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intro16
Angelos Tzotsos 2019-08-02 12:08:02 +03:00
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GSoC-2015/Access to Geospatial data/.ipynb_checkpoints/OSSIM Quickstart-checkpoint.ipynb
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GSoC-2015/Access to Geospatial data/GDAL-OGR Quickstart.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Access to Geospatial data](../Access to Geospatial data)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 22.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">GDAL/OGR Quickstart</span></h1></b>\n",
"\n",
"The first Notebook is dedicated to the use of the Geospatial Data Abstraction Library (**GDAL**) from the bash command line. GDAL is a powerful translator library for raster and vector geospatial data formats. It presents a single raster abstract data model and vector abstract data model for all supported formats.\n",
"\n",
"This Notebook is derived from the original [GDAL-OGR quickstart](http://localhost/osgeolive/en/quickstart/gdal_quickstart.html) adapted to run interactively in an IPython notebook and is composed by two main parts **GDAL** (to handle raster data) and **OGR** (to work with vector data)\n",
"\n",
"<h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">GDAL</span></h1>\n",
"\n",
"* Explore your image data with [```gdalinfo```](#gdalinfo)\n",
"* Format translations, Rescaling, Resizing, Splitting with [```gdal_translate```](#gdal_translate)\n",
" * [```Format translations```](#Format-translation)\n",
" * [```Resizing```](#Resizing)\n",
" * [```Rescaling```](#Rescaling)\n",
" * [```Splitting```](#Splitting)\n",
"* Reproject with [```gdalwarp```](#Reprojecting)\n",
"* Raster tileindex with [```gdaltindex```](#gdaltindex)\n",
"* Image Mosaic with ```gdal_warp``` or [```gdal_merge.py```](#Mosaicking)\n",
"\n",
"<h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">OGR </span></h1>\n",
"* get information about your data with [```ogrinfo```](#ogrinfo)\n",
"* use [```ogr2ogr```](#ogr2ogr) to transform your data to other formats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Get to know GDAL</span></h1></b> \n",
"\n",
"\n",
"You will find the demo data at ```/usr/local/share/data```. We want to have a look at the [naturalearth dataset](http://localhost/osgeolive/en/overview/naturalearth_overview.html) data in this quickstart. We want to work with a copy of the data. So the first step is to copy the data to your home directory."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from IPython.core.display import Image"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Set the PATH to the natural earth dataset used in this notebook**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"DATADIR='/home/user/data/natural_earth2'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"OUTPUTDIR='/home/user/jupyter/notebooks/GSoC-2015/OUTPUT/'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">gdalinfo</span></h1></b> \n",
"\n",
"<b><h2 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">get information about the raster data</span></h2></b> "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo --help-general"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo {DATADIR}/HYP_50M_SR_W.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"Note:\n",
"* Driver is “GTiff/GeoTIFF”\n",
"* Size is 10800x5400\n",
"* 3 Bands of type Byte.\n",
"* Coordinates\n",
"* Coordinate system is World Geodetic System 84"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Listing available Drivers</span></h1></b> "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First get to know your drivers. The ```--formats``` commandline switch of gdalinfo can be used to see a list of available format drivers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"List all the available formats:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo --formats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Each format reports if it is:\n",
"* read only (ro),\n",
"* read/write (rw) or\n",
"* read/write/update (rw+)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is also possible to ask for specific formats details:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo --format GTiff"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">gdal_translate</span></h1></b> \n",
"\n",
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Format translation</span></h1></b> \n",
"\n",
