{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# User Guide\n",
    "\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/imartinezl/cpab/HEAD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CPAB library allows to create transformations $\\phi(x,t)$ based on the integration of a continuous piecewise affine velocity field $v(x)$. Let us bring some clarity to this sentence by including some definitions:\n",
    "\n",
    "- The transformation $\\phi(x,t)$ is created by the integration of a velocity field. For that, we need to solve a differential equation of the form: \n",
    "\n",
    "$$\\frac{\\partial\\phi(x,t)}{\\partial t} = v(\\phi(x))$$\n",
    "\n",
    "The transformation $\\phi(x,t)$ depend on two variables $x$ (spatial dimension) and $t$ (integration time).\n",
    "\n",
    "- The velocity field $v(x)$ can be a function of any form and shape, but in this library we focus on an specific type of functions, which are continuous piecewise affine functions.\n",
    "\n",
    "- Continous function: there are no discontinuities in the function domain\n",
    "- Piecewise function: is a function that is defined by parts\n",
    "- Affine: is a geometric transformation that consist on a linear transformation + a translation.\n",
    "\n",
    "Thus, a continous, piecewise, and affine function is just a set of lines joined together. \n",
    "In summary, in this library integrate (efficiently) these functions to create diffeomorphic transformations $\\phi(x,t)$ that are very useful for a lot of tasks in machine learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading libraries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we need to import the necessary Python libraries: ``cpab`` library to compute the transformations, ``matplotlib`` for data visualization, ``numpy`` for array manipulation and ``pytorch`` for autodifferentiation and gradient descent optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import cpab\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transformation parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to create a transformation $\\phi(x,t)$, several options need to be specified. CPAB transformations are built by integrating a continuous piecewise affine velocity field $v(x)$. Such velocity field is defined onto a regular grid, or tesselation. In this example, we will set the number of intervals to 5 (``tess_size=5``).\n",
    "\n",
    "The ``backend`` option let us choose between ``numpy`` backend and the ``pytorch`` backend, the preferred option for optimization tasks. These computations can be also executed on CPU or GPU ``device`` (for the ``pytorch`` backend). \n",
    "\n",
    "The ``zero_boundary`` condition set to ``True`` constraints the velocity $v(x)$ at the tesselation boundary to 0, so $v(0)=0$ and $v(1)=0$. \n",
    "\n",
    "The ``basis`` option let us choose between {``svd``, ``sparse``, ``rref``, ``qr``}, and it represents the method to obtain the null space representation for continuous piecewise affine functions with ``tess_size`` intervals. In this case, we have used the QR decomposition to build the basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tess_size = 5\n",
    "backend = \"numpy\" # [\"pytorch\", \"numpy\"]\n",
    "device = \"cpu\" # [\"cpu\", \"gpu\"]\n",
    "zero_boundary = True # [True, False]\n",
    "basis = \"qr\" # [\"svd\", \"sparse\", \"rref\", \"qr\"]\n",
    "\n",
    "T = cpab.Cpab(tess_size, backend, device, zero_boundary, basis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transformation example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we need to create the one-dimensional grid that is going to be transformed. For that, we use the ``uniform_meshgrid`` method, and we set the number of equally spaced points in the grid to 100. \n",
    "\n",
    "The velocity field $v(x)$ in CPAB transformations are parameterized by a vector $\\theta$. In this example, taking into account the zero velocity constraints at the boundary, only 4 dimensions or degree of freedom are left to play with, and that indeed is the dimensionality of $\\theta$, a vector of 4 values.\n",
    "\n",
    "Finally, we can pass the ``grid`` and the ``theta`` parameters to the ``transform_grid`` method and compute the transformed grid ``grid_t`` $\\phi(x)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "outsize = 100\n",
    "grid = T.uniform_meshgrid(outsize)\n",
    "\n",
    "batch_size = 1\n",
    "theta = T.identity(batch_size, epsilon=2)\n",
    "\n",
    "grid_t = T.transform_grid(grid, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the methods ``visualize_velocity`` and ``visualize_deformgrid`` to plot the velocity field $v(x)$ and the transformed grid $\\phi(x,t)$ respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T.visualize_velocity(theta);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T.visualize_deformgrid(theta);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dotted black line represents the identity tranformation $\\phi(x,t) = x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integration details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the velocity field is integrated up to $t==1$. The following figure shows the how the transformed grid changes along the integration time $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = T.uniform_meshgrid(outsize)\n",
    "theta = T.identity(batch_size, epsilon=2)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax_zoom = fig.add_axes([0.2,0.58,0.2,0.25])\n",
    "\n",
    "ax.axline((0,0),(1,1), color=\"blue\", ls=\"dashed\")\n",
    "ax_zoom.axline((0,0),(1,1), color=\"blue\", ls=\"dashed\")\n",
    "\n",
