diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index b0107b33f..fbbc2f22f 100644
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diff --git a/doc/LectureNotes/_build/.doctrees/exercisesweek41.doctree b/doc/LectureNotes/_build/.doctrees/exercisesweek41.doctree
index fd44b902b..e97f6e506 100644
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diff --git a/doc/LectureNotes/_build/html/_images/exercisesweek41_16_2.png b/doc/LectureNotes/_build/html/_images/exercisesweek41_16_2.png
index 641eb1729..e5435f4eb 100644
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diff --git a/doc/LectureNotes/_build/html/_images/exercisesweek41_22_2.png b/doc/LectureNotes/_build/html/_images/exercisesweek41_22_2.png
new file mode 100644
index 000000000..bcbc69131
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diff --git a/doc/LectureNotes/_build/html/_images/exercisesweek41_5_1.png b/doc/LectureNotes/_build/html/_images/exercisesweek41_5_1.png
index 43447c4d5..8c31b59a8 100644
Binary files a/doc/LectureNotes/_build/html/_images/exercisesweek41_5_1.png and b/doc/LectureNotes/_build/html/_images/exercisesweek41_5_1.png differ
diff --git a/doc/LectureNotes/_build/html/_sources/exercisesweek41.ipynb b/doc/LectureNotes/_build/html/_sources/exercisesweek41.ipynb
index 5030d4af7..341ad034c 100644
--- a/doc/LectureNotes/_build/html/_sources/exercisesweek41.ipynb
+++ b/doc/LectureNotes/_build/html/_sources/exercisesweek41.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "59b40432",
+   "id": "e3354581",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c67e680",
+   "id": "8d5fc499",
    "metadata": {
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@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c36ec93d",
+   "id": "d3ef3596",
    "metadata": {
     "editable": true
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@@ -82,7 +82,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38303814",
+   "id": "9940e21b",
    "metadata": {
     "editable": true
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@@ -92,7 +92,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f68b9c20",
+   "id": "6559d6d2",
    "metadata": {
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@@ -105,7 +105,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "4dfe5e82",
+   "id": "021b66d2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -184,7 +184,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9671e6bc",
+   "id": "d8e7110b",
    "metadata": {
     "editable": true
    },
@@ -197,7 +197,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d74a9cd",
+   "id": "74a7859a",
    "metadata": {
     "editable": true
    },
@@ -212,7 +212,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8abf1570",
+   "id": "619df8e8",
    "metadata": {
     "editable": true
    },
@@ -224,7 +224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17a32c59",
+   "id": "c759cfc4",
    "metadata": {
     "editable": true
    },
@@ -242,7 +242,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2956cf09",
+   "id": "0a4571f9",
    "metadata": {
     "editable": true
    },
@@ -261,7 +261,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c55e40e",
+   "id": "9bebfdd9",
    "metadata": {
     "editable": true
    },
@@ -273,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b60fe832",
+   "id": "c9e635e8",
    "metadata": {
     "editable": true
    },
@@ -283,7 +283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51c2673d",
+   "id": "eb544f8b",
    "metadata": {
     "editable": true
    },
@@ -297,7 +297,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1801af52",
+   "id": "d088ad85",
    "metadata": {
     "editable": true
    },
@@ -317,7 +317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0c6253b",
+   "id": "937063d3",
    "metadata": {
     "editable": true
    },
@@ -332,7 +332,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "dcd56458",
+   "id": "e08215a6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -392,7 +392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6502c1ea",
+   "id": "623ad923",
    "metadata": {
     "editable": true
    },
@@ -403,7 +403,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "fa89613b",
+   "id": "b7fe53c1",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -467,7 +467,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac5271c6",
+   "id": "749000b3",
    "metadata": {
     "editable": true
    },
@@ -478,7 +478,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "0def25cd",
+   "id": "e7b4abe1",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -527,7 +527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a8fec1d",
+   "id": "d47c2b1c",
    "metadata": {
     "editable": true
    },
@@ -539,7 +539,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "00658ea8",
+   "id": "e2b04ba9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -623,7 +623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "584dbef3",
+   "id": "f6d7455a",
    "metadata": {
     "editable": true
    },
@@ -634,7 +634,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "2908775e",
+   "id": "40a68e4f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -712,7 +712,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5b4691f",
+   "id": "d1f7f38d",
    "metadata": {
     "editable": true
    },
@@ -728,7 +728,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e0f6972",
+   "id": "b85cc96c",
    "metadata": {
     "editable": true
    },
@@ -739,7 +739,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "5c39eaa6",
+   "id": "3ced9e13",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -798,7 +798,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "234e9738",
+   "id": "ed1fa9e4",
    "metadata": {
     "editable": true
    },
@@ -808,7 +808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53f908ed",
+   "id": "787b2b5e",
    "metadata": {
     "editable": true
    },
@@ -824,7 +824,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab2867c0",
+   "id": "ac61b6e0",
    "metadata": {
     "editable": true
    },
@@ -835,7 +835,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "cb5dcea3",
+   "id": "5febac4f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -900,7 +900,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c415477",
+   "id": "ee8a6301",
    "metadata": {
     "editable": true
    },
@@ -916,7 +916,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bf0aa76",
+   "id": "b2d0f16b",
    "metadata": {
     "editable": true
    },
@@ -927,7 +927,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "17bd80f0",
+   "id": "59349e6f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -997,7 +997,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f16e27bd",
+   "id": "1d490115",
    "metadata": {
     "editable": true
    },
@@ -1013,7 +1013,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "279eb2a4",
+   "id": "3bc7785a",
    "metadata": {
     "editable": true
    },
@@ -1024,7 +1024,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "a88c09b3",
+   "id": "f1090d5e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1041,7 +1041,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd958e85",
+   "id": "ac6bf976",
    "metadata": {
     "editable": true
    },
@@ -1052,7 +1052,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "41d78257",
+   "id": "ed55121d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1097,7 +1097,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4755b5a9",
+   "id": "4a994430",
    "metadata": {
     "editable": true
    },
@@ -1108,7 +1108,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "a74afe50",
+   "id": "863db98d",
    "metadata": {
     "collapsed": false,
     "editable": true
diff --git a/doc/LectureNotes/_build/html/exercisesweek41.html b/doc/LectureNotes/_build/html/exercisesweek41.html
index 3f9567d98..ce03ed498 100644
--- a/doc/LectureNotes/_build/html/exercisesweek41.html
+++ b/doc/LectureNotes/_build/html/exercisesweek41.html
@@ -789,15 +789,15 @@ regression.</p>
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[3.97594511]
- [2.99866581]]
-Eigenvalues of Hessian Matrix:[0.39890447 3.73456649]
+[[3.83505053]
+ [3.09726322]]
+Eigenvalues of Hessian Matrix:[0.27717261 4.34154132]
 theta from own gd
-[[3.97594511]
- [2.99866581]]
+[[3.83505053]
+ [3.09726322]]
 theta from own sdg
-[[3.94814932]
- [2.97879245]]
+[[3.77589027]
+ [3.07286416]]
 </pre></div>
 </div>
 <img alt="_images/exercisesweek41_5_1.png" src="_images/exercisesweek41_5_1.png" />
@@ -919,14 +919,14 @@ first example shows results with ordinary leats squares.</p>
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[4.09527217]
- [3.02622906]]
-Eigenvalues of Hessian Matrix:[0.34998197 4.32265589]
+[[3.81651921]
+ [3.10399758]]
+Eigenvalues of Hessian Matrix:[0.30971881 4.52950417]
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
-[[4.09527217]
- [3.02622906]]
+[[3.81651921]
+ [3.10399758]]
 </pre></div>
 </div>
 <img alt="_images/exercisesweek41_16_2.png" src="_images/exercisesweek41_16_2.png" />
@@ -997,73 +997,73 @@ Eigenvalues of Hessian Matrix:[0.34998197 4.32265589]
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
 [[4.]
  [3.]]