"Translations are accomplished with the gdal_translate command. The default output format is GeoTIFF. The ```-of``` flag is used to select an output format and the ```-co``` flag is used to specify a creation option:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The web browser is not happy with tif files so to have a quick look at the image we convert it to a web friendly format (JPG) using ```gdal_translate``` (this requires few seconds)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -of JPEG -co QUALITY=10 {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/HYP_50M_SR_W.jpg"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Image Display</span></h1></b> "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'/HYP_50M_SR_W.jpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The -ot switch can be used to alter the output data type."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -ot Int16 {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/HYP_50M_SR_W_Int16.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use gdalinfo to verify data type."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo {DATADIR}/HYP_50M_SR_W.tif | grep Band"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo {OUTPUTDIR}/HYP_50M_SR_W_Int16.tif | grep Band"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Resizing</span></h1></b> \n",
"\n",
"The -outsize switch can be used to set the size of the output file."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -outsize 50% 50% {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/HYP_50M_SR_W_small.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use gdalinfo to verify the size."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo {DATADIR}/HYP_50M_SR_W.tif | grep Size"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo {OUTPUTDIR}/HYP_50M_SR_W_small.tif | grep Size"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Rescaling</span></h1></b> "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The -scale switch can be used to rescale the data range of a given image. Explicit control of the input and output ranges is also available. The gdalinfo ```-mm``` switch can be used to see pixel min/max values.\n",
"\n",
"The output will display a computed Min/Max value for each band in the raster imput (3 band in our case)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo -mm {OUTPUTDIR}/HYP_50M_SR_W_small.tif | grep Min/Max"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To rescale a specific band we can use the \"-scale_bn\" syntax where bn is a band number (e.g. \"-scale_2\" for the 2nd band of the output dataset), in the example below we will rescale the 3 bands of the HYP_50M_SR_W GeoTiff to be in the range 0-255 :"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -scale_1 62.000 255.000 0 255.000 \\\n",
" -scale_2 85.000 255.000 0 255.000 \\\n",
" -scale_3 79.000 255.000 0 255.000 \\\n",
" {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/HYP_50M_SR_W_scaled.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check the results with ```gdalinfo``` :"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo -mm {OUTPUTDIR}/HYP_50M_SR_W_scaled.tif | grep Min/Max"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's convert the scaled output to JPG for a quick display, notice the color rearrangement."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -of JPEG -co QUALITY=40 {OUTPUTDIR}/HYP_50M_SR_W_scaled.tif {OUTPUTDIR}/HYP_50M_SR_W_scaled.jpg"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'/HYP_50M_SR_W_scaled.jpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"compare with [original image](#Image-Display)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Splitting</span></h1></b> "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let’s split our image into two with ```-srcwin``` which makes a copy based on pixel/line location (xoff yoff xsize ysize). You also could use ```-projwin``` and define the corners in georeferenced coordinates (ulx uly lrx lry)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -srcwin 0 0 5400 5400 {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/west.tif\n",
"!gdal_translate -srcwin 5400 0 5400 5400 {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/east.tif"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -of JPEG -co QUALITY=40 {OUTPUTDIR}/east.tif {OUTPUTDIR}/east.jpg\n",
"!gdal_translate -of JPEG -co QUALITY=40 {OUTPUTDIR}/west.tif {OUTPUTDIR}/west.jpg"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">gdalwarp</span></h1></b> \n",
"\n",
"\n",
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Reprojecting</span></h1></b> \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this process we assume that HYP_50M_SR_W.tif has been properly created with bounds. As we saw before with gdalinfo HYP_50M_SR_W has a proper coordinate system set. \n",
"\n",
"If the tif file we want work on doesn't have proper projection information (wich is the case in most *.tif* files when associated with a world file *.tfw*) it is possible to assign a coordinate system to the image with ```gdal_translate``` and the flag ```-a_srs``` e.g :\n",
