{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive PDE discretizations on Cartesian grids\n",
    "## Volume : Algorithmic tools\n",
    "## Part : Generalized acuteness\n",
    "## Chapter : Norms defined by a Hooke tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The propagation speed of seismic waves is governed by the elastic properties of the medium, encoded in a Hooke tensor $c$. The dependency is anisotropic, non-linear and rather complex from the algebraic point of view, involving for instance a polynomial constraint of degree six in three variables. In this notebook, we provide some detail on the definition and numerical computation of these quantities, implemented in the `Hooke` class of norms (`agd.Metrics.Seismic.Hooke`). We also extract some quantities of interest for the fast marching method used to solve the related eikonal equations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[**Summary**](Summary.ipynb) of volume Algorithmic tools, this series of notebooks.\n",
    "\n",
    "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n",
    "\tbook of notebooks, including the other volumes.\n",
    "\n",
    "# Table of contents\n",
    "  * [1. Geometric distorsion](#1.-Geometric-distorsion)\n",
    "    * [1.1 Considered norms](#1.1-Considered-norms)\n",
    "    * [1.2 Half sphere sampling](#1.2-Half-sphere-sampling)\n",
    "    * [1.3 Length distorsion](#1.3-Length-distorsion)\n",
    "    * [1.4 Angular distortion](#1.4-Angular-distortion)\n",
    "  * [2. Convexity of the constraint](#2.-Convexity-of-the-constraint)\n",
    "    * [2.1 Quasi-concavity](#2.1-Quasi-concavity)\n",
    "    * [2.2 Convexity of $\\exp(-\\alpha f_c)$.](#2.2-Convexity-of-$\\exp(-\\alpha-f_c)$.)\n",
    "  * [3. Computation of a frame of reference](#3.-Computation-of-a-frame-of-reference)\n",
    "    * [3.1 Alternative projections](#3.1-Alternative-projections)\n",
    "    * [3.2 Optimization routines](#3.2-Optimization-routines)\n",
    "    * [3.3 Two dimensions](#3.3-Two-dimensions)\n",
    "    * [3.4 Three dimensions](#3.4-Three-dimensions)\n",
    "  * [4 GPU acceleration of the TTI projection](#4-GPU-acceleration-of-the-TTI-projection)\n",
    "    * [4.1 Taking advantage of VTI rotational invariance](#4.1-Taking-advantage-of-VTI-rotational-invariance)\n",
    "    * [4.2 Validation tests](#4.2-Validation-tests)\n",
    "\n",
    "\n",
    "\n",
    "**Acknowledgement.** Some of the experiments presented in these notebooks are part of \n",
    "ongoing research with Ludovic Métivier and Da Chen.\n",
    "\n",
    "Copyright Jean-Marie Mirebeau, Centre Borelli, ENS Paris-Saclay, CNRS, University Paris-Saclay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Importing the required libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:40.799496Z",
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     "shell.execute_reply": "2024-04-30T08:46:40.809035Z"
    }
   },
   "outputs": [],
   "source": [
    "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n",
    "#from Miscellaneous import TocTools; print(TocTools.displayTOC('SeismicNorm','Algo'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
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    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "from agd.Metrics.Seismic import Hooke,Thomsen,TTI\n",
    "from agd.Metrics import Riemann\n",
    "from agd import Sphere\n",
    "from agd import LinearParallel as lp\n",
    "from agd import AutomaticDifferentiation as ad\n",
    "from agd.Plotting import SetTitle3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:41.065792Z",
     "iopub.status.busy": "2024-04-30T08:46:41.065663Z",
     "iopub.status.idle": "2024-04-30T08:46:41.067351Z",
     "shell.execute_reply": "2024-04-30T08:46:41.067116Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import copy\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Geometric distorsion\n",
    "\n",
    "Norms arising in seismology have a fairly complex expression, but eventually their anisotropy is rather mild in comparison with other applications.\n",
    "We illustrate this point by computing the length distortion associated with several geologic materials, as well as their angular distortion. \n",
    "\n",
    "This allows to choose a discretization stencil for the eikonal equation, ensuring the causality property and the  applicability of the fast marching method.\n",
    "Note that for other applications involving stronger anisotropies, more complex (data adaptive, anisotropic) strategies are used in the design of the discretization stencil, see [Stern-Brocot tree](SternBrocot.ipynb) and [Voronoi vectors](VoronoiVectors.ipynb).\n",
    "\n",
    "The algebraic expression of a `Hooke` norm is not used in this section, or any of its properties, except for symmetry (which allows to consider only half of the unit sphere)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Considered norms\n",
    "\n",
    "The various geologic materials yield different types of anisotropies. We select a few for illustration.\n",
    "The level sets of the norm illustrate the distance that the seismic waves can reach in a given time, which depends on their direction of propagation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:41.068747Z",
     "iopub.status.busy": "2024-04-30T08:46:41.068670Z",
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     "shell.execute_reply": "2024-04-30T08:46:41.070710Z"
    }
   },
   "outputs": [],
   "source": [
    "# Two specific examples\n",
    "norm2 = Hooke.mica[0].extract_xz().rotate_by(0.3) \n",
    "norm3 = Hooke.mica[0].rotate_by(0.8,axis=(1,2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:41.072282Z",
     "iopub.status.busy": "2024-04-30T08:46:41.072202Z",
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     "shell.execute_reply": "2024-04-30T08:46:41.075661Z"
    }
   },
   "outputs": [],
   "source": [
    "# Some more examples\n",
    "norms2 = [\n",
    "    (\"riemann2\",Riemann.from_diagonal([1,3**2]).rotate_by(0.7)),\n",
    "    (\"mica2\",Hooke.mica[0].extract_xz().rotate_by(1.2)),\n",
    "    (\"stishovite2\",Hooke.stishovite[0].extract_xz().rotate_by(-0.5)),\n",
    "    (\"mudshale2\",Hooke.from_ThomsenElastic(\n",
    "        Thomsen.ThomsenData[\"Mesaverde (4903) mudshale\"])[0].extract_xz().rotate_by(-0.5)),\n",
    "]\n",
    "norms3 = [\n",
    "    (\"mica3\",Hooke.mica[0].rotate_by(0.3,axis=(1,2,3))),\n",
    "    (\"stishovite3\",Hooke.stishovite[0].rotate_by(0.8,axis=(1,1,1))),\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2024-04-30T08:46:41.486499Z"
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aX = np.linspace(-1,1)\n",
    "X = np.meshgrid(aX,aX,indexing='ij')\n",
    "plt.title(\"Level sets of a two dimensional norm\"); plt.axis('equal');\n",
    "plt.contourf(*X,norm2.norm(X)); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:41.488409Z",
     "iopub.status.busy": "2024-04-30T08:46:41.488302Z",
     "iopub.status.idle": "2024-04-30T08:46:42.694077Z",
     "shell.execute_reply": "2024-04-30T08:46:42.693815Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15,3])\n",
    "for i,(name,norm) in enumerate(norms2):\n",
    "    plt.subplot(1,len(norms2),1+i)\n",
    "    plt.title(name); plt.axis('equal')\n",
    "    plt.contourf(*X,norm.norm(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Half sphere sampling\n",
    "\n",
    "We sample our norms on the Euclidean unit sphere, so as to quantify their length distortion and other distortion.\n",
    "Since the norms considered in this notebook are symmetric w.r.t the origin, it is enough to sample the half sphere.\n",
    "\n",
    "We use $40$ points for the two dimensional half-sphere, and $40^2$ points for the three dimensional one. This sampling is dense enough to extract the desired numerical information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.695687Z",
     "iopub.status.busy": "2024-04-30T08:46:42.695576Z",
     "iopub.status.idle": "2024-04-30T08:46:42.698515Z",
     "shell.execute_reply": "2024-04-30T08:46:42.698298Z"
    }
   },
   "outputs": [],
   "source": [
    "def HalfSphereSampling(vdim,dens=40):\n",
    "    \"\"\"\n",
    "    Produces a rather uniform sampling of the upper half of the unit sphere.\n",
    "    - vdim (in [2,3]) : dimension of the sphere\n",
    "    - dens : sampling density. dens**(vdim-1) points are returned.\n",
    "    \"\"\"\n",
    "    if vdim==2: \n",
    "        θs = np.linspace(0,np.pi,dens,endpoint=False)\n",
    "        return np.array([np.cos(θs),np.sin(θs)])\n",
    "    elif vdim==3:\n",
    "        θs = np.linspace(0,np.pi/2,dens//2)\n",
    "        ϕs = np.linspace(0,2*np.pi,2*dens,endpoint=False)\n",
    "        return np.array([(np.cos(θ)*np.cos(ϕ), np.cos(θ)*np.sin(ϕ), np.sin(θ)) for θ in θs for ϕ in ϕs]).T\n",
    "    else: \n",