-Eigenvalues of Hessian Matrix:[0.28837459 4.42584543]
-0 [-15.52856208] [-17.65196615]
-1 [-0.3842967] [0.3228044]
-2 [-0.3592571] [0.30177145]
-3 [-0.335849] [0.28210895]
-4 [-0.3139661] [0.26372759]
-5 [-0.29350903] [0.2465439]
-6 [-0.27438488] [0.23047985]
-7 [-0.25650679] [0.21546249]
-8 [-0.23979359] [0.20142361]
-9 [-0.22416937] [0.18829946]
-10 [-0.20956318] [0.17603044]
-11 [-0.19590868] [0.16456084]
-12 [-0.18314387] [0.15383855]
-13 [-0.17121077] [0.1438149]
-14 [-0.1600552] [0.13444436]
-15 [-0.14962649] [0.12568438]
-16 [-0.13987729] [0.11749517]
-17 [-0.13076331] [0.10983954]
-18 [-0.12224317] [0.10268273]
-19 [-0.11427818] [0.09599224]
-20 [-0.10683216] [0.08973767]
-21 [-0.0998713] [0.08389064]
-22 [-0.09336399] [0.07842458]
-23 [-0.08728068] [0.07331468]
-24 [-0.08159374] [0.06853772]
-25 [-0.07627734] [0.06407201]
-26 [-0.07130734] [0.05989727]
-27 [-0.06666117] [0.05599455]
-28 [-0.06231773] [0.05234611]
-29 [-0.0582573] [0.0489354]
+Eigenvalues of Hessian Matrix:[0.28641189 4.39287528]
+0 [-15.65565751] [-18.44347438]
+1 [-0.02618169] [0.02215597]
+2 [-0.02447466] [0.02071142]
+3 [-0.02287894] [0.01936105]
+4 [-0.02138725] [0.01809873]
+5 [-0.01999282] [0.01691871]
+6 [-0.0186893] [0.01581562]
+7 [-0.01747077] [0.01478446]
+8 [-0.01633169] [0.01382052]
+9 [-0.01526688] [0.01291943]
+10 [-0.01427149] [0.0120771]
+11 [-0.013341] [0.01128968]
+12 [-0.01247118] [0.0105536]
+13 [-0.01165807] [0.00986552]
+14 [-0.01089797] [0.00922229]
+15 [-0.01018743] [0.00862101]
+16 [-0.00952322] [0.00805892]
+17 [-0.00890232] [0.00753349]
+18 [-0.00832189] [0.00704231]
+19 [-0.00777931] [0.00658316]
+20 [-0.00727211] [0.00615394]
+21 [-0.00679797] [0.00575271]
+22 [-0.00635475] [0.00537764]
+23 [-0.00594042] [0.00502702]
+24 [-0.00555311] [0.00469926]
+25 [-0.00519105] [0.00439287]
+26 [-0.0048526] [0.00410646]
+27 [-0.00453622] [0.00383872]
+28 [-0.00424046] [0.00358844]
+29 [-0.00396398] [0.00335448]
 theta from own gd
-[[3.81114345]
- [3.15863713]]
-0 [-0.05446143] [0.04574692]
-1 [-0.05091289] [0.04276619]
-2 [-0.046531] [0.03908546]
-3 [-0.04218461] [0.03543455]
-4 [-0.03813208] [0.03203047]
-5 [-0.03443175] [0.02892224]
-6 [-0.03107818] [0.02610528]
-7 [-0.02804715] [0.02355925]
-8 [-0.02531037] [0.0212604]
-9 [-0.02284019] [0.01918548]
-10 [-0.02061094] [0.01731293]
-11 [-0.01859922] [0.01562311]
-12 [-0.01678384] [0.01409821]
-13 [-0.01514564] [0.01272215]
-14 [-0.01366733] [0.01148039]
-15 [-0.01233332] [0.01035984]
-16 [-0.01112952] [0.00934865]
-17 [-0.01004321] [0.00843617]
-18 [-0.00906293] [0.00761275]
-19 [-0.00817834] [0.0068697]
-20 [-0.00738008] [0.00619918]
-21 [-0.00665974] [0.0055941]
-22 [-0.00600971] [0.00504808]
-23 [-0.00542313] [0.00455536]
-24 [-0.0048938] [0.00411073]
-25 [-0.00441613] [0.0037095]
-26 [-0.00398509] [0.00334743]
-27 [-0.00359612] [0.0030207]
-28 [-0.00324512] [0.00272586]
-29 [-0.00292838] [0.0024598]
+[[3.98706221]
+ [3.01094846]]
+0 [-0.00370554] [0.00313577]
+1 [-0.00346394] [0.00293132]
+2 [-0.00316561] [0.00267887]
+3 [-0.00286972] [0.00242847]
+4 [-0.00259385] [0.00219502]
+5 [-0.00234197] [0.00198187]
+6 [-0.00211371] [0.00178871]
+7 [-0.00190742] [0.00161414]
+8 [-0.00172117] [0.00145652]
+9 [-0.00155308] [0.00131428]
+10 [-0.00140139] [0.00118591]
+11 [-0.00126452] [0.00107008]
+12 [-0.00114101] [0.00096557]
+13 [-0.00102956] [0.00087126]
+14 [-0.000929] [0.00078616]
+15 [-0.00083826] [0.00070937]
+16 [-0.00075639] [0.00064009]
+17 [-0.00068251] [0.00057757]
+18 [-0.00061585] [0.00052115]
+19 [-0.0005557] [0.00047025]
+20 [-0.00050142] [0.00042432]
+21 [-0.00045244] [0.00038288]
+22 [-0.00040825] [0.00034548]
+23 [-0.00036838] [0.00031174]
+24 [-0.0003324] [0.00028129]
+25 [-0.00029993] [0.00025381]
+26 [-0.00027064] [0.00022902]
+27 [-0.0002442] [0.00020665]
+28 [-0.00022035] [0.00018647]
+29 [-0.00019883] [0.00016826]
 theta from own gd wth momentum
-[[3.99083639]
- [3.00769731]]
+[[3.9993736 ]
+ [3.00053008]]
 </pre></div>
 </div>
 </div>
@@ -1116,17 +1116,17 @@ theta from own gd wth momentum
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[3.83190841]
- [2.9998542 ]]
-Eigenvalues of Hessian Matrix:[0.27971414 4.455592  ]
-0 [-12.5786304] [-15.41021561]
-1 [-2.79550688e-15] [-2.24968001e-16]
-2 [-2.2941718e-16] [-4.20820528e-16]
-3 [4.95697233e-16] [5.72742343e-16]
-4 [4.95697233e-16] [5.72742343e-16]
+[[3.92351924]
+ [3.025027  ]]
+Eigenvalues of Hessian Matrix:[0.33104875 3.95055425]
+0 [-11.75315452] [-11.48461009]
+1 [3.84783351e-15] [-1.7484672e-15]
+2 [-4.8897518e-16] [-4.48356153e-16]
+3 [4.61653285e-16] [3.79106945e-16]
+4 [-4.8897518e-16] [-4.48356153e-16]
 beta from own Newton code
-[[3.83190841]
- [2.9998542 ]]
+[[3.92351924]
+ [3.025027  ]]
 </pre></div>
 </div>
 </div>
@@ -1215,18 +1215,20 @@ beta from own Newton code
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[3.93988393]
- [3.06578047]]
-Eigenvalues of Hessian Matrix:[0.34100913 4.27547557]
-theta from own gd
-[[3.93988393]
- [3.06578047]]
+[[4.08928088]
+ [2.79578306]]
+Eigenvalues of Hessian Matrix:[0.31588332 4.45642521]
 </pre></div>
 </div>
-<img alt="_images/exercisesweek41_22_1.png" src="_images/exercisesweek41_22_1.png" />
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
+[[4.08928088]
+ [2.79578306]]
+</pre></div>
+</div>
+<img alt="_images/exercisesweek41_22_2.png" src="_images/exercisesweek41_22_2.png" />
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
-[[3.92648983]
- [3.07020234]]
+[[4.10188623]
+ [2.87242312]]
 </pre></div>
 </div>
 </div>
@@ -1308,15 +1310,15 @@ theta from own gd
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[4.12998822]
- [2.78886274]]
-Eigenvalues of Hessian Matrix:[0.3303366  4.33020191]
+[[3.84094234]
+ [3.01300561]]
+Eigenvalues of Hessian Matrix:[0.26776828 4.97262227]
 theta from own gd
-[[4.12921833]
- [2.78951443]]
+[[3.83774539]
+ [3.01544605]]
 theta from own sdg with momentum
-[[4.10156593]
- [2.7748567 ]]
+[[3.8186717 ]
+ [3.06511966]]
 </pre></div>
 </div>
 </div>
@@ -1391,9 +1393,9 @@ theta from own sdg with momentum
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
-[[1.9978254 ]
- [3.01066976]
- [3.98914003]]
+[[2.00019432]
+ [2.99888222]
+ [4.00105497]]
 </pre></div>
 </div>
 </div>
@@ -1475,9 +1477,9 @@ theta from own sdg with momentum
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
-[[1.99984215]
- [2.99767262]
- [3.99944037]]
+[[1.9996357 ]
+ [3.00788598]
+ [3.99589367]]
 </pre></div>
 </div>
 </div>
@@ -1563,9 +1565,9 @@ theta from own sdg with momentum
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
-[[1.99988325]
- [3.00072412]
- [3.99932732]]
+[[2.0001042 ]
+ [2.99949077]
+ [4.00048049]]
 </pre></div>
 </div>
 </div>
@@ -1638,7 +1640,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
   return asarray(x, dtype=self.dtype)
 </pre></div>
 </div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x11df37280&gt;]
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x1268ba940&gt;]
 </pre></div>
 </div>
 <img alt="_images/exercisesweek41_39_2.png" src="_images/exercisesweek41_39_2.png" />
@@ -1677,7 +1679,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
   return asarray(x, dtype=self.dtype)
 </pre></div>
 </div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x11de12520&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x1162c32b0&gt;
 </pre></div>
 </div>
 <img alt="_images/exercisesweek41_41_2.png" src="_images/exercisesweek41_41_2.png" />
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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Project 2 on Machine Learning, deadline November 13 (Midnight)","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Statistical interpretation of Linear Regression and Resampling techniques","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network 