"\n",
" gdal_translate -a_srs WGS84 HYP_50M_SR_W.tif HYP_50M_SR_W_4326.tif\n",
" \n",
" \n",
"Given a proper georeferenced raster file the ```gdalwarp``` command can be used to assign a new Spatial Reference System to it. Here we reproject the WGS84 geographic image to the Mercator projection:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalwarp -t_srs '+proj=merc +datum=WGS84' {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/mercator.tif"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -of JPEG -co QUALITY=40 {OUTPUTDIR}/mercator.tif {OUTPUTDIR}/mercator.png"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'/mercator.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we reproject to the Ortho projection."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalwarp -t_srs '+proj=ortho +datum=WGS84' {DATADIR}/HYP_50M_SR_W.tif {OUTPUTDIR}/ortho.tif 2>/dev/null"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -of JPEG -co QUALITY=40 {OUTPUTDIR}/ortho.tif {OUTPUTDIR}/ortho.png"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'/ortho.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">gdaltindex</span></h1></b> \n",
"\n",
"\n",
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Raster tileindex with gdaltindex</span></h1></b> \n",
"You can build a shapefile as a raster tileindex. For every image a polygon is generated with the bounds of the extent of the polygon and the path to the file."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdaltindex {OUTPUTDIR}/index_natural_earth.shp {OUTPUTDIR}/*st.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The command above just created a new ESRI Shape File (default vector format), we will see how to work on vector files later on in the **OGR** section."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Mosaicking</span></h1></b> \n",
"\n",
"```gdal_merge.py``` is a python script that can be used for simple mosaicking tasks. Mosaic the east.tif and west.tif into a single file:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_merge.py {OUTPUTDIR}/east.tif {OUTPUTDIR}/west.tif -o {OUTPUTDIR}/merged.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Convert to jpg to display in the notebook and you can see the original image recomposed"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdal_translate -of JPEG -co QUALITY=40 {OUTPUTDIR}/merged.tif {OUTPUTDIR}/merged.jpg"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'/merged.jpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The same task can be accomplished with gdalwarp. gdalwarp has a variety of advantages over gdal_merge, but can be slow to merge many files:\n",
"\n",
" gdalwarp east.tif west.tif warpmerged.tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Get to know OGR</span></h1></b> \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">ogrinfo</span></h1></b> \n",
"\n",
"Like we did with raster using ```gdalinfo```, is possible to retrieve descriptive information from a vector datasource using the command line too ```ogrinfo```.\n",
"Let's run ```ogrinfo``` on the previously generated shapefile ```index_natural_earth.shp```:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ogrinfo {OUTPUTDIR}/index_natural_earth.shp index_natural_earth"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get a summary about your data with ogrinfo together with -so."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ogrinfo -ro -so {DATADIR}/ne_10m_admin_0_countries.shp ne_10m_admin_0_countries"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you run ogrinfo without a parameter you will get a summary about your data and afterwards a section for every dataset. You can forward the result from ogrinfo to grep to filter and get only the attribute COUNTRY."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ogrinfo -ro {DATADIR}/ne_10m_admin_0_countries.shp ne_10m_admin_0_countries | grep 'admin '"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The shape file we just created can not be rendered directly in the notebook. Later in the python tutorial we'll learn how to use libraries like *shapely* to render directly vector data. \n",
"For now to display the results of our processing in the notebook we'll use the ```shp2img``` command line tool (provided by *[mapserver](http://localhost/osgeolive/en/overview/mapserver_overview.html)* ).\n",
"```shp2img``` require a *mapserver mapfile* as input to generate a rendered image.\n",
"Below we'll write a mapfile with 3 layers :\n",
"* west.tif\n",
"* east.tif\n",
"* index_natural_earth.shp\n",
"Note: the shapefile color has been classified based on the shapefile attribute ```location``` with a translarency to show the 2 raster images underneat."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"index_natural_earth=\"\"\"\n",
