Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:07.711707Z",
     "start_time": "2021-04-23T13:47:06.938597Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from swsm import SWSM # this library"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Determining key wake steering parameters from cross-sections\n",
    "\n",
    "This section describes how to use the Multiple 1D Gaussian code on vertical cross-sections to obtain the key wake steering parameters used in SWSM.\n",
    "In this example, we have simulated the interaction between a Neutral Boundary Layer and a NREL 5MW turbine (hub height = 90 m, rotor diameter = 126 m).\n",
    "Three yaw angles are considered: 0$^{\\circ}$ ($yaw\\_00.nc$), +30$^{\\circ}$ ($yaw\\_30.nc$) and -30$^{\\circ}$ ($yaw\\_-30.nc$). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.423357Z",
     "start_time": "2021-04-23T13:47:07.713069Z"
    },
    "code_folding": [
     0
    ],
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Determining key wake steering parameters\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/luuk/anaconda3/lib/python3.8/site-packages/scipy/optimize/minpack.py:828: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  warnings.warn('Covariance of the parameters could not be estimated',\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done\n"
     ]
    }
   ],
   "source": [
    "sims = ['yaw_00','yaw_30','yaw_-30'] ## Names of simulations\n",
    "testcase = SWSM()\n",
    "testcase.determine_key_parameters(sims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object SWSM is the main API for this model as is here renamed as wake_model. \n",
    "The first step is to determine the key wake steering parameters from an existing dataset, which is done in $.determine\\_key\\_parameters(sims)$. This function read the netcdf files in $load\\_crosssections(path\\_to\\_file)$. In this example, the netCDF files contain the following information:\n",
    "* x: distance downstream of turbine normalized by rotor diameter; x = 1 .. 10 D\n",
    "* y: lateral location, centered around turbine location and normalized by rotor diameter; -2 D < y < 2 D\n",
    "* z: z: vertical location, centered around hub height and normalized by rotor diameter; -0.7 D < z < 2 D\n",
    "* $u_{normdef}$: the wake deficit normalized by the wind speed at hub height: $u_{normdef} = \\frac{u_{wake} - u_{\\infty}}{u_{\\infty,hh}}$.\n",
    "This variable contains data on each grid point (∆ = 5 m), structured as (z, y, x).\n",
    "\n",
    "If a different data structure is used, it is advised to make changes in this function.\n",
    "\n",
    "Next, $.determine\\_key\\_parameters(sims)$ calls the  $multi1Dgaus(z, y, u)$  function. This function computes the key wake steering parameters for each cross-section.\n",
    "\n",
    "The $determine\\_key\\_parameters(sims)$ function is a wrapper that loops over all simulations (sims) and downstream distances and collects all key wake steering paramters in a dataframe saved as $.key\\_parameters$.\n",
    "\n",
    "This dataframe is structured as follows:\n",
    "* The rows contain the simulations\n",
    "* The columns contain all key wake steering parameters for all downstream locations\n",
    "\n",
    "For example, this test case results a dataframe of size 3x90:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.444494Z",
     "start_time": "2021-04-23T13:47:09.424886Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A_z1</th>\n",
       "      <th>mu_y1</th>\n",
       "      <th>mu_z1</th>\n",
       "      <th>sigma_y1</th>\n",
       "      <th>sigma_z1</th>\n",
       "      <th>c1</th>\n",
       "      <th>t1</th>\n",
       "      <th>s_a1</th>\n",
       "      <th>s_b1</th>\n",
       "      <th>A_z2</th>\n",
       "      <th>...</th>\n",
       "      <th>s_b9</th>\n",
       "      <th>A_z10</th>\n",
       "      <th>mu_y10</th>\n",
       "      <th>mu_z10</th>\n",