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No:[3,4,6,9,30,32,34,36],Not:[0,1,5,6,30,31,32,33,36,37],OR:27,Of:27,On:[0,3,15,26,27,28,29,30],One:[0,1,3,4,5,6,7,8,11,12,13,17,20,21,24,27,31,33,34,35,36,37],Or:[0,1,6,24,30,34],Such:[0,6,12,16,27,33,34,35,36,37],That:[0,5,7,10,11,12,14,19,24,27,30,32,33,34,37],The:[4,10,13,14,15,16,18,19,20,21,23,24,25,26,27,28,29],Their:37,Then:[0,1,6,8,9,10,11,12,13,14,23,24,30,31,33,34,35,36,37],There:[0,3,4,5,6,8,9,11,12,14,23,24,26,27,28,30,31,32,34,35,36,37],These:[0,2,3,4,5,8,9,10,11,12,13,14,15,16,23,24,25,27,28,30,31,32,35,36,37],To:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,21,23,24,25,27,32,33,34,35,36,37],With:[0,5,6,8,9,10,11,12,14,18,23,24,25,27,30,31,33,36,37],_0:[5,8,10,11,13,31,34,35],_1:[2,5,6,8,10,11,12,13,14,23,31,32,33,34,35,36,37],_2:[2,5,8,11,12,13,23,31,35,36,37],_3:23,_4:23,_9:[13,35,36],_:[0,1,2,4,5,6,7,8,9,10,11,12,13,17,18,19,21,23,24,30,31,32,33,34,35,36,37],_________________________________________________________________:4,__call__:[3,4],__class__:10,__doc__:[6,33],__future__:[8,9],__getattr__:32,__getitem__:2,__init__:[1,2,3,32,37],__main__:2,__name__:[2,10,32],__traceback__:[3,4],_auto10:[6,12,36,37],_auto11:[6,36],_auto12:[6,36],_auto1:[2,3,4,5,6,7,12,13,21,23,27,31,34,35,36,37],_auto2:[2,3,4,5,6,12,13,23,27,35,36,37],_auto3:[3,4,5,6,12,13,23,35,36,37],_auto4:[4,6,12,13,23,35,36,37],_auto5:[4,6,12,13,23,35,36,37],_auto6:[4,6,12,23,36,37],_auto7:[4,6,12,23,36,37],_auto8:[6,12,36,37],_auto9:[6,12,36,37],_base:8,_build:[0,17,19,22,24,29,30],_build_call_output:[3,4],_c:[1,37],_call:[3,4],_call_flat:[3,4],_check_optimize_result:[7,11,34],_compon:11,_decor:[0,30],_depth:9,_distn_infrastructur:34,_eagerdefinedfunct:[3,4],_fraction:9,_handl:[3,4],_i:[0,1,2,5,6,7,8,11,12,13,15,16,17,19,24,30,31,32,33,34,35,36,37],_inference_funct:[3,4],_interpolatefunctionerror:[3,4],_j:[0,1,2,3,5,6,8,13,17,19,24,31,32,33,35,37],_jit_compil:[3,4],_k:[13,34,35,36],_l:[12,36,37],_lambda:[6,30],_leaf:9,_lock:[3,4],_logist:[7,11,34],_m:10,_make_vjp:[2,13,36],_maybe_define_funct:[3,4],_multilayer_perceptron:37,_n:[2,5,8,11,13,31,34,35],_node:[2,9,13,36],_notokstatusexcept:[3,4],_num_output:[3,4],_p:[5,8,31],_process_traceback_fram:[3,4],_r:[3,4],_ratio:11,_sampl:9,_select_forward_and_backward_funct:[3,4],_split:[6,9,24],_src:21,_stateful_fn:[3,4],_stateless_fn:[3,4],_t:[13,21,35,36],_test:[6,24],_trace:[2,13,36],_unpad:2,_valu:[2,13,36],_varianc:11,_weight:9,a0:3,a0faa0:[9,10],a1:[0,30],a2:[0,30],a3:[0,30],a4:[0,30],a_0:[0,21,25,30],a_1a:[0,30],a_1x:[21,25],a_2a:[0,30],a_2x:[21,25],a_3:[0,30],a_3a:[0,30],a_4:[0,30],a_4a:[0,30],a_:[0,1,16,23,30,31,37],a_h:[1,37],a_i:[0,1,2,12,30,37],a_j:[1,12,37],a_k:[0,1,12,37],aaron:29,ab:[0,2,5,13,14,21,30,31,32,35,36],ab_channel:22,abandon:1,abbrevi:26,abid:27,abil:[0,10,30],abl:[0,1,4,5,6,7,10,12,13,16,24,31,34,35,36,37],about:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,22,23,24,25,28,32,33,34,35,36,37],abov:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,21,23,24,25,27,29,30,31,33,34,35,36,37],abovement:[6,33],abscissa:[13,34,35],absolut:[0,2,5,6,13,30,31,32,33,35,36],absorb:[31,32],acceler:[13,21,35,36],accept:[0,3,6,9,24,30,31],access:[0,3,11,27,31],accid:[4,6,33,34],accompani:[0,30,31],accomplish:[8,9,13,35,36],accord:[0,1,2,5,6,9,12,13,14,15,16,27,30,32,33,34,35,36,37],accordingli:11,account:[0,3,5,13,15,27,30,32,33,35,36],accumul:[12,13,21,27,35,36,37],accur:[0,3,4,6,10,13,33,35,36],accuraci:[0,1,3,4,5,6,7,9,10,11,12,25,30,31,34,36,37],accuracy_scor:[0,1,10,30,37],accuracy_score_numpi:[1,37],achiev:[0,1,5,6,8,12,23,30,32,33,36,37],aco:27,acquaint:[22,30],acquir:[1,22,30],acr:[0,31],across:[1,3,6,9,22,30,33,37],act:[1,3,23,37],action:27,activ:[0,2,3,4,9,26,28,30,33,34,35],actual:[0,1,4,5,6,8,11,16,23,27,30,31,32,33],ad:[1,3,4,5,8,13,15,16,23,32,33,34,35],ada_clf:10,adaboostclassifi:10,adadelta:[13,35,36],adagrad:25,adam:[1,3,4,25,28,30],adapt:[4,6,13,29,31,33,34],add:[0,1,2,3,4,5,6,8,10,11,12,15,16,17,21,24,25,27,30,31,32,33,35,37],add_outgrad:2,add_subplot:[1,7,12,14,34,36,37],addendum:5,addit:[0,2,3,5,6,7,8,9,10,12,13,15,17,21,22,23,24,27,28,29,30,31,32,33,34,35,36,37],addition:[12,13,34,35,36,37],address:[1,9,11,13,30,35,36],adjac:[3,12,36,37],adjoint:[5,31,32],adjust:[0,5,12,13,34,35,36],admir:[0,30],advanc:[4,6,12,29,30,33,36,37],advantag:[1,3,5,6,10,13,23,32,33,34,35,36,37],adversari:30,afecionado:30,affect:3,affin:[0,3,8,11,31],afford:3,aficionado:30,aforement:14,african:[0,31],after:[0,1,2,4,5,6,9,11,12,13,15,20,21,22,23,24,25,27,30,31,32,33,35,36,37],afterward:[0,30],ag:[0,7,26,30,31,34],ag_0:2,again:[0,1,4,5,6,7,8,10,11,12,13,15,16,21,24,25,27,30,31,32,33,35,36,37],against:[1,4,7,10,21,25,34,37],agegroup:[7,34],agegroupmean:[7,34],aggreg:[9,10],agorithm:10,agre:[5,6,27,32,33],agreement:[13,21,35,36],ahead:9,ai:[0,25,29],aid:[11,20],aim:[0,1,4,6,7,11,14,15,16,22,23,24,25,31,33,34],ainv:5,airplan:3,aka:[5,32,33],al:[0,2,4,15,16,17,25,29,30,31,32,33,34,35,36,37],alarm:[5,7,32,33],algebra:[0,3,5,13,21,22,31,32,33,35,36],algorithm:[0,1,2,4,5,6,7,8,13,14,22,23,24,27,29,30,32,33,34],align:[0,2,5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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Project 2 on Machine Learning, deadline November 13 (Midnight)","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Statistical interpretation of Linear Regression and Resampling techniques","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network 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iew:[0,4,10,31],visual:[1,9,37],vs:3,wai:[9,21,33],warm:21,wave:2,we:[21,30,35,36],wednesdai:32,week:[15,16,17,18,19,20,21,30,31,32,33,34,35,36,37],weekend:34,weekli:[26,33],weight:37,what:[0,30,31,32,33],when:[35,36],which:[1,21,35,36],why:[30,31,33,36,37],wisconsin:[7,34],wrap:[31,33],write:[4,11,25,32],x:[31,32],xgboost:10,xor:[36,37],yet:32,you:30,your:[0,10,15,16,25,30,31],yourself:34,z_j:37}})
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb
index 6dfba1160..4a84c43ea 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "59b40432",
+   "id": "e3354581",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c67e680",
+   "id": "8d5fc499",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c36ec93d",
+   "id": "d3ef3596",
    "metadata": {
     "editable": true
    },
@@ -82,7 +82,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38303814",
+   "id": "9940e21b",
    "metadata": {
     "editable": true
    },
@@ -92,7 +92,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f68b9c20",
+   "id": "6559d6d2",
    "metadata": {
     "editable": true
    },
@@ -105,7 +105,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "4dfe5e82",
+   "id": "021b66d2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -116,20 +116,20 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.97594511]\n",
-      " [2.99866581]]\n",
-      "Eigenvalues of Hessian Matrix:[0.39890447 3.73456649]\n",
+      "[[3.83505053]\n",
+      " [3.09726322]]\n",
+      "Eigenvalues of Hessian Matrix:[0.27717261 4.34154132]\n",
       "theta from own gd\n",
-      "[[3.97594511]\n",
-      " [2.99866581]]\n",
+      "[[3.83505053]\n",
+      " [3.09726322]]\n",
       "theta from own sdg\n",
-      "[[3.94814932]\n",
-      " [2.97879245]]\n"
+      "[[3.77589027]\n",
+      " [3.07286416]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -215,7 +215,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9671e6bc",
+   "id": "d8e7110b",
    "metadata": {
     "editable": true
    },
@@ -228,7 +228,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d74a9cd",
+   "id": "74a7859a",
    "metadata": {
     "editable": true
    },
@@ -243,7 +243,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8abf1570",
+   "id": "619df8e8",
    "metadata": {
     "editable": true
    },
@@ -255,7 +255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17a32c59",
+   "id": "c759cfc4",
    "metadata": {
     "editable": true
    },
@@ -273,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2956cf09",
+   "id": "0a4571f9",
    "metadata": {
     "editable": true
    },
@@ -292,7 +292,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c55e40e",
+   "id": "9bebfdd9",
    "metadata": {
     "editable": true
    },
@@ -304,7 +304,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b60fe832",
+   "id": "c9e635e8",
    "metadata": {
     "editable": true
    },
@@ -314,7 +314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51c2673d",
+   "id": "eb544f8b",
    "metadata": {
     "editable": true
    },
@@ -328,7 +328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1801af52",
+   "id": "d088ad85",
    "metadata": {
     "editable": true
    },
@@ -348,7 +348,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0c6253b",
+   "id": "937063d3",
    "metadata": {
     "editable": true
    },
@@ -363,7 +363,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "dcd56458",
+   "id": "e08215a6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -374,9 +374,9 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[4.09527217]\n",
-      " [3.02622906]]\n",
-      "Eigenvalues of Hessian Matrix:[0.34998197 4.32265589]\n"
+      "[[3.81651921]\n",
+      " [3.10399758]]\n",
+      "Eigenvalues of Hessian Matrix:[0.30971881 4.52950417]\n"
      ]
     },
     {
@@ -384,13 +384,13 @@
      "output_type": "stream",
      "text": [
       "theta from own gd\n",
-      "[[4.09527217]\n",
-      " [3.02622906]]\n"
+      "[[3.81651921]\n",
+      " [3.10399758]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6502c1ea",
+   "id": "623ad923",
    "metadata": {
     "editable": true
    },
@@ -468,7 +468,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "fa89613b",
+   "id": "b7fe53c1",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -481,73 +481,73 @@
       "Own inversion\n",
       "[[4.]\n",
       " [3.]]\n",
-      "Eigenvalues of Hessian Matrix:[0.28837459 4.42584543]\n",
-      "0 [-15.52856208] [-17.65196615]\n",
-      "1 [-0.3842967] [0.3228044]\n",
-      "2 [-0.3592571] [0.30177145]\n",
-      "3 [-0.335849] [0.28210895]\n",
-      "4 [-0.3139661] [0.26372759]\n",
-      "5 [-0.29350903] [0.2465439]\n",
-      "6 [-0.27438488] [0.23047985]\n",
-      "7 [-0.25650679] [0.21546249]\n",
-      "8 [-0.23979359] [0.20142361]\n",
-      "9 [-0.22416937] [0.18829946]\n",
-      "10 [-0.20956318] [0.17603044]\n",
