Development_OptimizationSingleTarget.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from lowEBMs.Packages.Configuration import importer, add_sellersparameters, parameterinterpolatorstepwise, reset\n",
    "from lowEBMs.Packages.Configuration import import_parallelparameter, allocate_parallelparameter, write_parallelparameter\n",
    "from lowEBMs.Packages.Variables import variable_importer\n",
    "from lowEBMs.Packages.RK4 import rk4alg, controlrun\n",
    "from lowEBMs.Packages.ModelEquation import model_equation\n",
    "from lowEBMs.Packages.Variables import Vars,reset, trackerreset, datareset\n",
    "from lowEBMs.Packages.Functions import plotmeanstd\n",
    "from lowEBMs import update_plotstyle\n",
    "import builtins\n",
    "import matplotlib\n",
    "update_plotstyle()\n",
    "matplotlib.rcParams['lines.linewidth']=1.1\n",
    "time_sec_year=60*60*24*365\n",
    "def moving_average(signal, period):\n",
    "    buffer = [np.nan] * period\n",
    "    for i in range(period,len(signal)):\n",
    "        buffer.append(signal[i-period:i].mean())\n",
    "    return buffer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(a,b):\n",
    "    data=(a)**2+b**4\n",
    "    return data\n",
    "    \n",
    "def coremodule(config,P0,P_pert,Pmin,Pmax,labels,ZMT,GMT,grid,maxlength,targetmode,target,targetfunction,elevation,precision,num_paras,gamma0,control,controlconfig):\n",
    "    F=np.reshape(np.zeros(maxlength*(2*num_paras+1)),(maxlength,2*num_paras+1))\n",
    "    #F=np.reshape(np.zeros(maxlength*(num_paras+1)),(maxlength,num_paras+1))\n",
    "    dF=np.reshape(np.zeros(maxlength*(num_paras)),(maxlength,num_paras))\n",
    "    P=np.reshape(np.zeros(maxlength*(num_paras)),(maxlength,num_paras))\n",
    "    Ptrans=np.reshape(np.zeros(maxlength*(num_paras)),(maxlength,num_paras))\n",
    "    gamma=np.zeros(maxlength)\n",
    "    if targetmode=='Single':\n",
    "        dataout=np.reshape(np.zeros(maxlength*(2*num_paras+1)),(maxlength,(2*num_paras+1)))\n",
    "    elif targetmode=='ZMT':\n",
    "        dataout=np.reshape(np.zeros(maxlength*len(grid)*(2*num_paras+1)),(maxlength,(2*num_paras+1),len(grid)))\n",
    "    elif targetmode=='GMT':\n",
    "        dataout=np.reshape(np.zeros(maxlength*int(number_of_integration/data_readout)),(maxlength,int(number_of_integration/data_readout)))\n",
    "    #data=np.reshape(np.zeros(maxlength*(2*num_paras+1)),(maxlength,2*num_paras+1))\n",
    "    for i in range(maxlength):\n",
    "        if i==0:\n",
    "            P[i]=P0\n",
    "            Ptrans[i]=(P0-Pmin)/(Pmax-Pmin)\n",
    "            #Ptrans_pert1=(P_pert-Pmin)/(Pmax-Pmin)\n",
    "            Ptrans_pert=Ptrans[i]*P_pert[0]/P0[0]\n",
    "            #print(Ptrans_pert1,Ptrans_pert)\n",
    "        #data[i][0]=(func(*P[i]))\n",
    "        \"\"\"for k in range(0,num_paras):\n",
    "            Pk=np.zeros(num_paras)\n",
    "            Pk[k]=P_pert[k]\n",
    "            data[i][k+1]=(func(*P[i]+Pk))\"\"\"\n",
    "  \n",
    "        \n",
    "        \n",
    "        #for k in range(0,2*num_paras):\n",
    "            #Pk=np.zeros(num_paras)\n",
    "            #Pk[int(k/2)]=(-1)**k*P_pert[int(k/2)]\n",
    "            #print(Pk)\n",
    "            \n",
    "            #data[i]=(func(*P[i]+Pk))\n",
    "        data=run_model(config,P[i],P_pert,labels,ZMT,GMT,targetmode,control,controlconfig)\n",
    "        dataout[i]=data\n",
    "        F[i]=target_comparison(data,targetmode,target,targetfunction,grid,num_paras,elevation)\n",
    "\n",
    "        #dF[i]=local_gradient1(F[i],P_pert)\n",
    "        dF[i]=local_gradient1(F[i],Ptrans_pert)\n",
    "        \n",
    "        if i==0:\n",
    "            gamma[i]=gamma0\n",
    "        else:\n",
    "            #gamma[i]=step_weighting(dF[i-1],dF[i],P[i-1],P[i])\n",
    "            gamma[i]=step_weighting(dF[i-1],dF[i],Ptrans[i-1],Ptrans[i])\n",
    "            \n",
