2024-07-15_caustique-Granet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.668239Z",
     "iopub.status.busy": "2022-09-16T06:50:17.667940Z",
     "iopub.status.idle": "2022-09-16T06:50:17.670759Z",
     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "\n",
    "# the higher PRECISION, the bigger the file\n",
    "# PRECISION = 4  # debugging\n",
    "# PRECISION = 10 # good quality\n",
    "PRECISION = 12 # for production\n",
    "# PRECISION = 13 # for production\n",
    "\n",
    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
    "from dataclasses import dataclass\n",
    "\n",
    "@dataclass\n",
    "class init:\n",
    "    figpath: str = '2024-07-15_caustique-Granet' # Folder to store images\n",
    "    phi: float = 1.61803 # beauty is gold\n",
    "    tag: str = 'caustique' # Tag\n",
    "    ext: str = 'png' # Extension for output\n",
    "    nx: int = 5*2**PRECISION # number of pixels (vertical)\n",
    "    ny: int = 5*2**PRECISION # number of pixels (horizontal)\n",
    "    nframe: int = 1 # number of frames\n",
    "    bin_dens: int = 1 # relative bin density\n",
    "    bin_spectrum: int = 1 # bin spacing in spectrum (lower is more CPU)\n",
    "    seed: int = 2024 # seed for RNG\n",
    "    H: float = 20.0 # depth of the pool\n",
    "    variation: float = .20 # variation of diffraction index: http://www.philiplaven.com/p20.html 1.40 at 400 nm and 1.37 at 700nm makes a 2% variation\n",
    "    scale: float = .50*2**PRECISION # period in pixels\n",
    "    B_sf: float = 0.75 # bandwidth in sf\n",
    "    V_Y: float = 0.3 # horizontal speed\n",
    "    V_X: float = 0.3 # vertical speed\n",
    "    B_V: float = 1.0 # bandwidth in speed\n",
    "    zmin: float = 0.2 # gradient of wave height\n",
    "    # theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
    "    theta: float = np.pi/2 # angle with the horizontal\n",
    "    B_theta: float = 60*np.pi/180 # bandwidth in theta\n",
    "    min_lum: float = .1 # diffusion level for the rendering\n",
    "    gamma: float = 2.9 # Gamma exponant to convert luminosity to luminance\n",
    "    fps: float = 18 # frames per second\n",
    "    multispectral: bool = True # Compute caustics on the full spectrogram.\n",
    "    cache: bool = False # Cache intermediate output.\n",
    "    verbose: bool = True # Displays more verbose output.\n",
    "    do_display: bool = True # Displays images in notebook.\n",
    "    do_recompute: bool = False # Restart each computation    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.688713Z",
     "iopub.status.busy": "2022-09-16T06:50:17.688504Z",
     "iopub.status.idle": "2022-09-16T06:50:17.691583Z",
     "shell.execute_reply": "2022-09-16T06:50:17.691125Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving our simulations in=2024-07-15_caustique-Granet\n"
     ]
    }
   ],
   "source": [
    "opt = init()\n",
    "print(f'Saving our simulations in={opt.figpath}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "if opt.nframe==1: opt.ext = 'png'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
     "iopub.status.idle": "2022-09-16T06:50:17.734829Z",
     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "init(figpath='2024-07-15_caustique-Granet',\n",
      "     phi=1.61803,\n",
      "     tag='caustique',\n",
      "     ext='tiff',\n",
      "     nx=20480,\n",
      "     ny=20480,\n",
      "     nframe=1,\n",
      "     bin_dens=1,\n",
      "     bin_spectrum=1,\n",
      "     seed=2024,\n",
      "     H=20.0,\n",
      "     variation=0.2,\n",
      "     scale=2048.0,\n",
      "     B_sf=0.75,\n",
      "     V_Y=0.3,\n",
      "     V_X=0.3,\n",
      "     B_V=1.0,\n",
      "     zmin=0.2,\n",
      "     theta=1.5707963267948966,\n",
      "     B_theta=1.0471975511965976,\n",
      "     min_lum=0.1,\n",
      "     gamma=2.9,\n",
      "     fps=18,\n",
      "     multispectral=True,\n",
      "     cache=False,\n",
      "     verbose=True,\n",