    "        raise ValueError(\"Unsupported dimension\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.699972Z",
     "iopub.status.busy": "2024-04-30T08:46:42.699873Z",
     "iopub.status.idle": "2024-04-30T08:46:42.767967Z",
     "shell.execute_reply": "2024-04-30T08:46:42.767724Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Sampling of the two dimensional half sphere\")\n",
    "plt.scatter(*HalfSphereSampling(2));plt.axis('equal');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.769506Z",
     "iopub.status.busy": "2024-04-30T08:46:42.769416Z",
     "iopub.status.idle": "2024-04-30T08:46:42.862129Z",
     "shell.execute_reply": "2024-04-30T08:46:42.861813Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "SetTitle3D(ax,\"Sampling of the three dimensional half sphere\")\n",
    "ax.scatter(*HalfSphereSampling(3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Length distorsion\n",
    "\n",
    "A natural measure of the anisotropy associated with a norm is its maximal length distortion\n",
    "$$\n",
    "    \\mu(N) := \\max_{|u|=|v|=1} \\frac {N(u)}{N(v)}.\n",
    "$$\n",
    "This quantity is to the ratio of the largest propagation speed, divided by the smallest propagation speed, over all space orientations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.864007Z",
     "iopub.status.busy": "2024-04-30T08:46:42.863886Z",
     "iopub.status.idle": "2024-04-30T08:46:42.865809Z",
     "shell.execute_reply": "2024-04-30T08:46:42.865578Z"
    }
   },
   "outputs": [],
   "source": [
    "def LengthDistortion(norm,**kwargs):\n",
    "    p = HalfSphereSampling(norm.vdim,**kwargs)\n",
    "    Np = norm.norm(p)\n",
    "    return np.max(Np)/np.min(Np)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mica medium has a length distortion of approximately $1.8$, which is large for a geological material (that is because mica is a crystal). Note that, with other types of norms, the HFM library routinely handles norms with length distortion exceeding $10$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.867291Z",
     "iopub.status.busy": "2024-04-30T08:46:42.867193Z",
     "iopub.status.idle": "2024-04-30T08:46:42.884789Z",
     "shell.execute_reply": "2024-04-30T08:46:42.884550Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.826531520777687"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LengthDistortion(norm2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By construction, length distortion is invariant under rotation of the norm. The (very small) difference arises because we use a finite sampling of the sphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.886275Z",
     "iopub.status.busy": "2024-04-30T08:46:42.886177Z",
     "iopub.status.idle": "2024-04-30T08:46:42.901271Z",
     "shell.execute_reply": "2024-04-30T08:46:42.901015Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.827030499135136"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LengthDistortion(norm2.rotate_by(np.pi/3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because mica is transversally isotropic, the length distortion of the three dimensional mica norm is equivalent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:42.902719Z",
     "iopub.status.busy": "2024-04-30T08:46:42.902635Z",
     "iopub.status.idle": "2024-04-30T08:46:43.229258Z",
     "shell.execute_reply": "2024-04-30T08:46:43.228987Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8283196290043453"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LengthDistortion(norm3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For Riemannian norms, the length distortion can be computed in closed form, and is provided as the `anisotropy` member function. (In contrast, there is no simple closed form expression for the anisotropy of `Hooke` norms to our knowledge, and the `anisotropy` method is thus not implemented.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:43.230861Z",
     "iopub.status.busy": "2024-04-30T08:46:43.230751Z",
     "iopub.status.idle": "2024-04-30T08:46:43.232867Z",
     "shell.execute_reply": "2024-04-30T08:46:43.232595Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm : riemann2. Length distortion : approximate 2.999373021225438, exact 2.9999999999999996\n"
     ]
    }
   ],
   "source": [
    "name,norm = norms2[0]\n",
    "print(f\"Norm : {name}. Length distortion : approximate {LengthDistortion(norm)}, exact {norm.anisotropy()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:43.234326Z",
     "iopub.status.busy": "2024-04-30T08:46:43.234227Z",
     "iopub.status.idle": "2024-04-30T08:46:43.925821Z",
     "shell.execute_reply": "2024-04-30T08:46:43.925549Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm riemann2. Length distortion 2.999373021225438\n",
      "Norm mica2. Length distortion 1.8240126561699312\n",
      "Norm stishovite2. Length distortion 1.3083676315734571\n",
      "Norm mudshale2. Length distortion 1.0697929978210605\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm mica3. Length distortion 1.8282899187030752\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm stishovite3. Length distortion 1.3084655222014128\n"
     ]
    }
   ],
   "source": [
    "for name,norm in norms2+norms3:\n",
    "    print(f\"Norm {name}. Length distortion {LengthDistortion(norm)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Angular distortion\n",
    "\n",
    "The Fast-Marching method relies on a *causality property*, ensuring that the front arrival time at a given point can be computed in terms of neighbors earlier reached, and thus that the non-linear system of equations discretizing the PDE can be solved in a single pass.\n",
    "\n",
    "For `Hooke` norms, we rely on a semi-lagrangian discretization of the eikonal equation, based on fixed stencils (illustrated below). In this context, the *causality property* follows from a geometrical *acuteness property*, as already observed by Sethian et al. The acuteness property requires that \n",
    "$$\n",
    "    \\Theta(N) + \\Theta(V) < \\pi/2,\n",
    "$$\n",
    "where $N$ is the norm, and $V$ is the stencil used for the PDE discretization.\n",
    "We denoted:\n",
    "* $\\Theta(N)$ the angular distortion of the norm, defined as the largest (unoriented) angle between $p$ and $\\nabla N(p)$, for each non-zero vector $p$. (By homogeneity, it suffices to consider the unit sphere, and by symmetry the half unit sphere.)\n",
    "* $\\Theta(V)$ the angular width of the stencil, defined as the largest (unoriented) angle between two vertices of a facet of the stencil."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some standard stencils are illustrate below, whose angular width $\\Theta(V)$ is easily computed:\n",
    "\n",
    "Stencil | Dimension | Angular width $\\Theta(V)$\n",
    "--- | --- | ---\n",
    "Square | 2 | $\\pi/4$\n",
    "Cut-cube | 3 | $\\pi/3$\n",
    "Cube | 3 | $0.955..$\n",
    "Spiky-cube | 3 | $\\pi/4$\n",
    "\n",
    "(The exact angular width of the cube stencil is $\\arccos(1/\\sqrt 3)$.)\n",
    "\n",
    "**In practice, for `Hooke` norms.** Most geologic materials are only midly anisotropic, so that the square stencil can be used in two dimensions, and the cut-cube in three dimensions. This is not true however of crystals, such as mica which exhibits stronger anisotropy and require more the refined spiky-cube stencil in three dimensions. \n",
    "\n",
    "**In practice, for strongly anisotropic norms arising in other applications.** The use of fixed stencils is inadequate when the anisotropy is strong, and one must instead produce adaptive and anisotropic stencils, using mathematical tools such as the [Stern-Brocot tree](SternBrocot.ipynb) and [Voronoi vectors](VoronoiVectors.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](Illustrations/SeismicNorm/FixedStencils.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The angular distortion of a norm is numerically evaluated by the next function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:43.927527Z",
     "iopub.status.busy": "2024-04-30T08:46:43.927418Z",
     "iopub.status.idle": "2024-04-30T08:46:43.929489Z",
     "shell.execute_reply": "2024-04-30T08:46:43.929253Z"
    }
   },
   "outputs": [],
   "source": [
    "def AngularDistortion(norm,**kwargs):\n",
    "    p = HalfSphereSampling(norm.vdim,**kwargs)\n",
    "    dNp = norm.gradient(p)\n",
    "    ratio = lp.dot_VV(p,dNp)/np.linalg.norm(dNp,ord=2,axis=0)\n",
    "    return np.arccos(np.min(ratio))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The angular distortion of the mica medium is less than $\\pi/4$, which allows using the square stencil (in two dimensions), and the spiky cube stencil (in three dimensions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:43.930840Z",
     "iopub.status.busy": "2024-04-30T08:46:43.930737Z",