    "        if precision_check(dF[0],dF[i],precision):\n",
    "            print('stop',i)\n",
    "            P=P[:i]\n",
    "            Ptrans=Ptrans[:i]\n",
    "            F=F[:i]\n",
    "            gamma=gamma[:i]\n",
    "            break\n",
    "                \n",
    "        #P_next=new_parameters(P[i],gamma[i],dF[i])        \n",
    "        Ptrans_next=new_parameters(Ptrans[i],gamma[i],dF[i])\n",
    "\n",
    "        for k in range(num_paras):\n",
    "            if Ptrans_next[k]<0:\n",
    "                Ptrans_next[k]=0.\n",
    "            if Ptrans_next[k]>1:\n",
    "                Ptrans_next[k]=1.\n",
    "\n",
    "        if i<maxlength-1:\n",
    "            Ptrans[i+1]=Ptrans_next\n",
    "            P[i+1]=Pmin+Ptrans_next*(Pmax-Pmin)\n",
    "            #P[i+1]=P_next    \n",
    "            print(P[i+1])\n",
    "            print(Ptrans[i+1])\n",
    "    return F, dF, P , Ptrans, gamma, dataout\n",
    "    \n",
    "def target_comparison(data,targetmode,target,targetfunction,grid,num_paras,elevation):\n",
    "    F=np.zeros(2*num_paras+1)\n",
    "    if targetfunction=='LeastSquare':\n",
    "        if targetmode=='Single':\n",
    "            F=(np.array(data)-target)**2\n",
    "        elif targetmode=='ZMT':\n",
    "            for i in range(len(data)):\n",
    "                data[i]=data[i]+elevation\n",
    "            for i in range(len(F)):\n",
    "                F[i]=np.sum(((data[i]-target)*np.cos(grid*np.pi/180)/np.mean(np.cos(grid*np.pi/180)))**2)\n",
    "        elif targetmode=='GMT':\n",
    "            for i in range(len(F)):\n",
    "                F[i]=np.sum((data[i]-target)**2)\n",
    "\n",
    "    print(F)\n",
    "    return F\n",
    "\n",
    "def parameter_gradient(P0,P1):\n",
    "    dP=P1-P0\n",
    "    return dP\n",
    "\n",
    "def local_gradient(F,P_pert):\n",
    "    dF=(F[1:]-F[0])/P_pert\n",
    "    return dF\n",
    "\n",
    "def local_gradient1(F,P_pert):\n",
    "    dF=np.zeros(len(P_pert))\n",
    "    for k in range(len(P_pert)):\n",
    "        #print(2*(k+1)-1,2*(k+1))\n",
    "        #print(F[2*(k+1)-1]-F[2*(k+1)])\n",
    "        dF[k]=(F[2*(k+1)-1]-F[2*(k+1)])/(2*P_pert[k])\n",
    "    return dF\n",
    "\n",
    "def step_weighting(dF0,dF1,P0,P1):\n",
    "    gamma=np.abs(np.dot(P1-P0,dF1-dF0)/np.dot(dF1-dF0,dF1-dF0))\n",
    "    return gamma\n",
    "\n",
    "def precision_check(dF0,dF,precision):\n",
    "    dFabs=np.sqrt(np.dot(dF,dF))\n",
    "    dF0abs=np.sqrt(np.dot(dF0,dF0))\n",
    "    if dFabs/dF0abs <= precision:\n",
    "        return True\n",
    "    \n",
    "def new_parameters(P,gamma,dF):\n",
    "    #print(gamma,dF)\n",
    "    P_next=P-gamma*dF\n",
    "    return P_next\n",
    "#def gradient_descent(xn,)\n",
    "\n",
    "def run_model(config,P,P_pert,labels,ZMT,GMT,targetmode,control,controlconfig):\n",
    "    \n",
    "    if control==True:\n",
    "        config_CTRL=importer(controlconfig)\n",
    "        variable_importer(config_CTRL,parallel=False)\n",
    "\n",
    "        config_CTRL,ParasCTRL=add_sellersparameters(config_CTRL,\\\n",
    "                                        parameterinterpolatorstepwise,'SellersParameterization.ini',2,0,True,True)\n",
    "        config_CTRL=add_parameters(config_CTRL,P,labels)\n",
    "        data_CTRL=rk4alg(model_equation,config_CTRL['eqparam'],config_CTRL['funccomp'])\n",
    "        ZMT,GMT=data_CTRL[1][-1],data_CTRL[2][-1]\n",
    "        \n",
    "    P_config=reshape_parameters(P,P_pert)\n",
    "    setup={'number_of_parameters': len(P), 'number_of_cycles': 1, 'number_of_parallels': len(P)*2+1}\n",
    "    \n",
    "    datareset()\n",
    "    variable_importer(config,parallel=True,parallel_config=setup)\n",
    "    config=add_parameters(config,P_config,labels)\n",
    "    \n",
    "    if control==True:\n",
    "        Vars.T,Vars.T_global=np.array([ZMT]*int(len(P)*2+1)),np.array([GMT]*int(len(P)*2+1))\n",