-      "11 [-0.19590868] [0.16456084]\n",
-      "12 [-0.18314387] [0.15383855]\n",
-      "13 [-0.17121077] [0.1438149]\n",
-      "14 [-0.1600552] [0.13444436]\n",
-      "15 [-0.14962649] [0.12568438]\n",
-      "16 [-0.13987729] [0.11749517]\n",
-      "17 [-0.13076331] [0.10983954]\n",
-      "18 [-0.12224317] [0.10268273]\n",
-      "19 [-0.11427818] [0.09599224]\n",
-      "20 [-0.10683216] [0.08973767]\n",
-      "21 [-0.0998713] [0.08389064]\n",
-      "22 [-0.09336399] [0.07842458]\n",
-      "23 [-0.08728068] [0.07331468]\n",
-      "24 [-0.08159374] [0.06853772]\n",
-      "25 [-0.07627734] [0.06407201]\n",
-      "26 [-0.07130734] [0.05989727]\n",
-      "27 [-0.06666117] [0.05599455]\n",
-      "28 [-0.06231773] [0.05234611]\n",
-      "29 [-0.0582573] [0.0489354]\n",
+      "Eigenvalues of Hessian Matrix:[0.28641189 4.39287528]\n",
+      "0 [-15.65565751] [-18.44347438]\n",
+      "1 [-0.02618169] [0.02215597]\n",
+      "2 [-0.02447466] [0.02071142]\n",
+      "3 [-0.02287894] [0.01936105]\n",
+      "4 [-0.02138725] [0.01809873]\n",
+      "5 [-0.01999282] [0.01691871]\n",
+      "6 [-0.0186893] [0.01581562]\n",
+      "7 [-0.01747077] [0.01478446]\n",
+      "8 [-0.01633169] [0.01382052]\n",
+      "9 [-0.01526688] [0.01291943]\n",
+      "10 [-0.01427149] [0.0120771]\n",
+      "11 [-0.013341] [0.01128968]\n",
+      "12 [-0.01247118] [0.0105536]\n",
+      "13 [-0.01165807] [0.00986552]\n",
+      "14 [-0.01089797] [0.00922229]\n",
+      "15 [-0.01018743] [0.00862101]\n",
+      "16 [-0.00952322] [0.00805892]\n",
+      "17 [-0.00890232] [0.00753349]\n",
+      "18 [-0.00832189] [0.00704231]\n",
+      "19 [-0.00777931] [0.00658316]\n",
+      "20 [-0.00727211] [0.00615394]\n",
+      "21 [-0.00679797] [0.00575271]\n",
+      "22 [-0.00635475] [0.00537764]\n",
+      "23 [-0.00594042] [0.00502702]\n",
+      "24 [-0.00555311] [0.00469926]\n",
+      "25 [-0.00519105] [0.00439287]\n",
+      "26 [-0.0048526] [0.00410646]\n",
+      "27 [-0.00453622] [0.00383872]\n",
+      "28 [-0.00424046] [0.00358844]\n",
+      "29 [-0.00396398] [0.00335448]\n",
       "theta from own gd\n",
-      "[[3.81114345]\n",
-      " [3.15863713]]\n",
-      "0 [-0.05446143] [0.04574692]\n",
-      "1 [-0.05091289] [0.04276619]\n",
-      "2 [-0.046531] [0.03908546]\n",
-      "3 [-0.04218461] [0.03543455]\n",
-      "4 [-0.03813208] [0.03203047]\n",
-      "5 [-0.03443175] [0.02892224]\n",
-      "6 [-0.03107818] [0.02610528]\n",
-      "7 [-0.02804715] [0.02355925]\n",
-      "8 [-0.02531037] [0.0212604]\n",
-      "9 [-0.02284019] [0.01918548]\n",
-      "10 [-0.02061094] [0.01731293]\n",
-      "11 [-0.01859922] [0.01562311]\n",
-      "12 [-0.01678384] [0.01409821]\n",
-      "13 [-0.01514564] [0.01272215]\n",
-      "14 [-0.01366733] [0.01148039]\n",
-      "15 [-0.01233332] [0.01035984]\n",
-      "16 [-0.01112952] [0.00934865]\n",
-      "17 [-0.01004321] [0.00843617]\n",
-      "18 [-0.00906293] [0.00761275]\n",
-      "19 [-0.00817834] [0.0068697]\n",
-      "20 [-0.00738008] [0.00619918]\n",
-      "21 [-0.00665974] [0.0055941]\n",
-      "22 [-0.00600971] [0.00504808]\n",
-      "23 [-0.00542313] [0.00455536]\n",
-      "24 [-0.0048938] [0.00411073]\n",
-      "25 [-0.00441613] [0.0037095]\n",
-      "26 [-0.00398509] [0.00334743]\n",
-      "27 [-0.00359612] [0.0030207]\n",
-      "28 [-0.00324512] [0.00272586]\n",
-      "29 [-0.00292838] [0.0024598]\n",
+      "[[3.98706221]\n",
+      " [3.01094846]]\n",
+      "0 [-0.00370554] [0.00313577]\n",
+      "1 [-0.00346394] [0.00293132]\n",
+      "2 [-0.00316561] [0.00267887]\n",
+      "3 [-0.00286972] [0.00242847]\n",
+      "4 [-0.00259385] [0.00219502]\n",
+      "5 [-0.00234197] [0.00198187]\n",
+      "6 [-0.00211371] [0.00178871]\n",
+      "7 [-0.00190742] [0.00161414]\n",
+      "8 [-0.00172117] [0.00145652]\n",
+      "9 [-0.00155308] [0.00131428]\n",
+      "10 [-0.00140139] [0.00118591]\n",
+      "11 [-0.00126452] [0.00107008]\n",
+      "12 [-0.00114101] [0.00096557]\n",
+      "13 [-0.00102956] [0.00087126]\n",
+      "14 [-0.000929] [0.00078616]\n",
+      "15 [-0.00083826] [0.00070937]\n",
+      "16 [-0.00075639] [0.00064009]\n",
+      "17 [-0.00068251] [0.00057757]\n",
+      "18 [-0.00061585] [0.00052115]\n",
+      "19 [-0.0005557] [0.00047025]\n",
+      "20 [-0.00050142] [0.00042432]\n",
+      "21 [-0.00045244] [0.00038288]\n",
+      "22 [-0.00040825] [0.00034548]\n",
+      "23 [-0.00036838] [0.00031174]\n",
+      "24 [-0.0003324] [0.00028129]\n",
+      "25 [-0.00029993] [0.00025381]\n",
+      "26 [-0.00027064] [0.00022902]\n",
+      "27 [-0.0002442] [0.00020665]\n",
+      "28 [-0.00022035] [0.00018647]\n",
+      "29 [-0.00019883] [0.00016826]\n",
       "theta from own gd wth momentum\n",
-      "[[3.99083639]\n",
-      " [3.00769731]]\n"
+      "[[3.9993736 ]\n",
+      " [3.00053008]]\n"
      ]
     }
    ],
@@ -609,7 +609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac5271c6",
+   "id": "749000b3",
    "metadata": {
     "editable": true
    },
@@ -620,7 +620,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "0def25cd",
+   "id": "e7b4abe1",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -631,17 +631,17 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.83190841]\n",
-      " [2.9998542 ]]\n",
-      "Eigenvalues of Hessian Matrix:[0.27971414 4.455592  ]\n",
-      "0 [-12.5786304] [-15.41021561]\n",
-      "1 [-2.79550688e-15] [-2.24968001e-16]\n",
-      "2 [-2.2941718e-16] [-4.20820528e-16]\n",
-      "3 [4.95697233e-16] [5.72742343e-16]\n",
-      "4 [4.95697233e-16] [5.72742343e-16]\n",
+      "[[3.92351924]\n",
+      " [3.025027  ]]\n",
+      "Eigenvalues of Hessian Matrix:[0.33104875 3.95055425]\n",
+      "0 [-11.75315452] [-11.48461009]\n",
+      "1 [3.84783351e-15] [-1.7484672e-15]\n",
+      "2 [-4.8897518e-16] [-4.48356153e-16]\n",
+      "3 [4.61653285e-16] [3.79106945e-16]\n",
+      "4 [-4.8897518e-16] [-4.48356153e-16]\n",
       "beta from own Newton code\n",
-      "[[3.83190841]\n",
-      " [2.9998542 ]]\n"
+      "[[3.92351924]\n",
+      " [3.025027  ]]\n"
      ]
     }
    ],
@@ -688,7 +688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a8fec1d",
+   "id": "d47c2b1c",
    "metadata": {
     "editable": true
    },
@@ -700,7 +700,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "00658ea8",
+   "id": "e2b04ba9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -711,24 +711,30 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.93988393]\n",
-      " [3.06578047]]\n",
-      "Eigenvalues of Hessian Matrix:[0.34100913 4.27547557]\n",
+      "[[4.08928088]\n",
+      " [2.79578306]]\n",
+      "Eigenvalues of Hessian Matrix:[0.31588332 4.45642521]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "theta from own gd\n",
-      "[[3.93988393]\n",
-      " [3.06578047]]\n"
+      "[[4.08928088]\n",
+      " [2.79578306]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
      },
      "metadata": {
       "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_22_1.png"
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_22_2.png"
       }
      },
      "output_type": "display_data"
@@ -738,8 +744,8 @@
      "output_type": "stream",
      "text": [
       "theta from own sdg\n",
-      "[[3.92648983]\n",
-      " [3.07020234]]\n"
+      "[[4.10188623]\n",
+      " [2.87242312]]\n"
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@@ -821,7 +827,7 @@
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      "output_type": "stream",
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       "Own inversion\n",
-      "[[4.12998822]\n",
-      " [2.78886274]]\n",
-      "Eigenvalues of Hessian Matrix:[0.3303366  4.33020191]\n",
+      "[[3.84094234]\n",
+      " [3.01300561]]\n",
+      "Eigenvalues of Hessian Matrix:[0.26776828 4.97262227]\n",
       "theta from own gd\n",
-      "[[4.12921833]\n",
-      " [2.78951443]]\n",
+      "[[3.83774539]\n",
+      " [3.01544605]]\n",
       "theta from own sdg with momentum\n",
-      "[[4.10156593]\n",
-      " [2.7748567 ]]\n"
+      "[[3.8186717 ]\n",
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@@ -927,7 +933,7 @@
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-      "[[1.9978254 ]\n",
-      " [3.01066976]\n",
-      " [3.98914003]]\n"
+      "[[2.00019432]\n",
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@@ -1034,7 +1040,7 @@
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@@ -1092,9 +1098,9 @@
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       "theta from own RMSprop\n",
-      "[[1.99984215]\n",
-      " [2.99767262]\n",
-      " [3.99944037]]\n"
+      "[[1.9996357 ]\n",
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@@ -1157,7 +1163,7 @@
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@@ -1184,7 +1190,7 @@
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@@ -1205,9 +1211,9 @@
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-      "[[1.99988325]\n",
-      " [3.00072412]\n",
-      " [3.99932732]]\n"
+      "[[2.0001042 ]\n",
+      " [2.99949077]\n",