       "      <th>sigma_y10</th>\n",
       "      <th>sigma_z10</th>\n",
       "      <th>c10</th>\n",
       "      <th>t10</th>\n",
       "      <th>s_a10</th>\n",
       "      <th>s_b10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>yaw_00</th>\n",
       "      <td>-0.606948</td>\n",
       "      <td>-0.025295</td>\n",
       "      <td>0.058914</td>\n",
       "      <td>0.444261</td>\n",
       "      <td>0.611884</td>\n",
       "      <td>0.090099</td>\n",
       "      <td>-0.020752</td>\n",
       "      <td>-2.180993</td>\n",
       "      <td>0.012736</td>\n",
       "      <td>-0.638517</td>\n",
       "      <td>...</td>\n",
       "      <td>0.083182</td>\n",
       "      <td>-0.192698</td>\n",
       "      <td>-0.067398</td>\n",
       "      <td>0.052294</td>\n",
       "      <td>0.563203</td>\n",
       "      <td>0.635817</td>\n",
       "      <td>0.092917</td>\n",
       "      <td>0.003870</td>\n",
       "      <td>0.049468</td>\n",
       "      <td>0.043853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yaw_30</th>\n",
       "      <td>-0.481027</td>\n",
       "      <td>0.047651</td>\n",
       "      <td>0.032145</td>\n",
       "      <td>0.355417</td>\n",
       "      <td>0.625283</td>\n",
       "      <td>0.035730</td>\n",
       "      <td>0.002431</td>\n",
       "      <td>-2.155771</td>\n",
       "      <td>0.050517</td>\n",
       "      <td>-0.499684</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.291038</td>\n",
       "      <td>-0.161804</td>\n",
       "      <td>0.398014</td>\n",
       "      <td>0.109881</td>\n",
       "      <td>0.426172</td>\n",
       "      <td>0.770508</td>\n",
       "      <td>-0.868518</td>\n",
       "      <td>0.474557</td>\n",
       "      <td>0.171546</td>\n",
       "      <td>-0.282656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yaw_-30</th>\n",
       "      <td>-0.481809</td>\n",
       "      <td>-0.094644</td>\n",
       "      <td>0.066922</td>\n",
       "      <td>0.352879</td>\n",
       "      <td>0.564390</td>\n",
       "      <td>0.143943</td>\n",
       "      <td>-0.022738</td>\n",
       "      <td>-2.145079</td>\n",
       "      <td>-0.068347</td>\n",
       "      <td>-0.497378</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.611295</td>\n",
       "      <td>-0.142702</td>\n",
       "      <td>-0.707627</td>\n",
       "      <td>0.208671</td>\n",
       "      <td>0.501055</td>\n",
       "      <td>0.563897</td>\n",
       "      <td>1.218063</td>\n",
       "      <td>-0.450020</td>\n",
       "      <td>0.916674</td>\n",
       "      <td>-0.605879</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 90 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             A_z1     mu_y1     mu_z1  sigma_y1  sigma_z1        c1        t1  \\\n",
       "yaw_00  -0.606948 -0.025295  0.058914  0.444261  0.611884  0.090099 -0.020752   \n",
       "yaw_30  -0.481027  0.047651  0.032145  0.355417  0.625283  0.035730  0.002431   \n",
       "yaw_-30 -0.481809 -0.094644  0.066922  0.352879  0.564390  0.143943 -0.022738   \n",
       "\n",
       "             s_a1      s_b1      A_z2  ...      s_b9     A_z10    mu_y10  \\\n",
       "yaw_00  -2.180993  0.012736 -0.638517  ...  0.083182 -0.192698 -0.067398   \n",
       "yaw_30  -2.155771  0.050517 -0.499684  ... -0.291038 -0.161804  0.398014   \n",
       "yaw_-30 -2.145079 -0.068347 -0.497378  ... -0.611295 -0.142702 -0.707627   \n",
       "\n",
       "           mu_z10  sigma_y10  sigma_z10       c10       t10     s_a10  \\\n",
       "yaw_00   0.052294   0.563203   0.635817  0.092917  0.003870  0.049468   \n",
       "yaw_30   0.109881   0.426172   0.770508 -0.868518  0.474557  0.171546   \n",
       "yaw_-30  0.208671   0.501055   0.563897  1.218063 -0.450020  0.916674   \n",
       "\n",
       "            s_b10  \n",
       "yaw_00   0.043853  \n",
       "yaw_30  -0.282656  \n",
       "yaw_-30 -0.605879  \n",