      "     do_display=True,\n",
      "     do_recompute=True)\n"
     ]
    }
   ],
   "source": [
    "from pprint import pprint\n",
    "pprint(opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## utilities\n",
    "\n",
    "Transfoming a sequence of PNG frames into gif or mp4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.737334Z",
     "iopub.status.busy": "2022-09-16T06:50:17.737126Z",
     "iopub.status.idle": "2022-09-16T06:50:17.741165Z",
     "shell.execute_reply": "2022-09-16T06:50:17.740716Z"
    }
   },
   "outputs": [],
   "source": [
    "def make_gif(gifname, fnames, fps, do_delete=True):\n",
    "    import imageio\n",
    "\n",
    "    with imageio.get_writer(gifname, mode='I', fps=fps) as writer:\n",
    "        for fname in fnames:\n",
    "            writer.append_data(imageio.imread(fname))\n",
    "\n",
    "    from pygifsicle import optimize\n",
    "    optimize(str(gifname))\n",
    "    if do_delete: \n",
    "        for fname in fnames: os.remove(fname)\n",
    "    return gifname\n",
    "\n",
    "# https://moviepy.readthedocs.io/en/latest/getting_started/videoclips.html#imagesequenceclip\n",
    "def make_mp4(mp4name, fnames, fps, do_delete=True):\n",
    "    import moviepy.editor as mpy\n",
    "    clip = mpy.ImageSequenceClip(fnames, fps=fps)\n",
    "    clip.write_videofile(mp4name, fps=fps, codec='libx264', verbose=False, logger=None)\n",
    "    if do_delete: \n",
    "        for fname in fnames: os.remove(fname)\n",
    "    return mp4name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Utilities to compute the spectrum of the blue sky and convert them later to RGB values (check out https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for details)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
     "iopub.status.busy": "2022-09-16T06:50:17.743461Z",
     "iopub.status.idle": "2022-09-16T06:50:17.757701Z",
     "shell.execute_reply": "2022-09-16T06:50:17.757282Z"
    }
   },
   "outputs": [],
   "source": [
    "from lambda2color import Lambda2color, xyz_from_xy\n",
    "\n",
    "# borrowed from https://github.com/gummiks/gummiks.github.io/blob/master/scripts/astro/planck.py\n",
    "def planck(wav, T):\n",
    "    import scipy.constants as const\n",
    "    c = const.c # c = 3.0e+8\n",
    "    h = const.h # h = 6.626e-34\n",
    "    k = const.k # k = 1.38e-23\n",
    "    a = 2.0*h*c**2\n",
    "    b = h*c/(wav*k*T)\n",
    "    intensity = a / ( (wav**5) * (np.exp(b) - 1.0) )\n",
    "    return intensity\n",
    "\n",
    "def scattering(wav, a=0.005, p=1.3, b=0.45):\n",
    "    \"\"\"\n",
    "    b is  proportionate  to  the  column  density  of  aerosols\n",
    "    along  the  path  of  sunlight,  from  outside  the  atmosphere\n",
    "    to  the  point  of  observation\n",
    "    \n",
    "    see https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for more details\n",
    "\n",
    "    \"\"\"\n",
    "    # converting wav in µm:\n",
    "    intensity = np.exp(-a/((wav/1e-6)**4)) # Rayleigh extinction by nitrogen\n",
    "    intensity *= (wav/1e-6)**-4\n",
    "    intensity *= np.exp(-b/((wav/1e-6)**p)) # Aerosols\n",
    "    return intensity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## computing the caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.012647Z",
     "iopub.status.busy": "2022-09-16T06:50:17.012413Z",
     "iopub.status.idle": "2022-09-16T06:50:17.665184Z",
     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm, trange\n",
    "import shutil\n",
    "import hashlib\n",
    "import MotionClouds as mc\n",
    "\n",
    "class Caustique:\n",
    "    def __init__(self, opt):\n",
    "        \"\"\"\n",
    "        Image coordinates follow 'ij' indexing, that is,\n",
    "        * their origin at the top left,\n",
    "        * the X axis is vertical and goes \"down\",\n",
    "        * the Y axis is horizontal and goes \"right\".\n",
    "\n",
    "        \"\"\"\n",
    "        self.mc = mc\n",