"MAP\n",
" EXTENT -180 -89.999999999982 179.999999999964 90\n",
" IMAGETYPE \"png\"\n",
" NAME \"simplepolygon\"\n",
" SIZE 600 600\n",
" STATUS ON\n",
" UNITS DD\n",
"\n",
" OUTPUTFORMAT\n",
" NAME \"png\"\n",
" MIMETYPE \"image/png\"\n",
" DRIVER \"AGG/PNG\"\n",
" EXTENSION \"png\"\n",
" IMAGEMODE RGB\n",
" TRANSPARENT TRUE\n",
" END # OUTPUTFORMAT\n",
"\n",
" PROJECTION\n",
" \"proj=longlat\"\n",
" \"datum=WGS84\"\n",
" \"no_defs\"\n",
" END # PROJECTION\n",
"\n",
" LAYER\n",
" DATA \"{OUTPUTDIR}/west.tif\"\n",
" EXTENT -180 -89.999999999982 -1.79596892913025e-11 90\n",
" METADATA\n",
" \"ows_title\"\t\"west\"\n",
" END # METADATA\n",
" NAME \"west\"\n",
" PROJECTION\n",
" \"proj=longlat\"\n",
" \"datum=WGS84\"\n",
" \"no_defs\"\n",
" END # PROJECTION\n",
" STATUS ON\n",
" TILEITEM \"location\"\n",
" TYPE RASTER\n",
" UNITS METERS\n",
" END # LAYER\n",
"\n",
" LAYER\n",
" DATA \"{OUTPUTDIR}/east.tif\"\n",
" EXTENT -1.79596892913025e-11 -89.999999999982 179.999999999964 90\n",
" METADATA\n",
" \"ows_title\"\t\"east\"\n",
" END # METADATA\n",
" NAME \"east\"\n",
" PROJECTION\n",
" \"proj=longlat\"\n",
" \"datum=WGS84\"\n",
" \"no_defs\"\n",
" END # PROJECTION\n",
" STATUS ON\n",
" TILEITEM \"location\"\n",
" TYPE RASTER\n",
" UNITS METERS\n",
" END # LAYER\n",
" \n",
" LAYER\n",
" DATA \"{OUTPUTDIR}/index_natural_earth.shp\"\n",
" EXTENT -180 -89.999999999982 179.999999999964 90\n",
" NAME \"index_natural_earth\"\n",
" PROJECTION\n",
" \"proj=longlat\"\n",
" \"datum=WGS84\"\n",
" \"no_defs\"\n",
" END # PROJECTION\n",
" STATUS ON\n",
" TILEITEM \"location\"\n",
" TYPE POLYGON\n",
" UNITS METERS\n",
" CLASS\n",
" NAME \"{OUTPUTDIR}/east.tif\"\n",
" EXPRESSION (\"[location]\" =\"{OUTPUTDIR}/east.tif\")\n",
" STYLE\n",
" OPACITY 50\n",
" COLOR 218 57 57\n",
" END # STYLE\n",
" STYLE\n",
" OUTLINECOLOR 0 0 0\n",
" WIDTH 0.26\n",
" END # STYLE\n",
" END # CLASS\n",
" CLASS\n",
" NAME \"{OUTPUTDIR}/west.tif\"\n",
" EXPRESSION (\"[location]\" =\"{OUTPUTDIR}/west.tif\")\n",
" STYLE\n",
" OPACITY 50\n",
" COLOR 18 211 14\n",
" END # STYLE\n",
" STYLE\n",
" OUTLINECOLOR 0 0 0\n",
" WIDTH 0.26\n",
" END # STYLE\n",
" END # CLASS\n",
" END # LAYER \n",
"END # MAP\n",
"\"\"\".format(OUTPUTDIR=OUTPUTDIR)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"mapfile=open('index_natural_earth.map','w')\n",
"mapfile.write(index_natural_earth)\n",
"mapfile.close()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!shp2img -m index_natural_earth.map -i PNG -o index_natural_earth.png"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image('index_natural_earth.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 18.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">Use ogr2ogr to convert data between file formats</span></h1></b> \n",
"\n",
"\n",
"Like with ```gdalinfo``` You can use ogr2ogr to converts simple features data between file formats. You can use –formats to get the list of the supported formats with read/write information."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ogrinfo --formats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Convert the countries to GeoJson."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b><h1 style=\"margin: 0.0px 0.0px 0.0px 0.0px; line-height: 15.4px; font: 16.0px 'Lucida Sans'; color: #004d87; -webkit-text-stroke: #004d87; background-color: #ffffff\"><span class=\"s1\">ogr2ogr</span></h1></b>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!rm -rf {DATADIR}/countries.json\n",
"!ogr2ogr -f GeoJSON {OUTPUTDIR}/countries.json {DATADIR}/ne_10m_admin_0_countries.shp"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Notebooks---Access-to-Geospatial-data)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

232
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@ -1,232 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Access to Geospatial data](../Access to Geospatial data)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook is heavily based on the [Python GDAL/OGR Cookbook](https://pcjericks.github.io/py-gdalogr-cookbook/)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this first example we'll learn how to generate a proper OGR geometry of type \"Geometry Collection\" which allows us to store multiple types of geometry (point, line, polygon) in a single vector file (note: this is a great advantage compared with the \"standard but obsolete\" ESRI Shape File data format, which is limited to only one type of geometry). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's re-use the example from the notebook in [Numerical Cartograph/The Geodesic Problem](../Numerical Cartography/The Geodesic Problem.ipynb), where using [geograhiclib]() we compute the shortest path (geodesic) from New York, (NY) to Delhi, (India):"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from geographiclib.geodesic import Geodesic\n",
