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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "76315cb9-11f7-42b2-b393-692511f6d67a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# ces_01\n",
    "%matplotlib inline\n",
    "\n",
    "from math import exp, pi, sin, cos, tan, atan, sqrt, floor, log10, nan, log   # math functions\n",
    "import numpy as np\n",
    "import scipy.linalg as la             # linear algebra functions\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt  # general plotting \n",
    "from matplotlib.colors import ListedColormap\n",
    "import time;\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "# function to make a numpy N-by-1 column vector\n",
    "# c=eda_cvec(v1, v2, ...) from a list of several\n",
    "# array-like entities v1, v2, including a number\n",
    "# a list of numbers, a tuple of numbers, an N-by-0 np array\n",
    "# and a N-by-1 np array. The function\n",
    "# also insures that, if v is an np array, that\n",
    "# c is a copy, as contrasted to a view, of it\n",
    "# It promotes integers to floats, and integers\n",
    "# and floats to complex, by context.\n",
    "# This version concatenates many argments,\n",
    "# whereas c=eda_cvec1(v1) takes just one argiment.\n",
    "# I recommend always using eda_cvec(v1, v2, ...)\n",
    "def gda_cvec(*argv):\n",
    "    t = int;\n",
    "    Nt = 0;\n",
    "    for a in argv:\n",
    "        v = gda_cvec1(a);\n",
    "        N,M = np.shape(v);\n",
    "        Nt = Nt + N;\n",
    "        if( N==0 ):\n",
    "            continue; # skip vector of zero length\n",
    "        if (t==int) and isinstance(v[0,0],float):\n",
    "            t=float;\n",
    "        elif isinstance(v[0,0],complex):\n",
    "            t=complex;\n",
    "    w = np.zeros((Nt,1),dtype=t);\n",
    "    Nt = 0;\n",
    "    for a in argv:\n",
    "        v = gda_cvec1(a);\n",
    "        N,M = np.shape(v);\n",
    "        w[Nt:Nt+N,0:1] = v;  # patch 20230418 was #w[Nt:Nt+N,0] = v[0:N,0];\n",
    "        Nt = Nt + N;\n",
    "    return w;\n",
    "\n",
    "# function to make a numpy N-by-1 column vector\n",
    "# c=gda_cvec1(v) from entity v that is array-like,\n",
    "# including a number, a list of numbers, a tuple\n",
    "# of numbers, an N-by-0 np array and a N-by1 np array.\n",
    "# It promotes integers to floats, and integers\n",
    "# and floats to complex, by context. The function\n",
    "# also insures that, if v is an np array, that\n",
    "# c is a copy, as contrasted to a view, of it.\n",
    "# This version takes just one input argment.\n",
    "# whereas c=gda_cvec(v1,v2,...) concatenates\n",
    "# many argiments.\n",
    "def gda_cvec1(v):\n",
    "    if isinstance(v, int) or isinstance(v, np.int32):\n",
    "        w = np.zeros((1,1),dtype=int);\n",
    "        w[0,0] = v;\n",
    "        return w;\n",
    "    elif isinstance(v, float):\n",
    "        w = np.zeros((1,1),dtype=float);\n",
    "        w[0,0] = v;\n",
    "        return w;\n",
    "    elif isinstance(v, complex):\n",
    "        w = np.zeros((1,1),dtype=complex);\n",
    "        w[0,0] = v;\n",
    "        return w;\n",
    "    elif isinstance(v, np.ndarray):\n",
    "        s = np.shape(v);\n",
    "        if len(s) == 1:\n",
