2022-12-02_caustique_single_dataclass_image.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# source code\n",
    "\n",
    "- single frame\n",
    "- dataclass\n",
    "- **image**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2022-09-16T06:50:17.009225Z"
    }
   },
   "outputs": [],
   "source": [
    "figpath = '2022-12-02_caustique_single_dataclass_image'\n",
    "if figpath is None:\n",
    "    import datetime\n",
    "    date = datetime.datetime.now().date().isoformat()\n",
    "    figpath = f'{date}_caustique'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
    }
   },
   "outputs": [],
   "source": [
    "PRECISION = 4 # the higher, the bigger the file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.673182Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.674999Z"
    }
   },
   "outputs": [],
   "source": [
    "PRECISION = 10 # the higher, the bigger the file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "import os\n",
    "import datetime\n",
    "import numpy as np\n",
    "\n",
    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
    "from dataclasses import dataclass, asdict, field\n",
    "\n",
    "@dataclass\n",
    "class Params:\n",
    "    figpath: str = figpath # Folder to store images\n",
    "    fig_width: float = 12 # width of figure\n",
    "    phi: float = 1.61803 # beauty is gold\n",
    "    N_PG_show: float = 5 # number of PG to show in plot_PG\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 = 4 # relative bin density\n",
    "    bin_spectrum: int = 3 # bin spacing in spectrum\n",
    "    seed: int = 8601 # seed for RNG\n",
    "    H: float = 1.5 # depth of the pool\n",
    "    variation: float = .4 # 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 = 200 # sf\n",
    "    B_sf: float = 0.25 # 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",
    "    theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
    "    B_theta: float = 2*np.pi/3 # bandwidth in theta\n",
    "    min_lum: float = .2 # diffusion level for the rendering\n",
    "    gamma: float = 2.8 # 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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.722173Z",
     "iopub.status.busy": "2022-09-16T06:50:17.721924Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.725292Z"
    }
   },
   "outputs": [],
   "source": [
    "opt = Params()\n",
    "opt.figpath = figpath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Params(figpath='2022-12-02_caustique_single_dataclass_image', fig_width=12, phi=1.61803, N_PG_show=5, tag='caustique', ext='png', nx=5120, ny=5120, nframe=1, bin_dens=4, bin_spectrum=3, seed=8601, H=1.5, variation=0.4, scale=200, B_sf=0.25, V_Y=0.3, V_X=0.3, B_V=1.0, theta=2.399988291783386, B_theta=2.0943951023931953, min_lum=0.2, gamma=2.8, fps=18, multispectral=True, cache=True, verbose=False, do_display=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## utilities\n",
    "\n",
    "Transfoming a sequence of PNG frames into gif or mp4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.737334Z",
     "iopub.status.busy": "2022-09-16T06:50:17.737126Z",
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     "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": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
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     "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": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.760440Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.822569Z"
    }
   },
   "outputs": [],
   "source": [
    "import shutil\n",
    "from tqdm.notebook import tqdm, trange\n",
    "import MotionClouds as mc\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",
    "\n",
    "\n",
    "    def wave(self):\n",
    "        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'\n",
    "        if os.path.isfile(filename):\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\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, output_filename=None, dpi=50):\n",
    "\n",
    "        # 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",
    "        if output_filename is None:\n",
    "            output_filename=f'{self.opt.figpath}/{self.opt.tag}.{self.opt.ext}'\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 tqdm(range(self.opt.nframe)):\n",
    "                for ii_wavelength, i_wavelength in enumerate(range(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",
    "                    # print(i_wavelength, N_wavelengths, modulation)\n",