    "        self.ratio = opt.ny/opt.nx # ratio between height and width (>1 for portrait, <1 for landscape)\n",
    "        X = np.linspace(0, 1, opt.nx, endpoint=False) # vertical\n",
    "        Y = np.linspace(0, self.ratio, opt.ny, endpoint=False) # horizontal\n",
    "        self.xv, self.yv = np.meshgrid(X, Y, indexing='ij')\n",
    "        self.opt = opt\n",
    "        # https://stackoverflow.com/questions/16878315/what-is-the-right-way-to-treat-python-argparse-namespace-as-a-dictionary\n",
    "        self.d = vars(opt)\n",
    "        os.makedirs(self.opt.figpath, exist_ok=True)\n",
    "        self.cachepath = os.path.join('/tmp', self.opt.figpath)\n",
    "        if opt.verbose: print(f'{self.cachepath=}')\n",
    "        os.makedirs(self.cachepath, exist_ok=True)\n",
    "\n",
    "        # a standard white:\n",
    "        # illuminant_D65 = xyz_from_xy(0.3127, 0.3291), \n",
    "        illuminant_sun = xyz_from_xy(0.325998, 0.335354)\n",
    "        # color conversion class\n",
    "        self.cs_srgb = Lambda2color(red=xyz_from_xy(0.64, 0.33),\n",
    "                               green=xyz_from_xy(0.30, 0.60),\n",
    "                               blue=xyz_from_xy(0.15, 0.06),\n",
    "                               white=illuminant_sun)\n",
    "        self.wavelengths = self.cs_srgb.cmf[:, 0]*1e-9\n",
    "        self.N_wavelengths = len(self.wavelengths)\n",
    "        # multiply by the spectrum of the sky\n",
    "        intensity5800 = planck(self.wavelengths, 5800.)\n",
    "        scatter = scattering(self.wavelengths)\n",
    "        self.spectrum_sky = intensity5800 * scatter\n",
    "        self.spectrum_sky /= self.spectrum_sky.max()\n",
    "\n",
    "    def wave(self):\n",
    "        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'\n",
    "        if os.path.isfile(filename) and not(self.opt.do_recompute):\n",
    "            z = np.load(filename)\n",
    "        else:\n",
    "            # A simplistic model of a wave using https://github.com/NeuralEnsemble/MotionClouds\n",
    "            fx, fy, ft = mc.get_grids(self.opt.nx, self.opt.ny, self.opt.nframe)\n",
    "            env = mc.envelope_gabor(fx, fy, ft, V_X=self.opt.V_Y, V_Y=self.opt.V_X, B_V=self.opt.B_V,\n",
    "                                    sf_0=1./self.opt.scale, B_sf=self.opt.B_sf/self.opt.scale,\n",
    "                                    theta=self.opt.theta, B_theta=self.opt.B_theta)\n",
    "            z = mc.rectif(mc.random_cloud(env, seed=self.opt.seed))\n",
    "            if self.opt.cache: np.save(filename, z)\n",
    "        return z * np.linspace(self.opt.zmin, 1., self.opt.nx)[:, None, None]\n",
    "\n",
    "    def transform(self, z_, modulation=1.):\n",
    "        xv, yv = self.xv.copy(), self.yv.copy()\n",
    "\n",
    "        dzdx = z_ - np.roll(z_, 1, axis=0)\n",
    "        dzdy = z_ - np.roll(z_, 1, axis=1)\n",
    "        xv = xv + modulation * self.opt.H * dzdx\n",
    "        yv = yv + modulation * self.opt.H * dzdy\n",
    "\n",
    "        xv = np.mod(xv, 1)\n",
    "        yv = np.mod(yv, self.ratio)\n",
    "\n",
    "        return xv, yv\n",
    "\n",
    "    def plot(self, z, image=None, do_color=True, dpi=50):\n",
    "        \"\"\"\n",
    "        \n",
    "        dpi: output resolution - sets the figure size as we ensure there is a one to one correspondance between pixels in the data and the output image\n",
    "        \"\"\"\n",
    "\n",
    "        # output filename        \n",
    "        md5 = hashlib.sha224((self.opt.figpath + self.opt.tag).encode()).hexdigest()[:8] # an unique identifier for future tagging\n",
    "        output_filename = f'{self.opt.figpath}/{self.opt.tag}_{md5}.{self.opt.ext}'\n",
    "        if os.path.isfile(output_filename) and not(self.opt.do_recompute):\n",
    "            return output_filename\n",
    "        else:\n",
    "            # 1/ do the raytracing of image through z:\n",
    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