     "iopub.status.idle": "2024-04-30T08:46:43.944452Z",
     "shell.execute_reply": "2024-04-30T08:46:43.944198Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Angular distortion of mica : 0.7509887694791147, pi/4 : 0.7853981633974483\n"
     ]
    }
   ],
   "source": [
    "μ = AngularDistortion(norm2)\n",
    "print(f\"Angular distortion of mica : {μ}, pi/4 : {np.pi/4}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that angular distortion is invariant under rotation (up to numerical accuracy due to the finite sampling of the sphere)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:43.945877Z",
     "iopub.status.busy": "2024-04-30T08:46:43.945790Z",
     "iopub.status.idle": "2024-04-30T08:46:43.960908Z",
     "shell.execute_reply": "2024-04-30T08:46:43.960639Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7497254150260353"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AngularDistortion(norm2.rotate_by(1.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the mica medium is transversally isotropic, the angular distortion of the three dimensional medium is identical (again up to numerical accuracy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:43.962379Z",
     "iopub.status.busy": "2024-04-30T08:46:43.962297Z",
     "iopub.status.idle": "2024-04-30T08:46:44.293056Z",
     "shell.execute_reply": "2024-04-30T08:46:44.292768Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7528581192017458"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AngularDistortion(norm3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Angular distortion is bounded in terms of the Length distortion : one has \n",
    "$$\n",
    "\\mu(N) \\cos \\Theta(N) \\geq 1.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:44.294565Z",
     "iopub.status.busy": "2024-04-30T08:46:44.294480Z",
     "iopub.status.idle": "2024-04-30T08:46:44.323859Z",
     "shell.execute_reply": "2024-04-30T08:46:44.323573Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3352210770062627"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LengthDistortion(norm2) * np.cos(AngularDistortion(norm2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of Riemannian metrics, the angular distortion has a closed form expression, as does the length distortion, and they are related by $(\\mu(N)+\\mu(N)^{-1})\\cos \\Theta(N) = 2$. Let us check this expression numerically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:44.325331Z",
     "iopub.status.busy": "2024-04-30T08:46:44.325230Z",
     "iopub.status.idle": "2024-04-30T08:46:44.327353Z",
     "shell.execute_reply": "2024-04-30T08:46:44.327109Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm riemann2. Angular distortion : approximate 0.9272937826526069, exact 0.9272952180016121 \n"
     ]
    }
   ],
   "source": [
    "name,norm = norms2[0]\n",
    "μ = norm.anisotropy()\n",
    "Θ = AngularDistortion(norm)\n",
    "print(f\"Norm {name}. Angular distortion : approximate {Θ}, exact {np.arccos(2/(μ+1/μ))} \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:44.328725Z",
     "iopub.status.busy": "2024-04-30T08:46:44.328626Z",
     "iopub.status.idle": "2024-04-30T08:46:45.017728Z",
     "shell.execute_reply": "2024-04-30T08:46:45.017434Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm riemann2. Angular distortion 0.9272937826526069\n",
      "Norm mica2. Angular distortion 0.7521110091600802\n",
      "Norm stishovite2. Angular distortion 0.3126982198178143\n",
      "Norm mudshale2. Angular distortion 0.12435235682165878\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm mica3. Angular distortion 0.752859677386624\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm stishovite3. Angular distortion 0.34104154422640154\n"
     ]
    }
   ],
   "source": [
    "for name,norm in norms2+norms3:\n",
    "    print(f\"Norm {name}. Angular distortion {AngularDistortion(norm)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The upper bound on the angular width $\\Theta(N)$ for the applicability of the fast-marching method with the cut-cube stencil, in three dimensions, is \n",
    "$\\pi/2 - \\Theta(\\text{cut-cube}) = \\pi/6$. As mentioned above, it is satisfied for all common geological materials, except crystals (such as mica)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.019413Z",
     "iopub.status.busy": "2024-04-30T08:46:45.019289Z",
     "iopub.status.idle": "2024-04-30T08:46:45.021459Z",
     "shell.execute_reply": "2024-04-30T08:46:45.021220Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5235987755982988"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi/6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Convexity of the constraint\n",
    "\n",
    "In this section, we discuss in more detail the computational aspects of `Hooke` norms. \n",
    "For that purpose, let us fix a Hooke tensor $c$ of components $c_{ijkl}$ where $i,j,k,l \\in \\{1,\\cdots,d\\}$.\n",
    "\n",
    "\n",
    "**Definition of the `Hooke` norm.**\n",
    "For each vector $v \\in R^d$ define a $d \\times d$ symmetric matrix $m(v)$ of components \n",
    "$$\n",
    "    m_c(v)_{ik} = \\sum_{j,l} c_{ijkl} v_j v_l.\n",
    "$$\n",
    "In view of energetic considerations, one assumes that the Hooke tensor $c$ is positive (in an appropriate sense), which implies that $m(v)$ is a positive semi-definite matrix for each $v \\in R^d$.\n",
    "\n",
    "The *dual norm* to a `Hooke` norm is defined as the square root of the largest eigenvalue of the matrix $m_c(v)$\n",
    "$$\n",
    "    N_c^*(v) := \\sqrt{\\lambda_{\\max}(m_c(v))},\n",
    "$$\n",
    "whereas the primal norm is defined dually, for all $w \\in R^d$\n",
    "$$\n",
    "    N_c(w) := \\max \\{<w,v>;\\ N_c^*(w) \\leq 1\\}.\n",
    "$$\n",
    "One can prove that $N_c^*$ is a norm, and in particular it is convex, so that $N_c$ is defined as the maximization of a linear objective function subject to a convex constraint.\n",
    "\n",
    "**Efficient numerical computation.**\n",
    "Despite being well posed, the above definition of $N_c$ is not very tractable numerically, due to the complex and costly evaluation of $N_c^*$.\n",
    "Instead, let us define \n",
    "$$\n",
    "    f_c(v) := \\det(I - m_c(v)),\n",
    "$$\n",
    "so that the (closed) dual unit ball $B_c^*$ admits the equivalent characterizations\n",
    "$$\n",
    "B_c^* \n",
    ":= \n",
    "\\{v; N_c^*(v) \\leq 1\\}\n",
    "=\n",
    "\\text{CC}_0(\\{f_c(v) \\geq 0\\}),\n",
    "$$\n",
    "where $\\text{CC}_x(X)$ denotes the connected component of the point $x$ in the set $X$. We can thus rephrase the definition of $N_c$, with a slight abuse of notation, as \n",
    "$$\n",
    "    N_c(w) := \\{<w,v>;\\ f_c(v) \\geq 0,\\ v \\in \\text{CC}_0\\}.\n",
    "$$\n",
    "We have replaced the highly non-linear constraint $N^*_c(v)\\leq 1$ with the polynomial constraint $f_c(v) \\geq 0$, which is much more tractable numerically (in particular it is easy to differentiate). Note that $f_c$ is an in-homogeneous polynomial of degree $2d$ in $d$ variables, where $f\\in \\{2,3\\}$ is the dimension.\n",
    "\n",
    "**Convexity.** \n",
    "The dual norm $N_c^*$ is convex, as mentioned above, but properties of $f_c$ are slightly more subtle. \n",
    "One can show that:\n",
    "* $f_c$ is quasi-concave on a neighborhood of $B_c^*$. (In other words the set $\\{v \\in B_c^*; f_c\\geq \\lambda\\}$ is convex for all $\\lambda$.)\n",
    "* $f_c^{\\frac 1 d}$ is strongly concave on $B_c^*$. Note that this function in not defined outside $B_c^*$.\n",
    "* $\\exp(-\\alpha f_c)$ is strongly convex on a neighborhood of $B_c^*$, for sufficiently large $\\alpha$.\n",
    "\n",
    "The constraint function $f_c$ is a hidden method of the dual norm, evidenced below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.022991Z",
     "iopub.status.busy": "2024-04-30T08:46:45.022874Z",
     "iopub.status.idle": "2024-04-30T08:46:45.024751Z",
     "shell.execute_reply": "2024-04-30T08:46:45.024450Z"
    }
   },
   "outputs": [],
   "source": [
    "def F(norm,v): return -norm._dual_level(v) # Constraint function f_c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Quasi-concavity\n",
    "\n",
    "The dual unit ball $B_c^*$ is the connected component of the origin delimited by the level set $f_c=0$, shown red.\n",
    "As announced, the level sets of $\\{f_c\\geq \\lambda\\}$ within this region are convex, reflecting the quasi-concavity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.026191Z",
     "iopub.status.busy": "2024-04-30T08:46:45.026092Z",
     "iopub.status.idle": "2024-04-30T08:46:45.028038Z",
     "shell.execute_reply": "2024-04-30T08:46:45.027787Z"
    }
   },
   "outputs": [],
   "source": [
    "aX = np.linspace(-0.3,0.3)\n",
    "X = np.array(np.meshgrid(aX,aX,indexing='ij'))\n",
    "X_ad = ad.Dense2.identity(constant=X,shape_free=(2,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.029474Z",