    "                    xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)\n",
    "                    hist_, edge_x, edge_y = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                           weights=image.ravel(),\n",
    "                                                           bins=[binsx, binsy],\n",
    "                                                           range=[[0, 1], [0, self.ratio]],\n",
    "                                                           density=True)\n",
    "\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",
    "                    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_, edge_x, edge_y = 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",
    "        # transform light into image:\n",
    "        fnames = []\n",
    "        for i_frame in range(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",
    "                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",
    "            imagefname = f'{self.opt.figpath}/{self.opt.tag}.png'\n",
    "            shutil.copyfile(fname, imagefname)\n",
    "            return imagefname\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} 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": 11,
   "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": [
       "(5120, 5120, 1)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": [
    "output_filename = f'{opt.figpath}/{opt.tag}.{opt.ext}'\n",
    "if not os.path.isfile(output_filename):\n",
    "    c = Caustique(opt)\n",
    "    z = c.wave()\n",
    "    output_filename = c.plot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [],
   "source": [
    "if opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# exploring parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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 = 9\n",
    "base = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## water depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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 = 0.750\n",
      "H = 0.892\n",
      "H = 1.061\n",
      "H = 1.261\n",
      "H = 1.500\n",
      "H = 1.784\n",
      "H = 2.121\n",
      "H = 2.523\n",
      "H = 3.000\n"
     ]
    }
   ],
   "source": [
    "opt = Params()\n",
    "opt.figpath = figpath\n",
    "\n",
    "c = Caustique(opt)\n",
    "# compute just once\n",
    "z = c.wave()\n",
    "\n",
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = Params()\n",
    "    opt.figpath = figpath\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    print(f'H = {H_:.3f}')\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{opt.tag}_H_{H_:.3f}'\n",
    "    output_filename = f'{opt.figpath}/{c.opt.tag}.{opt.ext}'\n",
    "    if not os.path.isfile(output_filename):\n",
    "        url=c.plot(z, output_filename=output_filename)\n",
    "    if opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## refraction index variation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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\n",
      "variation = 0.017\n",
      "variation = 0.028\n",
      "variation = 0.046\n",
      "variation = 0.077\n",
      "variation = 0.129\n",
      "variation = 0.215\n",
      "variation = 0.359\n",
      "variation = 0.599\n"
     ]
    }
   ],
   "source": [
    "opt = Params()\n",
    "opt.figpath = figpath\n",
    "\n",
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "\n",
    "for variation_ in np.logspace(-2, 0, N_scan, base=10, endpoint=False):\n",
    "    opt = Params()\n",
    "    opt.figpath = figpath\n",
    "    c = Caustique(opt)\n",
    "    print(f'variation = {variation_:.3f}')\n",
    "    c.opt.variation = variation_\n",
    "    c.opt.tag = f'{opt.tag}_variation_{variation_:.3f}'\n",
    "    output_filename = f'{opt.figpath}/{c.opt.tag}.{opt.ext}'\n",
    "    if not os.path.isfile(output_filename):\n",
    "        url=c.plot(z, output_filename=output_filename)\n",
    "    if opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## other variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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",
      "scale=scale(default)*0.500=1.000E+02\n",
      "scale=scale(default)*0.595=1.189E+02\n",
      "scale=scale(default)*0.707=1.414E+02\n",
      "scale=scale(default)*0.841=1.682E+02\n",
      "scale=scale(default)*1.000=2.000E+02\n",
      "scale=scale(default)*1.189=2.378E+02\n",
      "scale=scale(default)*1.414=2.828E+02\n",
      "scale=scale(default)*1.682=3.364E+02\n",