    "\n",
    "            # a fixed image in degree of contrast (from 0=black to 1=white)\n",
    "            if image is None: image = np.ones((self.opt.nx, self.opt.ny))\n",
    "\n",
    "            #hist = self.do_raytracing(z)\n",
    "            # binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
    "\n",
    "            subplotpars = matplotlib.figure.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)\n",
    "\n",
    "            if self.opt.multispectral:\n",
    "\n",
    "                #image_rgb = self.cs_srgb.spec_to_rgb(hist)\n",
    "                image_rgb = np.zeros((self.opt.nx//self.opt.bin_dens,  self.opt.ny//self.opt.bin_dens, 3, self.opt.nframe))\n",
    "                for i_frame in trange(self.opt.nframe):\n",
    "                    for i_wavelength in trange(self.opt.bin_spectrum//2, self.N_wavelengths, self.opt.bin_spectrum):\n",
    "                        modulation = 1. + self.opt.variation/2 - self.opt.variation*i_wavelength/self.N_wavelengths\n",
    "                        xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)\n",
    "                        hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                     bins=[binsx, binsy],\n",
    "                                                     weights=image.ravel(),\n",
    "                                                     range=[[0, 1], [0, self.ratio]],\n",
    "                                                     density=True)\n",
    "\n",
    "                        # we convert the spectrum into a color\n",
    "                        spec = np.zeros((self.N_wavelengths))\n",
    "                        spec[i_wavelength] = 1\n",
    "                        rgb = self.cs_srgb.spec_to_rgb(spec)\n",
    "                        rgb *= self.spectrum_sky[i_wavelength]\n",
    "                        # we add the color to the image\n",
    "                        image_rgb[:, :, :, i_frame] += hist_[:, :, None] * rgb[None, None, :]\n",
    "\n",
    "                image_rgb -= image_rgb.min()\n",
    "                image_rgb /= image_rgb.max()\n",
    "            else:\n",
    "                hist = np.zeros((binsx, binsy, self.opt.nframe))\n",
    "                for i_frame in trange(self.opt.nframe):\n",
    "                    xv, yv = self.transform(z[:, :, i_frame])\n",
    "                    hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                        bins=[binsx, binsy],\n",
    "                                                        range=[[0, 1], [0, self.ratio]],\n",
    "                                                        density=True)\n",
    "                #hist /= hist.max()\n",
    "\n",
    "            # 2/ transform light into image:\n",
    "            fnames = []\n",
    "            for i_frame in trange(self.opt.nframe):\n",
    "                fig, ax = plt.subplots(figsize=(self.opt.ny/self.opt.bin_dens/dpi, self.opt.nx/self.opt.bin_dens/dpi), subplotpars=subplotpars)\n",
    "                if self.opt.multispectral:\n",
    "                    ax.imshow(image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma), vmin=0, vmax=1)\n",
    "                else:\n",
    "                    if do_color:\n",
    "                        bluesky = np.array([0.268375, 0.283377]) # xyz\n",
    "                        sun = np.array([0.325998, 0.335354]) # xyz\n",
    "                        # ax.pcolormesh(edge_y, edge_x, hist[:, :, i_frame], vmin=0, vmax=1, cmap=plt.cm.Blues_r)\n",
    "                        # https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram\n",
    "                        L1 = 1 - hist[:, :, i_frame]\n",
    "                        L2 = hist[:, :, i_frame]\n",
    "                        image_denom = L1 / bluesky[1] + L2 / sun[1]\n",
    "                        image_x = (L1 * bluesky[0] / bluesky[1] + L2 * sun[0] / sun[1]) / image_denom\n",
    "                        image_y = (L1 + L2) / image_denom \n",
