scottyhq/pixel-function-test.ipynb

## pixel-function-test.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test gdal vrt pixel functions\n",
    "\n",
    "Use GDAL python pixel function to define how overlapping image regions are dealt with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import rasterio\n",
    "from rasterio.transform import Affine\n",
    "import rasterio.plot\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create two simple rasters, create vrts overlapping by 1 degree, use pixel functions to mosaiic\n",
    "x = np.linspace(-4.0, 4.0, 240)\n",
    "y = np.linspace(2.0, 8.0, 180)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z1 = np.ones_like(X)\n",
    "\n",
    "Z1[:10,:] = 0 #or np.nan?\n",
    "Z1[:,:10] = 0\n",
    "\n",
    "Z1c = Z1.astype('complex64') + 1j\n",
    "\n",
    "res = (x[-1] - x[0]) / 240.0\n",
    "transform1 = Affine.translation(x[0] - res / 2, y[-1] - res / 2) * Affine.scale(res, -res)\n",
    "transform1\n",
    "\n",
    "with rasterio.open('top-complex.tif', 'w',\n",
    "                    driver='GTiff',\n",
    "                    height=Z1c.shape[0],\n",
    "                    width=Z1c.shape[1],\n",
    "                    #nodata=np.nan, #0 #throwing KeyError: 'complex64'... likely a bug\n",
    "                    count=1,\n",
    "                    dtype=Z1c.dtype,\n",
    "                    crs='+proj=latlong',\n",
    "                    transform=transform1,\n",
    "                    # creation options\n",
    "                    blockxsize=128,\n",
    "                    blockysize=128,\n",
    "                    tiled=True,\n",
    "                    ) as dst:\n",
    "    dst.write(Z1c, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create two simple rasters, create vrts overlapping by 1 degree, use pixel functions to mosaiic\n",
    "x = np.linspace(-4.0, 4.0, 240)\n",
    "y = np.linspace(-3.0, 3.0, 180)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z2 = 2*np.ones_like(X)\n",
    "\n",
    "Z2[-10:,:] = 0\n",
    "Z2[:,-10:] = 0\n",
    "\n",
    "Z2c = Z2.astype('complex64') + 2j\n",
    "\n",
    "res = (x[-1] - x[0]) / 240.0\n",
    "transform2 = Affine.translation(x[0] - res / 2, y[-1] - res / 2) * Affine.scale(res, -res)\n",
    "transform2\n",
    "\n",
    "with rasterio.open('bottom-complex.tif', 'w',\n",
    "                    driver='GTiff',\n",
    "                    height=Z2c.shape[0],\n",
    "                    width=Z2c.shape[1],\n",
    "                    #nodata=np.nan,\n",
    "                    count=1,\n",
    "                    dtype=Z2c.dtype,\n",
    "                    crs='+proj=latlong',\n",
    "                    transform=transform2,\n",
    "                    # creation options\n",
    "                    blockxsize=128,\n",
    "                    blockysize=128,\n",
    "                    tiled=True,\n",
    "                    ) as dst:\n",
    "    dst.write(Z2c, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'driver': 'GTiff', 'dtype': 'complex64', 'nodata': None, 'width': 240, 'height': 180, 'count': 1, 'crs': CRS.from_epsg(4326), 'transform': Affine(0.03333333333333333, 0.0, -4.016666666666667,\n",
      "       0.0, -0.03333333333333333, 7.983333333333333), 'blockxsize': 128, 'blockysize': 128, 'tiled': True, 'interleave': 'band'}\n",
      "{'driver': 'GTiff', 'dtype': 'complex64', 'nodata': None, 'width': 240, 'height': 180, 'count': 1, 'crs': CRS.from_epsg(4326), 'transform': Affine(0.03333333333333333, 0.0, -4.016666666666667,\n",
      "       0.0, -0.03333333333333333, 2.9833333333333334), 'blockxsize': 128, 'blockysize': 128, 'tiled': True, 'interleave': 'band'}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-3, 8)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "\n",
    "with rasterio.open('top-complex.tif') as src:\n",
    "    print(src.profile)\n",
    "    data = src.read(1)\n",
    "    extent = (src.bounds.left, src.bounds.right, src.bounds.bottom, src.bounds.top) #(left, right, bottom, top)\n",
    "    plt.imshow(data.real, vmin=0, vmax=2, alpha=0.5, extent=extent)\n",
