Fix notebook layout.

docs/src/examples/spherically_symmetric.ipynb → docs/src/examples/1D_stellar_wind.ipynb

@@ -32,13 +32,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "---\n",
+    "\n",
     "## Model setup\n",
     "\n",
     "---\n",
     "\n",
     "### Geometry\n",
-    "\n",
-    "---\n",
     "The model box is given by the radial coordinate $r \\in [r_{\\star}, r_{\\text{out}}] = [1, 10^{4}] \\ \\text{au}$. The model is discretised on a logarithmically-spaced grid consisting of 1024 elements with $r \\in [r_{\\text{in}}, r_{\\text{out}}] = [10^{-1}, 10^{4}] \\ \\text{au}$.\n",
     "Note that $r_{\\text{in}} < r_{\\star}$, such that several rays hit the stellar surface, since, for concenience, we use the same discretisation for the impact parameters of the rays. We impose a boundary condition at $r=r_{\\star}$, such that the part of the model inside the star ($r<r_{\\star}$) does not contribute to the resulting observation, and thus cannot be reconstructed."
    ]
@@ -62,9 +62,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Velocity\n",
-    "\n",
     "---\n",
+    "\n",
+    "### Velocity\n",
     "For the velocity field, we assume a typical radially outward directed $\\beta$-law,\n",
     "\\begin{equation*}\n",
     "v(r) \\ = \\ v_{\\star} \\ + \\ \\left( v_{\\infty} - v_{\\star} \\right) \\left(1 - \\frac{r_{\\star}}{r}\\right)^{\\beta} ,\n",
@@ -91,10 +91,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Density\n",
-    "\n",
     "---\n",
     "\n",
+    "### Density\n",
     "We assume the density and velocity to be related through the conservation of mass, such that,\n",
     "\\begin{equation*}\n",
     "\\rho \\left( r \\right) \\ = \\ \\frac{\\dot{M}}{4 \\pi r^{2} \\, v(r)},\n",
@@ -117,10 +116,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### CO abundance\n",
-    "\n",
     "---\n",
     "\n",
+    "### CO abundance\n",
     "The CO abundance is assumed to be proportional to the density, such that, $n^{\\text{CO}}(r) = 3.0 \\times 10^{-4} \\, N_{A} \\, \\rho(r) / m^{\\text{H}_2}$, with $N_{A}$ Avogadro's number, and $m^{\\text{H}_2} = 2.02 \\ \\text{g}/\\text{mol}$, the molar mass of $\\text{H}_{2}$."
    ]
   },
@@ -138,10 +136,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Temperature\n",
-    "\n",
     "---\n",
     "\n",
+    "### Temperature\n",
     "For the gas temperature, we assume a power law,\n",
     "\\begin{equation*}\n",
     "T(r) \\ = \\ T_{\\star} \\left(\\frac{r_{\\star}}{r}\\right)^{\\epsilon} ,\n",
@@ -167,10 +164,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Micro-turbulence\n",
-    "\n",
     "---\n",
     "\n",
+    "### Micro-turbulence\n",
     "Finally, we assume a constant turbulent velocity $v_{\\text{turb}}(r) = 1 \\ \\text{km}/\\text{s}$."
    ]
   },
@@ -187,10 +183,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### TensorModel\n",
-    "\n",
     "---\n",
     "\n",
+    "### TensorModel\n",
     "With all the data in place, we can start building a pomme model.\n",
     "First, we store all model parameters as a TensorModel object and store this in an HDF5 file.\n",
     "We will use this later as the ground truth to verify our reconstructions against."
@@ -221,10 +216,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### SphericalModel\n",
-    "\n",
     "---\n",
     "\n",
+    "### SphericalModel\n",
     "First, we define the functions that can generate the model distributions from the model parameters."
    ]
   },
@@ -324,10 +318,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Spectral lines\n",
-    "\n",
     "---\n",
     "\n",
+    "### Spectral lines\n",
     "We base our reconstructions on synthetic observations of two commonly observed rotational CO lines $J = \\{(3-2), \\, (7-6)\\}$, which we observe, each in 50 frequency bins, centred around the lines, with a spacing of 1.02 km/s."
    ]
   },
@@ -373,10 +366,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Frequencies\n",
-    "\n",
     "---\n",
     "\n",
+    "### Frequencies\n",
     "Next, we define the velocity/frequency range of interest around the lines."
    ]
   },
@@ -397,10 +389,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Synthetic observations\n",
-    "\n",
     "---\n",
     "\n",
+    "## Synthetic observations\n",
