change of variables notebook changes for blog
This commit is contained in:
ritchie46 committed
1 parent
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commit
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1 file changed
+89
-54
@@ -28,24 +28,31 @@
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.0\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"1.0"
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"[<matplotlib.lines.Line2D at 0x7f90e9cb7208>]"
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]
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},
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"execution_count": 2,
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"execution_count": 17,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": 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truncated
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"image/png": 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truncated
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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"<Figure size 1152x288 with 1 Axes>"
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]
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},
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"metadata": {
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@@ -58,10 +65,12 @@
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"x = np.linspace(0.01, 2, num=100)\n",
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"\n",
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"base = stats.norm(1, 0.1)\n",
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"print(np.trapz(base.pdf(x), x))\n",
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"\n",
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"plt.plot(x, base.pdf(x))\n",
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"\n",
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"np.trapz(base.pdf(x), x)"
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"plt.figure(figsize=(16, 4))\n",
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"plt.xlabel(r'$x$')\n",
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"plt.ylabel(r'$p(x)$')\n",
|
||||
"plt.plot(x, base.pdf(x))"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -75,24 +84,31 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"5.641895835477563\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"5.641895835477563"
|
||||
"<matplotlib.legend.Legend at 0x7f90e98c6588>"
|
||||
]
|
||||
},
|
||||
"execution_count": 3,
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
"<Figure size 1152x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
@@ -105,10 +121,15 @@
|
||||
"def f(x):\n",
|
||||
" return x**2\n",
|
||||
"\n",
|
||||
"y = f(x)\n",
|
||||
"transformed = f(base.pdf(x))\n",
|
||||
"plt.plot(f(x), transformed)\n",
|
||||
"print(np.trapz(transformed, y))\n",
|
||||
"\n",
|
||||
"np.trapz(transformed, f(x))"
|
||||
"plt.figure(figsize=(16, 4))\n",
|
||||
"plt.xlim(0, 2)\n",
|
||||
"plt.plot(y, transformed, label=r'$P(y)$')\n",
|
||||
"plt.plot(x, base.pdf(x), label='$P(x)$', ls='-.')\n",
|
||||
