Localsaparamestim1variable.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using DiffEqSensitivity, OrdinaryDiffEq, DiffEqParamEstim,\n",
    "      ParameterizedFunctions, BlackBoxOptim, NLopt, Calculus, ForwardDiff, Optim, BenchmarkTools, RecursiveArrayTools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr}) (generic function with 2 methods)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitz  =  @ode_def FitzhughNagumo begin\n",
    "  dv = v - v^3/3 -w + 0.5\n",
    "  dw = 0.08*(v +  a - 0.8*w)\n",
    "end a "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mArray{Float64,1}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mtrue\u001b[0m\n",
       "timespan: (0.0, 3.0)\n",
       "u0: [1.0, 1.0]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p  =  [0.7]                      # Parameters used to construct the dataset\n",
    "r0 = [1.0; 1.0]                     # initial value\n",
    "tspan = (0.0, 3.0)                 # sample of 3000 observations over the (0,30) timespan\n",
    "prob = ODEProblem(fitz, r0, tspan,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: 1st order linear\n",
       "t: 1000-element Array{Float64,1}:\n",
       " 0.0                 \n",
       " 0.003003003003003003\n",
       " 0.006006006006006006\n",
       " 0.009009009009009009\n",
       " 0.012012012012012012\n",
       " 0.015015015015015015\n",
       " 0.018018018018018018\n",
       " 0.021021021021021023\n",
       " 0.024024024024024024\n",
       " 0.02702702702702703 \n",
       " 0.03003003003003003 \n",
       " 0.03303303303303303 \n",
       " 0.036036036036036036\n",
       " ⋮                   \n",
       " 2.966966966966967   \n",
       " 2.96996996996997    \n",
       " 2.972972972972973   \n",
       " 2.975975975975976   \n",
       " 2.978978978978979   \n",
       " 2.981981981981982   \n",
       " 2.984984984984985   \n",
       " 2.987987987987988   \n",
       " 2.990990990990991   \n",
       " 2.993993993993994   \n",
       " 2.996996996996997   \n",
       " 3.0                 \n",
       "u: 1000-element Array{Array{Float64,1},1}:\n",
       " [1.0, 1.0, 0.0, 0.0]                       \n",
       " [1.0005, 1.00022, -3.60698e-7, 0.000240217]\n",
       " [1.001, 1.00043, -1.4427e-6, 0.000480388]  \n",
       " [1.0015, 1.00065, -3.24584e-6, 0.000720512]\n",
       " [1.002, 1.00087, -5.76998e-6, 0.00096059]  \n",
       " [1.00249, 1.00108, -9.01496e-6, 0.00120062]\n",
       " [1.00299, 1.0013, -1.29806e-5, 0.0014406]  \n",
       " [1.00349, 1.00152, -1.76667e-5, 0.00168054]\n",
       " [1.00398, 1.00173, -2.30731e-5, 0.00192043]\n",
       " [1.00448, 1.00195, -2.91997e-5, 0.00216027]\n",
       " [1.00497, 1.00217, -3.60461e-5, 0.00240007]\n",
       " [1.00547, 1.00238, -4.36122e-5, 0.00263981]\n",
       " [1.00596, 1.0026, -5.18979e-5, 0.00287951] \n",
       " ⋮                                          \n",
       " [1.11497, 1.22039, -0.237672, 0.196355]    \n",
       " [1.11477, 1.22059, -0.238089, 0.196501]    \n",
       " [1.11457, 1.22079, -0.238506, 0.196646]    \n",
       " [1.11437, 1.22099, -0.238923, 0.196791]    \n",
       " [1.11416, 1.2212, -0.23934, 0.196936]      \n",
       " [1.11396, 1.2214, -0.239759, 0.197081]     \n",
       " [1.11375, 1.2216, -0.240177, 0.197225]     \n",
       " [1.11355, 1.2218, -0.240596, 0.19737]      \n",
       " [1.11334, 1.222, -0.241016, 0.197514]      \n",
       " [1.11313, 1.2222, -0.241436, 0.197659]     \n",
       " [1.11293, 1.2224, -0.241856, 0.197803]     \n",
       " [1.11272, 1.2226, -0.242277, 0.197947]     "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "global t = collect(range(0, stop=3.0, length=1000))\n",
    "data = Array(solve(prob,Tsit5(),saveat=t,abstol=1e-3,reltol=1e-3))\n",