    "            return np.copy(np.reshape(v,(s[0],1)));\n",
    "        else:\n",
    "            [r,c]=s;\n",
    "            if( c==1 ):\n",
    "                return(np.copy(v));\n",
    "            elif(r==1):\n",
    "                return(np.copy(v.T));\n",
    "            else:\n",
    "                raise TypeError(\"gda_cvec: %d by %d ndarray not allowed\" % (r, c));\n",
    "    elif isinstance(v, list):\n",
    "        r = len(v);\n",
    "        t = int;\n",
    "        for vi in v:\n",
    "            if isinstance(vi,int) or isinstance(vi, np.int32): #patch v->vi 20230418\n",
    "                pass;\n",
    "            elif isinstance(vi,float):\n",
    "                t=float;\n",
    "            elif isinstance(vi,complex):\n",
    "                t=complex;\n",
    "                break;\n",
    "            else:\n",
    "                raise TypeError(\"gda_cvec: list contains unsupported type %s\" % type(vi));\n",
    "        w = np.zeros((r,1),dtype=t);\n",
    "        w[:,0] = np.array(v); # patch v -> np.array(v)\n",
    "        return w;\n",
    "    elif isinstance(v, tuple):\n",
    "        r = len(v);\n",
    "        t = int;\n",
    "        for vi in v:\n",
    "            if isinstance(vi,int) or isinstance(vi, np.int32): #patch v->vi 20230418\n",
    "                pass;\n",
    "            elif isinstance(vi,float):\n",
    "                t=float;\n",
    "            elif isinstance(vi,complex):\n",
    "                t=complex;\n",
    "                break;\n",
    "            else:\n",
    "                raise TypeError(\"gda_cvec: tuple contains unsupported type %s\" % type(vi));\n",
    "        w = np.zeros((r,1),dtype=t);\n",
    "        w[:,0] = np.array(list(v)); # patch v -> np.array(list(v));\n",
    "        return w;\n",
    "    else:\n",
    "        raise TypeError(\"gda_cvec: %s not supported\" % type(v));\n",
    "\n",
    "        \n",
    "# gda_draw function makes a \"pictorial matrix equation\"\n",
    "# arguments are vectors, matrices and strings\n",
    "# which are plotted in the order that the appear\n",
    "# except that strings starting with 'title ' are plotted\n",
    "# under the subseqeunt matrix or vector\n",
    "# always returns a status of 1\n",
    "def gda_draw(*argv):\n",
    "    DOCOLOR=True;\n",
    "    if( DOCOLOR ):\n",
    "        bwcmap = matplotlib.colormaps['jet'];\n",
    "    else:\n",
    "        bw = np.zeros((256,4));\n",
    "        v = 0.9*(256 - np.linspace( 0, 255, 256 ))/255;\n",
    "        bw[:,0] = v;\n",
    "        bw[:,1] = v;\n",
    "        bw[:,2] = v;\n",
    "        bw[:,3] = np.ones(256);\n",
    "        bwcmap = ListedColormap(bw);\n",
    "    # size of plot\n",
    "    W = 16;\n",
    "    H = 4;\n",
    "    fig1 = plt.figure(1);\n",
    "    # figsize width and height in inches\n",
    "    fig1.set_size_inches(W,H);\n",
    "    ax1 = plt.subplot(1,1,1);\n",
    "    plt.axis([0, W, -H/2, H/2]);\n",
    "    plt.axis('off');\n",
    "    LM = W/6;    # matrix width and heoght\n",
    "    LV = W/40;   # vector width\n",
    "    FS = 0.12;    # character width\n",
    "    TO = 0.4;    # title vertical offset\n",
    "    SP = 0.2;    # space between objects\n",
    "    LS = 0.2;    # leading space\n",
