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@artirj
Created January 5, 2017 10:46
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Gradient descent vs Newton Raphson\n",
"\n",
"This compares these two popular methods for solving non-linear equations.\n",
"\n",
"We have a function $F(x)=x^2-4$. For gradient-descent, we cast the problem as the minimisation of the cost function $J(x)=\\frac{1}{2}\\lVert{F(x)-0}\\Vert^2$. But because we are cheap we know that is the same as minimising $J(x)=\\frac{1}{2}F(x)^2$ Its gradient is thus $\\nabla J(x)=F(x)\\nabla F(x)$"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn; seaborn.set()\n",
"h=1e-6 \n",
"nit=10\n",
"def gradient(func,x):\n",
" #f(x+h)-f(x-h) /2h\n",
" #return (func(x+h)-func(x-h))/(2*h)\n",
" return 2.0*x\n",
"\n",
"def func(x):\n",
" return np.square(x)\n",
"\n",
"def gradient_descent(func,x,alpha):\n",
" x_full=[x]\n",
" #Minimise distance to zero\n",
" for i in range(nit):\n",
" x-=alpha*func(x)*gradient(func,x) \n",
" x_full.append(x)\n",
" return x,x_full\n",
"\n",
"def newton_raphson(func,x,a):\n",
" x_full=[x]\n",
" for i in range(nit):\n",
" x-=a*func(x)/gradient(func,x)\n",
" x_full.append(x)\n",
" return x,x_full"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final solution and cost of Gradient descent:: 1.914218\n",
"Final solution and cost of Newton-Raphson: 0.004883\n"
]
},
{
"data": {
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isZLi+tIOn3/RGTG4mY3Y7HaWal9zERERkU7VY0Lm8OB4DK2b16eWZXT4/BB/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"text/plain": [
"<matplotlib.figure.Figure at 0x7f1bae2486a0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x,x_full=gradient_descent(func,5,0.005)\n",
"x2,x2_full=newton_raphson(func,5,1)\n",
"print(\"Final solution and cost of Gradient descent:: %f\" %x)\n",
"print(\"Final solution and cost of Newton-Raphson: %f\"%x2)\n",
"#x_full=np.array(x_full)\n",
"its=np.arange(nit+1)\n",
"plt.plot(its,x_full)\n",
"plt.plot(its,x2_full)\n",
"plt.legend(('Gradient descent','Newton Raphson'))\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But let's try now a different learning rate"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final solution and cost of Gradient descent:: 0.000000\n",
"Final solution and cost of Newton-Raphson: 0.004883\n"
]
},
{
"data": {
"image/png": 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e9smMXJ6mdr5SqXrdmd/vdBKJMi7p8nJemWWsK70NEonyYiG7i4b0tnh6zuTu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8AAAg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\nHUMoAAAAfPf/Gp8W/Pchrq4AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1bae318da0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x,x_full=gradient_descent(func,5,0.02)\n",
"x2,x2_full=newton_raphson(func,5,1.)\n",
"print(\"Final solution and cost of Gradient descent:: %f\" %x)\n",
"print(\"Final solution and cost of Newton-Raphson: %f\"%x2)\n",
"x3,x3_full=gradient_descent(func,5,0.04)\n",
"x4,x4_full=newton_raphson(func,5,1.99)\n",
"its=np.arange(nit+1)\n",
"plt.plot(its,x_full)\n",
"plt.plot(its,x2_full)\n",
"plt.plot(its,x3_full)\n",
"plt.plot(its,x4_full)\n",
"plt.legend(('Gradient descent (alpha=0.02)','Newton Raphson (alpha=1)','Gradient descent (alpha=0.03)','Newton Raphson (alpha=1.99)'))\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The performance of the algorithms seems to depends strongly on their learning rate. Very high values cause oscillations and instabilities. Low values cause slow convergence.\n",
"Let's now try 2D. $F(x,y)=x^2+y^2-4$. This is still a scalar function."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"h=1e-6 \n",
"nitmax=400\n",
"start=np.array([4,-5],dtype='float128')\n",
"x_full_sys=np.array(start)\n",
"\n",
"def gradient(x_loc,limit=False):\n",
" #f(x+h)-f(x-h) /2h\n",
" #return (func(x+h)-func(x-h))/(2*h)\n",
" grad=np.array(2.0*x_loc,dtype='float128')\n",
" if limit==False:\n",
" return grad\n",
" else:\n",
" larger=np.abs(grad)>1\n",
" grad[larger]=np.sign(grad[larger])*1\n",
" smaller=np.abs(grad)<0.01\n",
" grad[smaller]=np.sign(grad[smaller])*0.01\n",
" return grad\n",
" \n",
"\n",
"def func(x):\n",
" if x.ndim==1:\n",
" return np.square(x,dtype='float128').sum()-4\n",
" else:\n",
" return np.square(x,dtype='float128').sum(axis=1)-4\n",
" \n",
"def cost(x):\n",
" \n",
" return np.square(func(x),dtype='float128'),np.dot(func(x),gradient(x))\n",
"\n",
"\n",
"def acc(xp):\n",
" global x_full_sys\n",
" x_full_sys=np.vstack((x_full_sys,xp))\n",
" return 0\n",
"def norm(x):\n",
" return np.sqrt(x.dot(x))\n",
"\n",
"def gradient_descent(func,start,alpha,tol):\n",
" x_full=np.array(start)\n",