    "ourprob = ODELocalSensitivityProblem(fitz,r0,tspan,p)\n",
    "oursol = solve(ourprob,Tsit5(),saveat=t,abstol=1e-6,reltol=1e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "myl2loss (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function myl2loss(oursol_type, data)\n",
    "    my_l2loss = zero(eltype(data))\n",
    "    for i in 1:size(data)[1]\n",
    "        for j in 1:size(data)[2]\n",
    "            my_l2loss += (oursol_type[i,j] - data[i,j])^2\n",
    "        end\n",
    "    end\n",
    "    my_l2loss\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#15 (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_generator = (prob,p) -> remake(ourprob;p=p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#17 (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "costfunc = function (p)\n",
    "        tmp_prob = prob_generator(ourprob,p)\n",
    "        sol = solve(tmp_prob,Tsit5(),saveat=t,abstol=1e-6,reltol=1e-6)\n",
    "        loss = myl2loss(sol,data)\n",
    "        loss\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "costfunc_gradient (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function costfunc_gradient(p,grad)\n",
    "        tmp_prob = prob_generator(ourprob,p)\n",
    "        sol = solve(tmp_prob,Tsit5(),saveat=t,abstol=1e-6,reltol=1e-6)\n",
    "        myl2lossgradient!(grad,sol,data,length(p))\n",
    "        costfunc(p)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "myl2lossgradient! (generic function with 1 method)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function myl2lossgradient!(grad,oursol_type,data,num_p)\n",
    "    data_x_size = size(data)[1]\n",
    "    my_grad = -1 .*2 .*(data .- oursol_type[1:data_x_size,:])\n",
    "    for i in 1:num_p\n",
    "        for j in i*data_x_size+1:(i+1)*data_x_size\n",
    "            for k in 1:size(my_grad)[2]\n",
    "                grad[i] += my_grad[j-i*data_x_size,k]*oursol_type[j,k]\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0034862362357598866"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oursol[3,100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4591534767036414e-7"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = Array{Float64}(undef,1)\n",
    "p = [0.7]\n",
    "costfunc_gradient(p,out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 0.00010425580660985826"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 2.1219957915e-314"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = Array{Float64}(undef,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "Calculus.finite_difference!(costfunc,p,out,:central)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 0.00010425648566874457"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  575.72 KiB\n",
       "  allocs estimate:  2886\n",
       "  --------------\n",
       "  minimum time:     463.392 μs (0.00% GC)\n",
       "  median time:      534.183 μs (0.00% GC)\n",
       "  mean time:        614.679 μs (10.46% GC)\n",
       "  maximum time:     7.181 ms (84.50% GC)\n",
       "  --------------\n",
       "  samples:          8086\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = [0.5]\n",
    "@benchmark begin\n",
    "    out = Array{Float64}(undef,2)\n",
    "    costfunc_gradient(p,out)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1077934720011857"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = Array{Float64}(undef,1)\n",
    "costfunc_gradient(p,out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " -10.980977186241835"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 2.244801728e-314"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = Array{Float64}(undef,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  544.19 KiB\n",