"plt.legend()"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -144,24 +165,31 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"execution_count": 27,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0.9987379589284238\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"0.9987379589284238"
|
||||
"<matplotlib.legend.Legend at 0x7f90e9c442e8>"
|
||||
]
|
||||
},
|
||||
"execution_count": 4,
|
||||
"execution_count": 27,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
"<Figure size 1152x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
@@ -181,14 +209,14 @@
|
||||
"\n",
|
||||
"y = f(x)\n",
|
||||
"px = base.pdf(x)\n",
|
||||
"\n",
|
||||
"transformed = px * f_i_prime(f_i(y))\n",
|
||||
"print(np.trapz(transformed, y))\n",
|
||||
"\n",
|
||||
"plt.plot(x, px)\n",
|
||||
"plt.plot(y, transformed)\n",
|
||||
"plt.figure(figsize=(16, 4))\n",
|
||||
"plt.xlim(0, 2)\n",
|
||||
"\n",
|
||||
"np.trapz(transformed, y)"
|
||||
"plt.plot(y, transformed, label=r'$P(y)$')\n",
|
||||
"plt.plot(x, base.pdf(x), label='$P(x)$', ls='-.')\n",
|
||||
"plt.legend()\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -235,7 +263,6 @@
|
||||
"\n",
|
||||
"y = f(x)\n",
|
||||
"px = base.pdf(x)\n",
|
||||
"\n",
|
||||
"transformed = px * f_i_prime(f_i(y))\n",
|
||||
"\n",
|
||||
"plt.plot(x, px)\n",
|
||||
@@ -271,40 +298,50 @@
|
||||
"$$ \n",
|
||||
"\\begin{eqnarray}\n",
|
||||
"P(y)&=&P(f^{-1}(y)) \\cdot \\left| \\det \\frac{\\partial{ f(y)^{-1} }}{\\partial{y}} \\right| \\\\\n",
|
||||
"P(y)&=&P(f^{-1}(y)) \\cdot \\left| \\det \\mathbf{J}_{f^{-1}(y)} \\right| \\\\\n",
|
||||
"&=&P(f^{-1}(y)) \\cdot \\left| \\det \\mathbf{J}_{f^{-1}(y)} \\right| \\\\\n",
|
||||
"\\end{eqnarray}\n",
|
||||
"$$\n",
|
||||
"\n",
|
||||
"The geometric meaning of the determinant is a scaling factor. $\\det A$ tells us how much an n-dimensional volume is scaled by applying the transformation of $A$."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$Q(z') = Q(z) \\left| \\det \\frac{\\partial{f^{-1}}}{\\partial{z}} \\right| $$\n",
|
||||
"\n",
|
||||
"$$ f(x) $$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 259,
|
||||
"execution_count": 39,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0.9905751293230018\n",
|
||||
"(50, 50, 2)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.contour.QuadContourSet at 0x7f5f90e20ac8>"
|
||||
"0.9905751293230018"
|
||||
]
|
||||
},
|
||||
"execution_count": 259,
|
||||
"execution_count": 39,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAesAAAHWCAYAAABXF6HSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3d/69kdZ3n8de74TYQ+bZJw0BoviQsGbKaqGwHUZIJa3QiSOQXTJhETfylg2ETzI4x0R80s3+AMQ6rnY5ORuI4xvhtCQF2SEai/gATugWU6c4EZ1E7wKJO7IZIuoO894dbJdXVVbfOqfqc83l/Pp/nI+n07b517z2nTtV5ns/nnKpr7i4AABDXrtwLAAAAdkasAQAIjlgDABAcsQYAIDhiDQBAcMQaAIDgOsXazJ43s5+Z2VNm9uSCz5uZfcnMnjOzZ8zshvSLCgBAm87ucdv/5u6/XfK5WyVdN/nzLklfmfwNAAA2lGoa/A5J9/u2xyVdbGaXJ/reAAA0rWusXdI/mdkhM9u/4PNXSPr1zL+PTf4PAABsqOs0+M3u/oKZXSrpUTM76u4/mvm8LfiaM97HdBL6/ZJ0ls7+r285+z/1XmAAAEp14vXf/NbdL+n7dZ1i7e4vTP5+2cy+L+lGSbOxPibpypl/75X0woLvc1DSQUm6aOtSf8+eD/ddXgAAivXIS1/+5Tpft3Ia3MzeYmYXTD+W9JeSfj53swckfWxyVfhNko67+4vrLBAAADhdl5H1n0n6vplNb/9Nd3/EzO6WJHc/IOkhSbdJek7SHyR9fJjFBQCgPStj7e7/LuntC/7/wMzHLumetIsGAAAk3sEMAIDwiDUAAMERawAAgiPWAAAER6wBAAiOWAMAEByxBgAgOGINAEBwxBoAgOCINQAAwRFrAACCI9YAAARHrAEACI5