2021-08-26

source/FT_Interactive_animation.ipynb → build/doctrees/nbsphinx/FT_Interactive_animation_.ipynb

@@ -37,7 +37,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -82,37 +82,89 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 63/63 [00:19<00:00,  3.21it/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from tqdm import tqdm\n",
+    "n = 0\n",
+    "def F(omega,t):\n",
+    "    z = np.exp(-1j*omega*t)\n",
+    "    plt.arrow(0,0,z.real,z.imag,head_width=0.05, head_length=0.1)\n",
+    "    plt.xlim(-1.1,1.1)\n",
+    "    plt.ylim(-1.1,1.1)\n",
+    "    set_center_axis(plt.gca())\n",
+    "    ax1 = plt.gca()\n",
+    "    ax1.set_xlabel('real',position=(1,0),fontsize = 14)\n",
+    "    ax1.set_ylabel('imag',position=(0,1),fontsize = 14)\n",
+    "    set_center_axis(plt.gca())\n",
+    "    textstr = '\\n'.join((r'$e^{-i%.2f t}$' % (omega, ),))\n",
+    "    ax1.text(0.5,0.5,textstr,fontsize = 30)\n",
+    "    global n\n",
+    "    n += 1\n",
+    "    plt.savefig('img/e_'+str(n)+'.png')\n",
+    "    plt.close()\n",
+    "    \n",
+    "for omega in tqdm(np.arange(0,2*np.pi,0.1)):\n",
+    "    F(omega,1)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "844f1f7b416140468642d679ca0ceb6f",
+       "model_id": "bf34081fd4da40f79886b15b40429deb",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "interactive(children=(FloatSlider(value=-0.0031853071795859833, description='omega', max=6.283185307179586, mi…"
+       "interactive(children=(FloatSlider(value=3.1, description='omega', max=6.283185307179586), FloatSlider(value=3.…"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
+    "n = 0\n",
     "def F(omega,t):\n",
     "    z = np.exp(-1j*omega*t)\n",
     "    print(z)\n",
     "    plt.arrow(0,0,z.real,z.imag,head_width=0.05, head_length=0.1)\n",
     "    plt.xlim(-1.1,1.1)\n",
     "    plt.ylim(-1.1,1.1)\n",
+    "    ax1 = plt.gca()\n",
+    "    ax1.set_xlabel('real',position=(1,0),fontsize = 14)\n",
+    "    ax1.set_ylabel('imag',position=(0,1),fontsize = 14)\n",
     "    set_center_axis(plt.gca())\n",
+    "    textstr = '\\n'.join((r'$e^{-i%.2f t}$' % (omega, ),))\n",
+    "    ax1.text(0.5,0.5,textstr,fontsize = 30)\n",
+    "#     global n\n",
+    "#     n += 1\n",
+    "#     plt.savefig('img/e_'+str(n)+'.png')\n",
     "\n",
     "    \n",
-    "interactive_plot = interactive(F,omega=(-2*np.pi, 2*np.pi, 0.01),t=(0, 2*np.pi, 0.1))\n",
+    "interactive_plot = interactive(F,omega=(0, 2*np.pi, 0.1),t=(0, 2*np.pi, 0.1))\n",
     "output = interactive_plot.children[-1]\n",
     "output.layout.height = '600px'\n",
     "\n",
@@ -135,15 +187,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 39,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "0bf79c71fa134fae996aa284419a8fb9",
+       "model_id": "a7a227158e5f4e55b9fc10aac9ef7af1",
        "version_major": 2,
        "version_minor": 0
       },
@@ -174,7 +224,7 @@
     "    ax1.set_ylabel('imag',position=(0,1),fontsize = 14)\n",
     "    ax1.set_aspect(1)\n",
     "    textstr = '\\n'.join((r'$sin(2\\pi t)e^{-2\\pi it}\\cdot e^{%.2f}$' % (freq, ),))\n",
-    "    ax1.text(0.05,1.1,textstr,fontsize = 15)\n",
+    "    ax1.text(0.05,1.1,textstr,fontsize = 30)\n",
     "    ax2.scatter(ft_line[:,0],ft_line[:,1])\n",
     "    ax2.set_xlabel('$freq$',fontsize=14)\n",
     "    textstr2 = '\\n'.join((r'$ A = \\left|\\int^{+\\infty}_{-\\infty}sin(2\\pi t)e^{-2\\pi it}\\cdot e^{%.2f} dt\\right|$' % (freq, ),))\n",
@@ -187,6 +237,52 @@
     "interactive_plot"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 400/400 [02:53<00:00,  2.30it/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from tqdm import tqdm\n",
+    "n = 0\n",
+    "ft_line = np.empty(shape =(1,2))\n",
+    "def F(freq,t):\n",
+    "    global ft_line\n",
+    "    fig, (ax1, ax2) = plt.subplots(2, 1)\n",
+    "    t = np.linspace(0, np.pi, num=1000)\n",
+    "    ft = np.exp(2*np.pi*freq*1j*t) * np.sin(2*np.pi*t)\n",
+    "    Amp = abs(ft.sum())\n",
+    "    if ft_line.shape ==(1,2):\n",
+    "        ft_line = np.array([[freq,Amp]])\n",
+    "    ft_line = np.append(ft_line,np.array([[freq,Amp]]),axis=0)\n",
+    "    ax1.plot(ft.real,ft.imag)\n",
+    "    set_center_axis(ax1)\n",
+    "    ax1.set_xlabel('real',position=(1,0),fontsize = 14)\n",
+    "    ax1.set_ylabel('imag',position=(0,1),fontsize = 14)\n",
+    "    ax1.set_aspect(1)\n",
+    "    textstr = '\\n'.join((r'$sin(2\\pi t)e^{-2\\pi it}\\cdot e^{%.2f}$' % (freq, ),))\n",
+    "    ax1.text(0.05,1.1,textstr,fontsize = 30)\n",
+    "    ax2.scatter(ft_line[:,0],ft_line[:,1])\n",
+    "    ax2.set_xlabel('$freq$',fontsize=14)\n",
+    "    textstr2 = '\\n'.join((r'$ A = \\left|\\int^{+\\infty}_{-\\infty}sin(2\\pi t)e^{-2\\pi it}\\cdot e^{%.2f} dt\\right|$' % (freq, ),))\n",
+    "    ax2.set_ylabel(textstr2,fontsize = 14)\n",
+    "    global n\n",
+    "    n += 1\n",
+    "    plt.savefig('img/e_'+str(n)+'.png')\n",
+    "    plt.close()\n",
+    "    \n",
+    "for omega in tqdm(np.arange(-2,2,0.01)):\n",
+    "    F(omega,1)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

build/html/.buildinfo

@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 0a342fd571fd48c8e0f0149659b3a936
+config: c14f61d1e82ab4a58cbb0bbf18d3a4b8
 tags: 645f666f9bcd5a90fca523b33c5a78b7