       "  allocs estimate:  2887\n",
       "  --------------\n",
       "  minimum time:     450.946 μs (0.00% GC)\n",
       "  median time:      507.216 μs (0.00% GC)\n",
       "  mean time:        582.422 μs (10.36% GC)\n",
       "  maximum time:     5.007 ms (85.99% GC)\n",
       "  --------------\n",
       "  samples:          8552\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark Calculus.finite_difference!(costfunc,p,out,:central)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " -10.980978094091105"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.107793472001184, [0.5], :XTOL_REACHED)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt = Opt(:LD_MMA, 1)\n",
    "min_objective!(opt, costfunc_gradient)\n",
    "lower_bounds!(opt,[0.0])\n",
    "upper_bounds!(opt,[1.0])\n",
    "xtol_rel!(opt,1e-12)\n",
    "maxeval!(opt, 100000)\n",
    "(minf,minx,ret) = NLopt.optimize(opt,[0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "g! (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function g!(grad,p)\n",
    "    costfunc_gradient(p,grad)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: First function call produced NaNs. Exiting.\n",
      "└ @ OrdinaryDiffEq /Users/vaibhav/.julia/packages/OrdinaryDiffEq/c746g/src/initdt.jl:74\n",
      "┌ Warning: Automatic dt set the starting dt as NaN, causing instability.\n",
      "└ @ OrdinaryDiffEq /Users/vaibhav/.julia/packages/OrdinaryDiffEq/c746g/src/solve.jl:328\n",
      "┌ Warning: Instability detected. Aborting\n",
      "└ @ DiffEqBase /Users/vaibhav/.julia/packages/DiffEqBase/YSk7M/src/integrator_interface.jl:128\n"
     ]
    },
    {
     "ename": "BoundsError",
     "evalue": "BoundsError: attempt to access 1-element Array{Array{Float64,1},1} at index [2]",
     "output_type": "error",
     "traceback": [
      "BoundsError: attempt to access 1-element Array{Array{Float64,1},1} at index [2]",
      "",
      "Stacktrace:",
      " [1] getindex at ./array.jl:731 [inlined]",
      " [2] getindex at /Users/vaibhav/.julia/packages/RecursiveArrayTools/ukc19/src/vector_of_array.jl:44 [inlined]",
      " [3] myl2loss(::ODESolution{Float64,2,Array{Array{Float64,1},1},Nothing,Nothing,Array{Float64,1},Array{Array{Array{Float64,1},1},1},ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Array{Float64,1},ODELocalSensitvityFunction{true,FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr},Nothing,getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##8#14\")),DiffEqDiffTools.UJacobianWrapper{FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr},Float64,Array{Float64,1}},DiffEqDiffTools.ParamJacobianWrapper{FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr},Float64,Array{Float64,1}},Nothing,Nothing,DiffEqSensitivity.SensitivityAlg{0,true,DataType},Array{Float64,1},Float64,LinearAlgebra.UniformScaling{Bool}},CallbackSet{Tuple{},Tuple{}},DiffEqBase.StandardODEProblem},Tsit5,OrdinaryDiffEq.InterpolationData{ODELocalSensitvityFunction{true,FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr},Nothing,getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##8#14\")),DiffEqDiffTools.UJacobianWrapper{FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr},Float64,Array{Float64,1}},DiffEqDiffTools.ParamJacobianWrapper{FitzhughNagumo{getfield(Main, Symbol(\"##3#9\")),getfield(Main, Symbol(\"##4#10\")),getfield(Main, Symbol(\"##5#11\")),getfield(Main, Symbol(\"##6#12\")),getfield(Main, Symbol(\"##7#13\")),getfield(Main, Symbol(\"##8#14\")),Expr,Expr},Float64,Array{Float64,1}},Nothing,Nothing,DiffEqSensitivity.SensitivityAlg{0,true,DataType},Array{Float64,1},Float64,LinearAlgebra.UniformScaling{Bool}},Array{Array{Float64,1},1},Array{Float64,1},Array{Array{Array{Float64,1},1},1},OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}}}}, ::Array{Float64,2}) at ./In[5]:5",