       "\n",
       "[3 rows x 90 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# round(testcase.key_parameters,3)\n",
    "testcase.key_parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Specify input parameters\n",
    "In a separate dataframe, we have to specify the input parameters. For the test case, this information\n",
    "is provided in the file input.csv. It simply contains the $yaw$, $shear$ and $C_T$ values for these simulations. As discussed in the paper,\n",
    "other input parameters can be used as long as one cluster is represented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.457259Z",
     "start_time": "2021-04-23T13:47:09.445793Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>yaw</th>\n",
       "      <th>shear</th>\n",
       "      <th>Ct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>yaw_00</th>\n",
       "      <td>0</td>\n",
       "      <td>0.165</td>\n",
       "      <td>0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yaw_30</th>\n",
       "      <td>30</td>\n",
       "      <td>0.165</td>\n",
       "      <td>0.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yaw_-30</th>\n",
       "      <td>-30</td>\n",
       "      <td>0.165</td>\n",
       "      <td>0.61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         yaw  shear    Ct\n",
       "yaw_00     0  0.165  0.74\n",
       "yaw_30    30  0.165  0.61\n",
       "yaw_-30  -30  0.165  0.61"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_input = pd.read_csv('data/input.csv',index_col=0)\n",
    "df_input.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training\n",
    "\n",
    "Training of the SWMS is done by function $.train_coeffs(df_input,transformations,Ds)$. \n",
    "The input for this function is the following:\n",
    "\n",
    "* $df\\_input$: input parameters of $input.csv$\n",
    "\n",
    "* transformations: the transformations to be applied to the input parameters. Allowed are:\n",
    "    * '' = no transformation\n",
    "    * 'log' = logarithmic\n",
    "    * 'exp' = exponential\n",
    "    * 'rec' = reciprocal (1/x)\n",
    "    * 'sqrt' = square root\n",
    "\n",
    "* Ds: downstream distanced to be used in determination of coefficients. Since this method does not include a near wake description (such as a double Gaussian), it is advised to only consider distances larger than 4 x/D.\n",
    "\n",
    "The key wake steering parameters in $.key\\_parameters$ are used to determine the regression coefficients based on the provided input data. These coefficients are saved in a lookup table called $.dict\\_LUT$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.744165Z",
     "start_time": "2021-04-23T13:47:09.458271Z"
    },
    "code_folding": [
     0
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Determining coefficients\n",
      "Done\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "dict_keys(['predictors', 'transformations', 'x/D', 'A_z', 'A_z_i', 'mu_y', 'mu_y_i', 'mu_z', 'mu_z_i', 'sigma_y', 'sigma_y_i', 'sigma_z', 'sigma_z_i', 'c', 'c_i', 't', 't_i', 's_a', 's_a_i', 's_b', 's_b_i'])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ds = range(4,11) ## Distances downstream\n",
    "transformations = ['','',''] ## specify transformations ['','log','exp','rec','sqrt']\n",
    "testcase.train_coeffs(df_input,transformations,Ds) ## execute\n",
    "testcase.dict_LUT.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing\n",
    "The coefficients determined above can consequently be used to predict the key wake steering parameters when the input parameters are known.  \n",
    "\n",
    "The function $.run\\_wake\\_model(input\\_values)$ collects the data in the right format and calls the functions $wake\\_model()$. that computes the key wake steering parameters. and $wake\\_composition()$. that composes the a gridded cross-section of the wake from these parameters. Returned are the normalized y and z positions, as well as $u_{normdef}$ (z, y, x).\n",