    "    else:\n",
    "        Vars.T,Vars.T_global=ZMT,GMT\n",
    "    data=rk4alg(model_equation,config['eqparam'],config['funccomp'])\n",
    "    if targetmode=='Single':\n",
    "        data_out=data[2][-1]\n",
    "    elif targetmode=='ZMT':\n",
    "        data_out=data[1][-1]\n",
    "    elif targetmode=='GMT':\n",
    "        print(data[0][int(number_of_integration/2/data_readout)]/time_sec_year)\n",
    "        data_out=data[2][:-1,0]-data[2][0,0]\n",
    "\n",
    "    return data_out\n",
    "\n",
    "def reshape_parameters(P,P_pert):\n",
    "    num_para=len(P)\n",
    "    #Pk=np.zeros(num_paras)\n",
    "    P_config=np.reshape(np.zeros(num_para*(2*num_para+1)),(num_para,2*num_para+1))\n",
    "    #Ensemble_parameters=dict()\n",
    "    for i in range(num_para):\n",
    "        #Pk[int(k/2)]=(-1)**k*P_pert[int(k/2)]\n",
    "        P_config[i]=np.array([P[i]]*(2*num_para+1))\n",
    "        P_config[i][i*2+1]=P[i]+P_pert[i]\n",
    "        P_config[i][i*2+2]=P[i]-P_pert[i]\n",
    "    #print(P_config)\n",
    "    \"\"\"\n",
    "    j=1\n",
    "    for i in list(x0.keys()):\n",
    "        Ensemble_parameters.update({i:np.array([x0[i]]*(num_para+1))})\n",
    "        Ensemble_parameters[i][j]=x0[i]+dx[i]\n",
    "        j+=1\n",
    "    \"\"\"                             \n",
    "    return P_config\n",
    "             \n",
    "def add_parameters(config,P_config,labels):\n",
    "    num_para=len(P_config)\n",
    "    \"\"\"for i in list(Parameterlabels.keys()):\n",
    "        for j in Parameterlabels[i]:\n",
    "            config['funccomp']['funcparam'][i][j]=Ensemble_parameters\"\"\"\n",
    "    for i in range(num_para):\n",
    "        if labels[i][0][:4]=='func':\n",
    "            config['funccomp']['funcparam'][labels[i][0]][labels[i][1]]=P_config[i]\n",
    "        if labels[i][0]=='eqparam':\n",
    "            config[labels[i][0]][labels[i][1]]=P_config[i]\n",
    "    return config\n",
    "#Parameterlabels={'func1':['A','B'],'func2':['factor_oc','factor_kwv','factor_kair']}\n",
    "#Parameterlabels=[['func1','a'],['func1','b'],['func2','factor_oc'],['func2','factor_kwv'],['func2','factor_kair']]\n",
    "#Start_parameters=[230,2.5,1,1,1]\n",
    "#Start_pertubation=[1,0.1,0.05,0.05,0.05]\n",
    "#y=reshape_parameters(Start_parameters,Start_pertubation) \n",
    "#config_new=add_parameters(Config_Try1_base,y,Parameterlabels)\n",
    "#print(y)\n",
    "#print(config_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2. 2.]\n",
      "[1.8399968  0.71925753]\n",
      "[1.81281913 0.70825445]\n",
      "[1.31510759 0.51297074]\n",
      "[1.03693674 0.45577368]\n",
      "[0.77060153 0.40704015]\n",
      "[0.58343549 0.37420155]\n",
      "[0.43692919 0.34781564]\n",
      "[0.32715967 0.32661492]\n",
      "[0.24345494 0.30874067]\n",
      "[0.1798926  0.29334745]\n",
      "[0.1313287  0.27972058]\n",
      "[0.09406076 0.26734682]\n",
      "[0.06525677 0.25576543]\n",
      "[0.04286612 0.24452764]\n",
      "[0.02551825 0.23313945]\n",
      "[0.01256549 0.22105196]\n",
      "[0.00407107 0.20774095]\n",
      "stop 18\n",
      "[0.00407107 0.20774095] [3.53079192e-06 5.96279173e-06 4.47829184e-06 7.32595175e-06\n",
      " 1.58483182e-06]\n",
      "0 0.001879040160209674\n"
     ]
    }
   ],
   "source": [
    "precision=1e-7\n",
    "maxlength=int(1e4)\n",
    "target=0\n",
    "num_params=2\n",
    "P0=np.array([2,2])\n",
    "P_pert=P0/100\n",
    "gamma0=1e-3\n",
    "F,dF,P,gamma,data=coremodule(0,P0,P_pert,0,0,0,maxlength,target,'LeastSquare',precision,num_params,gamma0)\n",
    "print(P[-1],F[-1])\n",
    "print(target,func(*P[-1]))\n",
    "#print(gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Configuration from: Dev_Data/Optimization/Try1_Budyko_CTRL.ini\n",
      "Loading Parameters from: /Home/siv32/bsc029/.local/lib/python3.6/site-packages/lowEBMs/Tutorials/Config/Data/SellersParameterization.ini\n",
