D-FarhadifarModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Energy minimization for a 2.5D sheet in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import json\n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from scipy import optimize\n",
    "\n",
    "from tyssue import Sheet\n",
    "\n",
    "from tyssue import SheetGeometry as geom\n",
    "from tyssue.dynamics.sheet_vertex_model import SheetModel as model \n",
    "from tyssue.solvers.quasistatic import QSSolver\n",
    "from tyssue import config\n",
    "from tyssue.solvers.isotropic_solver import bruteforce_isotropic_relax\n",
    "\n",
    "from tyssue.draw.plt_draw import sheet_view\n",
    "import tyssue.draw.plt_draw as draw\n",
    "from tyssue.io import hdf5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>is_active</th>\n",
       "      <th>z</th>\n",
       "      <th>x</th>\n",
       "      <th>rho</th>\n",
       "      <th>old_idx</th>\n",
       "      <th>basal_shift</th>\n",
       "      <th>height</th>\n",
       "      <th>radial_tension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>80.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.110223e-15</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>8.881784e-17</td>\n",
       "      <td>-2.620126e-15</td>\n",
       "      <td>8.071634e+00</td>\n",
       "      <td>103.425000</td>\n",
       "      <td>2.216705e+00</td>\n",
       "      <td>5.854929e+00</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>5.743517e+00</td>\n",
       "      <td>0.402524</td>\n",
       "      <td>8.027290e+00</td>\n",
       "      <td>5.743517e+00</td>\n",
       "      <td>4.968335e-15</td>\n",
       "      <td>27.759261</td>\n",
       "      <td>4.468911e-16</td>\n",
       "      <td>5.000389e-15</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  y  is_active             z             x           rho  \\\n",
       "count  8.000000e+01  80.000000  8.000000e+01  8.000000e+01  8.000000e+01   \n",
       "mean   1.110223e-15   0.800000  8.881784e-17 -2.620126e-15  8.071634e+00   \n",
       "std    5.743517e+00   0.402524  8.027290e+00  5.743517e+00  4.968335e-15   \n",
       "\n",
       "          old_idx   basal_shift        height  radial_tension  \n",
       "count   80.000000  8.000000e+01  8.000000e+01            80.0  \n",
       "mean   103.425000  2.216705e+00  5.854929e+00             0.0  \n",
       "std     27.759261  4.468911e-16  5.000389e-15             0.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h5store = 'data/small_hexagonal.hf5'\n",
    "\n",
    "datasets = hdf5.load_datasets(h5store,\n",
    "                              data_names=['face', 'vert', 'edge'])\n",
    "specs = config.geometry.cylindrical_sheet()\n",
    "sheet = Sheet('emin', datasets, specs)\n",
    "sheet.sanitize(trim_borders=True, order_edges=True)\n",
    "\n",
    "geom.update_all(sheet)\n",
    "sheet.vert_df.describe().head(3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>area</th>\n",
       "      <th>z</th>\n",
       "      <th>y</th>\n",
       "      <th>is_alive</th>\n",
       "      <th>x</th>\n",
       "      <th>perimeter</th>\n",
       "      <th>old_idx</th>\n",
       "      <th>num_sides</th>\n",
       "      <th>vol</th>\n",
       "      <th>prefered_area</th>\n",
       "      <th>prefered_vol</th>\n",
       "      <th>contractility</th>\n",
       "      <th>vol_elasticity</th>\n",
       "      <th>prefered_height</th>\n",
       "      <th>basal_shift</th>\n",
       "      <th>basal_height</th>\n",
       "      <th>height</th>\n",
       "      <th>rho</th>\n",
       "      <th>id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>40.000000</td>\n",
       "      <td>4.000000e+01</td>\n",
       "      <td>4.000000e+01</td>\n",
       "      <td>40.0</td>\n",