    "\n",
    "The function $.plot(y,z,u)$ will plot the created cross section at one downstream distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.747155Z",
     "start_time": "2021-04-23T13:47:09.745200Z"
    }
   },
   "outputs": [],
   "source": [
    "input_values = [15,0.165,0.65] ## input values for new case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.858559Z",
     "start_time": "2021-04-23T13:47:09.748200Z"
    },
    "code_folding": [],
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicting wake for following settings: \n",
      " Input parameters: ['yaw', 'shear', 'Ct'] \n",
      " Input values [15, 0.165, 0.65] \n",
      " Transformations:  ['', '', ''] \n",
      " Distances downstream: [ 4  5  6  7  8  9 10]\n",
      "\n",
      "Sucess: The wake parameters(y,z,u_normdef) are saved in .wake_yzu\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/luuk/Desktop/python/SWSM_wrapper/Publishable/v1.0/swsm/wake_model.py:59: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return du*np.exp(-((y-mu)**2)/(2*sigma**2))\n"
     ]
    }
   ],
   "source": [
    "testcase.run_wake_model(input_values) ## execute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:09.868604Z",
     "start_time": "2021-04-23T13:47:09.859950Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'y': [-2.0,\n",
       "  -1.9603174603174602,\n",
       "  -1.9206349206349207,\n",
       "  -1.880952380952381,\n",
       "  -1.8412698412698412,\n",
       "  -1.8015873015873016,\n",
       "  -1.7619047619047619,\n",
       "  -1.7222222222222223,\n",
       "  -1.6825396825396826,\n",
       "  -1.6428571428571428,\n",
       "  -1.6031746031746033,\n",
       "  -1.5634920634920635,\n",
       "  -1.5238095238095237,\n",
       "  -1.4841269841269842,\n",
       "  -1.4444444444444444,\n",
       "  -1.4047619047619047,\n",
       "  -1.3650793650793651,\n",
       "  -1.3253968253968254,\n",
       "  -1.2857142857142858,\n",
       "  -1.246031746031746,\n",
       "  -1.2063492063492063,\n",
       "  -1.1666666666666667,\n",
       "  -1.126984126984127,\n",
       "  -1.0873015873015872,\n",
       "  -1.0476190476190477,\n",
       "  -1.007936507936508,\n",
       "  -0.9682539682539683,\n",
       "  -0.9285714285714286,\n",
       "  -0.8888888888888888,\n",
       "  -0.8492063492063492,\n",
       "  -0.8095238095238095,\n",
       "  -0.7698412698412699,\n",
       "  -0.7301587301587301,\n",
       "  -0.6904761904761905,\n",
       "  -0.6507936507936508,\n",
       "  -0.6111111111111112,\n",
       "  -0.5714285714285714,\n",
       "  -0.5317460317460317,\n",
       "  -0.49206349206349204,\n",
       "  -0.4523809523809524,\n",
       "  -0.4126984126984127,\n",
       "  -0.373015873015873,\n",
       "  -0.3333333333333333,\n",
       "  -0.29365079365079366,\n",
       "  -0.25396825396825395,\n",
       "  -0.21428571428571427,\n",
       "  -0.1746031746031746,\n",
       "  -0.1349206349206349,\n",
       "  -0.09523809523809523,\n",
       "  -0.05555555555555555,\n",
       "  -0.015873015873015872,\n",
       "  0.023809523809523808,\n",
       "  0.06349206349206349,\n",
       "  0.10317460317460317,\n",
       "  0.14285714285714285,\n",
       "  0.18253968253968253,\n",
       "  0.2222222222222222,\n",
       "  0.2619047619047619,\n",
       "  0.30158730158730157,\n",
       "  0.3412698412698413,\n",
       "  0.38095238095238093,\n",
       "  0.42063492063492064,\n",
       "  0.4603174603174603,\n",
       "  0.5,\n",
       "  0.5396825396825397,\n",
       "  0.5793650793650794,\n",
       "  0.6190476190476191,\n",
       "  0.6587301587301587,\n",
       "  0.6984126984126984,\n",
       "  0.7380952380952381,\n",
       "  0.7777777777777778,\n",
       "  0.8174603174603174,\n",
       "  0.8571428571428571,\n",
       "  0.8968253968253969,\n",
       "  0.9365079365079365,\n",
       "  0.9761904761904762,\n",