      "Starting simulation...\n"
     ]
    },
    {
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       "model_id": "a384425abf924eaf929ec55d39dc25b7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=43800), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Simulation finished within 49.36830019950867 seconds\n"
     ]
    }
   ],
   "source": [
    "config_CTRL=importer('Dev_Data/Optimization/Try1_Budyko_CTRL.ini')\n",
    "#setup={'number_of_parameters': 5, 'number_of_cycles': 1, 'number_of_parallels': 6}\n",
    "#allocated,setup=allocate_parallelparameter(raw)\n",
    "variable_importer(config_CTRL,parallel=False)#,parallel_config=setup)\n",
    "config_CTRL,ParasCTRL=add_sellersparameters(config_CTRL,\\\n",
    "                                    parameterinterpolatorstepwise,'SellersParameterization.ini',2,0,True,True)\n",
    "\n",
    "labels=[['eqparam','c_ao'],['func1','a'],['func1','b'],['func2','factor_oc'],['func2','factor_kwv'],['func2','factor_kair']]\n",
    "#P0=np.array([205,1.5,1,1,1])\n",
    "P0=np.array([70*4.2e6,205,1.5,1.165,1.165,1.165])\n",
    "#for i in range(2):\n",
    "#    Try['funccomp']['funcparam'][labels[i][0]][labels[i][1]]=P0[i]\n",
    "#P_pert=P0/1000\n",
    "#P_config=reshape_parameters(P0,P_pert)\n",
    "config_CTRL=add_parameters(config_CTRL,P0,labels)\n",
    "trackerreset()\n",
    "builtins.Runtime_Tracker=0\n",
    "data_CTRL=rk4alg(model_equation,config_CTRL['eqparam'],config_CTRL['funccomp'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "Zero_ZMT,Zero_GMT=np.array([data_CTRL[1][-1]]*13),np.array([data_CTRL[2][-1]]*13)\n",
    "#out=np.reshape(np.zeros(19*6),(6,19))\n",
    "#for i in range(6):\n",
    "#    out[i]=[Zero_GMT[i],*Zero_ZMT[i]]\n",
    "#np.savetxt('Data/Optimization_InputTemp.txt',out,delimiter=',')\"\"\"\n",
    "#print(Zero_ZMT,Zero_GMT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Configuration from: Dev_Data/Optimization/Try1_Budyko.ini\n",
      "Loading Parameters from: /Home/siv32/bsc029/.local/lib/python3.6/site-packages/lowEBMs/Tutorials/Config/Data/SellersParameterization.ini\n",
      "Starting simulation...\n"
     ]
    },
    {
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       "model_id": "89b86052ba314132800ed9c12fa3f9c5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=18250), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-24-fbebff7348db>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m F, dF, P, Ptrans , gamma, data=coremodule(config_base,P0,P_pert,Pmin,Pmax,labels,Zero_ZMT,Zero_GMT,grid,\\\n\u001b[0;32m---> 25\u001b[0;31m     maxlength,targetmode,target,targetfunction,elevation,precision,num_params,gamma0,control,controlconfig)\n\u001b[0m",
      "\u001b[0;32m<ipython-input-22-7336456b29cf>\u001b[0m in \u001b[0;36mcoremodule\u001b[0;34m(config, P0, P_pert, Pmin, Pmax, labels, ZMT, GMT, grid, maxlength, targetmode, target, targetfunction, elevation, precision, num_paras, gamma0, control, controlconfig)\u001b[0m\n\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m             \u001b[0;31m#data[i]=(func(*P[i]+Pk))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 40\u001b[0;31m         \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrun_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconfig\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP_pert\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mZMT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mGMT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtargetmode\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcontrol\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcontrolconfig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     41\u001b[0m         \u001b[0mdataout\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     42\u001b[0m         \u001b[0mF\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtarget_comparison\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtargetmode\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtarget\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtargetfunction\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mnum_paras\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0melevation\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-22-7336456b29cf>\u001b[0m in \u001b[0;36mrun_model\u001b[0;34m(config, P, P_pert, labels, ZMT, GMT, targetmode, control, controlconfig)\u001b[0m\n\u001b[1;32m    148\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    149\u001b[0m         \u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT_global\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mZMT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mGMT\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 150\u001b[0;31m     \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrk4alg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel_equation\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mconfig\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'eqparam'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mconfig\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'funccomp'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    151\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mtargetmode\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'Single'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    152\u001b[0m         \u001b[0mdata_out\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Desktop/Internship_Workspace/Model/Low-dimensional-EBMs/lowEBMs/Packages/RK4.py\u001b[0m in \u001b[0;36mrk4alg\u001b[0;34m(func, eqparam, funccomp)\u001b[0m\n\u001b[1;32m    188\u001b[0m         \u001b[0mbuiltins\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mRuntime_Tracker\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    189\u001b[0m         \u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mT0\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mk3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 190\u001b[0;31m         \u001b[0mk4\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meqparam\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfunccomp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    191\u001b[0m         \u001b[0mbuiltins\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mRuntime_Tracker\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Desktop/Internship_Workspace/Model/Low-dimensional-EBMs/lowEBMs/Packages/ModelEquation.py\u001b[0m in \u001b[0;36mmodel_equation\u001b[0;34m(eqparam, funccomp)\u001b[0m\n\u001b[1;32m     49\u001b[0m             \u001b[0mC_ao\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mC_ao\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC_ao\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumber_of_parallels\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mC_ao\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     50\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunclist\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 51\u001b[0;31m             \u001b[0my\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mfunclist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'func'\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfuncparam\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'func'\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m    \u001b[0;31m#Calling the selected function and sum them up\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     52\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mC_ao\u001b[0m           \u001b[0;31m#output of y, weighted with the heat capacity\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Desktop/Internship_Workspace/Model/Low-dimensional-EBMs/lowEBMs/Packages/Functions.py\u001b[0m in \u001b[0;36msellers\u001b[0;34m(funcparam)\u001b[0m\n\u001b[1;32m   1177\u001b[0m             \u001b[0;31m#calculating the current temperature