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EM5813/Gradient_descent.ipynb

Forked from rohanjoseph93/Gradient_descent.ipynb
Created June 23, 2020 00:22
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Gradient_descent.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"cur_x = 3 # The algorithm starts at x=3\n",
"rate = 0.01 # Learning rate\n",
"precision = 0.000001 #This tells us when to stop the algorithm\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) #Gradient of our function"
]
},
{
"cell_type": "code",
"execution_count": 4,
"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",
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"X value is -0.8927561797744419\n",
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"X value is -0.9749010561789531\n",
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"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",
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"X value is -1.9046087932144176\n",
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"X value is -1.9665166173501292\n",
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"X value is -2.0271862850031264\n",
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"X value is -2.0866425593030637\n",
"Iteration 51 \n",
"X value is -2.1449097081170025\n",
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"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 -3.534181005309697\n",
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"X value is -3.6479752309744553\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",
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"X value is -3.939043552841975\n",
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"X value is -3.9602626817851356\n",
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"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 -4.060159814856525\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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]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration 218 \n",
"X value is -4.902191975337089\n",
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"X value is -4.999933474551226\n",
"Iteration 580 \n",
"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 #Store current x value in prev_x\n",
" cur_x = cur_x - rate * df(prev_x) #Grad descent\n",
" previous_step_size = abs(cur_x - prev_x) #Change in x\n",
" iters = iters+1 #iteration count\n",
" print(\"Iteration\",iters,\"\\nX value is\",cur_x) #Print iterations\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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