     "We can now generate synthetic observations, directly from the SphericalModel object.\n",
     "We will use these later to derive our reconstructions."
    ]
@@ -452,10 +443,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Reconstruction setup\n",
-    "\n",
     "---\n",
     "\n",
+    "## Reconstruction setup\n",
     "In this example, we will try to reconstruct the CO abundance, velocity, and temperature distribution.\n",
     "First, we define the model object for the reconstruction. Note that in the smodel defined above, all the right parameters are already stored, so we need a new one for the reconstruction.\n",
     "We take, $n_{\\text{CO}}^{\\text{init}}(r) = 5.0 \\times 10^{14} \\, \\text{m}^{-3} \\, (r_{\\text{in}}/r)^{2} $, as initial guess for the CO abundance distribution, and initialise both the velocity and the temperature with the correct values."
@@ -495,11 +485,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "\n",
-    "### Loss functions\n",
-    "\n",
     "---\n",
     "\n",
+    "### Loss functions\n",
     "We first create Loss object that can conveniently store the different losses.\n",
     "We will use a reproduction loss (split into an averaged and relative component), a smoothness, and a continuity loss."
    ]
@@ -519,9 +507,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Reproduction loss\n",
-    "\n",
     "---\n",
+    "\n",
+    "#### Reproduction loss\n",
     "We split the reproduction loss into an averaged and a relative component,\n",
     "\\begin{equation*}\n",
     "\\mathcal{L}_{\\text{rep}}\\big(f(\\boldsymbol{m}), \\boldsymbol{o} \\big)\n",
@@ -559,9 +547,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Smoothness loss\n",
-    "\n",
     "---\n",
+    "\n",
+    "#### Smoothness loss\n",
     "The smoothnes loss in spherical symmetry is defined as, "
    ]
   },
@@ -587,9 +575,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Continuity loss\n",
-    "\n",
     "---\n",
+    "\n",
+    "#### Continuity loss\n",
     "In spherical symmetry, the regularisation loss that assumes a steady state and enforces the continuity equation, reads,\n",
     "\\begin{equation*}\n",
     "\\mathcal{L}[\\rho, v]\n",
@@ -626,15 +614,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Fit function\n",
-    "\n",
     "---\n",
+    "\n",
+    "### Fit function\n",
     "With everything in place, we can finally define the fit function."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -666,14 +654,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Experiments\n",
+    "---\n",
     "\n",
-    "---"
+    "## Experiments"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
@@ -682,7 +670,7 @@
      "text": [
       "  0%|          | 0/3 [00:00<?, ?it/s]/home/frederikd/.local/lib/python3.9/site-packages/torch/autograd/__init__.py:200: UserWarning: CUDA initialization: The NVIDIA driver on your system is too old (found version 9010). Please update your GPU driver by downloading and installing a new version from the URL: http://www.nvidia.com/Download/index.aspx Alternatively, go to: https://pytorch.org to install a PyTorch version that has been compiled with your version of the CUDA driver. (Triggered internally at ../c10/cuda/CUDAFunctions.cpp:109.)\n",
       "  Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass\n",
-      "100%|██████████| 3/3 [00:25<00:00,  8.64s/it]\n"
+      " 33%|███▎      | 1/3 [00:08<00:17,  8.99s/it]"
      ]
     }
    ],
@@ -701,14 +689,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "  8%|▊         | 8/100 [01:17<15:12,  9.92s/it]"
+      " 36%|███▌      | 36/100 [06:08<11:29, 10.77s/it]"
      ]
     }
    ],
@@ -724,6 +712,27 @@
     "losses.plot()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'losses' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mlosses\u001b[49m\u001b[38;5;241m.\u001b[39mplot()\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'losses' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "losses.plot()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -739,6 +748,13 @@
    "source": [
     "smodel_recon.model_1D.save('model_recon.h5')"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

docs/src/examples/index.rst

@@ -7,4 +7,5 @@ Some examples showcasing the use of pomme.
    :maxdepth: 1
    :caption: Contents:
 
-   spherically_symmetric
+   1D_stellar_wind
+   3D_stellar_wind