    "    p = LS; # starting x-position\n",
    "    istitle=0; # flags presence of a title\n",
    "    for a in argv:\n",
    "        if isinstance(a,np.ndarray):\n",
    "            sh = np.shape(a);\n",
    "            if len(sh) == 1:  # conversion to nx1 array\n",
    "                n = sh[0];\n",
    "                m = 1;\n",
    "                ap = a;\n",
    "                a = np.zeros((n,1));\n",
    "                a[:,0] = ap;\n",
    "            else:\n",
    "                n = sh[0];\n",
    "                m = sh[1];\n",
    "            if m==1:\n",
    "                pold=p;\n",
    "                left=p;\n",
    "                right=p+LV;\n",
    "                bottom=-LM/2;\n",
    "                top=LM/2;\n",
    "                plt.imshow( a, cmap=bwcmap, vmin=np.min(a), vmax=np.max(a), extent=(left,right,bottom,top) );\n",
    "                p = p+LV;\n",
    "                pm = (p+pold)/2;\n",
    "                if istitle:\n",
    "                    plt.text(pm,-(LM/2)-TO,titlestr,horizontalalignment='center');\n",
    "                    istitle=0;\n",
    "                p = p+SP;\n",
    "            else:\n",
    "                pold=p;\n",
    "                left=p;\n",
    "                right=p+LM;\n",
    "                bottom=-LM/2;\n",
    "                top=LM/2;\n",
    "                plt.imshow( a, cmap=bwcmap, vmin=np.min(a), vmax=np.max(a), extent=(left,right,bottom,top) );\n",
    "                p = p+LM;\n",
    "                pm = (p+pold)/2;\n",
    "                if istitle:\n",
    "                    plt.text(pm,-(LM/2)-TO,titlestr,horizontalalignment='center');\n",
    "                    istitle=0;\n",
    "                p = p+SP;\n",
    "        elif isinstance(a,str):\n",
    "            ns = len(a);\n",
    "            istitle=0;\n",
    "            if( ns>=6 ):\n",
    "                if 'title ' in a[0:6]:\n",
    "                    istitle=1;\n",
    "                    titlestr=a[6:];\n",
    "            if( istitle != 1):\n",
    "                plt.text(p,0,a);\n",
    "                p = p + ns*FS + SP;\n",
    "    plt.show();\n",
    "    return 1;"
   ]
  },
  {
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   "id": "0a829865-1891-43c3-9a8e-4cdc7ee43f73",
   "metadata": {
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   ],
   "source": [
    "# x axis\n",
    "Nx = 128;\n",
    "xmin = -1.0;\n",
    "xmax = 1.0;\n",
    "x = gda_cvec(np.linspace(xmin,xmax,Nx));\n",
    "Dx = x[1,0]-x[0,0];\n",
    "\n",
    "# y axis\n",
    "Ny = 128;\n",
    "ymin = -1.0;\n",
    "ymax = 1.0;\n",
    "y = gda_cvec(np.linspace(ymin,ymax,Ny));\n",
    "Dy = y[1,0]-y[0,0];\n",
    "\n",
    "# t axis\n",
    "Nt = 128;\n",
    "tmin = -1.0;\n",
    "tmax = 1.0;\n",
    "t = gda_cvec(np.linspace(tmin,tmax,Nt));\n",
    "Dt = t[1,0]-t[0,0];\n",
    "\n",
    "# kx axis\n",
    "Nkx = int(Nx/2)+1;\n",
    "kxmax = (2.0*pi)/(2.0*Dx);\n",
    "kxpos = gda_cvec(np.linspace(0.0,kxmax,Nkx));\n",
    "kx = np.concatenate( (kxpos,-np.flipud(kxpos[1:Nkx-1,0:1])), axis=0 );\n",
    "Dkx = kx[1,0]-kx[0,0];\n",
    "\n",
    "# ky axis\n",
    "Nky = int(Ny/2)+1;\n",
    "kymax = (2.0*pi)/(2.0*Dy);\n",
    "kypos = gda_cvec(np.linspace(0.0,kymax,Nky));\n",
