{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Sum\nThis example shows how to use the :py:class:`pylops.Sum` operator to stack\nvalues along an axis of a multi-dimensional array\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.gridspec as pltgs\n\nimport pylops\n\nplt.close('all')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's start by defining a 2-dimensional data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "ny, nx = 5, 7\nx   = (np.arange(ny*nx)).reshape(ny, nx)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can now create the operator and peform forward and adjoint\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "Sop = pylops.Sum(dims=(ny, nx), dir=0)\n\ny  = Sop * x.ravel()\nxadj = Sop.H * y\nxadj = xadj.reshape(ny, nx)\n\ngs = pltgs.GridSpec(1, 7)\nfig = plt.figure(figsize=(7, 3))\nax = plt.subplot(gs[0, 0:3])\nim = ax.imshow(x, cmap='rainbow', vmin=0, vmax=ny*nx)\nax.set_title('x', size=20, fontweight='bold')\nax.set_xticks(np.arange(nx-1)+0.5)\nax.set_yticks(np.arange(ny-1)+0.5)\nax.grid(linewidth=3, color='white')\nax.xaxis.set_ticklabels([])\nax.yaxis.set_ticklabels([])\nax.axis('tight')\nax = plt.subplot(gs[0, 3])\nax.imshow(y[:,np.newaxis], cmap='rainbow', vmin=0, vmax=ny*nx)\nax.set_title('y', size=20, fontweight='bold')\nax.set_xticks([])\nax.set_yticks(np.arange(nx-1)+0.5)\nax.grid(linewidth=3, color='white')\nax.xaxis.set_ticklabels([])\nax.yaxis.set_ticklabels([])\nax.axis('tight')\nax = plt.subplot(gs[0, 4:])\nax.imshow(xadj, cmap='rainbow', vmin=0, vmax=ny*nx)\nax.set_title('xadj', size=20, fontweight='bold')\nax.set_xticks(np.arange(nx-1)+0.5)\nax.set_yticks(np.arange(ny-1)+0.5)\nax.grid(linewidth=3, color='white')\nax.xaxis.set_ticklabels([])\nax.yaxis.set_ticklabels([])\nax.axis('tight')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Note that since the Sum operator creates and under-determined system of\nequations (data has always lower dimensionality than the model), an exact\ninverse is not possible for this operator.\n\n"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "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": "3.6.12"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}