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@@ -1275,7 +1281,7 @@
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@@ -1408,7 +1414,7 @@
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diff --git a/doc/LectureNotes/exercisesweek41.ipynb b/doc/LectureNotes/exercisesweek41.ipynb
index 5030d4af7..341ad034c 100644
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@@ -392,7 +392,7 @@
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@@ -1041,7 +1041,7 @@
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@@ -1052,7 +1052,7 @@
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-   "id": "a74afe50",
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diff --git a/doc/LectureNotes/figures/adam.png b/doc/LectureNotes/figures/adam.png
index 9d8d91cac..a3a39f025 100644
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diff --git a/doc/src/week41/.ipynb_checkpoints/exercisesweek41-checkpoint.ipynb b/doc/src/week41/.ipynb_checkpoints/exercisesweek41-checkpoint.ipynb
new file mode 100644
index 000000000..6ad2cfc15
--- /dev/null
+++ b/doc/src/week41/.ipynb_checkpoints/exercisesweek41-checkpoint.ipynb
@@ -0,0 +1,1066 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "961a498e",
+   "metadata": {},
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html exercisesweek41.do.txt  -->\n",
+    "<!-- dom:TITLE: Exercises week 41 -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "03c74797",
+   "metadata": {},
+   "source": [
+    "# Exercises week 41\n",
+    "**October 9-13, 2023**\n",
+    "\n",
+    "Date: **Deadline is Sunday October 15 at midnight**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ba796602",
+   "metadata": {},
+   "source": [
+    "# Overarching aims of the exercises this week\n",
+    "\n",
+    "The aim of the exercises this week is to get started with implementing\n",
+    "gradient methods of relevance for project 2. This exercise will also\n",
+    "be continued next week with the addition of automatic differentation.\n",
+    "Everything you develop here will be used in project 2. \n",
+    "\n",
+    "In order to get started, we will now replace in our standard ordinary\n",
+    "least squares (OLS) and Ridge regression codes (from project 1) the\n",
+    "matrix inversion algorithm with our own gradient descent (GD) and SGD\n",
+    "codes.  You can use the Franke function or the terrain data from\n",
+    "project 1. **However, we recommend using a simpler function like**\n",
+    "$f(x)=a_0+a_1x+a_2x^2$ or higher-order one-dimensional polynomials.\n",
+    "You can obviously test your final codes against for example the Franke\n",
+    "function. Automatic differentiation will be discussed next week.\n",
+    "\n",
+    "You should include in your analysis of the GD and SGD codes the following elements\n",
+    "1. A plain gradient descent with a fixed learning rate (you will need to tune it) using the analytical expression of the gradients\n",
+    "\n",
+    "2. Add momentum to the plain GD code and compare convergence with a fixed learning rate (you may need to tune the learning rate), again using the analytical expression of the gradients.\n",
+    "\n",
+    "3. Repeat these steps for stochastic gradient descent with mini batches and a given number of epochs. Use a tunable learning rate as discussed in the lectures from week 39. Discuss the results as functions of the various parameters (size of batches, number of epochs etc)\n",
+    "\n",
+    "4. Implement the Adagrad method in order to tune the learning rate. Do this with and without momentum for plain gradient descent and SGD.\n",
+    "\n",
+    "5. Add RMSprop and Adam to your library of methods for tuning the learning rate.\n",
+    "\n",
+    "The lecture notes from weeks 39 and 40 contain more information and code examples. Feel free to use these examples.\n",
+    "\n",
+    "In summary, you should \n",
+    "perform an analysis of the results for OLS and Ridge regression as\n",
+    "function of the chosen learning rates, the number of mini-batches and\n",
+    "epochs as well as algorithm for scaling the learning rate. You can\n",
+    "also compare your own results with those that can be obtained using\n",
+    "for example **Scikit-Learn**'s various SGD options.  Discuss your\n",
+    "results. For Ridge regression you need now to study the results as functions of  the hyper-parameter $\\lambda$ and \n",
+    "the learning rate $\\eta$.  Discuss your results.\n",
+    "\n",
+    "You will need your SGD code for the setup of the Neural Network and\n",
+    "Logistic Regression codes. You will find the Python [Seaborn\n",
+    "package](https://seaborn.pydata.org/generated/seaborn.heatmap.html)\n",
+    "useful when plotting the results as function of the learning rate\n",
+    "$\\eta$ and the hyper-parameter $\\lambda$ when you use Ridge\n",
+    "regression.\n",
+    "\n",
+    "We recommend reading chapter 8 on optimization from the textbook of [Goodfellow, Bengio and Courville](https://www.deeplearningbook.org/). This chapter contains many useful insights and discussions on the optimization part of machine learning."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "59ed943e",
+   "metadata": {},
+   "source": [
+    "# Code examples from week 39 and 40"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34d80618",
+   "metadata": {},
+   "source": [
+    "## Code with a Number of Minibatches which varies, analytical gradient\n",
+    "\n",
+    "In the code here we vary the number of mini-batches."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "43d8de2f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "# Importing various packages\n",
+    "from math import exp, sqrt\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = 2.0/n*X.T @ ((X @ theta)-y)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4677c5e8",
+   "metadata": {},
+   "source": [
+    "In the above code, we have use replacement in setting up the\n",
+    "mini-batches. The discussion\n",
+    "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n",
+    "useful."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2d5248ca",
+   "metadata": {},
+   "source": [
+    "## Momentum based GD\n",
+    "\n",
+    "The stochastic gradient descent (SGD) is almost always used with a\n",
+    "*momentum* or inertia term that serves as a memory of the direction we\n",
+    "are moving in parameter space.  This is typically implemented as\n",
+    "follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4bb0612d",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d5b889d0",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto1\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t},\n",
+    "\\label{_auto1} \\tag{1}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b7a2cc6e",
+   "metadata": {},
+   "source": [
+    "where we have introduced a momentum parameter $\\gamma$, with\n",
+    "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
+    "indicate the gradient is to be taken over a different mini-batch at\n",
+    "each step. We call this algorithm gradient descent with momentum\n",
+    "(GDM). From these equations, it is clear that $\\mathbf{v}_t$ is a\n",
+    "running average of recently encountered gradients and\n",
+    "$(1-\\gamma)^{-1}$ sets the characteristic time scale for the memory\n",
+    "used in the averaging procedure. Consistent with this, when\n",
+    "$\\gamma=0$, this just reduces down to ordinary SGD as discussed\n",
+    "earlier. An equivalent way of writing the updates is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7f0d00e7",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4d7fd3b5",
+   "metadata": {},
+   "source": [
+    "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1115897",
+   "metadata": {},
+   "source": [
+    "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
+    "\n",
+    "The algorithms we have implemented are well described in the text by [Goodfellow, Bengio and Courville, chapter 8](https://www.deeplearningbook.org/contents/optimization.html).\n",
+    "\n",
+    "The codes which implement these algorithms are discussed after our presentation of automatic differentiation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34dcaf8a",
+   "metadata": {},
+   "source": [
+    "## Practical tips\n",
+    "\n",
+    "* **Randomize the data when making mini-batches**. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.\n",
+    "\n",
+    "* **Transform your inputs**. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.\n",
+    "\n",
+    "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n",
+    "\n",
+    "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n",
+    "\n",
+    "Geron's text, see chapter 11, has several interesting discussions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61718b10",
+   "metadata": {},
+   "source": [
+    "## Using Automatic differentation with OLS\n",
+    "\n",
+    "We conclude the part on optmization by showing how we can make codes\n",
