{
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      },
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      "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"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.gridspec as pltgs\nimport matplotlib.pyplot as plt\nimport numpy as np\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), axis=0)\n\ny = Sop * x\nxadj = Sop.H * y\n\ngs = pltgs.GridSpec(1, 7)\nfig = plt.figure(figsize=(7, 4))\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\")\nplt.tight_layout()"
      ]
    },
    {
      "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"
      ]
    }
  ],
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      "display_name": "Python 3",
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      "file_extension": ".py",
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