" x=np.array(start)\n",
" #Minimise distance to zero\n",
" i=0\n",
" while cost(x)[0]>tol and i<nitmax:\n",
" x-=alpha*np.dot(func(x),gradient(x,limit=True))\n",
" x_full=np.vstack((x_full,x))\n",
" i+=1\n",
" return x,x_full,i\n",
"def minv(array):\n",
" if array.ndim==1:\n",
" return 1/array\n",
" else:\n",
" return np.linalg.inv(array)\n",
"\n",
"def newton_raphson(func,start,gamma,tol):\n",
" x_full=np.array(start)\n",
" x=np.array(start)\n",
" i=0\n",
" while cost(x)[0]>tol and i<nitmax:\n",
" x-=gamma*np.dot(func(x),minv(gradient(x,limit=True)))\n",
" x_full=np.vstack((x_full,x))\n",
" i+=1\n",
" return x,x_full,i"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
" fun: 2.180295075193263e-15\n",
" hess_inv: array([[ 0.6341257, 0.45734287],\n",
" [ 0.45734287, 0.42832141]], dtype=float128)\n",
" jac: array([ 1.1667712e-07, -1.458464e-07], dtype=float128)\n",
" message: 'Optimization terminated successfully.'\n",
" nfev: 11\n",
" nit: 10\n",
" njev: 11\n",
" status: 0\n",
" success: True\n",
" x: array([ 1.2493901, -1.5617376], dtype=float128)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import scipy.optimize\n",
"x_full_sys=np.array(start)\n",
"a=scipy.optimize.minimize(cost,start,callback=acc,tol=1e-6,jac=1)\n",
"nit_a=a.nit\n",
"x_sys=a.x\n",
"a"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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SrVt3unfvQatWrWncuAkzZz7Jxo0b6Nbt/wD4+OMPuPTSK/D5fDz66Giuv/7P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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1bae483a20>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost, solution, and iterations of Newton-Raphson: 0.000001 [ 0.92239283 -1.7743928] 12\n",
"Final cost, solution, and iterations of Gradient descent: 0.000001 [ 0.82306432 -1.8230643] 28\n",
"Final cost, solution, and iterations of Minimize: 0.000000 [ 1.2493901 -1.5617376] 10\n"
]
}
],
"source": [
"x,x_full,nit_1=gradient_descent(func,start,0.05,1e-6)\n",
"x2,x2_full,nit_2=newton_raphson(func,start,0.1,1e-6)\n",
"its_1=np.arange(nit_1+1)\n",
"its_2=np.arange(nit_2+1)\n",
"\n",
"its_sys=np.arange(nit_a+1)\n",
"plt.plot(its_1,cost(x_full)[0])\n",
"plt.plot(its_2,cost(x2_full)[0])\n",
"plt.plot(its_sys,cost(x_full_sys)[0])\n",
"plt.legend(('Gradient descent','Newton Raphson','System'))\n",
"plt.show()\n",
"print(\"Final cost, solution, and iterations of Newton-Raphson: %f\" %cost(x2)[0],x2,nit_2)\n",
"print(\"Final cost, solution, and iterations of Gradient descent: %f\"%cost(x)[0],x,nit_1)\n",
"print(\"Final cost, solution, and iterations of Minimize: %f\"%cost(x_sys)[0],x_sys,nit_a)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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67GzOv/MGhuzsu25Ll5JMzOSPS1xP7ehI7Smfm1SQjhgxmoCAQFavXsnvv69m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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1bae1b8518>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x_full[:,0],x_full[:,1],marker='o')\n",
"plt.plot(x2_full[:,0],x2_full[:,1],marker='o')\n",
"plt.plot(x_full_sys[:,0],x_full_sys[:,1],marker='o')\n",
"plt.plot(start[0],start[1], marker='x',linestyle='None')\n",
"plt.plot(0,0, marker='x',linestyle='None')\n",
"circle=plt.Circle(((0,0)), radius=2,fill=False)\n",
"plt.gca().add_patch(circle)\n",
"plt.legend(('Gradient descent','Newton Raphson','System'),loc=0)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000 loops, best of 3: 1.19 ms per loop\n",
"1000 loops, best of 3: 528 µs per loop\n"
]
}
],
"source": [
"%timeit x,x_full,nit_1=gradient_descent(func,start,0.05,1e-6)\n",
"%timeit x2,x2_full,nit_2=newton_raphson(func,start,0.1,1e-6)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000 loops, best of 3: 1.27 ms per loop\n"
]
}
],
"source": [
"%timeit a=scipy.optimize.minimize(cost,start,callback=acc,tol=1e-6,jac=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Seemingly, then, as much as I like NR, the pre-made solvers behave much better.\n",
"The pre-made solver, furthermore, does not require special finetuning of parameters.\n",
"Plot twist: going by the time it takes, newton-raphson seems to be actually faster... because we have finetuned its parameter to make it really fast\n",
"\n",
"So if one knows a priori about the problem, one can finetune custom solvers to go quite fast. Premade algorithms will be more stable, no matter what the starting conditions. On average, they will win."
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [conda root]",
"language": "python",
"name": "conda-root-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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