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rohanjoseph93/Gradient_Descent.ipynb

Created June 3, 2018 02:37
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Gradient_Descent.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [],
"source": [
"# From calculation, it is expected that the local minimum occurs at x=9/4\n",
"\n",
"cur_x = 3 # The algorithm starts at x=1\n",
"gamma = 0.01 # step size multiplier\n",
"precision = 0.000001\n",
"previous_step_size = 1 \n",
"max_iters = 10000 # maximum number of iterations\n",
"iters = 0 #iteration counter\n",
"df = lambda x: 2*(x+5)"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration 1 \n",
"X value is 2.84\n",
"Iteration 2 \n",
"X value is 2.6832\n",
"Iteration 3 \n",
"X value is 2.529536\n",
"Iteration 4 \n",
"X value is 2.37894528\n",
"Iteration 5 \n",
"X value is 2.2313663744\n",
"Iteration 6 \n",
"X value is 2.0867390469119997\n",
"Iteration 7 \n",
"X value is 1.9450042659737599\n",
"Iteration 8 \n",
"X value is 1.8061041806542846\n",
"Iteration 9 \n",
"X value is 1.669982097041199\n",
"Iteration 10 \n",
"X value is 1.5365824551003748\n",
"Iteration 11 \n",
"X value is 1.4058508059983674\n",
"Iteration 12 \n",
"X value is 1.2777337898784\n",
"Iteration 13 \n",
"X value is 1.152179114080832\n",
"Iteration 14 \n",
"X value is 1.0291355317992152\n",
"Iteration 15 \n",
"X value is 0.9085528211632309\n",
"Iteration 16 \n",
"X value is 0.7903817647399662\n",
"Iteration 17 \n",
"X value is 0.6745741294451669\n",
"Iteration 18 \n",
"X value is 0.5610826468562635\n",
"Iteration 19 \n",
"X value is 0.44986099391913825\n",
"Iteration 20 \n",
"X value is 0.3408637740407555\n",
"Iteration 21 \n",
"X value is 0.23404649855994042\n",
"Iteration 22 \n",
"X value is 0.1293655685887416\n",
"Iteration 23 \n",
"X value is 0.026778257216966764\n",
"Iteration 24 \n",
"X value is -0.07375730792737258\n",
"Iteration 25 \n",
"X value is -0.1722821617688251\n",
"Iteration 26 \n",
"X value is -0.2688365185334486\n",
"Iteration 27 \n",
"X value is -0.36345978816277963\n",
"Iteration 28 \n",
"X value is -0.45619059239952403\n",
"Iteration 29 \n",
"X value is -0.5470667805515336\n",
"Iteration 30 \n",
"X value is -0.6361254449405029\n",
"Iteration 31 \n",
"X value is -0.7234029360416929\n",
"Iteration 32 \n",
"X value is -0.8089348773208591\n",
"Iteration 33 \n",
"X value is -0.8927561797744419\n",
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"X value is -0.9749010561789531\n",
"Iteration 35 \n",
"X value is -1.055403035055374\n",
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"X value is -1.1342949743542665\n",
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"X value is -1.2116090748671813\n",
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"X value is -1.2873768933698377\n",
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"X value is -1.361629355502441\n",
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"X value is -1.4343967683923922\n",
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"X value is -1.5057088330245443\n",
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"X value is -1.5755946563640535\n",
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"X value is -1.6440827632367725\n",
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"X value is -1.711201107972037\n",
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"X value is -1.7769770858125964\n",
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"X value is -1.8414375440963444\n",
"Iteration 47 \n",
"X value is -1.9046087932144176\n",
"Iteration 48 \n",
"X value is -1.9665166173501292\n",
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"X value is -2.0271862850031264\n",
"Iteration 50 \n",
"X value is -2.0866425593030637\n",
"Iteration 51 \n",
"X value is -2.1449097081170025\n",
"Iteration 52 \n",
"X value is -2.2020115139546625\n",
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"X value is -2.257971283675569\n",
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"X value is -2.312811858002058\n",
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"X value is -2.3665556208420164\n",
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"X value is -2.419224508425176\n",
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"X value is -2.4708400182566725\n",
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"X value is -2.521423217891539\n",
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"X value is -2.570994753533708\n",
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"X value is -2.619574858463034\n",
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"X value is -2.667183361293773\n",
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"X value is -2.713839694067898\n",
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"X value is -2.75956290018654\n",
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"X value is -2.804371642182809\n",
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"X value is -2.8482842093391527\n",
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"X value is -2.8913185251523696\n",
