polys.ipynb

{
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   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Compat.AsyncCondition is deprecated, use Base.AsyncCondition instead.\n",
      "  likely near /Users/sascha/.julia/v0.6/IJulia/src/kernel.jl:31\n",
      "WARNING: Compat.AsyncCondition is deprecated, use Base.AsyncCondition instead.\n",
      "  likely near /Users/sascha/.julia/v0.6/IJulia/src/kernel.jl:31\n"
     ]
    }
   ],
   "source": [
    "import TypedPolynomials\n",
    "import DynamicPolynomials\n",
    "import MultivariatePolynomials\n",
    "using StaticArrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Compat.AsyncCondition is deprecated, use Base.AsyncCondition instead.\n",
      "  likely near /Users/sascha/.julia/v0.6/IJulia/src/kernel.jl:31\n",
      "WARNING: Compat.AsyncCondition is deprecated, use Base.AsyncCondition instead.\n",
      "  likely near /Users/sascha/.julia/v0.6/IJulia/src/kernel.jl:31\n"
     ]
    }
   ],
   "source": [
    "using BenchmarkTools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element MVector{3,Complex{Float64}}:\n",
       " 0.337939+0.625128im\n",
       " 0.921418+0.218451im\n",
       " 0.478515+0.968963im"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = @MVector rand(Complex128, 2)\n",
    "u = @MVector rand(Complex128, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = 5\n",
    "b = 4\n",
    "c = 3;\n",
    "\n",
    "#create the variables\n",
    "@TypedPolynomials.polyvar sθ cθ x0\n",
    "f1 = cθ^2 + sθ^2 - (1.0 + 0im)\n",
    "f2 = (a*cθ - b)^2 + (1.0 + 0im) * (a*sθ)^2 - c^2;\n",
    "h1 = cθ^2 + sθ^2 - (1.0 + 0im)*x0^2\n",
    "h2 = (a*cθ - b)^2 + (1.0 + 0im) * (a*sθ)^2 - c^2*x0^2;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "eval2 (generic function with 1 method)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eval2(p1, p2, x) = p1(MultivariatePolynomials.variables(p1)=>x) .+ p2(MultivariatePolynomials.variables(p2)=>x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  64 bytes\n",
       "  allocs estimate:  4\n",
       "  --------------\n",
       "  minimum time:     157.665 ns (0.00% GC)\n",
       "  median time:      161.373 ns (0.00% GC)\n",
       "  mean time:        180.488 ns (2.56% GC)\n",
       "  maximum time:     2.834 μs (84.59% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     796"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark eval2($f1, $f2, $v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  2.44 KiB\n",
       "  allocs estimate:  116\n",
       "  --------------\n",
       "  minimum time:     7.794 μs (0.00% GC)\n",
       "  median time:      8.053 μs (0.00% GC)\n",
       "  mean time:        9.156 μs (3.65% GC)\n",
       "  maximum time:     923.998 μs (96.95% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     4"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark eval2($h1, $h2, $u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#create the variables\n",
    "@DynamicPolynomials.polyvar sθ cθ x0\n",
    "# now construct the system\n",
    "# In the future we will be able to avoid to explicitly write complex coefficients\n",
    "f3 = cθ^2 + sθ^2 - (1.0 + 0im)\n",
    "f4 = (a*cθ - b)^2 + (1.0 + 0im) * (a*sθ)^2 - c^2;\n",
    "h3 = cθ^2 + sθ^2 - (1.0 + 0im)*x0^2\n",
    "h4 = (a*cθ - b)^2 + (1.0 + 0im) * (a*sθ)^2 - c^2*x0^2;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  640 bytes\n",
       "  allocs estimate:  16\n",
       "  --------------\n",
       "  minimum time:     383.030 ns (0.00% GC)\n",
       "  median time:      401.042 ns (0.00% GC)\n",
       "  mean time:        520.024 ns (17.16% GC)\n",
       "  maximum time:     19.084 μs (95.78% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     203"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark eval2($f3, $f4, $u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  800 bytes\n",
       "  allocs estimate:  20\n",
       "  --------------\n",
       "  minimum time:     464.838 ns (0.00% GC)\n",
       "  median time:      478.604 ns (0.00% GC)\n",
       "  mean time:        607.164 ns (15.62% GC)\n",
       "  maximum time:     27.392 μs (95.75% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     197"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark eval2($h3, $h4, $u)"
   ]
  }
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