     "iopub.status.busy": "2024-04-30T08:46:45.029357Z",
     "iopub.status.idle": "2024-04-30T08:46:45.101765Z",
     "shell.execute_reply": "2024-04-30T08:46:45.101481Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6)); plt.axis('equal');\n",
    "plt.title(\"The constraint is quasi convex, within the dual unit ball\")\n",
    "f = F(norm2,X)\n",
    "plt.contourf(*X,f,np.linspace(-0.2,1,10))\n",
    "plt.contour(*X,f,[0],colors='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function $f_c$ however is *not* concave in $B_c^*$. Indeed, as illustrated below, the determinant of the hessian of $f_c$ changes sign in this region. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.103396Z",
     "iopub.status.busy": "2024-04-30T08:46:45.103282Z",
     "iopub.status.idle": "2024-04-30T08:46:45.175935Z",
     "shell.execute_reply": "2024-04-30T08:46:45.175674Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6)); plt.axis('equal');\n",
    "plt.title(\"The constraint is not convex\")\n",
    "f_ad = F(norm2,X_ad)\n",
    "f = f_ad.value\n",
    "det_h = lp.det(f_ad.hessian())\n",
    "plt.contourf(*X,det_h)\n",
    "plt.contour(*X,det_h,[0])\n",
    "plt.contour(*X,f,[0],colors='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function $f_c^{\\frac 1 d}$ is strongly concave in $B_c^*$, and indeed its hessian is negative definite in the interior of this region. However $f_c^{\\frac 1 d}$ is not very nice to use numerically due to the singularity on the boundary of $B_c^*$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.177465Z",
     "iopub.status.busy": "2024-04-30T08:46:45.177363Z",
     "iopub.status.idle": "2024-04-30T08:46:45.248689Z",
     "shell.execute_reply": "2024-04-30T08:46:45.248409Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jean-mariemirebeau/Dropbox/Programmes/GithubM1/AdaptiveGridDiscretizations/agd/AutomaticDifferentiation/Base.py:45: RuntimeWarning: divide by zero encountered in power\n",
      "  def pow(x,n):\treturn (x**n,n*x**(n-1),(n*(n-1))*x**(n-2))\n",
      "/Users/jean-mariemirebeau/Dropbox/Programmes/GithubM1/AdaptiveGridDiscretizations/agd/AutomaticDifferentiation/Dense2.py:98: RuntimeWarning: invalid value encountered in multiply\n",
      "  return self.new(a,_add_dim(b)*self.coef1,_add_dim2(b)*self.coef2+_add_dim2(c)*mixed)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6)); plt.axis('equal');\n",
    "plt.title(\"The constraint power 1/d is convex\")\n",
    "f_pow_ad = np.maximum(0,F(norm2,X_ad))**(1/norm.vdim)\n",
    "det_h_pow = lp.det(f_pow_ad.hessian())\n",
    "plt.contourf(*X,det_h_pow>0)\n",
    "plt.contour(*X,f_ad.value,[0],colors='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Convexity of $\\exp(-\\alpha f_c)$.\n",
    "\n",
    "The function $\\exp(-\\alpha f_c)$ is known to be strongly convex on a neighborhood $B_c^*$, for sufficiently large $\\alpha$, but the theoretical analysis is not quantitative. \n",
    "The next function estimates numerically the lower bound on the values of $\\alpha$ which achieve this property.\n",
    "\n",
    "Note that the strong convexity of a smooth function $\\exp(-\\alpha f)$ is equivalent to the pointwise positive definiteness property\n",
    "$$\n",
    "    \\alpha \\nabla f \\nabla f^T - \\nabla^2 f \\succ 0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.250546Z",
     "iopub.status.busy": "2024-04-30T08:46:45.250438Z",
     "iopub.status.idle": "2024-04-30T08:46:45.253146Z",
     "shell.execute_reply": "2024-04-30T08:46:45.252884Z"
    }
   },
   "outputs": [],
   "source": [
    "def LowerAlpha(norm,**kwargs):\n",
    "    # Evaluate the dual norm on the Euclidean sphere\n",
    "    p = HalfSphereSampling(norm.vdim,**kwargs)\n",
    "    norm_pp = norm.contract(p)\n",
    "    dual_norm = np.sqrt(np.linalg.norm(norm_pp,ord=2,axis=(0,1)))\n",
    "    \n",
    "    # Produce a sampling of the dual unit sphere, evaluate the constraint and derivatives\n",
    "    q = p/dual_norm \n",
    "    q_ad = ad.Dense2.identity(constant=q,shape_free=(norm.vdim,))\n",
    "    dual_level_ad = norm._dual_level(q_ad)\n",
    "    assert np.allclose(dual_level_ad.value,0) \n",
    "    \n",
    "    # Compute the minimal relaxation parameter\n",
    "    h = dual_level_ad.hessian()\n",
    "    g = dual_level_ad.gradient()\n",
    "    λ = ad.Dense.identity(constant=1.)\n",
    "    det_ad = lp.det(h + λ * lp.outer_self(g)) # Polynomial of degree one w.r.t λ\n",
    "    α = -det_ad.value/det_ad.coef\n",
    "    \n",
    "    return np.max(α)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In practice, the exponential $\\exp(-\\alpha f_c)$ takes rather extreme values, which makes this quantity unfriendly from the numerical point of view due to the risk of overflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.254568Z",
     "iopub.status.busy": "2024-04-30T08:46:45.254461Z",
     "iopub.status.idle": "2024-04-30T08:46:45.257867Z",
     "shell.execute_reply": "2024-04-30T08:46:45.257623Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.129535935595026"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = LowerAlpha(norm2)\n",
    "α"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.259261Z",
     "iopub.status.busy": "2024-04-30T08:46:45.259180Z",
     "iopub.status.idle": "2024-04-30T08:46:45.323357Z",
     "shell.execute_reply": "2024-04-30T08:46:45.323074Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6));plt.axis('equal');\n",
    "exp_ad = np.exp(-α*F(norm2,X_ad))\n",
    "value = exp_ad.value\n",
    "det_h = lp.det(exp_ad.hessian())\n",
    "plt.contourf(*X,det_h)\n",
    "plt.contour(*X,det_h,[0])\n",
    "plt.contour(*X,value<=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As already mentioned, the hessian of $\\exp(-\\alpha f_c)$ is proportional to \n",
    "$$\n",
    "    \\alpha \\nabla f_c \\nabla f_c^T -\\nabla^2 f_c.\n",
    "$$\n",
    "We check in the following illustration that it is positive definite in the interior of $B_c^*$ with the value $\\alpha$ produced by the `LowerAlpha` function. In addition, this hessian degenerates on the boundary of $B_c^*$, showing that $\\alpha$ is indeed the lower bound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.324916Z",
     "iopub.status.busy": "2024-04-30T08:46:45.324811Z",
     "iopub.status.idle": "2024-04-30T08:46:45.388959Z",
     "shell.execute_reply": "2024-04-30T08:46:45.388689Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal')\n",
    "f_ad = F(norm2,X_ad)\n",
    "v = f_ad.value\n",
    "g = f_ad.gradient()\n",
    "h = f_ad.hessian()\n",
    "det_h = lp.det(α*lp.outer_self(g)-h)\n",
    "plt.contourf(*X,det_h)\n",
    "plt.contour(*X,det_h,[0])\n",
    "plt.contour(*X,v,[0],colors='red');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.390521Z",
     "iopub.status.busy": "2024-04-30T08:46:45.390408Z",
     "iopub.status.idle": "2024-04-30T08:46:45.442943Z",
     "shell.execute_reply": "2024-04-30T08:46:45.442663Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm mica2. Lower bound on α 10.131242536881315\n",
      "Norm stishovite2. Lower bound on α 3.496438839401178\n",
      "Norm mudshale2. Lower bound on α -0.05585949317270378\n",
      "Norm mica3. Lower bound on α 39.549249651079755\n",
      "Norm stishovite3. Lower bound on α 61.2186314407292\n"
     ]
    }
   ],
   "source": [
    "for name,norm in norms2[1:]+norms3:\n",
    "    print(f\"Norm {name}. Lower bound on α {LowerAlpha(norm)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a parameter $\\alpha$ has been determined (as above) such that $\\alpha \\nabla f_c \\nabla f_c^T -\\nabla^2 f_c \\succ 0$, then it can be taken into account in the  Sequential Quadratically Constrained Programming (SQCP) routine used to compute the norm. This ensures that all inverted matrices are positive definite, and is in principle safer. Note that SQCP is an iterative method for solving problems of the form\n",
    "$$\n",
    "    \\max \\{<w,v>; f(v) \\leq 0\\},\n",
    "$$\n",
    "which is based on successively approximating $f$ with its second order Taylor expansion (indeed the exact solution of this problem is known in closed form when the constraint is quadratic).\n",
    "\n",
    "In numerical experiments, somewhat surprisingly, the SQCP method is rather insensitive to the parameter $\\alpha$, even when values are used that do not enforce the positive definiteness of $-\\nabla^2 f_c$ on $B_c^*$. In practice leaving this parameter to the default value $\\alpha=0$ appears to be fine. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.444511Z",
     "iopub.status.busy": "2024-04-30T08:46:45.444424Z",
     "iopub.status.idle": "2024-04-30T08:46:45.446621Z",
     "shell.execute_reply": "2024-04-30T08:46:45.446397Z"
    }
   },
   "outputs": [],
   "source": [
    "def check_qconv(norm,α,**kwargs):\n",