    "    \n",
    "with rasterio.open('bottom-complex.tif') as src:\n",
    "    print(src.profile)\n",
    "    data = src.read(1)\n",
    "    extent = (src.bounds.left, src.bounds.right, src.bounds.bottom, src.bounds.top) \n",
    "    plt.imshow(data.real, vmin=0, vmax=2, alpha=0.5, extent=extent)\n",
    "\n",
    "plt.colorbar(ax.get_images()[0])\n",
    "plt.xlim(-4,4)\n",
    "plt.ylim(-3,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting merged-average-complex.vrt\n"
     ]
    }
   ],
   "source": [
    "%%writefile merged-average-complex.vrt\n",
    "\n",
    "<VRTDataset rasterXSize=\"240\" rasterYSize=\"330\">\n",
    "  <SRS>GEOGCS[\"WGS 84\",DATUM[\"unknown\",SPHEROID[\"WGS84\",6378137,298.257223563]],PRIMEM[\"Greenwich\",0],UNIT[\"degree\",0.0174532925199433]]</SRS>\n",
    "  <GeoTransform> -4.0166666666666666e+00,  3.3333333333333333e-02,  0.0000000000000000e+00,  7.9833333333333334e+00,  0.0000000000000000e+00, -3.3333333333333333e-02</GeoTransform>\n",
    "  <VRTRasterBand dataType=\"CFloat32\" band=\"1\" subClass=\"VRTDerivedRasterBand\">\n",
    "  \n",
    "    <PixelFunctionType>average</PixelFunctionType>\n",
    "    <PixelFunctionLanguage>Python</PixelFunctionLanguage>\n",
    "    <PixelFunctionCode><![CDATA[\n",
    "\n",
    "def average(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize, raster_ysize, buf_radius, gt, **kwargs):\n",
    "    \"\"\" Average overlapping VRTs where (data.reals != 0) \"\"\"\n",
    "    import numpy as np\n",
    "    stack = np.dstack(in_ar)\n",
    "    indValid = (stack.real != 0)\n",
    "    zero2nodata = np.where(indValid, stack, 0)\n",
    "    total = np.sum(zero2nodata, axis=-1)\n",
    "    count = np.sum(indValid.astype(int), axis=-1)\n",
    "    out_ar[:] = total / count\n",
    "    \n",
    "     ]]>\n",
    "    </PixelFunctionCode>\n",
    "    \n",
    "    <SimpleSource>\n",
    "      <SourceFilename relativeToVRT=\"1\">top-complex.tif</SourceFilename>\n",
    "      <SourceBand>1</SourceBand>\n",
    "      <SourceProperties RasterXSize=\"240\" RasterYSize=\"180\" DataType=\"CFloat32\" BlockXSize=\"128\" BlockYSize=\"128\" />\n",
    "      <SrcRect xOff=\"0\" yOff=\"0\" xSize=\"240\" ySize=\"180\" />\n",
    "      <DstRect xOff=\"0\" yOff=\"0\" xSize=\"240\" ySize=\"180\" />\n",
    "    </SimpleSource>\n",
    "    \n",
    "    <SimpleSource>\n",
    "      <SourceFilename relativeToVRT=\"1\">bottom-complex.tif</SourceFilename>\n",
    "      <SourceBand>1</SourceBand>\n",
    "      <SourceProperties RasterXSize=\"240\" RasterYSize=\"180\" DataType=\"CFloat32\" BlockXSize=\"128\" BlockYSize=\"128\" />\n",
    "      <SrcRect xOff=\"0\" yOff=\"0\" xSize=\"240\" ySize=\"180\" />\n",
    "      <DstRect xOff=\"0\" yOff=\"150\" xSize=\"240\" ySize=\"180\" />\n",
    "    </SimpleSource>\n",
    "    \n",
    "  </VRTRasterBand>\n",
    "</VRTDataset>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'driver': 'VRT', 'dtype': 'complex64', 'nodata': None, 'width': 240, 'height': 330, 'count': 1, 'crs': CRS.from_epsg(4326), 'transform': Affine(0.03333333333333333, 0.0, -4.016666666666667,\n",
      "       0.0, -0.03333333333333333, 7.983333333333333), 'blockxsize': 128, 'blockysize': 128, 'tiled': True}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "gdal_vrt_module_0x55cf1cb6f9c0:15: RuntimeWarning: invalid value encountered in true_divide\n"
     ]
    }
   ],
   "source": [
    "with rasterio.Env(GDAL_VRT_ENABLE_PYTHON=True):\n",
    "    with rasterio.open('merged-average-complex.vrt') as src:\n",
    "        print(src.profile)\n",
    "        #print(src.read(1)[0:5])\n",
    "        data = src.read(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,(ax1,ax2) = plt.subplots(1,2, figsize=(8,4))\n",
    "plt.sca(ax1)\n",
    "plt.imshow(data.real, vmin=1, vmax=2)\n",
    "plt.colorbar()\n",
    "plt.title('real part')\n",
    "\n",
    "plt.sca(ax2)\n",
    "plt.imshow(data.imag, vmin=1, vmax=2)\n",
    "plt.colorbar()\n",
    "plt.title('imaginary part');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}