From 1d4130d7b62752091d9bbb9ce15fda10d4353b97 Mon Sep 17 00:00:00 2001
From: Kees van Kempen <k.vankempen@student.science.ru.nl>
Date: Wed, 30 Mar 2022 09:19:00 +0200
Subject: [PATCH] Final: WIP: Fix comments in task 3.1 and execution numbers

---
 ...l - Tight-binding propagation method.ipynb | 23 +++++++++++--------
 1 file changed, 13 insertions(+), 10 deletions(-)

diff --git a/Final/Final - Tight-binding propagation method.ipynb b/Final/Final - Tight-binding propagation method.ipynb
index f476ce7..678da53 100644
--- a/Final/Final - Tight-binding propagation method.ipynb	
+++ b/Final/Final - Tight-binding propagation method.ipynb	
@@ -86,7 +86,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -135,7 +135,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -202,7 +202,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -289,7 +289,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -342,7 +342,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -398,7 +398,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -606,7 +606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 7,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -640,9 +640,12 @@
     "         for x_i in positions:\n",
     "             ret += -1./(np.abs(x - x_i) + 0.001)\n",
     "         return ret\n",
-    "    # Instead of using a loop, one could vectorize the problem by calculating all sum\n",
-    "    # elements in a len(x) by len(positions) matrix and then summing along the rows.\n",
+    "    # Instead of using a loop, one could vectorize the problem further by calculating all sum\n",
+    "    # terms as elements of a len(x) by len(positions) matrix and then summing along the rows.\n",
     "    # In testing I found that this was slower than using the loop, so I commented it out.\n",
+    "    # This might be due to the large memory overhead O(len(x)*len(positions)), and the fact that\n",
+    "    # the len(positions) iterations already do vectorized calculations on len(x) >> len(positions)\n",
+    "    # numbers, making the theoretical speed gain only plausible at larger len(positions). \n",
     "    #V = lambda x: np.sum( -1/( np.abs(np.subtract.outer(x, positions)) + 0.001 ), axis=1 )\n",
     "    \n",
     "    integrand = lambda x: atomic_basis(x, positions[i], sigma)*V(x)*atomic_basis(x, positions[j], sigma)\n",
@@ -660,7 +663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 119,
+   "execution_count": 8,
    "metadata": {
     "deletable": false,
     "nbgrader": {