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"X value is -2.9334921546493224\n",
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"X value is -2.974822311556336\n",
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"X value is -3.015325865325209\n",
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"X value is -3.055019348018705\n",
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"X value is -3.093918961058331\n",
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"X value is -3.1320405818371646\n",
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"X value is -3.1693997702004215\n",
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"X value is -3.206011774796413\n",
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"X value is -3.2418915393004846\n",
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"X value is -3.277053708514475\n",
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"X value is -3.3115126343441856\n",
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"X value is -3.345282381657302\n",
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"X value is -3.378376734024156\n",
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"X value is -3.4108091993436727\n",
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"X value is -3.534181005309697\n",
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"X value is -3.6479752309744553\n",
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"X value is -3.675015726354966\n",
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"X value is -3.7015154118278666\n",
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"X value is -3.7274851035913095\n",
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"X value is -3.7529354015194833\n",
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"X value is -3.7778766934890937\n",
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"X value is -3.8023191596193118\n",
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"X value is -3.8262727764269258\n",
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"X value is -3.8497473208983872\n",
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"X value is -3.8727523744804193\n",
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"X value is -3.895297326990811\n",
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"X value is -3.917391380450995\n",
"Iteration 100 \n",
"X value is -3.939043552841975\n",
"Iteration 101 \n",
"X value is -3.9602626817851356\n",
"Iteration 102 \n",
"X value is -3.981057428149433\n",
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"X value is -4.001436279586445\n",
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"X value is -4.021407553994716\n",
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"X value is -4.040979402914822\n",
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"X value is -4.060159814856525\n",
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"X value is -4.078956618559395\n",
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"X value is -4.097377486188207\n",
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"X value is -4.115429936464443\n",
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"X value is -4.133121337735154\n",
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"X value is -4.150458910980451\n",
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"X value is -4.167449732760842\n",
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"X value is -4.1841007381056246\n",
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"X value is -4.200418723343512\n",
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"X value is -4.444182804704305\n",
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"X value is -4.999934805060202\n",
"Iteration 581 \n",
"X value is -4.999936108958998\n",
"Iteration 582 \n",
"X value is -4.999937386779818\n",
"Iteration 583 \n",
"X value is -4.999938639044221\n",
"Iteration 584 \n",
"X value is -4.999939866263337\n",
"Iteration 585 \n",
"X value is -4.99994106893807\n",
"Iteration 586 \n",
"X value is -4.999942247559309\n",
"Iteration 587 \n",
"X value is -4.999943402608123\n",
"Iteration 588 \n",
"X value is -4.9999445345559606\n",
"Iteration 589 \n",
"X value is -4.999945643864842\n",
"Iteration 590 \n",
"X value is -4.999946730987545\n",
"Iteration 591 \n",
"X value is -4.999947796367794\n",
"Iteration 592 \n",
"X value is -4.999948840440438\n",
"Iteration 593 \n",
"X value is -4.999949863631629\n",
"Iteration 594 \n",
"X value is -4.999950866358997\n",
"Iteration 595 \n",
"X value is -4.9999518490318176\n",
"The local minimum occurs at -4.9999518490318176\n"
]
}
],
"source": [
"while previous_step_size > precision and iters < max_iters:\n",
" prev_x = cur_x\n",
" cur_x = cur_x - gamma * df(prev_x)\n",
" previous_step_size = abs(cur_x - prev_x)\n",
" iters = iters+1\n",
" print(\"Iteration\",iters,\"\\nX value is\",cur_x)\n",
" \n",
"print(\"The local minimum occurs at\", cur_x)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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