+    "for linear regression and logistic regression using **autograd**. The\n",
+    "first example shows results with ordinary leats squares."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "69f28955",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a803b75e",
+   "metadata": {},
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "4b035828",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x#+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 30\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "# Now improve with momentum gradient descent\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "for iter in range(Niterations):\n",
+    "    # calculate gradient\n",
+    "    gradients = training_gradient(theta)\n",
+    "    # calculate update\n",
+    "    new_change = eta*gradients+delta_momentum*change\n",
+    "    # take a step\n",
+    "    theta -= new_change\n",
+    "    # save the change\n",
+    "    change = new_change\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd wth momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a6cd3976",
+   "metadata": {},
+   "source": [
+    "## But noen of these can compete with Newton's method"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "bb1d1307",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Newton's method\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(beta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "# Note that here the Hessian does not depend on the parameters beta\n",
+    "invH = np.linalg.pinv(H)\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "beta = np.random.randn(2,1)\n",
+    "Niterations = 5\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(beta)\n",
+    "    beta -= invH @ gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"beta from own Newton code\")\n",
+    "print(beta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "75f73e7a",
+   "metadata": {},
+   "source": [
+    "## Including Stochastic Gradient Descent with Autograd\n",
+    "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "7dd791d5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4ffca685",
+   "metadata": {},
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "e204d159",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 100\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        # calculate update\n",
+    "        new_change = eta*gradients+delta_momentum*change\n",
+    "        # take a step\n",
+    "        theta -= new_change\n",
+    "        # save the change\n",
+    "        change = new_change\n",
+    "print(\"theta from own sdg with momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8d01366d",
+   "metadata": {},
+   "source": [
+    "## AdaGrad algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
+    "\n",
+    "<!-- dom:FIGURE: [figures/adagrad.png, width=600 frac=0.8] -->\n",
+    "<!-- begin figure -->\n",
+    "\n",
+    "<img src=\"figures/adagrad.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
+    "<!-- end figure -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "002a3fb6",
+   "metadata": {},
+   "source": [
+    "## Similar (second order function now) problem but now with AdaGrad"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "01052f97",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        Giter += gradients*gradients\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "        theta -= update\n",
+    "print(\"theta from own AdaGrad\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9ef98b6c",
+   "metadata": {},
+   "source": [
+    "Running this code we note an almost perfect agreement with the results from matrix inversion."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d8c41b4",
+   "metadata": {},
+   "source": [
+    "## RMSProp algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
+    "\n",
+    "<!-- dom:FIGURE: [figures/rmsprop.png, width=600 frac=0.8] -->\n",
+    "<!-- begin figure -->\n",
+    "\n",
+    "<img src=\"figures/rmsprop.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
+    "<!-- end figure -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ccc367e5",
+   "metadata": {},
+   "source": [
+    "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "7c672270",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameter rho\n",
+    "rho = 0.99\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "\t# Accumulated gradient\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        Giter = (rho*Giter+(1-rho)*gradients*gradients)\n",
+    "\t# Taking the diagonal only and inverting\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "\t# Hadamard product\n",
+    "        theta -= update\n",
+    "print(\"theta from own RMSprop\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e933539",
+   "metadata": {},
+   "source": [
+    "## ADAM algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
+    "\n",
+    "<!-- dom:FIGURE: [figures/adam.png, width=600 frac=0.8] -->\n",
+    "<!-- begin figure -->\n",
+    "\n",
+    "<img src=\"figures/adam.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
+    "<!-- end figure -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dba60a0e",
+   "metadata": {},
+   "source": [
+    "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "dded64ca",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameters beta1 and beta2, see https://arxiv.org/abs/1412.6980\n",
+    "beta1 = 0.9\n",
+    "beta2 = 0.999\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-7\n",
+    "iter = 0\n",
+    "for epoch in range(n_epochs):\n",
+    "    first_moment = 0.0\n",
+    "    second_moment = 0.0\n",
+    "    iter += 1\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        # Computing moments first\n",
+    "        first_moment = beta1*first_moment + (1-beta1)*gradients\n",
+    "        second_moment = beta2*second_moment+(1-beta2)*gradients*gradients\n",
+    "        first_term = first_moment/(1.0-beta1**iter)\n",
+    "        second_term = second_moment/(1.0-beta2**iter)\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        update = eta*first_term/(np.sqrt(second_term)+delta)\n",
+    "        theta -= update\n",
+    "print(\"theta from own ADAM\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cfcf6b3f",
+   "metadata": {},
+   "source": [
+    "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "**JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),\n",
+    "brought together for high-performance numerical computing and machine learning research.\n",
+    "It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3154e001",
+   "metadata": {},
+   "source": [
+    "### Getting started with Jax, note the way we import numpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "10302ddf",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax\n",
+    "import jax.numpy as jnp\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from jax import grad as jax_grad"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b502e49e",
+   "metadata": {},
+   "source": [
+    "### A warm-up example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "96d0b51e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def function(x):\n",
+    "    return x**2\n",
+    "\n",
+    "def analytical_gradient(x):\n",
+    "    return 2*x\n",
+    "\n",
+    "def gradient_descent(starting_point, learning_rate, num_iterations, solver=\"analytical\"):\n",
+    "    x = starting_point\n",
+    "    trajectory_x = [x]\n",
+    "    trajectory_y = [function(x)]\n",
+    "\n",
+    "    if solver == \"analytical\":\n",
+    "        grad = analytical_gradient    \n",
+    "    elif solver == \"jax\":\n",
+    "        grad = jax_grad(function)\n",
+    "        x = jnp.float64(x)\n",
+    "        learning_rate = jnp.float64(learning_rate)\n",
+    "\n",
+    "    for _ in range(num_iterations):\n",
+    "        \n",
+    "        x = x - learning_rate * grad(x)\n",
+    "        trajectory_x.append(x)\n",
+    "        trajectory_y.append(function(x))\n",
+    "\n",
+    "    return trajectory_x, trajectory_y\n",
+    "\n",
+    "x = np.linspace(-5, 5, 100)\n",
+    "plt.plot(x, function(x), label=\"f(x)\")\n",
+    "\n",
+    "descent_x, descent_y = gradient_descent(5, 0.1, 10, solver=\"analytical\")\n",
+    "jax_descend_x, jax_descend_y = gradient_descent(5, 0.1, 10, solver=\"jax\")\n",
+    "\n",
+    "plt.plot(descent_x, descent_y, label=\"Gradient descent\", marker=\"o\")\n",
+    "plt.plot(jax_descend_x, jax_descend_y, label=\"JAX\", marker=\"x\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "276504df",
+   "metadata": {},
+   "source": [
+    "### A more advanced example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "461c3059",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "backend = np\n",
+    "\n",
+    "def function(x):\n",
+    "    return x*backend.sin(x**2 + 1)\n",
+    "\n",
+    "def analytical_gradient(x):\n",
+    "    return backend.sin(x**2 + 1) + 2*x**2*backend.cos(x**2 + 1)\n",
+    "\n",
+    "\n",
+    "x = np.linspace(-5, 5, 100)\n",
+    "plt.plot(x, function(x), label=\"f(x)\")\n",