YAwAQHLEGACA4Yg0AQHDEGgCA4Ig1AADBEWsAAIIj1gAABEesAQAIjlgDABAcsQYAIDhiDQBAcMQaAIDgiDUAAMERawAAgiPWAAAER6wBAAiOWAMAEByxBgAgOGINAEBwxBoAgOCINQAAwRFrAACCI9YAAARHrAEACI5YAwAQHLEGACA4Yg0AQHDEGgCA4Ig1AADBEWsAAIIj1gAABEesAQAIjlgDABBc51ib2Vlm9lMze3DB524xs+Nm9tTkz+fSLiYAAO06u8dt75V0RNKFSz7/Y3e/ffNFAgAAszqNrM1sr6QPSvrqsIsDAADmdZ0G/6KkT0t6Y4fbvNvMnjazh83srYtuYGb7zexJM3vy1Buv9V1WAACatDLWZna7pJfd/dAONzss6Wp3f7ukv5X0g0U3cveD7r7P3fft3nXeWgsMAEBruoysb5b0ITN7XtK3JL3XzL4xewN3P+Hur04+fkjSlpntSb2wAAC0aGWs3f0z7r7X3a+RdJekf3b3j8zexswuMzObfHzj5Pv+boDlBQCgOX2uBj+Nmd0tSe5+QNKdkj5hZq9Lek3SXe7uaRYRAIC29Yq1uz8m6bHJxwdm/v8+SfelXDAAALBt7ZE1gHhOXb83yffZffRYku8DIA1iDRQgVYSH+HmEHRgesQYCGDvGKa1admIObI5YAyMqOcrrWrbORBzojlgDA2oxzl3N3zfEG1iOWAOJEObNEG9gOWINbIBAD4d4A28i1kAPxDmf2fuecKM1xBpYgUDHQ7jRGmINLEGky0C40QJiDcwg0GUj3KgVsUbzCHSdCDdqQqzRLCLdjum2JtooFbFGUwh02xhto1TEGk0g0pjHaBslIdaoGpHGKkQbJSDWqBKRRl9EG5ERa1SFSGNTRBsREWtUgUgjNaKNSIg1ikakMTSijQiINYpEpDE2oo2ciDWKQqSRG9FGDrtyLwDQFaFGJDweMSZG1giPnSKiYpSNsRBrhEWkUQqijaExDY5wTl2/l1CjSDxuMRRijVDY2aF0HGxiCMQaIbCDQ214PCMlYo3s2KmhVhyEIhUuMEM27MTSOn7tOcm/50W/OJn8e7bo1PV7ufgMGyHWyIJQ9zNEiFP9XILeDVeMYxPEGqMj1MvlivImli0zEV+MUTbWQawxGiJ9uhLD3Mei9SPg2wg2+iLWGAWhrj/OXczfBy3Hm2lx9EGsMbhWQ02cVyPejLLRDbHGYFqMNIHezOz911K4CTZWIdYYREuhJtDDaC3cTItjJ8QaybUQagI9run93Uq0CTbmEWskVXuoiXRerYy2CTbmEWskU2uoCXRMtYebYGMW7w2OJGoM9fFrzyHUhah1W9X4vMJ6GFljIzXuTGrc6beixnPbjLAhEWtsoKZQE+i61BZtgg1ijbXUEmoiXbeaos1Lu9rGOWv0RqhRmprOadfy/EM/nWNtZmeZ2U/N7MEFnzMz+5KZPWdmz5jZDWkXE1HUsKOoaceNfmrZ9jU8D9FPn5H1vZKOLPncrZKum/zZL+krGy4XAip9B1HLjhqbq+GxUPrzEf10irWZ7ZX0QUlfXXKTOyTd79sel3SxmV2eaBkRQMk7hhp2zBhG6Y+Nkp+X6KfryPqLkj4t6Y0ln79C0q9n/n1s8n+oQMk7hJJ3xBhPyY+Tkp+f6G7l1eBmdrukl939kJndsuxmC/7PF3yv/dqeJte5u87vsZjIpdQdQck739ReuXrR0/N0F/zyjKdrc0q+cpyXdtWvy0u3bpb0ITO7TdK5ki40s2+4+0dmbnNM0pUz/94r6YX5b+TuByUdlKSLti5l7xBciaFuJdJdAjzU96s97MevPYdgI5yVsXb3z0j6jCRNRtafmgu1JD0g6b+b2bckvUvScXd/MfGyYkSEOobUUU5h2TLVFPFSR9kEu15rvymKmd0tSe5+QNJDkm6T9JykP0j6eJKlQxalhbqWSEcMcx+Llr/0gJc4yibYdTL3PE+mi7Yu9ffs+XCWn43lCPV4So9zX6WHu7RoE+yYHnnpy4fcfV/fr+PtRvEnhHp4rQV61vy6lxbvEkfZqAexhqSyQl1apFsO9E5m75dSwl3SuWymw+tCrFGUUkJNoPspLdyljLIJdj2INYoZVUcPNYFOo5RwE2yMid+61bgSQh39LSFfudoI9UCi37eRH5ezSnieY2fEumElPIEj7wyjh6Qmke/r6AeTUyU837Ec0+CNKuGJG3EHGDUYrZje/xGnx0uZFkeZGFk3iFD3F3lk16Ko2yPa43ZeCc99LEasEU6kHV7UKGBbxO0T6fG7CMEuE7FuTOQnarRzf9EigOWiRTvS43iRyPsBLEasGxL5CRpp5xZtx4/uIm27SI/pRSLvD3AmYt2IyE/MKDu1SDt6bCbKtozy2Eb5iDWyirAzi7JjR3oRtmuEx/gykQ/icTpeutWAqE/ICDuxCDvzTZ286tTgP+OcX+0e/GcMJcLLvSK/rIt3OCsDsa4coV6utFCPEeW+P7ukiL9ytWUPthTzl4AQ7PiINUaXO9QlRDpnmPtYtJyRA84oG6Ui1hWLOKom1MuVEuhVZtcjarhzj7IjYnQdG7GuFKE+XcRI1xLnnUQOd85RdtTRNcGOi1hXiFCfLlKoWwj0MlHDnWuUHTXYiImXbqFqUUJ98qpTTYd63vT+iHKf5Hqc5D4ttEjEg30Q6+pEfKLl2CFFee10pCBFFeU+IthvirgfaR3T4BhUrlDnFCE8JYowTZ7rPDZT4liFkXVFoh0NtxbqKCPEGuS+L3M8jqKNsKPtT1pHrCsR7YnVUqhzh6VmBBvYRqyRXGuhxrByHgzlPqWSW7RBQMuIdQVaf0Ll2KEymh5frvt87MdXtNF16/uXKIg1khpzR5Pjim8inV+ObdB6sJEfsS5cpKPesUM9JiIdz9jbpOVgR9rPtIpYI4lIO5bUiHRsNQcbmOJ11gVr9Wh3rB1maZG+Zu9vkn6/549dkvT7DenkVadGe232mG9PGun117xveF7EulCRQl3j9HfkUKeO8jo/J2LIp9tsjGi3GmzkQ6yxEUI9vLHi3Mf8MkWK91ij7BaDzeg6H2JdoEij6rGMEeookY4Y51VmlzlCuMcaZfN7sTEWLjDD2sYaVbcS6mv2/qbIUM+brkeEdRlju4414xPlIs4WBwsRMLIuTJQnCqFOI0LQhhRhxD3GtPhYI2ymw9tFrBFWraGuPdDLTNc7R7RrCjbaxDR4QVoaVQ8d6hxvchJlaji3XPdDhFMdKTAd3iZijV6i7Cg