      "scale=scale(default)*2.000=4.000E+02\n",
      "======B_sf======\n",
      "B_sf=B_sf(default)*0.500=1.250E-01\n",
      "B_sf=B_sf(default)*0.595=1.487E-01\n",
      "B_sf=B_sf(default)*0.707=1.768E-01\n",
      "B_sf=B_sf(default)*0.841=2.102E-01\n",
      "B_sf=B_sf(default)*1.000=2.500E-01\n",
      "B_sf=B_sf(default)*1.189=2.973E-01\n",
      "B_sf=B_sf(default)*1.414=3.536E-01\n",
      "B_sf=B_sf(default)*1.682=4.204E-01\n",
      "B_sf=B_sf(default)*2.000=5.000E-01\n",
      "======B_theta======\n",
      "B_theta=B_theta(default)*0.500=1.047E+00\n",
      "B_theta=B_theta(default)*0.595=1.245E+00\n",
      "B_theta=B_theta(default)*0.707=1.481E+00\n",
      "B_theta=B_theta(default)*0.841=1.761E+00\n",
      "B_theta=B_theta(default)*1.000=2.094E+00\n",
      "B_theta=B_theta(default)*1.189=2.491E+00\n",
      "B_theta=B_theta(default)*1.414=2.962E+00\n",
      "B_theta=B_theta(default)*1.682=3.522E+00\n",
      "B_theta=B_theta(default)*2.000=4.189E+00\n",
      "======V_X======\n",
      "V_X=V_X(default)*0.500=1.500E-01\n",
      "V_X=V_X(default)*0.595=1.784E-01\n",
      "V_X=V_X(default)*0.707=2.121E-01\n",
      "V_X=V_X(default)*0.841=2.523E-01\n",
      "V_X=V_X(default)*1.000=3.000E-01\n",
      "V_X=V_X(default)*1.189=3.568E-01\n",
      "V_X=V_X(default)*1.414=4.243E-01\n",
      "V_X=V_X(default)*1.682=5.045E-01\n",
      "V_X=V_X(default)*2.000=6.000E-01\n",
      "======B_V======\n",
      "B_V=B_V(default)*0.500=5.000E-01\n",
      "B_V=B_V(default)*0.595=5.946E-01\n",
      "B_V=B_V(default)*0.707=7.071E-01\n",
      "B_V=B_V(default)*0.841=8.409E-01\n",
      "B_V=B_V(default)*1.000=1.000E+00\n",
      "B_V=B_V(default)*1.189=1.189E+00\n",
      "B_V=B_V(default)*1.414=1.414E+00\n",
      "B_V=B_V(default)*1.682=1.682E+00\n",
      "B_V=B_V(default)*2.000=2.000E+00\n",
      "======gamma======\n",
      "gamma=gamma(default)*0.500=1.400E+00\n",
      "gamma=gamma(default)*0.595=1.665E+00\n",
      "gamma=gamma(default)*0.707=1.980E+00\n",
      "gamma=gamma(default)*0.841=2.355E+00\n",
      "gamma=gamma(default)*1.000=2.800E+00\n",
      "gamma=gamma(default)*1.189=3.330E+00\n",
      "gamma=gamma(default)*1.414=3.960E+00\n",
      "gamma=gamma(default)*1.682=4.709E+00\n",
      "gamma=gamma(default)*2.000=5.600E+00\n"
     ]
    }
   ],
   "source": [
    "for variable in ['scale', 'B_sf', 'B_theta', 'V_X', 'B_V', 'gamma', ]: #  'theta', 'V_Y'\n",
    "    print(f'======{variable}======')\n",
    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
    "        opt = Params()\n",
    "        opt.figpath = figpath\n",
    "\n",
    "        c = Caustique(opt)\n",
    "        c.d[variable] *= modul\n",
    "        c.opt.tag = f'{opt.tag}_{variable}_modul_{modul:.3f}'\n",
    "        output_filename = f'{opt.figpath}/{c.opt.tag}.{opt.ext}'\n",
    "\n",
    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E}')\n",
    "        if not os.path.isfile(output_filename):\n",
    "            print('Doing ', output_filename)\n",
    "            z = c.wave()\n",
    "            mcname = f'{opt.figpath}/{c.opt.tag}'\n",
    "            if False: #not os.path.isfile(f'{mcname}{c.mc.ext}'): \n",
    "                print('Doing ', f'{mcname}{c.mc.ext}')\n",
    "                c.mc.anim_save(z.swapaxes(0, 1), f'{mcname}')\n",
    "            url=c.plot(z, output_filename=output_filename)\n",
    "        if opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42, 42)"
      ]
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     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "c = Caustique(Params())\n",
    "c.d['fps'] = 42\n",
    "c.d['fps'], c.opt.fps\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## installation\n",
    "\n",
    "Install [dependencies](https://pip.pypa.io/en/stable/user_guide/#requirements-files), then this notebook:\n",
    "\n",
    "```\n",
    "python3 -m pip install -r requirements.txt\n",
    "```"
   ]
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  {
   "cell_type": "code",
   "execution_count": 19,
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    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:23.689468Z",
     "iopub.status.busy": "2022-09-16T06:50:23.689202Z",
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     "shell.execute_reply": "2022-09-16T06:50:30.587403Z"
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   "source": [
    "# %pip install --upgrade -r requirements.txt"
   ]
  }
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