       "      <td>4.000000e+01</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>4.000000e+01</td>\n",
       "      <td>4.000000e+01</td>\n",
       "      <td>40.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>31.948614</td>\n",
       "      <td>-1.850372e-18</td>\n",
       "      <td>1.132427e-15</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-2.642331e-15</td>\n",
       "      <td>21.447238</td>\n",
       "      <td>27.500000</td>\n",
       "      <td>5.600000</td>\n",
       "      <td>187.056872</td>\n",
       "      <td>12.0</td>\n",
       "      <td>288.0</td>\n",
       "      <td>76.076404</td>\n",
       "      <td>1.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2.500252</td>\n",
       "      <td>-3.246161</td>\n",
       "      <td>5.854929e+00</td>\n",
       "      <td>8.071634e+00</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.890942</td>\n",
       "      <td>7.446702e+00</td>\n",
       "      <td>5.463498e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.463498e+00</td>\n",
       "      <td>0.549335</td>\n",
       "      <td>16.306362</td>\n",
       "      <td>0.496139</td>\n",
       "      <td>16.926260</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.520187e-15</td>\n",
       "      <td>2.544151e-15</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            area             z             y  is_alive             x  \\\n",
       "count  40.000000  4.000000e+01  4.000000e+01      40.0  4.000000e+01   \n",
       "mean   31.948614 -1.850372e-18  1.132427e-15       1.0 -2.642331e-15   \n",
       "std     2.890942  7.446702e+00  5.463498e+00       0.0  5.463498e+00   \n",
       "\n",
       "       perimeter    old_idx  num_sides         vol  prefered_area  \\\n",
       "count  40.000000  40.000000  40.000000   40.000000           40.0   \n",
       "mean   21.447238  27.500000   5.600000  187.056872           12.0   \n",
       "std     0.549335  16.306362   0.496139   16.926260            0.0   \n",
       "\n",
       "       prefered_vol  contractility  vol_elasticity  prefered_height  \\\n",
       "count          40.0      40.000000            40.0             40.0   \n",
       "mean          288.0      76.076404             1.0             24.0   \n",
       "std             0.0       0.000000             0.0              0.0   \n",
       "\n",
       "       basal_shift  basal_height        height           rho    id  \n",
       "count    40.000000     40.000000  4.000000e+01  4.000000e+01  40.0  \n",
       "mean      2.500252     -3.246161  5.854929e+00  8.071634e+00   0.0  \n",
       "std       0.000000      0.000000  2.520187e-15  2.544151e-15   0.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet.face_df.describe().head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dz</th>\n",
       "      <th>length</th>\n",
       "      <th>dx</th>\n",
       "      <th>dy</th>\n",
       "      <th>srce</th>\n",
       "      <th>trgt</th>\n",
       "      <th>face</th>\n",
       "      <th>old_jv0</th>\n",
       "      <th>old_jv1</th>\n",
       "      <th>old_cell</th>\n",
       "      <th>...</th>\n",
       "      <th>sz</th>\n",
       "      <th>tx</th>\n",
       "      <th>ty</th>\n",
       "      <th>tz</th>\n",
       "      <th>fx</th>\n",
       "      <th>fy</th>\n",
       "      <th>fz</th>\n",
       "      <th>rx</th>\n",
       "      <th>ry</th>\n",
       "      <th>rz</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>224.000000</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>2.240000e+02</td>\n",
       "      <td>2.240000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.965082e-18</td>\n",
       "      <td>3.829864</td>\n",
       "      <td>-1.982541e-17</td>\n",
       "      <td>-7.930164e-18</td>\n",
       "      <td>39.500000</td>\n",
       "      <td>39.500000</td>\n",
       "      <td>19.500000</td>\n",
