Problems that are slow to parse in cvxpy

gistfile1.json

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   "cells": [
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These are a list of problems where parsing is slow in CVXPY.\n",
      "\n",
      "The first four are all from the Convex.jl paper.\n",
      "\n",
      "Be careful when profiling CVXPY that you create a new problem each time.\n",
      "When you solve a problem it caches the cone program matrices, so if you solve it again it doesn't run the matrix stuffing algorithm."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Preparation:\n",
      "from cvxpy import *\n",
      "import numpy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Summation.\n",
      "n = 10000\n",
      "x = Variable()\n",
      "e = 0\n",
      "for i in range(n):\n",
      "    e = e + x\n",
      "p = Problem(Minimize(norm(e-1,2)), [x>=0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "# This generates the cone program matrices but doesn't solve the cone program.\n",
      "# 99% of the time here is spent in the matrix stuffing algorithm (going from LinOps to the final matrix).\n",
      "p = Problem(Minimize(norm(e-1,2)), [x>=0])\n",
      "p.get_problem_data(ECOS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 4.07 s per loop\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can replace %%timeit with %%prun to profile the script."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Indexing.\n",
      "n = 10000\n",
      "x = Variable(n)\n",
      "e = 0\n",
      "for i in range(n):\n",
      "    e += x[i];"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "p = Problem(Minimize(norm(e-1,2)), [x>=0])\n",
      "p.get_problem_data(ECOS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 10.9 s per loop\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Transpose\n",
      "n = 500\n",
      "A = numpy.random.randn(n,n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "X = Variable(n,n)\n",
      "p = Problem(Minimize(norm(X.T-A,'fro')), [X[1,1] == 1])\n",
      "p.get_problem_data(ECOS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 332 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Matrix constraint.\n",
      "# CVXPY actually does a pretty good job with this one.\n",
      "# Convex.jl and CVX are slower (at least when they were profiled for the paper).\n",
      "n = 500\n",
      "A = numpy.random.randn(n,n)\n",
      "B = numpy.random.randn(n,n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "X = Variable(n,n)\n",
      "p = Problem(Minimize(norm(X-A,'fro')), [X == B])\n",
      "p.get_problem_data(ECOS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 230 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Matrix product.\n",
      "# This one is a bit different, because the issue is that the coefficient for A.T*X*A has n^4 nonzeros.\n",
      "# A fix is to introduce the variable A.T*X = Y, and rewrite A.T*X*A as Y*A. \n",
      "# This will only add 2n^3 nonzeros.\n",
      "n = 50\n",
      "A = numpy.random.randn(n,n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "X = Variable(n,n)\n",
      "p = Problem(Minimize(norm(X,'fro')), [A.T*X*A >= 1])\n",
      "p.get_problem_data(ECOS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 3.37 s per loop\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# SVM with indexing.\n",
      "def gen_data(n):\n",
      "    pos = numpy.random.multivariate_normal([1.0,2.0],numpy.eye(2),size=n)\n",
      "    neg = numpy.random.multivariate_normal([-1.0,1.0],numpy.eye(2),size=n)\n",
      "    return pos, neg\n",
      "\n",
      "N = 2\n",
      "C = 10\n",
      "pos, neg = gen_data(500)\n",
      "\n",
      "w = Variable(N)\n",
      "b = Variable()\n",
      "xi_pos = Variable(pos.shape[0])\n",
      "xi_neg = Variable(neg.shape[0])\n",
      "cost = sum_squares(w) + C*sum_entries(xi_pos) + C*sum_entries(xi_neg)\n",
      "constrs = []\n",
      "for j in range(pos.shape[0]):\n",
      "    constrs += [w.T*pos[j,:] - b >= 1 - xi_pos[j]]\n",
      "    \n",
      "for j in range(neg.shape[0]):\n",
      "    constrs += [-(w.T*neg[j,:] - b) >= 1 - xi_neg[j]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "p = Problem(Minimize(cost), constrs)\n",
      "p.get_problem_data(ECOS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 3.71 s per loop\n"
       ]
      }
     ],
     "prompt_number": 35
    }
   ],
   "metadata": {}
  }
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