    "ky = np.concatenate( (kypos,-np.flipud(kypos[1:Nky-1,0:1])), axis=0 );\n",
    "Dky = ky[1,0]-ky[0,0];\n",
    "\n",
    "# w axis\n",
    "Nw = int(Nt/2)+1;\n",
    "wmax = (2.0*pi)/(2.0*Dt);\n",
    "wpos = gda_cvec(np.linspace(0.0,wmax,Nw));\n",
    "w = np.concatenate( (wpos,-np.flipud(wpos[1:Nw-1,0:1])), axis=0 );\n",
    "Dw = w[1,0]-w[0,0];\n",
    "\n",
    "# theory\n",
    "# the acoustic wave equation is \n",
    "# ( s2 d2/dt2 - d2/dx2 - d2/dx2) u = source(x,y) delta(t)\n",
    "# where  source(x,y) is the spatially variavle source\n",
    "\n",
    "# he source is the divergence of the force\n",
    "# so if (fx, fy) = (cosq , sinq) delta(x) delta(y)\n",
    "# and source = div(f) = (d/dx) fx  + (d/dy) fy\n",
    "# = cosq d/dx delta(x) delta(y) + sinq delta(x) d/dy deltay\n",
    "# which transforms to\n",
    "# cosg i kx + sin1 i ky\n",
    "\n",
    "# (-s2 w2 + kx2 + ky2) ubar = (cosq i kx + sinq i ky)\n",
    "# ubar = (cosq i kx + sinq i ky) / (kx2 + ky2 - w2 )\n",
    "#      = (cosq i kx + sinq i ky) (kx2 + ky2 - s2 w2  / (kx2 + ky2 - s2 w2 )\n",
    "#      (about equal) (cosq i kx + sinq i ky) (kx2 + ky2 - s2 w2  / [ (kx2 + ky2 - s2 w2 )  epsi2 ]\n",
    "\n",
    "# transform of field, note order ut[iw, ikx, iky] \n",
    "ut = np.zeros((Nt,Nx,Ny),dtype=complex);\n",
    "\n",
    "s=0.5;  # slowness\n",
    "s2=s**2;\n",
    "epsi = 40.0; # damping\n",
    "epsi2 = epsi**2;\n",
    "sigma = 1.0; # low pass filter frequency width\n",
    "sigma2 = sigma**2;\n",
    "i = complex(0.0,1.0);\n",
    "q = 0.0; # force orientation in degrees\n",
    "cosq = cos(pi*q/180.0);\n",
    "sinq = sin(pi*q/180.0);\n",
    "for iw in range(Nt):\n",
    "    for ikx in range(Nx):\n",
    "        for iky in range(Ny):\n",
    "            A = kx[ikx,0]**2 + ky[iky,0]**2 - s2*(w[iw,0]**2);\n",
    "            r2 = (kx[ikx,0]/kxmax)**2 + (ky[iky,0]/kymax)**2 + (w[iw,0]/wmax)**2;\n",
    "            F = exp(-0.5*r2/sigma2);\n",
    "            ut[iw,ikx,iky] = F * (cosq*i*kx[ikx,0]+sinq*i*ky[iky,0]) * A / (A**2 + epsi2 );\n",
    "\n",
    "# inverse fourier transform\n",
    "u = np.fft.ifftn(ut);\n",
    "u = np.real(u);\n",
    "\n",
    "for it in range(1,int(Nt/2),4):\n",
    "    # roll so that x=0 is in center of interval\n",
    "    uxy = np.squeeze( u[it,0:Nx,0:Ny] );\n",
    "    uxy = np.roll(uxy,int(Nx/2),axis=0);\n",
    "    uxy = np.roll(uxy,int(Ny/2),axis=1);\n",
    "\n",
    "    fig1 = plt.figure();\n",
    "    mycm = plt.get_cmap('jet');\n",
    "    plt.axis( [xmin, xmax, ymin, ymax ] );\n",
    "    plt.imshow(uxy,aspect='auto',extent=(xmin,xmax,ymin,ymax),cmap=mycm);\n",
    "    plt.colorbar();\n",
    "    plt.xlabel('y');\n",
    "    plt.ylabel('x');\n",
    "    plt.title(\"time %d\" % it );\n",
    "    plt.show();\n",
    "\n",
    "\n",
    "\n"
   ]
  },
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   "execution_count": 150,
   "id": "023b43ed-76c9-44d6-8a34-ae6a0b54cc48",
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       "YXRhAAAAAQAAAABMYXZmNTguNDUuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "[encoded data, 155984 characters]",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# to install ipython\n",
    "# conda install ipython\n",
    "\n",
    "# this demo from\n",