       "      <td>99.348214</td>\n",
       "      <td>106.031250</td>\n",
       "      <td>27.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2.727977e-15</td>\n",
       "      <td>1.268826e-15</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2.569373e-15</td>\n",
       "      <td>1.015061e-15</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.982541e-17</td>\n",
       "      <td>3.965082e-18</td>\n",
       "      <td>2.973812e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.593865e+00</td>\n",
       "      <td>0.652700</td>\n",
       "      <td>2.053231e+00</td>\n",
       "      <td>2.053231e+00</td>\n",
       "      <td>23.111351</td>\n",
       "      <td>23.111351</td>\n",
       "      <td>11.563046</td>\n",
       "      <td>27.073959</td>\n",
       "      <td>27.627631</td>\n",
       "      <td>16.132856</td>\n",
       "      <td>...</td>\n",
       "      <td>7.530508</td>\n",
       "      <td>5.720290e+00</td>\n",
       "      <td>5.720290e+00</td>\n",
       "      <td>7.530508</td>\n",
       "      <td>5.409339e+00</td>\n",
       "      <td>5.409339e+00</td>\n",
       "      <td>7.117109</td>\n",
       "      <td>1.860313e+00</td>\n",
       "      <td>1.860313e+00</td>\n",
       "      <td>2.460756e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 33 columns</p>\n",
       "</div>"
      ],
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       "                 dz      length            dx            dy        srce  \\\n",
       "count  2.240000e+02  224.000000  2.240000e+02  2.240000e+02  224.000000   \n",
       "mean   3.965082e-18    3.829864 -1.982541e-17 -7.930164e-18   39.500000   \n",
       "std    2.593865e+00    0.652700  2.053231e+00  2.053231e+00   23.111351   \n",
       "\n",
       "             trgt        face     old_jv0     old_jv1    old_cell  ...  \\\n",
       "count  224.000000  224.000000  224.000000  224.000000  224.000000  ...   \n",
       "mean    39.500000   19.500000   99.348214  106.031250   27.500000  ...   \n",
       "std     23.111351   11.563046   27.073959   27.627631   16.132856  ...   \n",
       "\n",
       "               sz            tx            ty          tz            fx  \\\n",
       "count  224.000000  2.240000e+02  2.240000e+02  224.000000  2.240000e+02   \n",
       "mean     0.000000 -2.727977e-15  1.268826e-15    0.000000 -2.569373e-15   \n",
       "std      7.530508  5.720290e+00  5.720290e+00    7.530508  5.409339e+00   \n",
       "\n",
       "                 fy          fz            rx            ry            rz  \n",
       "count  2.240000e+02  224.000000  2.240000e+02  2.240000e+02  2.240000e+02  \n",
       "mean   1.015061e-15    0.000000 -1.982541e-17  3.965082e-18  2.973812e-17  \n",
       "std    5.409339e+00    7.117109  1.860313e+00  1.860313e+00  2.460756e+00  \n",
       "\n",
       "[3 rows x 33 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet.edge_df.describe().head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non dimensionalisation and isotropic model\n",
    "\n",
    "\n",
    "For our 2D1/2 model, for a tissue energy is expressed as:\n",
    "$$\n",
    "E = N_f\\frac{K}{2}(V - V_0)^2 + N_f \\frac{\\Gamma}{2}L^2 + 3N_f\\Lambda \\ell \n",
    "$$\n",
    "In the case of a regular, infinite hexagonal lattice, There 6 edges per cell, each shared bteween 2 cells, hence $Ne = 3N_f$\n",
    "\n",
    "We can write this equation as a dimension-less one by dividing it by $N_f K V_0^2$. We define the dimension-less values: $\\bar\\Gamma = \\Gamma/K V_0^{4/3}$ and $\\bar\\Lambda = \\Lambda/K V_0^{5/3}$\n",
    "\n",
    "$$\n",
    "\\bar{E} = \\frac{\\left(V/V_0 - 1\\right)^2}{2} + \\bar\\Gamma \\frac{V_0^{-2/3}}{2}L^2 + 3\\bar\\Lambda V_0^{-1/3} \\ell\n",
    "$$\n",
    "\n",