       "  1.0158730158730158,\n",
       "  1.0555555555555556,\n",
       "  1.0952380952380953,\n",
       "  1.1349206349206349,\n",
       "  1.1746031746031746,\n",
       "  1.2142857142857142,\n",
       "  1.253968253968254,\n",
       "  1.2936507936507937,\n",
       "  1.3333333333333333,\n",
       "  1.373015873015873,\n",
       "  1.4126984126984128,\n",
       "  1.4523809523809523,\n",
       "  1.492063492063492,\n",
       "  1.5317460317460319,\n",
       "  1.5714285714285714,\n",
       "  1.6111111111111112,\n",
       "  1.6507936507936507,\n",
       "  1.6904761904761905,\n",
       "  1.7301587301587302,\n",
       "  1.7698412698412698,\n",
       "  1.8095238095238095,\n",
       "  1.8492063492063493,\n",
       "  1.8888888888888888,\n",
       "  1.9285714285714286,\n",
       "  1.9682539682539681],\n",
       " 'z': [-0.7142857142857143,\n",
       "  -0.6746031746031746,\n",
       "  -0.6349206349206349,\n",
       "  -0.5952380952380952,\n",
       "  -0.5555555555555556,\n",
       "  -0.5158730158730159,\n",
       "  -0.47619047619047616,\n",
       "  -0.4365079365079365,\n",
       "  -0.3968253968253968,\n",
       "  -0.35714285714285715,\n",
       "  -0.31746031746031744,\n",
       "  -0.2777777777777778,\n",
       "  -0.23809523809523808,\n",
       "  -0.1984126984126984,\n",
       "  -0.15873015873015872,\n",
       "  -0.11904761904761904,\n",
       "  -0.07936507936507936,\n",
       "  -0.03968253968253968,\n",
       "  0.0,\n",
       "  0.03968253968253968,\n",
       "  0.07936507936507936,\n",
       "  0.11904761904761904,\n",
       "  0.15873015873015872,\n",
       "  0.1984126984126984,\n",
       "  0.23809523809523808,\n",
       "  0.2777777777777778,\n",
       "  0.31746031746031744,\n",
       "  0.35714285714285715,\n",
       "  0.3968253968253968,\n",
       "  0.4365079365079365,\n",
       "  0.47619047619047616,\n",
       "  0.5158730158730159,\n",
       "  0.5555555555555556,\n",
       "  0.5952380952380952,\n",
       "  0.6349206349206349,\n",
       "  0.6746031746031746,\n",
       "  0.7142857142857143,\n",
       "  0.753968253968254,\n",
       "  0.7936507936507936,\n",
       "  0.8333333333333334,\n",
       "  0.873015873015873,\n",
       "  0.9126984126984127,\n",
       "  0.9523809523809523,\n",
       "  0.9920634920634921],\n",
       " 'u_normdef': array([[[-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         ...,\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00]],\n",
       " \n",
       "        [[-1.38124117e-16, -4.70544333e-12, -3.35371930e-10, ...,\n",
       "          -4.78090255e-09, -1.76692548e-08, -4.95527944e-08],\n",
       "         [-5.81053131e-16, -1.32898784e-11, -7.98970100e-10, ...,\n",
       "          -1.00493344e-08, -3.48872651e-08, -9.31510591e-08],\n",
       "         [-2.37072043e-15, -3.66854329e-11, -1.86668424e-09, ...,\n",
       "          -2.07756571e-08, -6.78463511e-08, -1.72657074e-07],\n",
       "         ...,\n",
       "         [-1.44027580e-18, -3.80909062e-15, -1.75777923e-13, ...,\n",
       "          -1.06696489e-11, -7.64004578e-11, -2.85666396e-10],\n",
       "         [-3.02532553e-19, -1.13987044e-15, -6.20221441e-14, ...,\n",
       "          -4.40761241e-12, -3.41044268e-11, -1.34870914e-10],\n",
       "         [-6.16334849e-20, -3.33381776e-16, -2.14617800e-14, ...,\n",
       "          -1.79079852e-12, -1.49946532e-11, -6.27847801e-11]],\n",
       " \n",
       "        [[-3.40991734e-10, -1.21805269e-07, -1.36061219e-06, ...,\n",
       "          -6.20767705e-06, -1.28952041e-05, -2.24633297e-05],\n",
       "         [-7.72838113e-10, -2.20617338e-07, -2.23790033e-06, ...,\n",
       "          -9.49591910e-06, -1.90265926e-05, -3.22233791e-05],\n",
       "         [-1.72171863e-09, -3.94473248e-07, -3.64071273e-06, ...,\n",
       "          -1.43909447e-05, -2.78347571e-05, -4.58589180e-05],\n",
       "         ...,\n",