      " [4] (::getfield(Main, Symbol(\"##17#18\")))(::Array{Float64,1}) at ./In[7]:4",
      " [5] value!!(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at /Users/vaibhav/.julia/packages/NLSolversBase/Cvvki/src/interface.jl:9",
      " [6] value!(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at /Users/vaibhav/.julia/packages/NLSolversBase/Cvvki/src/interface.jl:31",
      " [7] value!(::Optim.ManifoldObjective{OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}}, ::Array{Float64,1}) at /Users/vaibhav/.julia/packages/Optim/fabGe/src/Manifolds.jl:31",
      " [8] (::getfield(LineSearches, Symbol(\"#ϕ#1\")){Optim.ManifoldObjective{OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}},Array{Float64,1},Array{Float64,1},Array{Float64,1}})(::Float64) at /Users/vaibhav/.julia/packages/LineSearches/SrdrY/src/LineSearches.jl:25",
      " [9] _hzI12(::Float64, ::Optim.ManifoldObjective{OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Float64, ::Float64, ::Float64, ::Float64, ::Float64, ::Float64, ::Bool, ::Base.RefValue{Bool}) at /Users/vaibhav/.julia/packages/LineSearches/SrdrY/src/initialguess.jl:225",
      " [10] InitialHagerZhang at /Users/vaibhav/.julia/packages/LineSearches/SrdrY/src/initialguess.jl:196 [inlined]",
      " [11] perform_linesearch!(::Optim.ConjugateGradientState{Array{Float64,1},Float64,Array{Float64,1}}, ::ConjugateGradient{Float64,Nothing,getfield(Optim, Symbol(\"##33#35\")),LineSearches.InitialHagerZhang{Float64},LineSearches.HagerZhang{Float64,Base.RefValue{Bool}}}, ::Optim.ManifoldObjective{OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}}) at /Users/vaibhav/.julia/packages/Optim/fabGe/src/utilities/perform_linesearch.jl:32",
      " [12] update_state!(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Optim.ConjugateGradientState{Array{Float64,1},Float64,Array{Float64,1}}, ::ConjugateGradient{Float64,Nothing,getfield(Optim, Symbol(\"##33#35\")),LineSearches.InitialHagerZhang{Float64},LineSearches.HagerZhang{Float64,Base.RefValue{Bool}}}) at /Users/vaibhav/.julia/packages/Optim/fabGe/src/multivariate/solvers/first_order/cg.jl:153",
      " [13] optimize(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}, ::ConjugateGradient{Float64,Nothing,getfield(Optim, Symbol(\"##33#35\")),LineSearches.InitialHagerZhang{Float64},LineSearches.HagerZhang{Float64,Base.RefValue{Bool}}}, ::Optim.Options{Float64,Nothing}, ::Optim.ConjugateGradientState{Array{Float64,1},Float64,Array{Float64,1}}) at /Users/vaibhav/.julia/packages/Optim/fabGe/src/multivariate/optimize/optimize.jl:57",
      " [14] optimize at /Users/vaibhav/.julia/packages/Optim/fabGe/src/multivariate/optimize/optimize.jl:33 [inlined]",
      " [15] #optimize#88(::Bool, ::Symbol, ::Function, ::Function, ::Function, ::Array{Float64,1}, ::ConjugateGradient{Float64,Nothing,getfield(Optim, Symbol(\"##33#35\")),LineSearches.InitialHagerZhang{Float64},LineSearches.HagerZhang{Float64,Base.RefValue{Bool}}}, ::Optim.Options{Float64,Nothing}) at /Users/vaibhav/.julia/packages/Optim/fabGe/src/multivariate/optimize/interface.jl:121",
      " [16] optimize(::Function, ::Function, ::Array{Float64,1}, ::ConjugateGradient{Float64,Nothing,getfield(Optim, Symbol(\"##33#35\")),LineSearches.InitialHagerZhang{Float64},LineSearches.HagerZhang{Float64,Base.RefValue{Bool}}}, ::Optim.Options{Float64,Nothing}) at /Users/vaibhav/.julia/packages/Optim/fabGe/src/multivariate/optimize/interface.jl:119 (repeats 2 times)",
      " [17] top-level scope at In[24]:1"
     ]
    }
   ],
   "source": [
    "Optim.optimize(costfunc, g!, [0.5], ConjugateGradient())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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