    "We define the scaling factor $\\delta$ such that $V/V_0 = \\delta^3$. On a regular hexagonal grid, the perimeter $L=6\\ell$ and the area is A=$3\\sqrt{3}/2\\,\\ell^2$. The volume is $V = Ah$. As the (pseudo-)height is arbitrary, we can chose its prefered value. We set $h_0 = V_0^{1/3}$.\n",
    "\n",
    "We thus have $A_0 = V_0^{2/3}$, $A = \\delta^2 V_0^{2/3}$ and \n",
    "$\\ell = \\delta (\\frac{2}{3\\sqrt{3}})^{1/2} V_0^{1/3}$. We define the constant $\\mu = 2^{3/2}3^{1/4}$ to simplify further the equation:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\bar{E} &=& \\frac{(\\delta^3 - 1)^2}{2} + \\frac{12}{\\sqrt{3}}\\bar\\Gamma\\delta^2 + \\frac{6}{\\sqrt{3}}\\bar\\Lambda \\delta \\\\\n",
    "\\bar{E} &=& \\frac{(\\delta^3 - 1)^2}{2} + \\frac{\\mu^2}{2}\\bar\\Gamma\\delta^2 + \\frac{\\mu}{2}\\bar\\Lambda \\delta \\\\\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "\n",
    "The root of this polynomial corresponds to the lowest energy possible for this set of paramters.\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This analytic model is implemented bellow\n",
    "\n",
    "It is now a bit too specific to warrant a module in tyssue, and was thus removed\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Isotropic energy model from Farhadifar et al. 2007 article\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "\n",
    "mu = 2 ** 1.5 * 3 ** 0.25\n",
    "\n",
    "\n",
    "def elasticity(delta):\n",
    "    return (delta ** 3 - 1) ** 2 / 2.0\n",
    "\n",
    "\n",
    "def contractility(delta, gamma):\n",
    "    return gamma * mu ** 2 * delta ** 2 / 2.0\n",
    "\n",
    "\n",
    "def tension(delta, lbda):\n",
    "    return lbda * mu * delta / 2.0\n",
    "\n",
    "\n",
    "def isotropic_energies(sheet, model, geom, deltas, nondim_specs):\n",
    "\n",
    "    # bck_face_shift = sheet.face_df['basal_shift']\n",
    "    # bck_vert_shift = sheet.vert_df['basal_shift']\n",
    "    # ## Faces only area and height\n",
    "\n",
    "    V_0 = sheet.specs[\"face\"][\"prefered_vol\"]\n",
    "    vol_avg = sheet.face_df[sheet.face_df[\"is_alive\"] == 1].vol.mean()\n",
    "    rho_avg = sheet.vert_df.rho.mean()\n",
    "\n",
    "    # ## Set height and volume to height0 and V0\n",
    "    delta_0 = (V_0 / vol_avg) ** (1 / 3)\n",
    "    geom.scale(sheet, delta_0, sheet.coords)\n",
    "\n",
    "    h_0 = V_0 ** (1 / 3)\n",
    "\n",
    "    sheet.face_df[\"basal_shift\"] = rho_avg * delta_0 - h_0\n",
    "    sheet.vert_df[\"basal_shift\"] = rho_avg * delta_0 - h_0\n",
    "    geom.update_all(sheet)\n",
    "\n",
    "    energies = np.zeros((deltas.size, 3))\n",
    "    for n, delta in enumerate(deltas):\n",
    "        geom.scale(sheet, delta, sheet.coords + [\"basal_shift\"])\n",
    "        geom.update_all(sheet)\n",
    "        Et, Ec, Ev = model.compute_energy(sheet, full_output=True)\n",
    "        energies[n, :] = [Et.sum(), Ec.sum(), Ev.sum()]\n",
    "        geom.scale(sheet, 1 / delta, sheet.coords + [\"basal_shift\"])\n",
    "        geom.update_all(sheet)\n",
    "    energies /= sheet.face_df[\"is_alive\"].sum()\n",
    "    isotropic_relax(sheet, nondim_specs)\n",
    "\n",
    "    return energies\n",
    "\n",
    "\n",
    "def isotropic_relax(sheet, nondim_specs, geom=geom):\n",
    "    \"\"\"Deforms the sheet so that the faces pseudo-volume is at their\n",
    "    isotropic optimum (on average)\n",
    "    The specified model specs is assumed to be non-dimentional\n",
    "    \"\"\"\n",
    "\n",
    "    vol0 = sheet.face_df[\"prefered_vol\"].mean()\n",
    "    h_0 = vol0 ** (1 / 3)\n",
    "    live_faces = sheet.face_df[sheet.face_df.is_alive == 1]\n",
    "    vol_avg = live_faces.vol.mean()\n",
    "    rho_avg = sheet.vert_df.rho.mean()\n",
    "\n",
    "    # ## Set height and volume to height0 and vol0\n",
    "    delta = (vol0 / vol_avg) ** (1 / 3)\n",
    "    geom.scale(sheet, delta, coords=sheet.coords)\n",