    "N = 11\n",
    "for i in range(N):\n",
    "    time = i / (N-1)\n",
    "    grid_t = T.transform_grid(grid, theta, time=time)\n",
    "    ax.plot(grid, grid_t.T, label=round(time, 2), color=\"black\", alpha=time)\n",
    "    ax_zoom.plot(grid, grid_t.T, label=round(time, 2), color=\"black\", alpha=time)\n",
    "\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"Original Time\")\n",
    "ax.set_ylabel(\"Transformed Time\")\n",
    "\n",
    "sm = plt.cm.ScalarMappable(cmap=\"gray_r\")\n",
    "cbar = plt.colorbar(sm, ax=ax)\n",
    "cbar.ax.get_yaxis().labelpad = 15\n",
    "cbar.ax.set_ylabel('Integration time', rotation=270)\n",
    "\n",
    "ax_zoom.grid()\n",
    "ax_zoom.set_xlim(.25, .35)\n",
    "ax_zoom.set_ylim(.25, .35)\n",
    "ax_zoom.set_xticklabels([])\n",
    "ax_zoom.set_yticklabels([])\n",
    "ax_zoom.xaxis.set_ticks_position('none')\n",
    "ax_zoom.yaxis.set_ticks_position('none')\n",
    "\n",
    "from matplotlib.patches import Rectangle\n",
    "import matplotlib.lines as lines\n",
    "r = Rectangle((.25,.25), 0.1, 0.1, edgecolor=\"red\", facecolor=\"none\", lw=1)\n",
    "ax.add_patch(r)\n",
    "\n",
    "line = lines.Line2D([0.085,0.25], [0.62, 0.35], color=\"red\", lw=1)\n",
    "ax.add_line(line)\n",
    "line = lines.Line2D([0.435,0.35], [0.62, 0.35], color=\"red\", lw=1)\n",
    "ax.add_line(line);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling and squaring\n",
    "\n",
    "The CPAB library allows to use the scaling and squaring method to approximate the velocity field integration. This method uses the following property of diffeomorphic transformations to accelerate the computation of the integral:\n",
    "\n",
    "$$\\phi(x,t+s) = \\phi(x,t) \\circ \\phi(x,s)$$\n",
    "\n",
    "Thus, computing the transformation $\\phi$ at time $t+s$ is equivalent to composing the transformations at time $t$ and $s$. In the scaling and squaring method, we impose $t=s$, so that we need to compute only one transformation and self-compose it: \n",
    "\n",
    "$$\\phi(x,2t) = \\phi(x,t) \\circ \\phi(x,t)$$\n",
    "\n",
    "Repeating this procedure multiple times (N), we can efficienty approximate the integration:\n",
    "\n",
    "$$\\phi(x,t^{2N}) = \\phi(x,t) \\; \\underbrace{\\circ \\; \\cdots \\; \\circ}_{N} \\; \\phi(x,t)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = T.uniform_meshgrid(outsize)\n",
    "theta = T.identity(batch_size, epsilon=2)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax_zoom = fig.add_axes([0.2,0.58,0.2,0.25])\n",
    "\n",
    "ax.axline((0,0),(1,1), color=\"blue\", ls=\"dashed\")\n",
    "ax_zoom.axline((0,0),(1,1), color=\"blue\", ls=\"dashed\")\n",
    "\n",
    "N = 11\n",
    "for i in range(N):\n",
    "    alpha = i / (N-1)\n",
    "    grid_t = T.transform_grid_ss(grid, theta / 2**N, N=i+1)\n",
    "    ax.plot(grid, grid_t.T, label=round(time, 2), color=\"black\", alpha=alpha)\n",
    "    ax_zoom.plot(grid, grid_t.T, label=round(time, 2), color=\"black\", alpha=alpha)\n",
    "\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"Original Time\")\n",
    "ax.set_ylabel(\"Transformed Time\")\n",
    "\n",
    "sm = plt.cm.ScalarMappable(cmap=\"gray_r\")\n",
    "cbar = plt.colorbar(sm, ax=ax)\n",
    "cbar.ax.get_yaxis().labelpad = 15\n",
    "cbar.ax.set_ylabel('Scaling-Squaring iteration', rotation=270)\n",
    "\n",
    "ax_zoom.grid()\n",
    "ax_zoom.set_xlim(.25, .35)\n",
    "ax_zoom.set_ylim(.25, .35)\n",
    "ax_zoom.set_xticklabels([])\n",
    "ax_zoom.set_yticklabels([])\n",
    "ax_zoom.xaxis.set_ticks_position('none')\n",
    "ax_zoom.yaxis.set_ticks_position('none')\n",
    "\n",
    "from matplotlib.patches import Rectangle\n",
    "import matplotlib.lines as lines\n",
    "r = Rectangle((.25,.25), 0.1, 0.1, edgecolor=\"red\", facecolor=\"none\", lw=1)\n",
    "ax.add_patch(r)\n",
    "\n",
    "line = lines.Line2D([0.085,0.25], [0.62, 0.35], color=\"red\", lw=1)\n",
    "ax.add_line(line)\n",
    "line = lines.Line2D([0.435,0.35], [0.62, 0.35], color=\"red\", lw=1)\n",
    "ax.add_line(line);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data transformation\n",
    "\n",
    "The time series data must have a shape (batch, length, channels). In this example, we have created a sinusoidal dataset of one batch, 50 points in length, and 2 channels. Then, to transform time series data, we can use the ``transform_data`` method and pass as arguments:\n",
    "\n",
    "- data: n-dimensional array of shape (batch, length, channels)\n",
    "- theta: transformation parameters\n",
    "- outsize: length of the transformed data, with final shape (batch, outsize, channels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 1\n",
    "length = 50\n",
    "channels = 2\n",
    "outsize = 100\n",
    "\n",
    "# Generation\n",
    "m = np.ones((batch_size, channels))\n",
    "x = np.linspace(m*0, m*2*np.pi, length, axis=1)\n",
    "data = np.sin(x)\n",
    "\n",
    "theta = T.identity(batch_size, epsilon=1)\n",
    "data_t = T.transform_data(data, theta, outsize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can visualize this data transformation with the ``visualize_deformdata`` method. The <span style=\"color:red\">red</span> curves represent the original data and the <span style=\"color:blue\">blue</span> ones are the transformed data after applying the transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T.visualize_deformdata(data, theta);"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "4b938bf18a8eb7cb5fa05106e7497f4f8071eeeb8765801a6a264d061d1944e0"
  },
  "kernelspec": {
   "display_name": "Python 3.7.9 64-bit ('.venv': venv)",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}