    "                        image_xyz = np.dstack((image_x, image_y, 1 - image_x - image_y))\n",
    "                        image_rgb = self.cs_srgb.xyz_to_rgb(image_xyz)\n",
    "                        image_L = self.opt.min_lum + (1-self.opt.min_lum)* L2 ** .61803\n",
    "                        ax.imshow(image_L[:, :, None]*image_rgb, vmin=0, vmax=1)\n",
    "\n",
    "                    else:\n",
    "                        ax.imshow(1-image_L, vmin=0, vmax=1)\n",
    "\n",
    "                fname = f'{self.cachepath}/{self.opt.tag}_frame_{i_frame:04d}.png'\n",
    "                fig.savefig(fname, dpi=dpi)\n",
    "                fnames.append(fname)\n",
    "                plt.close('all')\n",
    "\n",
    "            if self.opt.nframe==1:\n",
    "                shutil.copyfile(fname, output_filename)\n",
    "                return output_filename\n",
    "            else:\n",
    "                if self.opt.ext == 'gif':\n",
    "                    return make_gif(output_filename, fnames, fps=self.opt.fps)\n",
    "                else:\n",
    "                    return make_mp4(output_filename, fnames, fps=self.opt.fps)\n",
    "\n",
    "    def show(self, output_filename, width=1024):\n",
    "        from IPython.display import HTML, Image, display\n",
    "        if self.opt.nframe==1:\n",
    "            display(Image(url=output_filename.replace(self.opt.ext, 'png'), width=width))\n",
    "        else:\n",
    "            if self.opt.ext == 'gif':\n",
    "                return display(Image(url=output_filename, width=width))\n",
    "            else:\n",
    "                #import moviepy.editor as mpy\n",
    "                #return mpy.ipython_display(output_filename, width=width)\n",
    "                # https://github.com/NeuralEnsemble/MotionClouds/blob/master/MotionClouds/MotionClouds.py#L858\n",
    "                opts = ' loop=\"1\" autoplay=\"1\" controls '\n",
    "                html = HTML(f'<video {opts} width=\"{width}\"> <source src=\"{output_filename}\" type=\"video/{self.opt.ext}\" />  </video>')\n",
    "                html.reload()\n",
    "                return display(html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# the selected caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.864888Z",
     "iopub.status.busy": "2022-09-16T06:50:17.864663Z",
     "iopub.status.idle": "2022-09-16T06:50:19.896847Z",
     "shell.execute_reply": "2022-09-16T06:50:19.896285Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "self.cachepath='/tmp/2024-07-15_caustique-Granet'\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(20480, 20480, 1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mLe noyau s’est bloqué lors de l’exécution du code dans une cellule active ou une cellule précédente. \n",
      "\u001b[1;31mVeuillez vérifier le code dans la ou les cellules pour identifier une cause possible de l’échec. \n",
      "\u001b[1;31mCliquez <a href='https://aka.ms/vscodeJupyterKernelCrash'>ici</a> pour plus d’informations. \n",
      "\u001b[1;31mPour plus d’informations, consultez Jupyter <a href='command:jupyter.viewOutput'>log</a>."
     ]
    }
   ],
   "source": [
    "def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
    "    # image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
    "    # image = (image>=1) * 1.\n",
    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "self.cachepath='/tmp/2024-07-15_caustique-Granet'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [44:51<00:00, 33.22s/it]\n",
      "100%|██████████| 1/1 [44:51<00:00, 2691.02s/it]\n",
      "  0%|          | 0/1 [00:00<?, ?it/s]"
     ]
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.figpath}-{PRECISION=}'\n",
    "output_filename = c.plot(z, image)\n",
    "pprint(output_filename)\n",
    "# c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c.show(output_filename)"
   ]
  }
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