       "         [-7.02595069e-11, -5.90145554e-09, -4.83624278e-08, ...,\n",
       "          -4.05766952e-07, -1.12050689e-06, -2.17457538e-06],\n",
       "         [-2.95045227e-11, -3.02384255e-09, -2.71684559e-08, ...,\n",
       "          -2.48563073e-07, -7.16344632e-07, -1.43396114e-06],\n",
       "         [-1.21787035e-11, -1.52954958e-09, -1.50959730e-08, ...,\n",
       "          -1.50848486e-07, -4.54070315e-07, -9.38114983e-07]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[-3.59088145e-45, -1.46219245e-36, -5.66778138e-33, ...,\n",
       "          -1.04839259e-29, -7.16978408e-28, -1.65603737e-26],\n",
       "         [-2.03702756e-43, -3.86864425e-35, -1.04725202e-31, ...,\n",
       "          -1.28154924e-28, -7.30247813e-27, -1.48824661e-25],\n",
       "         [-1.06314300e-41, -9.55887601e-34, -1.82156618e-30, ...,\n",
       "          -1.49063974e-27, -7.10538501e-26, -1.28093620e-24],\n",
       "         ...,\n",
       "         [-2.30979256e-45, -2.40786694e-38, -1.39463112e-33, ...,\n",
       "          -1.06223080e-25, -2.01362414e-23, -3.49337272e-22],\n",
       "         [-3.71249013e-47, -7.81585784e-40, -6.90477031e-35, ...,\n",
       "          -9.98119299e-27, -2.32783681e-24, -4.56180211e-23],\n",
       "         [-5.48980074e-49, -2.36927021e-41, -3.21806456e-36, ...,\n",
       "          -8.92425683e-28, -2.57086824e-25, -5.70526449e-24]],\n",
       " \n",
       "        [[-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         ...,\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n",
       "         [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00, ...,\n",
       "          -0.00000000e+00, -0.00000000e+00, -0.00000000e+00]],\n",
       " \n",
       "        [[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "           0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "         [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "           0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "         [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "           0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "         ...,\n",
       "         [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "           0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "         [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "           0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "         [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "           0.00000000e+00,  0.00000000e+00,  0.00000000e+00]]])}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testcase.wake_yzu ## y, z, and u_normdef data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:10.255790Z",
     "start_time": "2021-04-23T13:47:09.870156Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "testcase.plot(D=1) ## 2nd calculated downstream distance, so 5 D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-23T13:47:10.458701Z",
     "start_time": "2021-04-23T13:47:10.257394Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "testcase.plot(D=4) ## 5th calculated downstream distance, so 8 D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding optimum solution\n",
    "This test case simply computes the coefficients based on one set of input parameters and transformations, but does not test for an optimal solution.\n",
    "If desired, one should execute the following steps:\n",
    "* Generate coefficient ($.dict\\_LUT$) with set of input parameters and transformations (Training)\n",
    "* Use these coefficients in the wake model to compute key wake steering parameters and compose the wake (Testing)\n",
    "* Calculate power (or other measure of quality) and compare to original LES\n",
    "* Repeat with other input parameters and transformations until optimum is found"
   ]
  }
 ],
 "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",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}