "    [2]           0.465478           True\n",
       "    [1]           0.465478           True\n",
       "    [0]           0.465478           True\n",
-      "   [2, 3]         0.212675           True\n",
-      "   [1, 3]         0.183738           True\n",
-      "   [1, 2]         0.217453           True\n",
-      "   [0, 3]         0.200206           True\n",
-      "   [0, 2]         0.301332           True\n",
-      "   [0, 1]         0.215681           True\n",
-      " [1, 2, 3]        0.058427           True\n",
-      " [0, 2, 3]        0.075037           True\n",
-      " [0, 1, 3]        0.056030           True\n",
-      " [0, 1, 2]        0.077350           True\n",
-      "[0, 1, 2, 3]     -0.082403           False\n"
+      "   [2, 3]         0.207789           True\n",
+      "   [1, 3]         0.179513           True\n",
+      "   [1, 2]         0.179239           True\n",
+      "   [0, 3]         0.315586           True\n",
+      "   [0, 2]         0.205222           True\n",
+      "   [0, 1]         0.327619           True\n",
+      " [1, 2, 3]        0.049226           True\n",
+      " [0, 2, 3]        0.088339           True\n",
+      " [0, 1, 3]        0.098730           True\n",
+      " [0, 1, 2]        0.081731           True\n",
+      "[0, 1, 2, 3]     -0.133914           False\n"
      ]
     }
    ],
@@ -148,12 +149,11 @@
     "# compute the dissipation operators `S_TK` for each `K ⊆ {1,2,...,d}``:\n",
     "S, beta_T = dissipation_operators(shape=[N, N], A=A);\n",
     "\n",
-    "data = [];\n",
-    "for K, S_TK, b in sorted(S, key=lambda x: len(x[0])):\n",
-    "    data.append((K, b, True if b >= -MACHINE_EPS else False))\n",
-    "\n",
     "repr = tabulate(\n",
-    "    tabular_data = data,\n",
+    "    tabular_data = [\n",
+    "        (K, b, True if b >= -MACHINE_EPS else False)\n",
+    "        for K, S_TK, b in sorted(S, key=lambda x: len(x[0]))\n",
+    "    ],\n",
     "    headers      = ['K', 'min σ(S_{T,K})', 'S_{T,K} >= 0?'],\n",
     "    showindex    = False,\n",
     "    floatfmt = '.6f',\n",
@@ -165,7 +165,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -173,7 +173,7 @@
      "output_type": "stream",
      "text": [
       "\n",
-      "β_T = min_K min σ(S_{T,K}) = -0.082403\n",
+      "β_T = min_K min σ(S_{T,K}) = -0.133914\n",
       "⟹ T is not compeletely dissipative.\n",
       "⟹ (by Thm 1.1) T does not have a regular unitary dilation.\n"
      ]