    "    norm_ = copy.copy(norm)\n",
    "    norm_.qconv_sqp = α # Parameter such that α grad(f_c) grad (f_c)^T - hess(f_c) > 0\n",
    "    norm_.niter_sqp = 12 # A few more iterations than default\n",
    "    p = HalfSphereSampling(norm.vdim,**kwargs)\n",
    "    return np.max(np.abs(norm.norm(p)-norm_.norm(p))) # Largest absolute error on unit ball"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.447954Z",
     "iopub.status.busy": "2024-04-30T08:46:45.447877Z",
     "iopub.status.idle": "2024-04-30T08:46:45.488963Z",
     "shell.execute_reply": "2024-04-30T08:46:45.488683Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lower bound of α ensuring strong convexity :  10.129535935595026\n"
     ]
    }
   ],
   "source": [
    "print(\"Lower bound of α ensuring strong convexity : \", LowerAlpha(norm2))\n",
    "# Norm is correctly computed in both cases, with identical value\n",
    "assert check_qconv(norm2,60.)<1e-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:45.490343Z",
     "iopub.status.busy": "2024-04-30T08:46:45.490259Z",
     "iopub.status.idle": "2024-04-30T08:46:46.565700Z",
     "shell.execute_reply": "2024-04-30T08:46:46.565282Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lower bound of α ensuring strong convexity :  39.54959545329993\n"
     ]
    }
   ],
   "source": [
    "print(\"Lower bound of α ensuring strong convexity : \", LowerAlpha(norm3))\n",
    "assert check_qconv(norm3,60.) <1e-12 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:46.567341Z",
     "iopub.status.busy": "2024-04-30T08:46:46.567256Z",
     "iopub.status.idle": "2024-04-30T08:46:48.635022Z",
     "shell.execute_reply": "2024-04-30T08:46:48.634742Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm mica2, effect of $α$ 5.551115123125783e-17\n",
      "Norm stishovite2, effect of $α$ 2.0816681711721685e-17\n",
      "Norm mudshale2, effect of $α$ 1.6263032587282567e-19\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm mica3, effect of $α$ 5.551115123125783e-17\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm stishovite3, effect of $α$ 1.5265566588595902e-15\n"
     ]
    }
   ],
   "source": [
    "for name,norm in norms2[1:]+norms3:\n",
    "    print(f\"Norm {name}, effect of $α$ {check_qconv(norm,60.)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Computation of a frame of reference\n",
    "\n",
    "Most materials arising in geology which are *anisotropic* inherit this property from a *layered structure*, which can have various and independent origins:\n",
    "* (Atom scale) In a crystal, due to the periodic arrangement of atoms.\n",
    "* (Centimeter scale) Successive deposits on the sea floor, whose constitutents may vary periodically.\n",
    "* (Kilometer scale) Fault interfaces produce anisotropic elastic response along them.\n",
    "\n",
    "If a frame of reference aligned with the layers is used, then the Hooke tensor typically takes a block-diagonal structure. Depending on the some shared coefficient values, the material symmetry is known as *hexagonal*, *tetragonal*, or *orthorombic*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.636617Z",
     "iopub.status.busy": "2024-04-30T08:46:48.636525Z",
     "iopub.status.idle": "2024-04-30T08:46:48.638934Z",
     "shell.execute_reply": "2024-04-30T08:46:48.638685Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mica in a frame of reference :\n",
      " [[178.   42.4  14.5   0.    0.    0. ]\n",
      " [ 42.4 178.   14.5   0.    0.    0. ]\n",
      " [ 14.5  14.5  54.9   0.    0.    0. ]\n",
      " [  0.    0.    0.   12.2   0.    0. ]\n",
      " [  0.    0.    0.    0.   12.2   0. ]\n",
      " [  0.    0.    0.    0.    0.   67.8]]\n",
      "\n",
      "Mudshale in a frame of reference :\n",
      " [[21906646.  5949886. 11051999.        0.        0.        0.]\n",
      " [ 5949886. 21906646. 11051999.        0.        0.        0.]\n",
      " [11051999. 11051999. 20511841.        0.        0.        0.]\n",
      " [       0.        0.        0.  7306209.        0.        0.]\n",
      " [       0.        0.        0.        0.  7306209.        0.]\n",
      " [       0.        0.        0.        0.        0.  7978380.]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Mica in a frame of reference :\\n\", Hooke.mica[0].hooke)\n",
    "print(\"\\nMudshale in a frame of reference :\\n\",Hooke.from_ThomsenElastic(\n",
    "    Thomsen.ThomsenData[\"Mesaverde (4903) mudshale\"])[0].hooke.round())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In dimension $d=2$, the reference structure of interest is built of a $2\\times 2$ block, and an additional diagonal coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.640369Z",
     "iopub.status.busy": "2024-04-30T08:46:48.640269Z",
     "iopub.status.idle": "2024-04-30T08:46:48.642467Z",
     "shell.execute_reply": "2024-04-30T08:46:48.642217Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[178. ,  14.5,   0. ],\n",
       "       [ 14.5,  54.9,   0. ],\n",
       "       [  0. ,   0. ,  12.2]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hooke.mica[0].extract_xz().hooke"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When a rotation is applied to the medium, this block structure lost, is obviously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.643882Z",
     "iopub.status.busy": "2024-04-30T08:46:48.643784Z",
     "iopub.status.idle": "2024-04-30T08:46:48.645914Z",
     "shell.execute_reply": "2024-04-30T08:46:48.645694Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[128.3,  36.8,  39.4,  -0.2, -43.1,   3. ],\n",
       "       [ 36.8, 176.9,  20.6,   7.6, -10.9,   3.8],\n",
       "       [ 39.4,  20.6,  54.9,   0.9,  -6.3,  -2.6],\n",
       "       [ -0.2,   7.6,   0.9,  23.9,  -1.9, -22. ],\n",
       "       [-43.1, -10.9,  -6.3,  -1.9,  37.2,   1.3],\n",
       "       [  3. ,   3.8,  -2.6, -22. ,   1.3,  56.5]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm3.hooke.round(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Hooke` class can handle general elliptic Hooke tensors, hence the frame of reference has no particular interest to it. However there are other numerical methods, such as the `TTI` (Tilted Transversally Isotropic) class of geological materials in the `agd` library, which require it. The frame of reference is often not available in the input data, if for instance it arises from the homogeneization of a complex material, and therefore it must be approximated or computed. \n",
    "\n",
    "Inspired by works of Paul Cupillard, we propose to approximate a frame of reference using numerical optimization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.647265Z",
     "iopub.status.busy": "2024-04-30T08:46:48.647165Z",
     "iopub.status.idle": "2024-04-30T08:46:48.649540Z",
     "shell.execute_reply": "2024-04-30T08:46:48.649323Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def proj_orthorombic(c):\n",
    "    \"\"\"Project onto the vector space of Hooke tensors corresponding to orthorombic materials in their frame of reference\"\"\"\n",
    "    to_orthorombic = (c[0,0],c[0,1],c[0,2],c[1,1],c[1,2],c[2,2],c[3,3],c[4,4],c[5,5]) # Seismologists start at 1 ...\n",
    "    return Hooke.from_orthorombic(*to_orthorombic).hooke\n",
    "\n",
    "def frame_score(c,proj,r):\n",
    "    \"\"\"Score for wether c coincides with its projection in the frame defined by r\"\"\"\n",
    "    c = c.rotate(lp.transpose(r)) # Put in specified frame\n",
    "    c.hooke -= proj(c.hooke) # Substract projection \n",
    "    return (c.to_Mandel()**2).sum(axis=(0,1)) # Return frobenius norm squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By construction, the score vanishes if the correct frame is produced, and is positive otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.650878Z",
     "iopub.status.busy": "2024-04-30T08:46:48.650780Z",
     "iopub.status.idle": "2024-04-30T08:46:48.653731Z",
     "shell.execute_reply": "2024-04-30T08:46:48.653503Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vanishing score in the correct frame :  9.442701583533177e-27\n",
      "Positive score otherwise :  14066.444179546052\n"
     ]
    }
   ],
   "source": [
    "r = lp.rotation(np.pi/3,axis=(1,2,3))\n",
    "norm = Hooke.mica[0].rotate(r)\n",
    "print(\"Vanishing score in the correct frame : \",frame_score(norm,proj_orthorombic,r))\n",
    "print(\"Positive score otherwise : \",frame_score(norm,proj_orthorombic,np.eye(3)))      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reference frame reconstruction problem for a Hooke tensor thus be rephrased as \n",
    "$$\n",
    "    min_{r \\in SO_d} f(r),\n",
    "$$\n",
    "where $f(r) = $`frame_score(norm,proj_orthorombic,r)`. Alternatively, projections onto the hexagonal and tetragonal symmetries may be used as well.\n",
    "\n",
