diff --git a/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf b/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf new file mode 100644 index 000000000..caf451ded Binary files /dev/null and b/doc/HandWrittenNotes/2025/FYSSTKweek37.pdf differ diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb index 8e275c56f..ff7fc79f0 100644 --- a/doc/pub/week37/ipynb/week37.ipynb +++ b/doc/pub/week37/ipynb/week37.ipynb @@ -106,7 +106,10 @@ "id": "2a8c5baa", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, "outputs": [], "source": [ @@ -347,13 +350,38 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "02d7e401", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.29918563 4.58469793]\n", + "[[4.04503963]\n", + " [2.96930082]]\n", + "[[-3.92478381e+176]\n", + " [-4.83829315e+176]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "%matplotlib inline\n", "\n", @@ -383,7 +411,7 @@ "print(theta_linreg)\n", "theta = np.random.randn(2,1)\n", "\n", - "eta = 1.0/np.max(EigValues)\n", + "eta = 2.5/np.max(EigValues)\n", "Niterations = 1000\n", "\n", "for iter in range(Niterations):\n", @@ -527,13 +555,38 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "id": "2909407a", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.28267705 4.52578812]\n", + "[[4.39166208]\n", + " [2.57978284]]\n", + "[[4.38905562]\n", + " [2.58193415]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from random import random, seed\n", "import numpy as np\n", @@ -636,13 +689,63 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "id": "ac420f7a", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.59779819]) = 0.35736\n", + ">2 f([0.47823856]) = 0.22871\n", + ">3 f([0.38259084]) = 0.14638\n", + ">4 f([0.30607268]) = 0.09368\n", + ">5 f([0.24485814]) = 0.05996\n", + ">6 f([0.19588651]) = 0.03837\n", + ">7 f([0.15670921]) = 0.02456\n", + ">8 f([0.12536737]) = 0.01572\n", + ">9 f([0.10029389]) = 0.01006\n", + ">10 f([0.08023512]) = 0.00644\n", + ">11 f([0.06418809]) = 0.00412\n", + ">12 f([0.05135047]) = 0.00264\n", + ">13 f([0.04108038]) = 0.00169\n", + ">14 f([0.0328643]) = 0.00108\n", + ">15 f([0.02629144]) = 0.00069\n", + ">16 f([0.02103315]) = 0.00044\n", + ">17 f([0.01682652]) = 0.00028\n", + ">18 f([0.01346122]) = 0.00018\n", + ">19 f([0.01076897]) = 0.00012\n", + ">20 f([0.00861518]) = 0.00007\n", + ">21 f([0.00689214]) = 0.00005\n", + ">22 f([0.00551372]) = 0.00003\n", + ">23 f([0.00441097]) = 0.00002\n", + ">24 f([0.00352878]) = 0.00001\n", + ">25 f([0.00282302]) = 0.00001\n", + ">26 f([0.00225842]) = 0.00001\n", + ">27 f([0.00180673]) = 0.00000\n", + ">28 f([0.00144539]) = 0.00000\n", + ">29 f([0.00115631]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -713,13 +816,63 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "id": "687e9d89", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.54175461]) = 0.29350\n", + ">2 f([0.37175575]) = 0.13820\n", + ">3 f([0.24640494]) = 0.06072\n", + ">4 f([0.15951871]) = 0.02545\n", + ">5 f([0.1015491]) = 0.01031\n", + ">6 f([0.0638484]) = 0.00408\n", + ">7 f([0.03976851]) = 0.00158\n", + ">8 f([0.02459084]) = 0.00060\n", + ">9 f([0.01511937]) = 0.00023\n", + ">10 f([0.00925406]) = 0.00009\n", + ">11 f([0.00564365]) = 0.00003\n", + ">12 f([0.0034318]) = 0.00001\n", + ">13 f([0.00208188]) = 0.00000\n", + ">14 f([0.00126053]) = 0.00000\n", + ">15 f([0.00076202]) = 0.00000\n", + ">16 f([0.00046006]) = 0.00000\n", + ">17 f([0.00027746]) = 0.00000\n", + ">18 f([0.00016719]) = 0.00000\n", + ">19 f([0.00010067]) = 0.00000\n", + ">20 f([6.05804744e-05]) = 0.00000\n", + ">21 f([3.64373635e-05]) = 0.00000\n", + ">22 f([2.19069576e-05]) = 0.00000\n", + ">23 f([1.31664443e-05]) = 0.00000\n", + ">24 f([7.91100141e-06]) = 0.00000\n", + ">25 f([4.75216828e-06]) = 0.00000\n", + ">26 f([2.85408468e-06]) = 0.00000\n", + ">27 f([1.71384267e-06]) = 0.00000\n", + ">28 f([1.02900153e-06]) = 0.00000\n", + ">29 f([6.17748881e-07]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -1078,7 +1231,10 @@ "id": "102b1658", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, "outputs": [], "source": [ @@ -1179,7 +1335,10 @@ "id": "cfc48413", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, "outputs": [], "source": [ @@ -1223,13 +1382,43 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "id": "cc1e51cd", "metadata": { "collapsed": false, - "editable": true + "editable": true, + "jupyter": { + "outputs_hidden": false + } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.08805934]\n", + " [2.86802426]]\n", + "Eigenvalues of Hessian Matrix:[0.26504701 4.42519896]\n", + "theta from own gd\n", + "[[4.08805934]\n", + " [2.86802426]]\n", + "theta from own sdg\n", + "[[4.10653666]\n", + " [2.86499207]]\n" + ] + }, + { + "data": { + "image/png": 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", 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