differences and wind patterns\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1178\u001b[0m             \u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtempdif\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mearthsystem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtemperature_difference_latitudes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1179\u001b[0;31m             \u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmeridional\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mearthsystem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmeridionalwind_sel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mre\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1180\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1181\u001b[0m             \u001b[0;31m#calculating the 3 transfer components\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Desktop/Internship_Workspace/Model/Low-dimensional-EBMs/lowEBMs/Packages/Functions.py\u001b[0m in \u001b[0;36mmeridionalwind_sel\u001b[0;34m(a, re)\u001b[0m\n\u001b[1;32m   2694\u001b[0m                         \u001b[0mv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtempdif\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mT_av\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2695\u001b[0m                     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2696\u001b[0;31m                         \u001b[0mv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mVars\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtempdif\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mT_av\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2697\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2698\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "labels=[['func1','a'],['func1','b'],['func2','factor_oc'],['func2','factor_kwv'],['func2','factor_kair']]\n",
    "P0=np.array([70*4.2e6,205,1.5,1.165,1.165,1.165])\n",
    "P_pert=P0/1000\n",
    "Pmin=np.array([30*4.2e6,190,1.3,0.9,0.9,0.9])\n",
    "Pmax=np.array([100*4.2e6,250,4,1.3,1.3,1.3])\n",
    "precision=1e-6\n",
    "maxlength=int(30)\n",
    "targetmode='Single'\n",
    "target=286.39\n",
    "targetfunction='LeastSquare'\n",
    "num_params=6\n",
    "gamma0=1e-3\n",
    "setup={'number_of_parameters': 6, 'number_of_cycles': 1, 'number_of_parallels': 13}\n",
    "grid=0\n",
    "elevation=0\n",
    "control=False\n",
    "controlconfig=0\n",
    "\n",
    "config_base=importer('Dev_Data/Optimization/Try1_Budyko.ini')\n",
    "variable_importer(config_base,parallel=True,parallel_config=setup)\n",
    "config_base,ParasCTRL=add_sellersparameters(config_base,\\\n",
    "                                    parameterinterpolatorstepwise,'SellersParameterization.ini',2,0,True,True)\n",
    "\n",
    "F, dF, P, Ptrans , gamma, data=coremodule(config_base,P0,P_pert,Pmin,Pmax,labels,Zero_ZMT,Zero_GMT,grid,\\\n",
    "    maxlength,targetmode,target,targetfunction,elevation,precision,num_params,gamma0,control,controlconfig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#print(local_gradient1(data[2],P_pert))\n",
    "fig,ax=plt.subplots(2,3,figsize=(16,9))\n",
    "for k in range(2):\n",
    "    for j in range(3):\n",
    "        for i in range(30):\n",
    "            ax[k][j].scatter(P[i][k+j],local_gradient1(data[i],P_pert)[k+j])\n",
    "#plt.plot(np.arange(30),data[:,0]-target)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting simulation...\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2a37f597b49c4a00b7aebdd34170ee34",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=3650), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Simulation finished within 11.577050924301147 seconds\n"
     ]
    }
   ],
   "source": [
    "data=run_model(config_base,P0,P_pert,labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[201.63311768 201.23311721 204.38376606 201.63311766 201.63311767\n",
      " 201.63311758]\n"
     ]