2QaRjyHG/DL3tWzt/jfEQ60K0dBQ75A4vR6ixs7GjXUuw0RZijc5Kn/4eM9SMpvsb8z6rIdgRRtctDSJy4wKzArTyhKgh1AR6c2NdiDbmO54Bm2JkjU4iHMWvi1CXqfRRNqNrpESssVLJ099jhJop7+GMdd+WHGy0gVgH18JRa+mhxvBKvp+HDjaj6zYQa+xo6B1BqaFmND2+oe/vkl+HHSHYGNbKC8zM7FxJP5J0zuT233H3z8/d5hZJ/1vS/5381/fc/X+mXdT2cLQaUymRfv9lR3t/zaMvXT/AkqQz9MVnQ73TGe9uhk11uRr8pKT3uvurZrYl6Sdm9rC7Pz53ux+7++3pFxG5MKo+U8RQrxPlvt8rWsSv2fsbgj0n9/uG837hw1oZa3d3Sa9O/rk1+cMhIkJqIdQp47zuz4wQ7xKDDayr0+uszewsSYck/WdJ/8vdn1hws3eb2dOSXpD0KXd/Nt1itif3FHiJo+qhQh0h0jkCvZPZ5ckZ7iGDPQRG11hXp1i7+x8lvcPMLpb0fTN7m7v/fOYmhyVdPZkqv03SDyRdN/99zGy/pP2SdO6u8zdeeJSppJez5Ax1tEAvkzvcQwWb0TUi6XU1uLv/XtJjkj4w9/8n3P3VyccPSdoysz0Lvv6gu+9z9327d523/lJXrvZR9RCGGFXnCPX7Lzv6pz8lyrXsQ22rIR5XJR2sIo6VsTazSyYjapnZeZLeJ+no3G0uMzObfHzj5Pv+Lv3ionSlTH+PHeqSA71IjvUh2NtyH2zLine truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
"<Figure size 576x576 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
@@ -323,9 +360,12 @@
|
||||
"\n",
|
||||
"# field of all possible events X\n",
|
||||
"x_field = np.concatenate([x1_s[..., None], x2_s[..., None]], axis=-1)\n",
|
||||
"print(x_field.shape)\n",
|
||||
"\n",
|
||||
"plt.contourf(x1_s, x2_s, base.pdf(x_field))"
|
||||
"print(np.trapz(np.trapz(base.pdf(x_field), x_field[:, 0, 1], axis=0), x_field[0, :, 0]))\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(8, 8))\n",
|
||||
"plt.contourf(x1_s, x2_s, base.pdf(x_field))\n",
|
||||
"np.trapz(np.trapz(base.pdf(x_field), x_field[:, 0, 1], axis=0), x_field[0, :, 0])"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -347,18 +387,9 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 275,
|
||||
"execution_count": 35,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"/opt/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
|
||||
" import sys\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def f(x1, x2):\n",
|
||||
" return torch.exp(x1 / 3), x2**2\n",
|
||||
@@ -373,7 +404,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 276,
|
||||
"execution_count": 36,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -401,32 +432,32 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 277,
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"/opt/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:5: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
|
||||
" \"\"\"\n"
|
||||
"/opt/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
|
||||
" \n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.contour.QuadContourSet at 0x7f5f90d534a8>"
|
||||
"<matplotlib.contour.QuadContourSet at 0x7f90e4f80208>"
|
||||
]
|
||||
},
|
||||
"execution_count": 277,
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
"<Figure size 576x576 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
@@ -438,7 +469,11 @@
|
||||
"source": [
|
||||
"px = base.pdf(x_field)\n",
|
||||
"transformed = px * np.abs(create_det_jac(y_field))\n",
|
||||
"plt.contourf(y_field[..., 0], y_field[..., 1], transformed)"
|
||||
"\n",
|
||||
"plt.figure(figsize=(8, 8))\n",
|
||||
"plt.contourf(y_field[..., 0], y_field[..., 1], transformed)\n",
|
||||
"\n",
|
||||
"print(np.trapz(np.trapz(transformed, y_field[:, 0, 1], axis=0), y_field[0, :, 0]))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
Reference in new issue
Block a user