From 32166931f1998118f66ea4d33b41e4f95768b18c Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Wed, 11 Oct 2023 16:33:42 +0200 Subject: [PATCH] Update exercisesweek41.ipynb --- doc/src/week41/exercisesweek41.ipynb | 246 ++++++++++++++++----------- 1 file changed, 151 insertions(+), 95 deletions(-) diff --git a/doc/src/week41/exercisesweek41.ipynb b/doc/src/week41/exercisesweek41.ipynb index fb52a5a71..b828548e8 100644 --- a/doc/src/week41/exercisesweek41.ipynb +++ b/doc/src/week41/exercisesweek41.ipynb @@ -103,25 +103,27 @@ "output_type": "stream", "text": [ "Own inversion\n", - "[[4.11317647]\n", - " [2.89590113]]\n", - "Eigenvalues of Hessian Matrix:[0.30572664 4.2933372 ]\n", + "[[4.28776768]\n", + " [2.88377084]]\n", + "Eigenvalues of Hessian Matrix:[0.30773954 4.59131906]\n", "theta from own gd\n", - "[[4.11317647]\n", - " [2.89590113]]\n", + "[[4.28776768]\n", + " [2.88377084]]\n", "theta from own sdg\n", - "[[4.11054282]\n", - " [2.90860481]]\n" + "[[4.2916904 ]\n", + " [2.90327755]]\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "
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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -427,73 +429,73 @@ "Own inversion\n", "[[4.]\n", " [3.]]\n", - "Eigenvalues of Hessian Matrix:[0.3114293 4.37490988]\n", - "0 [-11.29166089] [-12.67848646]\n", - "1 [-0.32626599] [0.27511094]\n", - "2 [-0.30304065] [0.25552709]\n", - "3 [-0.28146861] [0.23733731]\n", - "4 [-0.26143218] [0.22044238]\n", - "5 [-0.24282205] [0.20475012]\n", - "6 [-0.22553668] [0.19017492]\n", - "7 [-0.20948179] [0.17663726]\n", - "8 [-0.19456976] [0.16406329]\n", - "9 [-0.18071925] [0.15238439]\n", - "10 [-0.1678547] [0.14153686]\n", - "11 [-0.15590591] [0.13146152]\n", - "12 [-0.1448077] [0.12210339]\n", - "13 [-0.13449952] [0.11341142]\n", - "14 [-0.12492513] [0.10533819]\n", - "15 [-0.1160323] [0.09783966]\n", - "16 [-0.1077725] [0.09087491]\n", - "17 [-0.10010068] [0.08440596]\n", - "18 [-0.09297498] [0.07839749]\n", - "19 [-0.08635653] [0.07281674]\n", - "20 [-0.08020922] [0.06763326]\n", - "21 [-0.0744995] [0.06281877]\n", - "22 [-0.06919623] [0.05834699]\n", - "23 [-0.06427047] [0.05419354]\n", - "24 [-0.05969536] [0.05033576]\n", - "25 [-0.05544593] [0.04675259]\n", - "26 [-0.05149899] [0.0434245]\n", - "27 [-0.04783302] [0.04033331]\n", - "28 [-0.04442801] [0.03746217]\n", - "29 [-0.04126539] [0.03479541]\n", + "Eigenvalues of Hessian Matrix:[0.28076442 4.37589157]\n", + "0 [-10.1056039] [-11.51537034]\n", + "1 [-0.16830135] [0.14316669]\n", + "2 [-0.15750286] [0.13398088]\n", + "3 [-0.14739722] [0.12538445]\n", + "4 [-0.13793997] [0.11733958]\n", + "5 [-0.12908951] [0.10981087]\n", + "6 [-0.12080692] [0.10276523]\n", + "7 [-0.11305575] [0.09617164]\n", + "8 [-0.1058019] [0.09000111]\n", + "9 [-0.09901348] [0.08422649]\n", + "10 [-0.09266061] [0.07882238]\n", + "11 [-0.08671535] [0.07376501]\n", + "12 [-0.08115155] [0.06903212]\n", + "13 [-0.07594474] [0.06460291]\n", + "14 [-0.071072] [0.06045788]\n", + "15 [-0.0665119] [0.0565788]\n", + "16 [-0.06224439] [0.05294861]\n", + "17 [-0.05825068] [0.04955134]\n", + "18 [-0.05451322] [0.04637205]\n", + "19 [-0.05101557] [0.04339674]\n", + "20 [-0.04774232] [0.04061233]\n", + "21 [-0.0446791] [0.03800658]\n", + "22 [-0.04181241] [0.03556801]\n", + "23 [-0.03912966] [0.03328591]\n", + "24 [-0.03661904] [0.03115023]\n", + "25 [-0.0342695] [0.02915158]\n", + "26 [-0.03207071] [0.02728117]\n", + "27 [-0.030013] [0.02553076]\n", + "28 [-0.02808732] [0.02389267]\n", + "29 [-0.02628519] [0.02235967]\n", "theta from own gd\n", - "[[3.87692905]\n", - " [3.10377473]]\n", - "0 [-0.0383279] [0.03231849]\n", - "1 [-0.03559952] [0.03001789]\n", - "2 [-0.03224684] [0.02719088]\n", - "3 [-0.02894554] [0.02440718]\n", - "4 [-0.02589465] [0.02183464]\n", - "5 [-0.02313606] [0.01950857]\n", - "6 [-0.02066154] [0.01742203]\n", - "7 [-0.01844838] [0.01555587]\n", - "8 [-0.01647118] [0.01388868]\n", - "9 [-0.01470552] [0.01239985]\n", - "10 [-0.013129] [0.01107051]\n", - "11 [-0.01172145] [0.00988365]\n", - "12 [-0.01046479] [0.00882403]\n", - "13 [-0.00934286] [0.007878]\n", - "14 [-0.0083412] [0.00703339]\n", - "15 [-0.00744693] [0.00627933]\n", - "16 [-0.00664854] [0.00560612]\n", - "17 [-0.00593575] [0.00500508]\n", - "18 [-0.00529937] [0.00446848]\n", - "19 [-0.00473122] [0.00398941]\n", - "20 [-0.00422398] [0.0035617]\n", - "21 [-0.00377112] [0.00317985]\n", - "22 [-0.00336682] [0.00283894]\n", - "23 [-0.00300586] [0.00253457]\n", - "24 [-0.0026836] [0.00226284]\n", - "25 [-0.00239589] [0.00202024]\n", - "26 [-0.00213902] [0.00180365]\n", - "27 [-0.00190969] [0.00161027]\n", - "28 [-0.00170495] [0.00143764]\n", - "29 [-0.00152216] [0.00128351]\n", + "[[3.91238674]\n", + " [3.07452882]]\n", + "0 [-0.02459869] [0.02092504]\n", + "1 [-0.0230204] [0.01958246]\n", + "2 [-0.02106988] [0.01792324]\n", + "3 [-0.01913285] [0.01627549]\n", + "4 [-0.01732414] [0.0147369]\n", + "5 [-0.01566999] [0.01332978]\n", + "6 [-0.01416833] [0.01205238]\n", + "7 [-0.01280877] [0.01089586]\n", + "8 [-0.01157907] [0.00984981]\n", + "9 [-0.01046722] [0.00890402]\n", + "10 [-0.00946208] [0.00804898]\n", + "11 [-0.00855343] [0.00727603]\n", + "12 [-0.00773203] [0.00657731]\n", + "13 [-0.00698952] [0.00594568]\n", + "14 [-0.0063183] [0.00537471]\n", + "15 [-0.00571154] [0.00485856]\n", + "16 [-0.00516305] [0.00439199]\n", + "17 [-0.00466724] [0.00397022]\n", + "18 [-0.00421904] [0.00358895]\n", + "19 [-0.00381387] [0.0032443]\n", + "20 [-0.00344762] [0.00293274]\n", + "21 [-0.00311654] [0.00265111]\n", + "22 [-0.00281725] [0.00239652]\n", + "23 [-0.00254671] [0.00216637]\n", + "24 [-0.00230214] [0.00195833]\n", + "25 [-0.00208106] [0.00177027]\n", + "26 [-0.00188122] [0.00160027]\n", + "27 [-0.00170056] [0.00144659]\n", + "28 [-0.00153725] [0.00130767]\n", + "29 [-0.00138963] [0.0011821]\n", "theta from own gd wth momentum\n", - "[[3.99563634]\n", - " [3.00367949]]\n" + "[[3.99552586]\n", + " [3.00380596]]\n" ] } ], @@ -619,10 +621,45 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "id": "e2b04ba9", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.6259946 ]\n", + " [3.13054971]]\n", + "Eigenvalues of Hessian Matrix:[0.31026823 4.41529307]\n", + "theta from own gd\n", + "[[3.6259946 ]\n", + " [3.13054971]]\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta from own sdg\n", + "[[3.54608489]\n", + " [3.1531006 ]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -807,10 +844,25 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "id": "3ced9e13", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own AdaGrad\n", + "[[2.00059687]\n", + " [2.99708164]\n", + " [4.00299455]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n", "# OLS example\n", @@ -1084,7 +1136,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 5, "id": "f1090d5e", "metadata": {}, "outputs": [], @@ -1107,7 +1159,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 6, "id": "ed55121d", "metadata": {}, "outputs": [ @@ -1115,28 +1167,30 @@ "name": "stderr", "output_type": "stream", "text": [ - "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:173: UserWarning: Explicitly requested dtype float64 requested in asarray is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + "/opt/homebrew/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:164: UserWarning: Explicitly requested dtype float64 requested in asarray is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", " return asarray(x, dtype=self.dtype)\n" ] }, { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 3, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -1187,7 +1241,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 7, "id": "863db98d", "metadata": {}, "outputs": [ @@ -1195,28 +1249,30 @@ "name": "stderr", "output_type": "stream", "text": [ - "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:173: UserWarning: Explicitly requested dtype float64 requested in asarray is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + "/opt/homebrew/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:164: UserWarning: Explicitly requested dtype float64 requested in asarray is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", " return asarray(x, dtype=self.dtype)\n" ] }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 4, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -1268,7 +1324,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.10" + "version": "3.9.16" } }, "nbformat": 4,