"\n",
"lat1,lon1 = (40.7143528, -74.0059731) # New York, NY\n",
"lat2,lon2 = (1.359, 103.989) # Delhi, India\n",
"g = Geodesic.WGS84.Inverse(lat1, lon1, lat2, lon2)\n",
"g"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now compute a list of points along the geodesic curve with a fixed distance of 100000m"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"gc = [Geodesic.WGS84.Direct(lat1, lon1, g['azi1'], i) for i in range(0,int(g['s12']),100000)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's start with OGR! \n",
"\n",
"We will first create a geometry collection with:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from osgeo import ogr\n",
"geomcol = ogr.Geometry(ogr.wkbGeometryCollection)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"let's add 2 point features for the 2 location we used to compute the geodesic curve:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"point1 = ogr.Geometry(ogr.wkbPoint)\n",
"point1.AddPoint(lon1,lat1)\n",
"geomcol.AddGeometry(point1)\n",
"\n",
"point2 = ogr.Geometry(ogr.wkbPoint)\n",
"point2.AddPoint(lon2,lat2)\n",
"geomcol.AddGeometry(point2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's add to our GeometryCollection a new line feature:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"line = ogr.Geometry(ogr.wkbLineString)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And let's populate the newly generated line feature looping through the list of coordinates of our geodesic path."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"[line.AddPoint(i['lon2'],i['lat2']) for i in gc]\n",
"geomcol.AddGeometry(line)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And finally export the data as GeoJSON string and paste it online for easy visualization on github:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"data = geomcol.ExportToJson()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To save on file the new dataset we will ```echo``` the ```geojson``` string to a file"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!echo '{data}' > /tmp/geojson.geojson"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ```gist``` utility (not installed on the live) can be used to paste the content of a text file online as a *gist* for easy visualization on github"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#!gist -p /tmp/geojson.geojson"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from CesiumWidget import CesiumWidget"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cesiumExample = CesiumWidget(width=\"100%\",geojson=data, enable_lighting=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cesiumExample"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

56
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@ -1,56 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Access to Geospatial data](../Access to Geospatial data) - [Introduction ](../Access to Geospatial data/Introduction to Access to Geospatial data.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Access to Geospatial data\n",
"\n",
"In this set of notebook two of the most important open source software libraries are introduced:\n",
"\n",
"* [GDAL](http://localhost/osgeolive/en/overview/gdal_overview.html) (Geospatial Data Abstraction Library) \n",
"* [OSSIM](http://localhost/osgeolive/en/overview/ossim_overview.html) (Open Source Software Image Mapping). \n",
"\n",
"Both libraries are the state of the art in software for reading and translating geospatial data between several formats, and the contain tools to reproject, mosaic and subset geospatial dataset.\n",
"\n",
"The two libraries have a lot in common but differ in some particular features. **GDAL** presents a complete set of software utilities to work with both raster and vector data. It includes support for sql-like query processing, a very wide range of driver to access both raster and vector for all the most common data formats and a complete set of API accessible trough scripting languages such Python. **OSSIM** is more oriented to photogrammetry with its hi-performance hi-precision raster processing engine. It offers parallel processing support, an unique orthorectification system which enables the processing of satellite-sensor specific data products. \n",
"\n",
"In the notebooks below we'll explore the tools offered by the *command line utilities* for both software plus the Python scripting capabilities pf GDAL.\n",
"\n",
"* [GDAL-OGR Quickstart - bash](GDAL-OGR Quickstart.ipynb)\n",
"\n",
"* [OSSIM Quickstart](OSSIM Quickstart.ipynb)\n",
"\n",
"* [GDAL-OGR with Python](GDAL-OGR with Python.ipynb)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

