Notebook_8_SphericalHarmonics.ipynb

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    "%matplotlib widget\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from scipy.special import sph_harm \n",
    "\n",
    "#initial values\n",
    "l0 = 0\n",
    "ml0 = 0\n",
    "\n",
    "#create data\n",
    "theta = np.linspace(0, np.pi, 91)\n",
    "phi   = np.linspace(0, 2*np.pi, 181)\n",
    "theta, phi = np.meshgrid(theta, phi)\n",
    "xyz = np.array([np.sin(theta) * np.sin(phi),\n",
    "                np.sin(theta) * np.cos(phi),\n",
    "                np.cos(theta)]) \n",
    "\n",
    "#helper function for equal plots\n",
    "def set_axes_equal(ax):\n",
    "    x_limits = ax.get_xlim3d()\n",
    "    y_limits = ax.get_ylim3d()\n",
    "    z_limits = ax.get_zlim3d()\n",
    "    x_range = abs(x_limits[1] - x_limits[0])\n",
    "    x_middle = np.mean(x_limits)\n",
    "    y_range = abs(y_limits[1] - y_limits[0])\n",
    "    y_middle = np.mean(y_limits)\n",
    "    z_range = abs(z_limits[1] - z_limits[0])\n",
    "    z_middle = np.mean(z_limits)\n",
    "    plot_radius = 0.5*max([x_range, y_range, z_range])\n",
    "    ax.set_xlim3d([x_middle - plot_radius, x_middle + plot_radius])\n",
    "    ax.set_ylim3d([y_middle - plot_radius, y_middle + plot_radius])\n",
    "    ax.set_zlim3d([z_middle - plot_radius, z_middle + plot_radius])\n",
    "\n",
    "#prepare plotting\n",
    "fig = plt.figure(figsize=plt.figaspect(0.5))\n",
    "colormap = plt.cm.ScalarMappable( cmap=plt.get_cmap(\"coolwarm\"))\n",
    "colormap.set_clim(-.45, .45)\n",
    "colormap2 = plt.cm.ScalarMappable( cmap=plt.get_cmap(\"summer\"))\n",
    "colormap2.set_clim(-.45, .45)\n",
    "limit = 0.6\n",
    "Y_lml = sph_harm(ml0, l0, phi, theta)\n",
    "    \n",
    "#create real part plot\n",
    "ax1 = fig.add_subplot(1, 2, 1, projection='3d')\n",
    "r_real = abs(Y_lml.real)*xyz\n",
    "surf1 = ax1.plot_surface(r_real[0], r_real[1], r_real[2],\n",
    "                         rstride=2, cstride=2,\n",
    "                         facecolors=colormap.to_rgba(Y_lml.real))\n",
    "ax1.set_xlim(-limit,limit)\n",
    "ax1.set_ylim(-limit,limit)\n",
    "ax1.set_zlim(-limit,limit)\n",
    "ax1.set_title('Realteil')\n",
    "ax1.set_xlabel('x')\n",
    "ax1.set_ylabel('y')\n",
    "ax1.set_zlabel('z')\n",
    "set_axes_equal(ax1)\n",
    "\n",
    "#create imaginary part plot\n",
    "ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
    "r_imag = abs(Y_lml.imag)*xyz\n",
    "surf2 = ax2.plot_surface(r_imag[0], r_imag[1], r_imag[2],\n",
    "                         rstride=2, cstride=2,\n",
    "                         facecolors=colormap.to_rgba(Y_lml.imag))\n",
    "ax2.set_xlim(-limit,limit)\n",
    "ax2.set_ylim(-limit,limit)\n",
    "ax2.set_zlim(-limit,limit)\n",
    "ax2.set_title('Imaginärteil')\n",
    "ax2.set_xlabel('x')\n",
    "ax2.set_ylabel('y')\n",
    "ax2.set_zlabel('z')\n",
    "set_axes_equal(ax2)\n",
    "\n",
    "#interactivity\n",
    "l_slider = widgets.IntSlider(min=0, max=3, value=0)\n",
    "ml_slider = widgets.IntSlider(min=0, max=0)\n",
    "\n",
    "def update_ml_range(*args):\n",
    "    ml_slider.min = -l_slider.value\n",
    "    ml_slider.max = l_slider.value\n",
    "    \n",
    "l_slider.observe(update_ml_range, 'value')\n",
    "\n",
    "def update(l=l0, ml=ml0):\n",
    "    global surf1, surf2, colormap, colormap2\n",
    "    Y_lml = sph_harm(ml, l, phi, theta)\n",
    "    r_real = abs(Y_lml.real)*xyz\n",
    "    r_imag = abs(Y_lml.imag)*xyz\n",
    "    surf1.remove()\n",
    "    surf1 = ax1.plot_surface(r_real[0], r_real[1], r_real[2],\n",
    "                                    rstride=4, cstride=4,\n",
    "                                    facecolors=colormap.to_rgba(Y_lml.real))\n",
    "    surf2.remove()\n",
    "    surf2 = ax2.plot_surface(r_imag[0], r_imag[1], r_imag[2],\n",
    "                                    rstride=4, cstride=4,\n",
    "                                    facecolors=colormap2.to_rgba(Y_lml.imag))\n",
    "    plt.draw()\n",
    "\n",
    "i=widgets.interact(update,l=l_slider,ml=ml_slider)"
   ]
  }
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