2024-08-15_caustique-bands.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Requirement already satisfied: jsonpointer>1.13 in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from jsonschema[format-nongpl]>=4.18.0->jupyter-events>=0.9.0->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (3.0.0)\n",
      "Requirement already satisfied: uri-template in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from jsonschema[format-nongpl]>=4.18.0->jupyter-events>=0.9.0->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (1.3.0)\n",
      "Requirement already satisfied: webcolors>=24.6.0 in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from jsonschema[format-nongpl]>=4.18.0->jupyter-events>=0.9.0->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (24.8.0)\n",
      "Requirement already satisfied: cffi>=1.0.1 in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from argon2-cffi-bindings->argon2-cffi>=21.1->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (1.17.0)\n",
      "Requirement already satisfied: pycparser in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from cffi>=1.0.1->argon2-cffi-bindings->argon2-cffi>=21.1->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (2.22)\n",
      "Requirement already satisfied: arrow>=0.15.0 in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from isoduration->jsonschema[format-nongpl]>=4.18.0->jupyter-events>=0.9.0->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (1.3.0)\n",
      "Requirement already satisfied: types-python-dateutil>=2.8.10 in /Users/laurentperrinet/.venv/lib/python3.12/site-packages (from arrow>=0.15.0->isoduration->jsonschema[format-nongpl]>=4.18.0->jupyter-events>=0.9.0->jupyter-server<3,>=2.4.0->notebook->jupyter->-r requirements.txt (line 15)) (2.9.0.20240316)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -U -r requirements.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.9.2'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib\n",
    "matplotlib.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.gridspec as gs\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "# import imageio\n",
    "import cv2\n",
    "\n",
    "# the higher PRECISION, the bigger the file\n",
    "PRECISION = 4  # debugging\n",
    "PRECISION = 10 # good quality\n",
    "PRECISION = 12 # good quality\n",
    "# PRECISION = 14 # very good quality\n",
    "# PRECISION = 15 # 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 = '2024-08-15_caustique-bands' # 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 = 8*2**PRECISION # number of pixels (vertical)\n",
    "    ny: int = 1*2**PRECISION # number of pixels (horizontal)\n",
    "    nframe: int = 1 # number of frames\n",
    "    bin_dens: int = 4 # 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 = 40.0 # 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 = .95*2**PRECISION # period in pixels\n",
    "    B_sf: float = 1.61 # 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 = 0.10 # relative minimal value of wave height at the top to generate a gradient (set to 1. to have no gradient)\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 = .01 # global diffusion level for the rendering giving the pedestal value\n",
    "    n_bits: int = 16 # bits to save images\n",
    "    gamma: float = 3. # 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 = True # Cache intermediate output.\n",
    "    verbose: bool = False # Displays more verbose output.\n",
    "    do_display: bool = False # Displays images in notebook.\n",
    "    do_recompute: bool = False # Restart each computation    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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=2024-08-15_caustique-bands\n"
     ]
    }
   ],
   "source": [
    "opt = init()\n",
    "print(f'Saving our simulations in={opt.figpath}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# if opt.nframe==1: opt.ext = 'png'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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='2024-08-15_caustique-bands',\n",
      "     tag='caustique',\n",
      "     ext='png',\n",
      "     nx=32768,\n",
      "     ny=4096,\n",
      "     nframe=1,\n",
      "     bin_dens=4,\n",
      "     bin_spectrum=1,\n",
      "     seed=2024,\n",
      "     H=40.0,\n",
      "     variation=0.2,\n",
      "     scale=3891.2,\n",
      "     B_sf=1.61,\n",
      "     V_Y=0.3,\n",
      "     V_X=0.3,\n",
      "     B_V=1.0,\n",
      "     zmin=0.1,\n",
      "     theta=1.5707963267948966,\n",
      "     B_theta=1.0471975511965976,\n",
      "     min_lum=0.01,\n",
      "     n_bits=16,\n",
      "     gamma=3.0,\n",
      "     fps=18,\n",
      "     multispectral=True,\n",
      "     cache=True,\n",
      "     verbose=False,\n",
      "     do_display=False,\n",
      "     do_recompute=False)\n"
     ]
    }
   ],
   "source": [
    "from pprint import pprint\n",
    "pprint(opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Screen size=100cm=39.370in, dpi=208dpi\n"
     ]
    }
   ],
   "source": [
    "screen_size_cm = 100 # cm\n",