963
GSoC-2015/Access to Geospatial data/OSSIM Quickstart.ipynb
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@ -1,963 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Access to Geospatial data](../Access to Geospatial data)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# OSSIM Command Line Applications\n",
"The following command line applications are distributed with OSSIM.\n",
"\n",
"## Core Programs\n",
"\n",
"* [```ossim-info```](#ossim-info) Used to run ossim utility function and to display metadata for imagery, maps, terrain, and vector data.\n",
" * [Utility functions](#Utility-functions)\n",
" * [radians from degrees](#radians-from-degrees)\n",
" * [degrees from radians](#degrees-from-radians)\n",
" * [meters from feet](#meters-from-feet)\n",
" * [meters to feet](#meters-to-feet)\n",
" * [Meters per degree](#Meters-per-degrees)\n",
" * [height](#height)\n",
" * [Projections](#Projections)\n",
" * [Datums](#Datums)\n",
" * [Explore raster data](#Explore-raster-data)\n",
" * [ground center](#ground-center)\n",
" * [image center](#image-center)\n",
" * [ground and image center](#ground-and-image-center)\n",
" * [general image information](#general-image-information)\n",
" * [meta data image information](#meta-data-image-information)\n",
" * [image projection information](#image-projection-information)\n",
" * [image rectangle](#image-rectangle)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Utilities to Create Support Files\n",
"\n",
"The following tools are used to create OSSIM support files:\n",
"\n",
"* [```ossim-img2rr```](#ossim-img2rr) Create reduced resolution data sets for an image.\n",
"* [```ossim-cmm```](#ossim-cmm) Determine the min/max pixel values of an image.\n",
"* [```ossim-create-histo```](#ossim-create-histo) Compute a histogram for an image.\n",
"* [```ossim-img2md```](#ossim-img2md) Create metadata files.\n",
"* [```ossim-tfw2ogeom```]() Create a geom file from a TIFF World File.\n",
"* [```ossim-extract-vertices```]() Compute the valid vertices (corners) of an image.\n",
"* [```ossim-preproc```]() Create reduced resolution data sets, histograms, and so on. The application does directory walking and is threaded at a file level.\n",
"* [```ossim-applanix2ogeom```]() Create a geom file for Applanix Images.\n",
"* [```ossim-create-cg```]() Create an ossim coarse grid.\n",
"* [```ossim-ecg2ocg```]() Convert an enhanced coarse grid to an ossim coarse grid.\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## OSSIM-Applications\n",
"\n",
" * [```ossim-band-merge```](#ossim-band-merge) Merge multiple images files into a single n-band dataset.\n",
" * [```ossim-chipper```](#ossim-chipper) Render elevation data (e.g. shaded relief).\n",
" * [```ossim-icp```](#ossim-icp) Convert an image from one format to another.\n",
" * [```ossim-igen```](#ossim-igen) Execute image chains specified in a spec file.\n",
" * [```ossim-orthoigen```](#ossim-orthoigen) Tool to orthorectify, mosaic, and convert raster data between different formats. It provides a number of operations including subsetting, resampling, histogram matching, and reprojection of data.\n",
" * [```ossim-rpf```](#ossim-rpf) Various utilities for managing RPF data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Import IPython utility to display images**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from IPython.core.display import Image"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Set the PATH to the natural earth dataset used in this notebook**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"DATADIR='/home/user/data/landsat/'\n",
"OUTPUTDIR='/home/user/jupyter/notebooks/GSoC-2015/OUTPUT/'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# we'll use the north_carolina image dataset\n",
"!ls {DATADIR} | grep tif"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-info```\n",
"\n",
"[top](#Core-Programs)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Utility functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### radians from degrees\n",
"\n",
"```ossim-info --deg2rad <degrees>```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --deg2rad 20.54"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### degrees from radians\n",
" ```ossim-info --rad2deg <radians>```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --rad2deg 0.35849"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### meters from feet \n",
"- 0.3048 meters per foot\n",
"\n",
" ```ossim-info --ft2mtrs <feet>``` "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --ft2mtrs 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 0.3048006096 meters per foot\n",
" \n",
" ```ossim-info --ft2mtrs-us-survey <feet>``` "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --ft2mtrs-us-survey 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### meters to feet\n",