    "    sheet.face_df[\"basal_shift\"] = rho_avg * delta - h_0\n",
    "    sheet.vert_df[\"basal_shift\"] = rho_avg * delta - h_0\n",
    "    geom.update_all(sheet)\n",
    "\n",
    "    # ## Optimal value for delta\n",
    "    delta_o = find_grad_roots(nondim_specs)\n",
    "    if not np.isfinite(delta_o):\n",
    "        raise ValueError(\"invalid parameters values\")\n",
    "    sheet.delta_o = delta_o\n",
    "    # ## Scaling\n",
    "    geom.scale(sheet, delta_o, coords=sheet.coords + [\"basal_shift\"])\n",
    "    geom.update_all(sheet)\n",
    "\n",
    "\n",
    "def isotropic_energy(delta, mod_specs):\n",
    "    \"\"\"\n",
    "    Computes the theoritical energy per face for the given\n",
    "    parameters.\n",
    "    \"\"\"\n",
    "    lbda = mod_specs[\"edge\"][\"line_tension\"]\n",
    "    gamma = mod_specs[\"face\"][\"contractility\"]\n",
    "    elasticity_ = (delta ** 3 - 1) ** 2 / 2.0\n",
    "    contractility_ = gamma * mu ** 2 * delta ** 2 / 2.0\n",
    "    tension_ = lbda * mu * delta / 2.0\n",
    "    energy = elasticity_ + contractility_ + tension_\n",
    "    return energy\n",
    "\n",
    "\n",
    "def isotropic_grad_poly(mod_specs):\n",
    "    lbda = mod_specs[\"edge\"][\"line_tension\"]\n",
    "    gamma = mod_specs[\"face\"][\"contractility\"]\n",
    "\n",
    "    grad_poly = [3, 0, 0, -3, mu ** 2 * gamma, mu * lbda / 2.0]\n",
    "    return grad_poly\n",
    "\n",
    "\n",
    "def isotropic_grad(mod_specs, delta):\n",
    "    grad_poly = isotropic_grad_poly(mod_specs)\n",
    "    return np.polyval(grad_poly, delta)\n",
    "\n",
    "\n",
    "def find_grad_roots(mod_specs):\n",
    "    poly = isotropic_grad_poly(mod_specs)\n",
    "    roots = np.roots(poly)\n",
    "    good_roots = np.real([r for r in roots if np.abs(r) == r])\n",
    "    np.sort(good_roots)\n",
    "    if len(good_roots) == 1:\n",
    "        return good_roots\n",
    "    elif len(good_roots) > 1:\n",
    "        return good_roots[0]\n",
    "    else:\n",
    "        return np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Reseting column contractility of the face dataset with new specs\n",
      "Reseting column vol_elasticity of the face dataset with new specs\n",
      "Reseting column prefered_height of the face dataset with new specs\n",
      "Reseting column prefered_area of the face dataset with new specs\n",
      "Reseting column prefered_vol of the face dataset with new specs\n",
      "Reseting column radial_tension of the vert dataset with new specs\n",
      "Reseting column is_active of the vert dataset with new specs\n",
      "Reseting column ux of the edge dataset with new specs\n",
      "Reseting column uy of the edge dataset with new specs\n",
      "Reseting column uz of the edge dataset with new specs\n",
      "Reseting column line_tension of the edge dataset with new specs\n",
      "Reseting column is_active of the edge dataset with new specs\n"
     ]
    }
   ],
   "source": [
    "nondim_specs = config.dynamics.quasistatic_sheet_spec()\n",
    "dim_model_specs = model.dimensionalize(nondim_specs)\n",
    "\n",
    "sheet.update_specs(dim_model_specs, reset=True)\n",
    "sheet.edge_df.is_active = (sheet.upcast_face(sheet.face_df.is_alive)\n",
    "                           & sheet.upcast_srce(sheet.vert_df.is_active))\n",
    "res = bruteforce_isotropic_relax(sheet, geom, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total energy: 18.662021831602555\n"
     ]
    }
   ],
   "source": [
    "Et, Ec, Ev = model.compute_energy(sheet, full_output=True)\n",
    "energy = model.compute_energy(sheet, full_output=False)\n",
    "print('Total energy: {}'.format(energy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_analytical_to_numeric_comp(sheet, model, geom, nondim_specs):\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(8, 8))\n",