+    "\n",
+    "descent_x, descent_y = gradient_descent(1, 0.01, 300, solver=\"analytical\")\n",
+    "\n",
+    "# Change the backend to JAX\n",
+    "backend = jnp\n",
+    "jax_descend_x, jax_descend_y = gradient_descent(1, 0.01, 300, solver=\"jax\")\n",
+    "\n",
+    "plt.scatter(descent_x, descent_y, label=\"Gradient descent\", marker=\"v\", s=10, color=\"red\") \n",
+    "plt.scatter(jax_descend_x, jax_descend_y, label=\"JAX\", marker=\"x\", s=5, color=\"black\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/doc/src/week41/exercisesweek41.ipynb b/doc/src/week41/exercisesweek41.ipynb
new file mode 100644
index 000000000..341ad034c
--- /dev/null
+++ b/doc/src/week41/exercisesweek41.ipynb
@@ -0,0 +1,1144 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "e3354581",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html exercisesweek41.do.txt  -->\n",
+    "<!-- dom:TITLE: Exercises week 41 -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8d5fc499",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Exercises week 41\n",
+    "**October 9-13, 2023**\n",
+    "\n",
+    "Date: **Deadline is Sunday October 15 at midnight**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d3ef3596",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Overarching aims of the exercises this week\n",
+    "\n",
+    "The aim of the exercises this week is to get started with implementing\n",
+    "gradient methods of relevance for project 2. This exercise will also\n",
+    "be continued next week with the addition of automatic differentation.\n",
+    "Everything you develop here will be used in project 2. \n",
+    "\n",
+    "In order to get started, we will now replace in our standard ordinary\n",
+    "least squares (OLS) and Ridge regression codes (from project 1) the\n",
+    "matrix inversion algorithm with our own gradient descent (GD) and SGD\n",
+    "codes.  You can use the Franke function or the terrain data from\n",
+    "project 1. **However, we recommend using a simpler function like**\n",
+    "$f(x)=a_0+a_1x+a_2x^2$ or higher-order one-dimensional polynomials.\n",
+    "You can obviously test your final codes against for example the Franke\n",
+    "function. Automatic differentiation will be discussed next week.\n",
+    "\n",
+    "You should include in your analysis of the GD and SGD codes the following elements\n",
+    "1. A plain gradient descent with a fixed learning rate (you will need to tune it) using the analytical expression of the gradients\n",
+    "\n",
+    "2. Add momentum to the plain GD code and compare convergence with a fixed learning rate (you may need to tune the learning rate), again using the analytical expression of the gradients.\n",
+    "\n",
+    "3. Repeat these steps for stochastic gradient descent with mini batches and a given number of epochs. Use a tunable learning rate as discussed in the lectures from week 39. Discuss the results as functions of the various parameters (size of batches, number of epochs etc)\n",
+    "\n",
+    "4. Implement the Adagrad method in order to tune the learning rate. Do this with and without momentum for plain gradient descent and SGD.\n",
+    "\n",
+    "5. Add RMSprop and Adam to your library of methods for tuning the learning rate.\n",
+    "\n",
+    "The lecture notes from weeks 39 and 40 contain more information and code examples. Feel free to use these examples.\n",
+    "\n",
+    "In summary, you should \n",
+    "perform an analysis of the results for OLS and Ridge regression as\n",
+    "function of the chosen learning rates, the number of mini-batches and\n",
+    "epochs as well as algorithm for scaling the learning rate. You can\n",
+    "also compare your own results with those that can be obtained using\n",
+    "for example **Scikit-Learn**'s various SGD options.  Discuss your\n",
+    "results. For Ridge regression you need now to study the results as functions of  the hyper-parameter $\\lambda$ and \n",
+    "the learning rate $\\eta$.  Discuss your results.\n",
+    "\n",
+    "You will need your SGD code for the setup of the Neural Network and\n",
+    "Logistic Regression codes. You will find the Python [Seaborn\n",
+    "package](https://seaborn.pydata.org/generated/seaborn.heatmap.html)\n",
+    "useful when plotting the results as function of the learning rate\n",
+    "$\\eta$ and the hyper-parameter $\\lambda$ when you use Ridge\n",
+    "regression.\n",
+    "\n",
+    "We recommend reading chapter 8 on optimization from the textbook of [Goodfellow, Bengio and Courville](https://www.deeplearningbook.org/). This chapter contains many useful insights and discussions on the optimization part of machine learning."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9940e21b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Code examples from week 39 and 40"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6559d6d2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Code with a Number of Minibatches which varies, analytical gradient\n",
+    "\n",
+    "In the code here we vary the number of mini-batches."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "021b66d2",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "# Importing various packages\n",
+    "from math import exp, sqrt\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = 2.0/n*X.T @ ((X @ theta)-y)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d8e7110b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In the above code, we have use replacement in setting up the\n",
+    "mini-batches. The discussion\n",
+    "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n",
+    "useful."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "74a7859a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Momentum based GD\n",
+    "\n",
+    "The stochastic gradient descent (SGD) is almost always used with a\n",
+    "*momentum* or inertia term that serves as a memory of the direction we\n",
+    "are moving in parameter space.  This is typically implemented as\n",
+    "follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "619df8e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c759cfc4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto1\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t},\n",
+    "\\label{_auto1} \\tag{1}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0a4571f9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have introduced a momentum parameter $\\gamma$, with\n",
+    "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
+    "indicate the gradient is to be taken over a different mini-batch at\n",
+    "each step. We call this algorithm gradient descent with momentum\n",
+    "(GDM). From these equations, it is clear that $\\mathbf{v}_t$ is a\n",
+    "running average of recently encountered gradients and\n",
+    "$(1-\\gamma)^{-1}$ sets the characteristic time scale for the memory\n",
+    "used in the averaging procedure. Consistent with this, when\n",
+    "$\\gamma=0$, this just reduces down to ordinary SGD as discussed\n",
+    "earlier. An equivalent way of writing the updates is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9bebfdd9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c9e635e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eb544f8b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
+    "\n",
+    "The algorithms we have implemented are well described in the text by [Goodfellow, Bengio and Courville, chapter 8](https://www.deeplearningbook.org/contents/optimization.html).\n",
+    "\n",
+    "The codes which implement these algorithms are discussed after our presentation of automatic differentiation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d088ad85",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Practical tips\n",
+    "\n",
+    "* **Randomize the data when making mini-batches**. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.\n",
+    "\n",
+    "* **Transform your inputs**. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.\n",
+    "\n",
+    "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n",
+    "\n",
+    "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n",
+    "\n",
+    "Geron's text, see chapter 11, has several interesting discussions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "937063d3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Automatic differentation with OLS\n",
+    "\n",
+    "We conclude the part on optmization by showing how we can make codes\n",
+    "for linear regression and logistic regression using **autograd**. The\n",
+    "first example shows results with ordinary leats squares."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "e08215a6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "623ad923",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "b7fe53c1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x#+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 30\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "# Now improve with momentum gradient descent\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "for iter in range(Niterations):\n",