    "One may parametrize direct rotations from a sphere\n",
    "* by their first column, which belongs to $S^1$, in dimension two. (This is a bijection.)\n",
    "* by the corresponding unit quaternion, which belongs to $S^3$, in dimension three. (This is a double cover.)\n",
    "\n",
    "Using this quadratic parametrization $R : S^n \\to SO_d$, we obtain a sphere constrained optimization problem, in four variables in dimension three (resp. two variables in dimension two). The objective function is a polynomial of degree $2 \\times 4 \\times 2 = 16$. There exists global methods for such problems, based on positive definite relaxations, but we shall not use them here now.\n",
    "Instead, we content ourselves with a combination of exhaustive search and Newton optimization. The sphere itself is parametrized by the equatorial projection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Alternative projections\n",
    "\n",
    "In addition to the three dimensional orthorombic materials, the hexagonal and tetragonal symmetries are also of interest, as well as the (2,1) block diagonal structure in two dimensions. Projections on these spaces of matrices are needed to optimize the corresponding frame.\n",
    "We use orthogonal projections in the Frobenius scalar product associated with the Mandel form of the Hooke tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.655201Z",
     "iopub.status.busy": "2024-04-30T08:46:48.655096Z",
     "iopub.status.idle": "2024-04-30T08:46:48.657146Z",
     "shell.execute_reply": "2024-04-30T08:46:48.656900Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def proj_hooke2(c):\n",
    "    \"\"\"Project onto the vector space of Hooke tensors with (2,1) block diagonal structure\"\"\"\n",
    "    z = np.zeros_like(c[0,0])\n",
    "    return ad.array([\n",
    "        [c[0,0],c[0,1],     z],\n",
    "        [c[1,0],c[1,1],     z],\n",
    "        [     z,     z,c[2,2]] ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.658528Z",
     "iopub.status.busy": "2024-04-30T08:46:48.658425Z",
     "iopub.status.idle": "2024-04-30T08:46:48.660797Z",
     "shell.execute_reply": "2024-04-30T08:46:48.660553Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def proj_tetragonal(c):\n",
    "    \"\"\"Tetragonal Hooke tensors share the coefficients c11=c22, c13=c23, c44=c55\"\"\"\n",
    "    c11,c12,c13,c22,c23,c33,c44,c55,c66 = ( # Seismologists start at 1 ...\n",
    "        c[0,0],c[0,1],c[0,2],c[1,1],c[1,2],c[2,2],c[3,3],c[4,4],c[5,5])\n",
    "    α=(c11+c22)/2\n",
    "    γ=(c13+c23)/2\n",
    "    δ=(c44+c55)/2\n",
    "    return Hooke.from_orthorombic(α,c12,γ,α,γ,c33,δ,δ,c66).hooke"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.662109Z",
     "iopub.status.busy": "2024-04-30T08:46:48.662011Z",
     "iopub.status.idle": "2024-04-30T08:46:48.664479Z",
     "shell.execute_reply": "2024-04-30T08:46:48.664245Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def proj_hexagonal(c):\n",
    "    \"\"\"Hexagonal Hooke tensors are tetragonal, with the additional property that c66=(c11-c12)/2\"\"\"\n",
    "    c11,c12,c13,c22,c23,c33,c44,c55,c66 = ( # Seismologists start at 1 ...\n",
    "        c[0,0],c[0,1],c[0,2],c[1,1],c[1,2],c[2,2],c[3,3],c[4,4],c[5,5])\n",
    "    α=(3*(c11+c22)+2*c12+4*c66)/8\n",
    "    β=(c11+c22+6*c12-4*c66)/8\n",
    "    γ=(c13+c23)/2\n",
    "    δ=(c44+c55)/2\n",
    "    return Hooke.from_orthorombic(α,β,γ,α,γ,c33,δ,δ,(α-β)/2).hooke"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Optimization routines\n",
    "\n",
    "We parametrize rotations from the unit ball, via quaternions in dimension three, and the simple angular parametrization in dimension two.\n",
    "A roughly uniform sampling of the unit ball is produced by an adequate function.\n",
    "\n",
    "The frame score is extremized via a Newton method, in a purely naive manner : no adaptive stepping is used, and no check of the positive definiteness of the Hessian. We look for a *minimum* of the frame score, but the method is blind to this, and it actually converges a local *maximum* in a large proportion of cases. Nevertheless, if one uses enough seeds, one of them is in practice usually caught in the attraction basin of the optimal frame, which is found by the Newton method, and is eventually selected and returned.\n",
    "\n",
    "<!---\n",
    "# Attempt to eliminate matrices with excessive condition number. Not very convincing.\n",
    "def newton_extremize(f,x,niter,max_cond=1e20):\n",
    "    \"\"\"\n",
    "    Runs niter steps of Newton's method for extremizing f. \n",
    "    (A.k.a, solve grad(f) = 0)\n",
    "    \"\"\"\n",
    "    x_ad = ad.Dense2.identity(constant=x,shape_free=(len(x),))\n",
    "    for i in range(niter):\n",
    "        f_ad = f(x_ad)\n",
    "        H = f_ad.hessian(); \n",
    "        bad=np.linalg.cond(np.moveaxis(H,(0,1),(-2,-1)))>max_cond\n",
    "        H[:,:,bad]=np.nan             \n",
    "        x_ad.value -= lp.solve_AV(H,f_ad.gradient())\n",
    "    return x_ad.value,f_ad.value\n",
    "--->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.665942Z",
     "iopub.status.busy": "2024-04-30T08:46:48.665839Z",
     "iopub.status.idle": "2024-04-30T08:46:48.667800Z",
     "shell.execute_reply": "2024-04-30T08:46:48.667532Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def rotation_from_ball(x):\n",
    "    \"\"\"\n",
    "    Produces a rotation matrix from an element of the unit ball\n",
    "    B_3 -> S_3 (lower half) -> SO_3, via quaternions\n",
    "    B_1 -> SO_2, via rotation of angle pi*x\n",
    "    \"\"\"\n",
    "    if   len(x)==3: return Sphere.rotation3_from_ball3(x)[0] \n",
    "    elif len(x)==1: return lp.rotation(np.pi*x[0])\n",
    "    else: raise ValueError(\"Unsupported dimension\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.669208Z",
     "iopub.status.busy": "2024-04-30T08:46:48.669100Z",
     "iopub.status.idle": "2024-04-30T08:46:48.671082Z",
     "shell.execute_reply": "2024-04-30T08:46:48.670845Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rotation \n",
      "[[-0.58778525 -0.80901699]\n",
      " [ 0.80901699 -0.58778525]]\n",
      " with parameter [0.7]\n",
      "\n",
      "Rotation \n",
      "[[-0.76802317 -0.60051821  0.22252705]\n",
      " [-0.25301021  0.60371895  0.75598232]\n",
      " [-0.58832495  0.52431032 -0.61560738]]\n",
      " with parameter [-0.2, 0.7, 0.3]\n"
     ]
    }
   ],
   "source": [
    "x=[0.7]; print(f\"Rotation \\n{rotation_from_ball(x)}\\n with parameter {x}\\n\")\n",
    "x=[-0.2,0.7,0.3]; print(f\"Rotation \\n{rotation_from_ball(x)}\\n with parameter {x}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.672424Z",
     "iopub.status.busy": "2024-04-30T08:46:48.672330Z",
     "iopub.status.idle": "2024-04-30T08:46:48.674454Z",
     "shell.execute_reply": "2024-04-30T08:46:48.674214Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def ball_samples(vdim,dens):\n",
    "    \"\"\"\n",
    "    Produce samples of the unit ball of dimension vdim.\n",
    "    Approx c(vdim) * dens^vdim elements.\n",
    "    \"\"\"\n",
    "    aB,h = np.linspace(-1,1,dens,retstep=True,endpoint=False)\n",
    "    B = np.array(np.meshgrid(*(aB,)*vdim,indexing='ij'))\n",
    "    B += h*np.random.rand(*B.shape) # Add random perturbations\n",
    "    B = B[:,np.linalg.norm(B,axis=0)<=1]\n",
    "    return B.reshape(vdim,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.675793Z",
     "iopub.status.busy": "2024-04-30T08:46:48.675699Z",
     "iopub.status.idle": "2024-04-30T08:46:48.739628Z",
     "shell.execute_reply": "2024-04-30T08:46:48.739336Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Uniform sampling of the unit ball'); plt.axis('equal')\n",
    "plt.scatter(*ball_samples(2,10));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.741437Z",
     "iopub.status.busy": "2024-04-30T08:46:48.741329Z",
     "iopub.status.idle": "2024-04-30T08:46:48.743540Z",
     "shell.execute_reply": "2024-04-30T08:46:48.743301Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def newton_extremize(f,x,niter,max_cond=1e10):\n",
    "    \"\"\"\n",
    "    Runs niter steps of Newton's method for extremizing f. \n",
    "    (A.k.a, solve grad(f) = 0)\n",
    "    \"\"\"\n",
    "    x_ad = ad.Dense2.identity(constant=x,shape_free=(len(x),))\n",
    "    for i in range(niter):\n",
    "        f_ad = f(x_ad)\n",
    "#        print(np.linalg.eigvalsh(f_ad.coef2[0]))\n",
    "        x_ad.value -= lp.solve_AV(f_ad.hessian(),f_ad.gradient())\n",
    "    return x_ad.value,f_ad.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.744850Z",
     "iopub.status.busy": "2024-04-30T08:46:48.744756Z",
     "iopub.status.idle": "2024-04-30T08:46:48.746964Z",
     "shell.execute_reply": "2024-04-30T08:46:48.746742Z"
    },
    "tags": [
     "ExportCode"
    ]
   },
   "outputs": [],
   "source": [