    }
   ],
   "source": [
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Configuration from: Dev_Data/Optimization/Try1_Budyko.ini\n",
      "Loading Parameters from: /Home/siv32/bsc029/.local/lib/python3.6/site-packages/lowEBMs/Tutorials/Config/Data/SellersParameterization.ini\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'dx' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-140-718a58f863f5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     18\u001b[0m     \u001b[0;31m#raw=import_parallelparameter('Dev_Data/Volc_Rout/Ensemble_Budyko_Pinatubo.ini')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m     \u001b[0mStart_parameters\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m     \u001b[0mStart_pertubation\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m     \u001b[0mEnsemble_parameters\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreshape_parameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mStart_parameters\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mStart_pertubation\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m     \u001b[0mConfig_new\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0madd_parameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mConfig_Try1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mEnsemble_parameters\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mParameterlabels\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'dx' is not defined"
     ]
    }
   ],
   "source": [
    "Config_Try1_base=importer('Dev_Data/Optimization/Try1_Budyko.ini')\n",
    "setup={'number_of_parameters': 5, 'number_of_cycles': 1, 'number_of_parallels': 6}\n",
    "#allocated,setup=allocate_parallelparameter(raw)\n",
    "variable_importer(Config_Try1_base,parallel=True,parallel_config=setup)\n",
    "Config_Try1,ParasCTRL=add_sellersparameters(Config_Try1_base,\\\n",
    "                                    parameterinterpolatorstepwise,'SellersParameterization.ini',2,0,True,True)\n",
    "\n",
    "Parameterlabels=[['func1','a'],['func1','b'],['func2','factor_oc'],['func2','factor_kwv'],['func2','factor_kair']]\n",
    "Initial_parameters=[230,2.5,1,1,1]\n",
    "Initial_pertubation=[1,0.1,0.05,0.05,0.05]\n",
    "Start_parameters=[]\n",
    "Start_pertubation=[]\n",
    "Ensemble_parameters=[]\n",
    "Start_parameters.append(Initial_parameters)\n",
    "Start_pertubation.append(Initial_pertubation)\n",
    "Target=15+273.15\n",
    "for i in range(2):\n",
    "    #raw=import_parallelparameter('Dev_Data/Volc_Rout/Ensemble_Budyko_Pinatubo.ini')\n",
    "    Start_parameters.append(x)\n",
    "    Start_pertubation.append(dx)\n",
    "    Ensemble_parameters.append(reshape_parameters(Start_parameters[i],Start_pertubation[i]))\n",
    "    Config_new=add_parameters(Config_Try1,Ensemble_parameters[i],Parameterlabels)\n",
    "    #Config_Try1=write_parallelparameter(Config_Try1,allocated,setup)\n",
    "    \n",
    "    trackerreset()\n",
    "    builtins.Runtime_Tracker=0\n",
    "    Try1=rk4alg(model_equation,Config_new['eqparam'],Config_new['funccomp'])\n",
    "    \n",
    "    T=Try1[2][-1]\n",
    "    S=deviation_function(T,Target,'Residual')\n",
    "    dF=calculate_gradient(S,0)\n",
    "    x,dx=new_parameters(Start_parameters[i],Start_pertubation[i],dF,0)\n",
    "    \n",
    "    \"\"\"setup={'number_of_parameters': 4, 'number_of_cycles': 1, 'number_of_parallels': 4}\n",
    "    variable_importer(configFuncDiffCTRL,parallel=True,parallel_config=setup)\n",
    "\n",
    "    configFuncDiffCTRL,ParasCTRL=add_sellersparameters(configFuncDiffCTRL,parameterinterpolatorstepwise,'SellersParameterization.ini',5,0,True,True)\n",
    "\n",
    "    Func1_4=np.array([[True,False,False,False],[False,True,False,False],[False,False,True,False],[False,False,False,True]])\n",
    "    for i in range(1,5):\n",
    "        configFuncDiffCTRL['funccomp']['funcparam']['func'+str(i)]['activation']=Func1_4[i-1]\"\"\"\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.005630112809163453\n",