    "cm_by_inch = 2.54\n",
    "screen_size_in = screen_size_cm/cm_by_inch\n",
    "dpi = (opt.nx // opt.bin_dens) / screen_size_in\n",
    "print(f'Screen size={screen_size_cm}cm={screen_size_in:.3f}in, dpi={dpi:.0f}dpi')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## utilities\n",
    "\n",
    "Transfoming a sequence of PNG frames into gif or mp4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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",
    "    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": 27,
   "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": 28,
   "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:193: SyntaxWarning: invalid escape sequence '\\>'\n",
      "<>:193: SyntaxWarning: invalid escape sequence '\\>'\n",
      "/var/folders/3s/q2x8bxzj43g4rdvb2wjt67640000gq/T/ipykernel_27236/1192703615.py:193: SyntaxWarning: invalid escape sequence '\\>'\n",
      "  html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n"
     ]
    }
   ],
   "source": [
    "import matplotlib\n",
    "subplotpars = matplotlib.gridspec.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)\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., edge_order=2):\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",
    "\n",
    "        # https://numpy.org/doc/stable/reference/generated/numpy.gradient.html\n",
    "        # dzdx = np.gradient(z_, axis=0, edge_order=edge_order)\n",
    "        # dzdy = np.gradient(z_, axis=1, edge_order=edge_order)\n",
    "        dzdx, dzdy = np.gradient(z_, edge_order=edge_order)\n",
    "\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=dpi):\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",
    "\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",
    "                    image_array = image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma)\n",
    "                    ax.imshow(image_array, 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) ** (1/self.opt.gamma)\n",
    "                        image_array = image_L[:, :, None]*image_rgb\n",
    "                        ax.imshow(image_array, vmin=0, vmax=1)\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",
    "                \n",
    "                # fig.savefig(fname, dpi=dpi)\n",
    "                np_dtype = np.uint8 if self.opt.n_bits==8 else np.uint16\n",
    "                # imageio.imsave(fname, image_array.astype(np_dtype), dpi=dpi, extension=opt.ext)\n",
    "                cv2.imwrite(fname, (image_array*(2**self.opt.n_bits-1)).astype(np_dtype))\n",
    "                fnames.append(fname)\n",
    "                plt.close(fig)\n",
    "\n",
    "            if self.opt.nframe==1:\n",
    "                shutil.move(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",
    "            display(Image(url=output_filename, 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} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n",
    "                html.reload()\n",
    "                return display(html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# a simple caustics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## generating the caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": [
    {
     "data": {
      "text/plain": [
       "(32768, 4096, 1)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'grating'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 492.126x3937.01 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_image(nx, ny, periods=.5, threshold=0.80, radius=.9):\n",
    "    Y, X = np.meshgrid(np.linspace(-1, 1, ny, endpoint=True), np.linspace(-1, 1, nx, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*Y*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",
    "\n",
    "fig, ax = plt.subplots(figsize=(opt.ny/opt.bin_dens/dpi, opt.nx/opt.bin_dens/dpi), subplotpars=subplotpars)\n",
    "\n",
    "ax.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.899518Z",
     "iopub.status.busy": "2022-09-16T06:50:19.899287Z",
     "iopub.status.idle": "2022-09-16T06:50:19.902454Z",
     "shell.execute_reply": "2022-09-16T06:50:19.902008Z"
    }
   },
   "outputs": [],
   "source": [
    "c = Caustique(opt)\n",
    "output_filename = c.plot(z, image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.904998Z",
     "iopub.status.busy": "2022-09-16T06:50:19.904782Z",
     "iopub.status.idle": "2022-09-16T06:50:19.908171Z",
     "shell.execute_reply": "2022-09-16T06:50:19.907731Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2024-08-15_caustique-bands/caustique_10537e39.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# exploring parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.910794Z",
     "iopub.status.busy": "2022-09-16T06:50:19.910587Z",
     "iopub.status.idle": "2022-09-16T06:50:19.913072Z",
     "shell.execute_reply": "2022-09-16T06:50:19.912580Z"
    }
   },
   "outputs": [],
   "source": [
    "N_scan = 7\n",
    "base = 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## water depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 10.000 -> output_filename='2024-08-15_caustique-bands/caustique_H_10.000_daf83814.png' \n",