    "def hooke_frame(c,proj,dens=8,niter=8):\n",
    "    \"\"\"\n",
    "    Optimize the frame score, via a Newton method, with a large number of initial seeds.\n",
    "    Return the best rotation and associated score.\n",
    "    \"\"\"\n",
    "    def f(x): return frame_score(c,proj,rotation_from_ball(x))\n",
    "    x = ball_samples({2:1,3:3}[c.vdim],dens) \n",
    "    x,f_x = newton_extremize(f,x,niter)\n",
    "    argmin = np.nanargmin(f_x)\n",
    "    return lp.transpose(rotation_from_ball(x[:,argmin])),f_x[argmin]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Two dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.748379Z",
     "iopub.status.busy": "2024-04-30T08:46:48.748288Z",
     "iopub.status.idle": "2024-04-30T08:46:48.749776Z",
     "shell.execute_reply": "2024-04-30T08:46:48.749538Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(42) # Reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.751089Z",
     "iopub.status.busy": "2024-04-30T08:46:48.751007Z",
     "iopub.status.idle": "2024-04-30T08:46:48.762064Z",
     "shell.execute_reply": "2024-04-30T08:46:48.761820Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hooke tensor : \n",
      "[[154.88711806  26.86228904  35.4467799 ]\n",
      " [ 26.86228904  53.28830387  -0.69303566]\n",
      " [ 35.4467799   -0.69303566  24.56228904]]\n",
      "found to be block diagonal in frame : \n",
      "[[-0.95533649 -0.29552021]\n",
      " [ 0.29552021 -0.95533649]],\n",
      "with score : 6.247778369350414e-28.\n",
      "In this frame of reference : \n",
      "[[ 1.78000000e+02  1.45000000e+01 -8.97253389e-15]\n",
      " [ 1.45000000e+01  5.49000000e+01  1.86710653e-15]\n",
      " [-1.24012868e-14  3.10068543e-15  1.22000000e+01]]\n"
     ]
    }
   ],
   "source": [
    "r,score = hooke_frame(norm2,proj_hooke2,dens=8)\n",
    "print(f\"Hooke tensor : \\n{norm2.hooke}\\nfound to be block diagonal in frame : \\n{r},\\nwith score : {score}.\")\n",
    "print(f\"In this frame of reference : \\n{norm2.rotate(r).hooke}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Likewise, a frame of reference with a negligible score residual is found for all our examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.763491Z",
     "iopub.status.busy": "2024-04-30T08:46:48.763412Z",
     "iopub.status.idle": "2024-04-30T08:46:48.789547Z",
     "shell.execute_reply": "2024-04-30T08:46:48.789327Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hooke tensor mica2 found frame [[-0.36235775 -0.93203909]\n",
      " [ 0.93203909 -0.36235775]] with score 4.827828739952593e-28.\n",
      "Hooke tensor stishovite2 found frame [[ 0.47942554  0.87758256]\n",
      " [-0.87758256  0.47942554]] with score 4.038967834731581e-27.\n",
      "Hooke tensor mudshale2 found frame [[ 0.87758256 -0.47942554]\n",
      " [ 0.47942554  0.87758256]] with score 2.1684043449710093e-18.\n"
     ]
    }
   ],
   "source": [
    "for name,norm in norms2[1:]:\n",
    "    r,score = hooke_frame(norm,proj_hooke2,dens=8)\n",
    "    print(f\"Hooke tensor {name} found frame {r} with score {score}.\")\n",
    "    assert score<1e-8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 Three dimensions\n",
    "\n",
    "**Note on performance.**\n",
    "The numerical code presented below is too slow to be usable in practice, but could easily be (greatly) optimized. A lot of overhead is related with instance creation within the custom automatic differentiation library. A gpu accelerated code, orders of magnitude faster, is presented at the end of this document.\n",
    "\n",
    "**Note on robustness.**\n",
    "The `np.linalg.solve` fails in to the presence of singular matrices. We often encounter these, since we run a Newton method on a rather arbitrary (polynomial) function, without any guarantees, and from many seed points. An easy fix would be to abort the Newton method for all those seed points which raise such a singular matrix exception."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.791008Z",
     "iopub.status.busy": "2024-04-30T08:46:48.790930Z",
     "iopub.status.idle": "2024-04-30T08:46:48.792633Z",
     "shell.execute_reply": "2024-04-30T08:46:48.792410Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(44) # Reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.793935Z",
     "iopub.status.busy": "2024-04-30T08:46:48.793858Z",
     "iopub.status.idle": "2024-04-30T08:46:48.832735Z",
     "shell.execute_reply": "2024-04-30T08:46:48.832462Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.254809  , -0.96504472,  0.0613275 ],\n",
       "        [-0.85672573,  0.25470969,  0.44849079],\n",
       "        [-0.44843438,  0.06173864, -0.89168097]]),\n",
       " 2.8985865812469996e-27)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hooke_frame(norm3,proj_orthorombic,dens=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.834127Z",
     "iopub.status.busy": "2024-04-30T08:46:48.834047Z",
     "iopub.status.idle": "2024-04-30T08:46:48.928812Z",
     "shell.execute_reply": "2024-04-30T08:46:48.928534Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hooke tensor mica3 found frame [[ 0.96705012  0.20405886 -0.15223022]\n",
      " [ 0.19169447 -0.97712804 -0.09205447]\n",
      " [-0.16753295  0.05983959 -0.98404875]] with score 7.004377435266216e-28.\n",
      "Hooke tensor stishovite3 found frame [[ 0.34276047  0.92847926  0.14297383]\n",
      " [-0.5152635   0.31306797 -0.79780447]\n",
      " [-0.78550544  0.19978664  0.5857188 ]] with score 2.853530775237862e-25.\n"
     ]
    }
   ],
   "source": [
    "for name,norm in norms3:\n",
    "    r,score = hooke_frame(norm,proj_orthorombic,dens=5)\n",
    "    print(f\"Hooke tensor {name} found frame {r} with score {score}.\")\n",
    "    assert score<1e-8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 GPU acceleration of the TTI projection\n",
    "\n",
    "In order to apply the above projection to meaningful test cases for seimic applications, which involve millions of Hooke tensors, computation time must be sped up dramatically. \n",
    "\n",
    "The proposed GPU implementation is based on : \n",
    "- the treatment of each different hooke Tensor in a different thread, in an embarassingly parallel manner\n",
    "- a specific optimization in dimension 3, taking advantage of the invariance of VTI metrics subject to rotations along the z-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T08:46:48.930420Z",
     "iopub.status.busy": "2024-04-30T08:46:48.930325Z",
     "iopub.status.idle": "2024-04-30T08:46:49.003284Z",
     "shell.execute_reply": "2024-04-30T08:46:49.002821Z"
    }
   },
   "outputs": [
    {
     "ename": "DeliberateNotebookError",
     "evalue": "Cupy library not found",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mDeliberateNotebookError\u001b[0m                   Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[59], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m ad\u001b[38;5;241m.\u001b[39mBase\u001b[38;5;241m.\u001b[39mcp \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m: \u001b[38;5;28;01mraise\u001b[39;00m ad\u001b[38;5;241m.\u001b[39mDeliberateNotebookError(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCupy library not found\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m      2\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01magd\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mEikonal\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mHFM_CUDA\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mProjectionTTI\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m ProjectionTTI\n",
      "\u001b[0;31mDeliberateNotebookError\u001b[0m: Cupy library not found"
     ]
    }
   ],
   "source": [
    "if ad.Base.cp is None: raise ad.DeliberateNotebookError(\"Cupy library not found\")\n",
    "from agd.Eikonal.HFM_CUDA.ProjectionTTI import ProjectionTTI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reload_packages():\n",
    "    from Miscellaneous.rreload import rreload\n",
    "    global ad,ProjectionTTI\n",
    "    Hooke,ad,ProjectionTTI, = rreload([Hooke,ad,ProjectionTTI],rootdir=\"../..\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Taking advantage of VTI rotational invariance\n",
    "\n",
    "**Three dimensions.**\n",
    "Let us consider a material which does *not* have a TTI structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm = Hooke.olivine[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And introduce the following rotations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "r0 = lp.rotation(0.8,(1,2,3)) # Some arbitrary rotation\n",
    "def rx(θ): return lp.rotation(θ,(1,0,0)) # A rotation along the x-axis\n",
    "def ry(θ): return lp.rotation(θ,(0,1,0)) # A rotation along the y-axis\n",