    "# http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-as-interactive-javascript-widgets/\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "fig, ax = plt.subplots();\n",
    "\n",
    "ax.set_xlim(( xmin, xmax));\n",
    "ax.set_ylim(( ymin, ymax));\n",
    "\n",
    "# roll so that x=0 is in center of interval\n",
    "it=4;\n",
    "uxy = np.squeeze( u[it,0:Nx,0:Ny] );\n",
    "uxy = np.roll(uxy,int(Nx/2),axis=0);\n",
    "uxy = np.roll(uxy,int(Ny/2),axis=1);\n",
    "\n",
    "dmin = np.min(u)/10;\n",
    "dmax = np.max(u)/10;\n",
    "mycm = plt.get_cmap('jet');\n",
    "plt.imshow(uxy, cmap=mycm, aspect='auto', extent=(xmin,xmax,ymin,ymax), vmin=dmin, vmax=dmax);\n",
    "im = ax.imshow([[]], cmap=mycm, aspect='auto', extent=(xmin,xmax,ymin,ymax), vmin=dmin, vmax=dmax);\n",
    "plt.xlabel('y');\n",
    "plt.ylabel('x');\n",
    "plt.colorbar();\n",
    "\n",
    "def init():\n",
    "    im.set_data([[]]);\n",
    "    return (im,)\n",
    "\n",
    "def animate(i):\n",
    "    uxy = np.squeeze( u[i,0:Nx,0:Ny] );\n",
    "    uxy = np.roll(uxy,int(Nx/2),axis=0);\n",
    "    uxy = np.roll(uxy,int(Ny/2),axis=1);\n",
    "    im.set_data(uxy);\n",
    "    return (im,)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=int(Nt/2), interval=int(20), \n",
    "                               blit=True)\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "c4962bc9-67e3-4404-b3cf-43681fabaa68",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 155984 characters]",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# to install ipython\n",
    "# conda install ipython\n",
    "\n",
    "# this demo from\n",
    "# http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-as-interactive-javascript-widgets/\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "fig, ax = plt.subplots();\n",
    "\n",
    "ax.set_xlim(( xmin, xmax));\n",
    "ax.set_ylim(( ymin, ymax));\n",
    "\n",
    "# roll so that x=0 is in center of interval\n",
    "it=4;\n",
    "uxy = np.squeeze( u[it,0:Nx,0:Ny] );\n",
    "uxy = np.roll(uxy,int(Nx/2),axis=0);\n",
    "uxy = np.roll(uxy,int(Ny/2),axis=1);\n",
    "\n",
    "dmin = np.min(u)/10;\n",
    "dmax = np.max(u)/10;\n",
    "mycm = plt.get_cmap('jet');\n",
    "plt.imshow(uxy, cmap=mycm, aspect='auto', extent=(xmin,xmax,ymin,ymax), vmin=dmin, vmax=dmax);\n",
    "im = ax.imshow([[]], cmap=mycm, aspect='auto', extent=(xmin,xmax,ymin,ymax), vmin=dmin, vmax=dmax);\n",
    "plt.xlabel('y');\n",
    "plt.ylabel('x');\n",
    "plt.colorbar();\n",
    "\n",
    "def init():\n",
    "    im.set_data([[]]);\n",
    "    return (im,)\n",
    "\n",
    "def animate(i):\n",
    "    uxy = np.squeeze( u[i,0:Nx,0:Ny] );\n",
    "    uxy = np.roll(uxy,int(Nx/2),axis=0);\n",
    "    uxy = np.roll(uxy,int(Ny/2),axis=1);\n",
    "    im.set_data(uxy);\n",
    "    return (im,)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=int(Nt/2), interval=int(20), \n",
    "                               blit=True)\n",
    "\n",
    "writer = animation.PillowWriter(fps=15);\n",
    "anim.save('sphericalwave.gif', writer=writer);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12307ff1-6184-4138-839a-ebf7125193be",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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