      "H = 15.874 -> output_filename='2024-08-15_caustique-bands/caustique_H_15.874_ae9d2d3e.png' \n",
      "H = 25.198 -> output_filename='2024-08-15_caustique-bands/caustique_H_25.198_bcf83f39.png' \n",
      "H = 40.000 -> output_filename='2024-08-15_caustique-bands/caustique_H_40.000_2e1735f4.png' \n",
      "H = 63.496 -> output_filename='2024-08-15_caustique-bands/caustique_H_63.496_11c4a412.png' \n",
      "H = 100.794 -> output_filename='2024-08-15_caustique-bands/caustique_H_100.794_50574803.png' \n",
      "H = 160.000 -> output_filename='2024-08-15_caustique-bands/caustique_H_160.000_95c9c011.png' \n"
     ]
    }
   ],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## refraction index variation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:21.644704Z",
     "iopub.status.busy": "2022-09-16T06:50:21.644457Z",
     "iopub.status.idle": "2022-09-16T06:50:23.391217Z",
     "shell.execute_reply": "2022-09-16T06:50:23.390608Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.010  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.010_49c216e5.png'\n",
      "variation = 0.019  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.019_f8db4ff9.png'\n",
      "variation = 0.037  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.037_6d76df11.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [22:53<00:00, 16.96s/it]\n",
      "100%|██████████| 1/1 [22:53<00:00, 1373.85s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.83it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.072  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.072_e2f27d3d.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [24:45<00:00, 18.34s/it]\n",
      "100%|██████████| 1/1 [24:45<00:00, 1485.39s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.17it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.139  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.139_761e6d4f.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [36:25<00:00, 26.98s/it]\n",
      "100%|██████████| 1/1 [36:25<00:00, 2185.03s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.268  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.268_ba15d1c6.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [17:31<00:00, 12.98s/it]\n",
      "100%|██████████| 1/1 [17:31<00:00, 1051.35s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.19it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.518  -> output_filename='2024-08-15_caustique-bands/caustique_variation_0.518_993a869a.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "for variation_ in np.logspace(-2, 0, N_scan, base=10, endpoint=False):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.variation = variation_\n",
    "    c.opt.tag = f'{opt.tag}_variation_{variation_:.3f}'\n",
    "\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'variation = {variation_:.3f}  -> {output_filename=}')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## other instances of the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [38:26<00:00, 28.47s/it]\n",
      "100%|██████████| 1/1 [38:26<00:00, 2306.31s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2024 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2024_e99a0613.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [37:50<00:00, 28.03s/it]\n",
      "100%|██████████| 1/1 [37:50<00:00, 2270.63s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2025 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2025_cfd342f9.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [24:19<00:00, 18.02s/it]\n",
      "100%|██████████| 1/1 [24:19<00:00, 1459.42s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.88it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2026 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2026_f4172f03.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [16:32<00:00, 12.25s/it]\n",
      "100%|██████████| 1/1 [16:32<00:00, 992.60s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.03it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2027 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2027_beefe2db.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [18:40<00:00, 13.84s/it]\n",
      "100%|██████████| 1/1 [18:40<00:00, 1120.98s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.73it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2028 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2028_7c6851af.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [18:50<00:00, 13.96s/it]\n",
      "100%|██████████| 1/1 [18:50<00:00, 1130.88s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2029 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2029_83041ca6.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [19:01<00:00, 14.09s/it]\n",
      "100%|██████████| 1/1 [19:01<00:00, 1141.44s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.03it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2030 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2030_8aa1fea0.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [18:42<00:00, 13.86s/it]\n",