"* 0.3048 meters per foot\n",
"\n",
" ```ossim-info --mtrs2ft <meters>```\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --mtrs2ft 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* 0.3048006096 meters per foot\n",
"\n",
" ```ossim-info --mtrs2ft-us-survey <meters>```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --mtrs2ft-us-survey 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### height\n",
"return the MSL and ellipoid height given a latitude longitude position\n",
"\n",
"```ossim-info --height <latitude-in-degrees> <longitude-in-degrees>``` "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# note we pass the path to the ossim_preference file to tell where the geoid file is\n",
"!ossim-info --height 47.54 157.40 -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Meters per degrees\n",
"Gives meters per degree and meters per minute for a given latitude. \n",
"```ossim-info --mtrsPerDeg <latitude>```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --mtrsPerDeg 65.45"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Datums\n",
"Prints datum list.\n",
"```ossim-info --datums``` \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --datums"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Projections\n",
"Prints projections list\n",
"```ossim-info --projections``` "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --projections"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Explore raster data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ground center\n",
"\n",
" ```ossim-info --cg filename```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --cg {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### image center\n",
"\n",
" ```ossim-info --ci filename``` "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info --ci {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ground and image center\n",
"\n",
" ```ossim-info -c filename```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info -c {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### general image information\n",
" \n",
" ```ossim-info -i filename```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info -i {DATADIR}/clip10.tif -P /usr/local/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### meta data image information\n",
"\n",
" ossim-info -m filename"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info -m {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### image projection information\n",
"\n",
" ossim-info -p filename"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info -p {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### image rectangle\n",
"\n",
" ossim-info -r filename"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-info -r {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-img2rr```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-img2rr {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-img2rr {DATADIR}/clip20.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-img2rr {DATADIR}/clip30.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-cmm``` "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-cmm {DATADIR}/clip10.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-cmm {DATADIR}/clip20.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-cmm {DATADIR}/clip30.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!cat {DATADIR}clip10.omd"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-img2md```\n",
"\n",
"\n",
" Usage: ossim-img2md [options] <metadata_writer> <input_file> <output_file>\n",
" \n",
" \n",
" * Valid metadata writer types:\n",
" * envi_header\t\n",
" * ers_header\t\n",
" * ossim_fgdc\t\n",
" * ossim_geometry\t\n",
" * ossim_readme\t\n",
" * tiff_world_file\t\n",
" * jpeg_world_file\t"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-img2md -P /usr/share/ossim/ossim_preference tiff_world_file {DATADIR}/clip10.tif {DATADIR}/clip10.tfw"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!cat {DATADIR}/clip10.tfw"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-band-merge```\n",
"\n",
"```ossim-band-merge [-h][-o][-w tile_width] <output_type> <input_file1> <input_file2> ... <output_file>```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example, create an RGB image from the single-band grayscale r,g,b images (Landsat 7)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-band-merge jpeg -P /usr/share/ossim/ossim_preference \\\n",
" {DATADIR}/clip30.tif \\\n",
" {DATADIR}/clip20.tif \\\n",
" {DATADIR}/clip10.tif \\\n",