+    "    # calculate gradient\n",
+    "    gradients = training_gradient(theta)\n",
+    "    # calculate update\n",
+    "    new_change = eta*gradients+delta_momentum*change\n",
+    "    # take a step\n",
+    "    theta -= new_change\n",
+    "    # save the change\n",
+    "    change = new_change\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd wth momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "749000b3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## But noen of these can compete with Newton's method"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "e7b4abe1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Newton's method\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(beta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "# Note that here the Hessian does not depend on the parameters beta\n",
+    "invH = np.linalg.pinv(H)\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "beta = np.random.randn(2,1)\n",
+    "Niterations = 5\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(beta)\n",
+    "    beta -= invH @ gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"beta from own Newton code\")\n",
+    "print(beta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d47c2b1c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Including Stochastic Gradient Descent with Autograd\n",
+    "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "e2b04ba9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f6d7455a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "40a68e4f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 100\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        # calculate update\n",
+    "        new_change = eta*gradients+delta_momentum*change\n",
+    "        # take a step\n",
+    "        theta -= new_change\n",
+    "        # save the change\n",
+    "        change = new_change\n",
+    "print(\"theta from own sdg with momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d1f7f38d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## AdaGrad algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
+    "\n",
+    "<!-- dom:FIGURE: [figures/adagrad.png, width=600 frac=0.8] -->\n",
+    "<!-- begin figure -->\n",
+    "\n",
+    "<img src=\"figures/adagrad.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
+    "<!-- end figure -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b85cc96c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Similar (second order function now) problem but now with AdaGrad"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "3ced9e13",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        Giter += gradients*gradients\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "        theta -= update\n",
+    "print(\"theta from own AdaGrad\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ed1fa9e4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Running this code we note an almost perfect agreement with the results from matrix inversion."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "787b2b5e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## RMSProp algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
+    "\n",
+    "<!-- dom:FIGURE: [figures/rmsprop.png, width=600 frac=0.8] -->\n",
+    "<!-- begin figure -->\n",
+    "\n",
+    "<img src=\"figures/rmsprop.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
+    "<!-- end figure -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ac61b6e0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "5febac4f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameter rho\n",
+    "rho = 0.99\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "\t# Accumulated gradient\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        Giter = (rho*Giter+(1-rho)*gradients*gradients)\n",
+    "\t# Taking the diagonal only and inverting\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "\t# Hadamard product\n",
+    "        theta -= update\n",
+    "print(\"theta from own RMSprop\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ee8a6301",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## ADAM algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
+    "\n",
+    "<!-- dom:FIGURE: [figures/adam.png, width=600 frac=0.8] -->\n",
+    "<!-- begin figure -->\n",
+    "\n",
+    "<img src=\"figures/adam.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
+    "<!-- end figure -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b2d0f16b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "59349e6f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameters beta1 and beta2, see https://arxiv.org/abs/1412.6980\n",
+    "beta1 = 0.9\n",
+    "beta2 = 0.999\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-7\n",
+    "iter = 0\n",
+    "for epoch in range(n_epochs):\n",
+    "    first_moment = 0.0\n",
+    "    second_moment = 0.0\n",
+    "    iter += 1\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        # Computing moments first\n",
+    "        first_moment = beta1*first_moment + (1-beta1)*gradients\n",
+    "        second_moment = beta2*second_moment+(1-beta2)*gradients*gradients\n",
+    "        first_term = first_moment/(1.0-beta1**iter)\n",
+    "        second_term = second_moment/(1.0-beta2**iter)\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        update = eta*first_term/(np.sqrt(second_term)+delta)\n",
+    "        theta -= update\n",
+    "print(\"theta from own ADAM\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1d490115",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "**JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),\n",
+    "brought together for high-performance numerical computing and machine learning research.\n",
+    "It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3bc7785a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Getting started with Jax, note the way we import numpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "f1090d5e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import jax\n",
+    "import jax.numpy as jnp\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from jax import grad as jax_grad"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ac6bf976",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### A warm-up example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "ed55121d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "def function(x):\n",
+    "    return x**2\n",
+    "\n",
+    "def analytical_gradient(x):\n",
+    "    return 2*x\n",
+    "\n",
+    "def gradient_descent(starting_point, learning_rate, num_iterations, solver=\"analytical\"):\n",
+    "    x = starting_point\n",
+    "    trajectory_x = [x]\n",
+    "    trajectory_y = [function(x)]\n",
+    "\n",
+    "    if solver == \"analytical\":\n",
+    "        grad = analytical_gradient    \n",
+    "    elif solver == \"jax\":\n",
+    "        grad = jax_grad(function)\n",
+    "        x = jnp.float64(x)\n",
+    "        learning_rate = jnp.float64(learning_rate)\n",
+    "\n",
+    "    for _ in range(num_iterations):\n",
+    "        \n",
+    "        x = x - learning_rate * grad(x)\n",
+    "        trajectory_x.append(x)\n",
+    "        trajectory_y.append(function(x))\n",
+    "\n",
+    "    return trajectory_x, trajectory_y\n",
+    "\n",
+    "x = np.linspace(-5, 5, 100)\n",
+    "plt.plot(x, function(x), label=\"f(x)\")\n",
+    "\n",
+    "descent_x, descent_y = gradient_descent(5, 0.1, 10, solver=\"analytical\")\n",
+    "jax_descend_x, jax_descend_y = gradient_descent(5, 0.1, 10, solver=\"jax\")\n",
+    "\n",
+    "plt.plot(descent_x, descent_y, label=\"Gradient descent\", marker=\"o\")\n",
+    "plt.plot(jax_descend_x, jax_descend_y, label=\"JAX\", marker=\"x\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a994430",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### A more advanced example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "863db98d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "backend = np\n",
+    "\n",
+    "def function(x):\n",
+    "    return x*backend.sin(x**2 + 1)\n",
+    "\n",
+    "def analytical_gradient(x):\n",
+    "    return backend.sin(x**2 + 1) + 2*x**2*backend.cos(x**2 + 1)\n",
+    "\n",
+    "\n",
+    "x = np.linspace(-5, 5, 100)\n",
+    "plt.plot(x, function(x), label=\"f(x)\")\n",
+    "\n",
+    "descent_x, descent_y = gradient_descent(1, 0.01, 300, solver=\"analytical\")\n",
+    "\n",
+    "# Change the backend to JAX\n",
+    "backend = jnp\n",
+    "jax_descend_x, jax_descend_y = gradient_descent(1, 0.01, 300, solver=\"jax\")\n",
+    "\n",
+    "plt.scatter(descent_x, descent_y, label=\"Gradient descent\", marker=\"v\", s=10, color=\"red\") \n",
+    "plt.scatter(jax_descend_x, jax_descend_y, label=\"JAX\", marker=\"x\", s=5, color=\"black\")"
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
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