      "100%|██████████| 1/1 [18:42<00:00, 1122.60s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.47it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2031 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2031_39325e89.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [23:31<00:00, 17.43s/it]\n",
      "100%|██████████| 1/1 [23:31<00:00, 1411.91s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.78it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2032 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2032_ca1fc04d.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [19:55<00:00, 14.76s/it]\n",
      "100%|██████████| 1/1 [19:55<00:00, 1195.30s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.94it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed=2033 -> output_filename='2024-08-15_caustique-bands/caustique_seed_2033_9c23f4f9.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "for seed_increment in range(10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.d['seed'] = c.d['seed'] + seed_increment\n",
    "    c.opt.tag = f'{c.opt.tag}_seed_{c.d['seed']}'\n",
    "    \n",
    "    z = c.wave()\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'seed={c.d['seed']} -> {output_filename=}')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## other variables on the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:23.394466Z",
     "iopub.status.busy": "2022-09-16T06:50:23.394219Z",
     "iopub.status.idle": "2022-09-16T06:50:23.686162Z",
     "shell.execute_reply": "2022-09-16T06:50:23.685512Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "======scale======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [20:51<00:00, 15.45s/it]\n",
      "100%|██████████| 1/1 [20:51<00:00, 1251.84s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.56it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*0.250=9.728E+02 -> output_filename='2024-08-15_caustique-bands/caustique_scale_modul_0.250_2b358f55.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [27:39<00:00, 20.49s/it]\n",
      "100%|██████████| 1/1 [27:39<00:00, 1659.94s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.10it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*0.397=1.544E+03 -> output_filename='2024-08-15_caustique-bands/caustique_scale_modul_0.397_1032c0c0.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [18:55<00:00, 14.02s/it]\n",
      "100%|██████████| 1/1 [18:55<00:00, 1135.43s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*0.630=2.451E+03 -> output_filename='2024-08-15_caustique-bands/caustique_scale_modul_0.630_6f1f241f.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [19:12<00:00, 14.23s/it]\n",
      "100%|██████████| 1/1 [19:12<00:00, 1152.39s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.80it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*1.000=3.891E+03 -> output_filename='2024-08-15_caustique-bands/caustique_scale_modul_1.000_577c21db.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [18:17<00:00, 13.55s/it]\n",
      "100%|██████████| 1/1 [18:17<00:00, 1097.17s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*1.587=6.177E+03 -> output_filename='2024-08-15_caustique-bands/caustique_scale_modul_1.587_3bae04b0.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [14:42<00:00, 10.90s/it]\n",
      "100%|██████████| 1/1 [14:42<00:00, 882.66s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  3.16it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*2.520=9.805E+03 -> output_filename='2024-08-15_caustique-bands/caustique_scale_modul_2.520_61506795.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1 [00:00<?, ?it/s]"
     ]
    }
   ],
   "source": [
    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
    "    print(f'======{variable}======')\n",
    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
    "        opt = init()\n",
    "        c = Caustique(opt)\n",
    "        c.d[variable] *= modul\n",
    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
    "        \n",
    "        z = c.wave()\n",
    "        output_filename = c.plot(z, image)\n",
    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
    "        if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## shining a grating image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, threshold=threshold)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{threshold:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.2e}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
    "    print(f'======{variable}======')\n",
    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
    "        opt = init()\n",
    "        c = Caustique(opt)\n",
    "        c.d[variable] *= modul\n",
    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
    "        z = c.wave()\n",
    "        image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "        output_filename = c.plot(z, image)\n",
    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
    "        if c.opt.do_display: c.show(output_filename)"
   ]
  }
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