    "\n",
    "    deltas = np.linspace(0.1, 1.8, 50)\n",
    "\n",
    "    lbda = nondim_specs[\"edge\"][\"line_tension\"]\n",
    "    gamma = nondim_specs[\"face\"][\"contractility\"]\n",
    "\n",
    "    ax.plot(\n",
    "        deltas,\n",
    "        isotropic_energy(deltas, nondim_specs),\n",
    "        \"k-\",\n",
    "        label=\"Analytical total\",\n",
    "    )\n",
    "    try:\n",
    "        ax.plot(sheet.delta_o, isotropic_energy(sheet.delta_o, nondim_specs), \"ro\")\n",
    "    except:\n",
    "        pass\n",
    "    ax.plot(deltas, elasticity(deltas), \"b-\", label=\"Analytical volume elasticity\")\n",
    "    ax.plot(\n",
    "        deltas,\n",
    "        contractility(deltas, gamma),\n",
    "        color=\"orange\",\n",
    "        ls=\"-\",\n",
    "        label=\"Analytical contractility\",\n",
    "    )\n",
    "    ax.plot(deltas, tension(deltas, lbda), \"g-\", label=\"Analytical line tension\")\n",
    "\n",
    "    ax.set_xlabel(r\"Isotropic scaling $\\delta$\")\n",
    "    ax.set_ylabel(r\"Isotropic energie $\\bar E$\")\n",
    "\n",
    "    energies = isotropic_energies(sheet, model, geom, deltas, nondim_specs)\n",
    "    # energies = energies / norm\n",
    "    ax.plot(\n",
    "        deltas,\n",
    "        energies[:, 2],\n",
    "        \"bo:\",\n",
    "        lw=2,\n",
    "        alpha=0.8,\n",
    "        label=\"Computed volume elasticity\",\n",
    "    )\n",
    "    ax.plot(\n",
    "        deltas, energies[:, 0], \"go:\", lw=2, alpha=0.8, label=\"Computed line tension\"\n",
    "    )\n",
    "    ax.plot(\n",
    "        deltas,\n",
    "        energies[:, 1],\n",
    "        ls=\":\",\n",
    "        marker=\"o\",\n",
    "        color=\"orange\",\n",
    "        label=\"Computed contractility\",\n",
    "    )\n",
    "    ax.plot(\n",
    "        deltas, energies.sum(axis=1), \"ko:\", lw=2, alpha=0.8, label=\"Computed total\"\n",
    "    )\n",
    "\n",
    "    ax.legend(loc=\"upper left\", fontsize=10)\n",
    "    ax.set_ylim(0, 1.2)\n",
    "    print(sheet.delta_o, deltas[energies.sum(axis=1).argmin()])\n",
    "\n",
    "    return fig, ax\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8865926873873902 0.8979591836734694\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plot_analytical_to_numeric_comp(sheet, model, geom, nondim_specs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Line tension', 'Contractility', 'Volume elasticity']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "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>gx</th>\n",
       "      <th>gy</th>\n",
       "      <th>gz</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>edge</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-668.132926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>668.132926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>112.700882</td>\n",
       "      <td>566.585593</td>\n",
       "      <td>335.679736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-112.700882</td>\n",
       "      <td>566.585593</td>\n",
       "      <td>-335.679736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>112.700882</td>\n",
       "      <td>-566.585593</td>\n",
       "      <td>335.679736</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              gx          gy          gz\n",
       "edge                                    \n",
       "0      -0.000000   -0.000000 -668.132926\n",
       "1      -0.000000   -0.000000  668.132926\n",
       "2     112.700882  566.585593  335.679736\n",
       "3    -112.700882  566.585593 -335.679736\n",
       "4     112.700882 -566.585593  335.679736"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradients = model.compute_gradient(sheet, components=True)\n",
    "gradients = {label: (srce, trgt) for label, (srce, trgt)\n",