      "0.00993827628197613\n",
      "0.024922214766503567\n",
      "0.04759448143982094\n",
      "0.10029767881882037\n",
      "0.1940339476686329\n",
      "0.35812582172776086\n",
      "0.47898058414066236\n",
      "0.636372168641202\n",
      "2.2330326209482934\n",
      "4.165174655667334\n",
      "0.7898948347868491\n",
      "0.4978253243717003\n",
      "0.49875530392581874\n",
      "15.883618570096505\n",
      "27.582652459850706\n",
      "68.4072107374806\n",
      "0.5219913560671585\n",
      "0.4998198606455038\n",
      "0.4998536319935656\n",
      "232.14855328264395\n",
      "398.1532080849546\n",
      "1158.4246746119416\n",
      "Minimum at -1.8385907364006245e-06 0.004576915113284614 23\n"
     ]
    }
   ],
   "source": [
    "next_x_0 = 1  # We start the search at x=6\n",
    "next_x=next_x_0\n",
    "next_y_0 = 4\n",
    "next_y=next_y_0\n",
    "gamma = 0.001  # Step size multiplier\n",
    "precision = 1e-8  # Desired precision of result\n",
    "max_iters = 10000  # Maximum number of iterations\n",
    "\n",
    "# Derivative function\n",
    "#F = lambda x,y: x**2+y**4\n",
    "#dfx = lambda x: 2*x\n",
    "#dfy = lambda y: 4*y**3\n",
    "F = lambda x,y: x**2+y**4+x**2*y**2\n",
    "dfx = lambda x,y: 2*x+2*x*y**2\n",
    "dfy = lambda x,y: 4*y**3+x**2*2*y\n",
    "\n",
    "x=[]\n",
    "y=[]\n",
    "for i in range(max_iters):\n",
    "    current_x = next_x\n",
    "    current_y = next_y\n",
    "    x.append(current_x)\n",
    "    y.append(current_y)\n",
    "    if i==0:\n",
    "        df0=np.sqrt(dfx(current_x,current_y)**2+dfy(current_x,current_y)**2)\n",
    "    if i>=1:\n",
    "        gamma=abs((x[i]-x[i-1])*(dfx(x[i],y[i])-dfx(x[i-1],y[i-1]))+(y[i]-y[i-1])*(dfy(x[i],y[i])-dfy(x[i-1],y[i-1])))\\\n",
    "                    /((dfx(x[i],y[i])-dfx(x[i-1],y[i-1]))**2+(dfy(x[i],y[i])-dfy(x[i-1],y[i-1]))**2)\n",
    "        print(gamma)\n",
    "    #print(np.sqrt(dfx(current_x,current_y)**2+dfy(current_x,current_y)**2))\n",
    "        #gamma_y=abs())/abs(dfy(y[i])-dfy(y[i-1]))**2\n",
    "    next_x = current_x - gamma * dfx(current_x,current_y)\n",
    "    next_y = current_y - gamma * dfy(current_y,current_y)\n",
    "    Fabs=abs(F(next_x,next_y)-F(current_x,current_y))\n",
    "    df=np.sqrt(dfx(current_x,current_y)**2+dfy(current_x,current_y)**2)\n",
    "    if df/df0 <= precision:\n",
    "        break\n",
    "    #if abs(step_x)<= precision and abs(step_y)<= precision :\n",
    "    #    break\n",
    "\n",
    "print(\"Minimum at\", next_x, next_y, i)\n",
    "t=np.linspace(-10,10,100)\n",
    "#plt.plot(t,df(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, 1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.scatter(next_x_0,next_y_0)\n",
    "plt.xlim(-1,1)\n",
    "plt.ylim(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx=np.array([np.linspace(-3,3,100)]*100)\n",
    "yy=np.transpose(np.array([np.linspace(-3,3,100)]*100))\n",
    "z=F(xx,yy)\n",
    "#print(z)\n",
    "plt.contourf(xx,yy,z)\n",
    "heatmap = plt.pcolor(z)\n",
    "cbar = plt.colorbar(heatmap)\n",
    "plt.clim(0,1)\n",
    "#plt.cbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "625000\n",
      "629392.5438200647\n",
      "625017.5000699877\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(-5,5,1000)\n",
    "x0=5\n",
    "plt.plot(x,x**4)\n",
    "def Res(x,x_t):\n",
    "    S=(x-x_t)**2\n",
    "    return S\n",
    "plt.plot(x,Res(x**4,0))\n",
    "S=[Res(x0**4,0),Res((x0+0.01)**4,0),Res((x0-0.01)**4,0)]\n",
    "print(2*(x0**4-0)*4*x0**3)\n",
    "print((S[1]-S[0])/0.01)\n",
    "print((S[1]-S[2])/0.02)\n",
    "#print(4*x0**3)\n",
    "#print(((x0+0.01)**4-x0**4)/(0.01))\n",
    "#print(((x0+0.01)**4-(x0-0.01)**4)/(2*0.01))"
   ]
  },
  {
   "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",
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