    "def rz(θ): return lp.rotation(θ,(0,0,1)) # A rotation along the z-axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that the objective is to find a frame which minimizes the VTI projection error.\n",
    "However, since the set of VTI tensors is invariant under the action of rotations along the z-axis, the projection error also is.\n",
    "\n",
    "We also have some invariance by symmetry around the $x$ and $y$-axes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = [frame_score(norm,proj_hexagonal,r0 @ rx(θx) @ ry(θy) @ rz(θz))\n",
    "          for θx in (0,np.pi) for θy in (0,np.pi) for θz in np.linspace(0,np.pi,10)]\n",
    "assert np.allclose(scores,scores[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any rotation matrix can be written as the composition\n",
    "$$\n",
    "    r(\\theta_x,\\theta_y,\\theta_z) := r_x(\\theta_x) r_y(\\theta_y) r_z(\\theta_z)\n",
    "$$\n",
    "of three rotations around the $x$, $y$ and $z$ axes.\n",
    "\n",
    "Based on the above invariance property, if one wants to optimize the TTI projection error, then it is sufficient to optimize the parameter $\\theta_x\\in [0,\\pi]$ and $\\theta_y \\in [0,\\pi]$, and one can set $\\theta_z=0$. \n",
    "\n",
    "Note that rotations along the $x$ and $y$ axes do not commute, but we have the identity\n",
    "$$\n",
    "    r_x(\\pi) r_y(\\theta_y) = r_y(-\\theta_y) r_x(\\pi).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Two dimensions.** There is a weaker invariance property, which that the set of VTI tensors is invariant under a rotation of $\\pi/2$, exchanging the roles of the $x$ and $y$ axes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Validation tests\n",
    "\n",
    "Since the implementation is embarassingly parallel, the computation time does not increase much until the number of Hooke tensors exceeds the number of threads of the GPU (about 2560 on a GTX 1080)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "norm = Hooke.olivine[0]\n",
    "nrand = 2500\n",
    "angle = np.random.uniform(0,np.pi,nrand)\n",
    "axis = np.random.uniform(size=(3,nrand))\n",
    "norms = norm.rotate_by(angle,axis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[398.52292 398.52243 398.52237 398.5226  398.52246 398.52267 398.52206\n",
      " 398.52283 398.52234 398.52252]\n",
      "CPU times: total: 2.84 s\n",
      "Wall time: 4.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "score,hexa,rotation = ProjectionTTI(norms.hooke)\n",
    "print(score[:10]) # Do not remove, otherwise false timing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this special case, we applied random rotations to a fixed norm. But then we inverse that process by finding the optimal frame of reference. As a result, the obtained TTI projection errors are all identical.\n",
    "(Note that there is some amount of roundoff error, since the Hooke tensor coefficients are rather large, and the GPU uses single precision.)\n",
    "\n",
    "Note that the original rotations, with the angles and axes defined above, *cannot* recovered, because of the $z$ rotational invariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.00195312, dtype=float32)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(score-score[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.allclose(score,score[0],atol=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We recover the projection error scores defined in this notebook, up to a factor two."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "score2 = 0.5*frame_score(norms,proj_hexagonal,rotation.get())\n",
    "assert np.allclose(score2,score[0],atol=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "tti_approx = Hooke.from_hexagonal(*hexa).rotate(rotation)\n",
    "tti_approx = Hooke(tti_approx.hooke.get())\n",
    "score3 = 0.5*np.sum( (tti_approx.to_Mandel()-norms.to_Mandel())**2,axis=(0,1) )\n",
    "assert np.allclose(score3,score[0],atol=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can build a TTI metric from the output of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "TTI.from_hexagonal(*hexa).rotate(rotation);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the ProjectionTTI implementation uses optimization over two angles. The quaternion approach was also implemented, for reproducibility, but it is slower and there should be no good reason to use it at this time. (The quaternion approach may be used in the future to compute projections onto a sets of Hooke tensors which are not $z$ rotationally invariant, such as orthorombic tensors.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[398.52292 398.52243 398.52237 398.5226  398.52246 398.52267 398.52206\n",
      " 398.52283 398.52234 398.52252]\n",
      "CPU times: total: 3.05 s\n",
      "Wall time: 3.06 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "score_quat,hexa,rotation = ProjectionTTI(norms.hooke,quaternion=True)\n",
    "print(score[:10]) # Do not remove, otherwise false timing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By construction, the projection error is the same. However the rotations are expected to differ from the previous ones, again due to $z$ rotational invariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.allclose(score_quat,score[0],atol=0.05)\n",
    "tti_approx = Hooke.from_hexagonal(*hexa).rotate(rotation)\n",
    "tti_approx = Hooke(tti_approx.hooke.get())\n",
    "score3 = 0.5*np.sum( (tti_approx.to_Mandel()-norms.to_Mandel())**2,axis=(0,1) )\n",
    "assert np.allclose(score3,score[0],atol=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we test the two dimensional implementation.\n",
    "Since all classical two dimensional materials are TTI, we build a random positive definite Hooke tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "A = np.random.rand(3,3)-0.5\n",
    "norm = Hooke(A.T @ A + 0.3*np.eye(3))\n",
    "angles = 2*np.pi*np.random.rand(nrand)\n",
    "norms = norm.rotate_by(angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00021021 0.00021021 0.00021021 0.00021021 0.00021021 0.00021021\n",
      " 0.00021021 0.00021021 0.00021021 0.00021021]\n",
      "CPU times: total: 391 ms\n",
      "Wall time: 391 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "score,hexa,rotation = ProjectionTTI(norms.hooke)\n",
    "print(score[:10]) # Do not remove, otherwise false timing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, since the same norm is subject to random rotations, the obtained projection errors are identical."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.allclose(score,score[0],atol=1e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "score2 = 0.5*frame_score(norms,proj_hooke2,rotation.get())\n",
    "assert np.allclose(score2,score[0],atol=1e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "tti_approx = Hooke.from_hexagonal(*hexa,vdim=2).rotate(rotation)\n",
    "tti_approx = Hooke(tti_approx.hooke.get())\n",
    "score3 = 0.5*np.sum( (tti_approx.to_Mandel()-norms.to_Mandel())**2,axis=(0,1) )\n",
    "assert np.allclose(score3,score[0],atol=1e-8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, one can build a TTI norm from the output of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "TTI.from_hexagonal(*hexa,vdim=2).rotate(rotation);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check visually the quality of the TTI approximation.\n",
    "In this case it is almost perfect. Note that exact reconstruction is not possible in general, since a two dimensional Hooke tensor is defined by $6$ parameters, whereas the TTI approximation is defined by $5$ parameters (4 coefficients and an angle)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "i0 = 10\n",
    "c11,_,c13,c33,c44 = hexa\n",
    "c11,c13,c33,c44 = [x[i0].get() for x in (c11,c13,c33,c44)]\n",
    "tti0 = TTI.from_hexagonal(c11,None,c13,c33,c44,vdim=2).rotate(rotation[:,:,i0].get())\n",
    "norm0 = norm.rotate_by(angles[i0])\n",
    "\n",
    "#import cupy as cp\n",
    "aX = np.linspace(-1.2,1.2)\n",
    "X = np.meshgrid(aX,aX,indexing='ij')\n",
    "plt.axis('equal')\n",
    "plt.contour(*X,tti0.norm(X),levels=[1.01],colors='red') # Red : tti approximation\n",
    "plt.contour(*X,norm0.norm(X),levels=[1],colors='blue'); # Blue : original hooke tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time, in contrast with the three dimensional case, one can recover the rotation angles, up to a multiple of $\\pi/2$ in view of the invariances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "score,hexa,θ = ProjectionTTI(norms.hooke,ret_rot=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff = θ.get()+angles # Note the different sign conventions\n",
    "diff = (diff - diff[0])/(np.pi/2) # convert to quarter turns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.max(np.abs(np.round(diff) - diff)) < 1e-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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