    "             in zip(model.labels, gradients)}\n",
    "gradients['Line tension'][0].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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>gx</th>\n",
       "      <th>gy</th>\n",
       "      <th>gz</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>srce</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.008983</td>\n",
       "      <td>-3.720720e-03</td>\n",
       "      <td>-0.001010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.008983</td>\n",
       "      <td>3.720720e-03</td>\n",
       "      <td>-0.001010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.018412</td>\n",
       "      <td>7.626655e-03</td>\n",
       "      <td>-0.009825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.013376</td>\n",
       "      <td>-7.127358e-17</td>\n",
       "      <td>-0.008121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.018412</td>\n",
       "      <td>-7.626655e-03</td>\n",
       "      <td>-0.009825</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gx            gy        gz\n",
       "srce                                  \n",
       "0    -0.008983 -3.720720e-03 -0.001010\n",
       "1    -0.008983  3.720720e-03 -0.001010\n",
       "2    -0.018412  7.626655e-03 -0.009825\n",
       "3    -0.013376 -7.127358e-17 -0.008121\n",
       "4    -0.018412 -7.626655e-03 -0.009825"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_i = model.compute_gradient(sheet, components=False)\n",
    "grad_i.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "geom.scale(sheet, 1.2, sheet.coords)\n",
    "geom.update_all(sheet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "scale = 5\n",
    "\n",
    "fig, ax = draw.plot_forces(sheet, geom, model, ['z', 'x'], scale)\n",
    "fig.set_size_inches(10, 12)\n",
    "for n, (vx, vy, vz) in sheet.vert_df[sheet.coords].iterrows():\n",
    "    shift = 0.6 * np.sign(vy)\n",
    "    ax.text(vz+shift-0.3, vx, str(n))\n",
    "\n",
    "app_grad_specs = config.draw.sheet_spec()['grad']\n",
    "app_grad_specs.update({'color':'r'})\n",
    "\n",
    "solver = QSSolver()    \n",
    "sheet.topo_changed = False\n",
    "\n",
    "\n",
    "def draw_approx_force(ax=None):\n",
    "    fig, ax = draw.plot_forces(sheet, geom, model,\n",
    "                              ['z', 'x'], scaling=scale, ax=ax,\n",
    "                              approx_grad=solver.approx_grad, **{'grad':app_grad_specs})\n",
    "    fig.set_size_inches(10, 12)\n",
    "    return fig, ax\n",
    "\n",
    "## Uncomment bellow to recompute\n",
    "fig, ax = draw_approx_force(ax=ax)\n",
    "#fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "http://scipy.github.io/devdocs/generated/scipy.optimize.check_grad.html#scipy.optimize.check_grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error on the gradient (non-dim, per vertex): 1.689e-05\n"
     ]
    }
   ],
   "source": [
    "\n",
    "grad_err = solver.check_grad(sheet, geom, model)\n",
    "grad_err /= sheet.Nv\n",
    "\n",
    "\n",
    "print(\"Error on the gradient (non-dim, per vertex): {:.3e}\".format(grad_err))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "settings = {\n",
    "        'options': {'disp':False,\n",
    "                    'ftol':1e-5,\n",
    "                    'gtol':1e-5},\n",
    "        }\n",
    "\n",
    "\n",
    "res = solver.find_energy_min(sheet, geom, model, **settings)\n",
    "print(res['success'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res['message']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4314576758601875"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res['fun']/sheet.face_df.is_alive.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = draw.plot_forces(sheet, geom, model, ['z', 'y'], 10)\n",
    "fig.set_size_inches(10, 12)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}