" {OUTPUTDIR}/rgb.jpeg"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-cmm {OUTPUTDIR}/rgb.jpeg -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!cat {OUTPUTDIR}/rgb.omd"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+\"rgb.jpeg\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-create-histo```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-create-histo {DATADIR}/clip30.tif \\\n",
"{DATADIR}/clip20.tif \\\n",
"{DATADIR}/clip10.tif"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-orthoigen --hist-auto-minmax {DATADIR}/clip30.tif {OUTPUTDIR}/clip30_histmm.tif -P /usr/share/ossim/ossim_preference\n",
"!ossim-orthoigen --hist-auto-minmax {DATADIR}/clip20.tif {OUTPUTDIR}/clip20_histmm.tif -P /usr/share/ossim/ossim_preference\n",
"!ossim-orthoigen --hist-auto-minmax {DATADIR}/clip10.tif {OUTPUTDIR}/clip10_histmm.tif -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-band-merge jpeg -P /usr/share/ossim/ossim_preference \\\n",
" {OUTPUTDIR}/clip30_histmm.tif \\\n",
" {OUTPUTDIR}/clip20_histmm.tif \\\n",
" {OUTPUTDIR}/clip10_histmm.tif \\\n",
" {OUTPUTDIR}/rgb_histmm.jpeg"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'rgb_histmm.jpeg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-chipper```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!wget https://gist.githubusercontent.com/anonymous/c339de8d38357a4a71bf/raw/428e9f193d29b25735b57960372d029691511a17/a.rb"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-chipper --color 255 255 255 \\\n",
" --azimuth 270 \\\n",
" --elevation 45 \\\n",
" --exaggeration 2.0 \\\n",
" --op hillshade \\\n",
" --color-table a.rb \\\n",
" --input-dem {DATADIR}/srtm.tif \\\n",
" {OUTPUTDIR}/hillshade.jpg -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(OUTPUTDIR+'hillshade.jpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-icp```\n",
"\n",
"```ossim-icp [options] <output_type> <input_file> <output_file>```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# A complete list of ossim writers (driver) is given by:\n",
"!ossim-info --writers -P /usr/share/ossim/ossim_preference"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#convert a geotiff to a geopdf\n",
"!ossim-icp ossim_pdf rgb_histmm.jpeg rgb_histmm.pdf"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#view the results in a pdf viewer\n",
"!nohup evince rgb_histmm.pdf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-igen```\n",
"\n",
"Execute image chains specified in a spec file.\n",
"\n",
"In the folowing example the spec file ```rgb.spec``` has been generated using [imagelinker](http://localhost/osgeolive/en/quickstart/ossim_quickstart.html) ```save spec only``` when saving a data product (this may be useful when batch processing a complex image chain, or when ossim is built with mpi support to redistribute the computation on more CPU's)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!ossim-igen /home/user/data/landsat/rgb.spec"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"Image(\"/home/user/data/landsat/rgb_spec.jpg\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Core-Programs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-orthoigen```\n",
"\n",
"```todo```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ```ossim-rpf```\n",
"\n",
"```todo```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[top](#Notebooks---Access-to-Geospatial-data)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

173
GSoC-2015/Geoprocessing with Vectors/Intro to Postgis.ipynb
View File

@ -1,173 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Geoprocessing with Vectors](../Geoprocessing with Vectors) - [Intro to Postgis](../Geoprocessing with Vectors/Intro to Postgis.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Postgis"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import psycopg2\n",
"paramstring = \"dbname='%s' user='%s' host='%s' password='%s'\" % ('natural_earth2','user','localhost','user')\n",
"conn = psycopg2.connect(paramstring)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"curs = conn.cursor()\n",
"curs.execute(\"\"\"SELECT table_name FROM information_schema.tables WHERE table_schema = 'public'\"\"\")\n",
"for table in curs.fetchall():\n",
" print(table)\n",
"conn.commit()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"curs = conn.cursor()\n",
"curs.execute(\"Select * FROM ne_10m_urban_areas\")\n",
"colnames = [desc[0] for desc in curs.description]\n",
"conn.commit()\n",
"colnames"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"curs = conn.cursor()\n",
"curs.execute(\"CREATE TABLE cities ( id int4 primary key, name varchar(50), the_geom geometry(POINT,4326));\")\n",
"conn.commit()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"table='cities'\n",
"col=\"id, the_geom, name\"\n",
"x=10\n",
"y=10\n",
"name='test'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"querytmplate=\"INSERT INTO %(table)s (%(col)s) VALUES (1,ST_GeomFromText('POINT(%(x)f %(y)f)',4326),'%(name)s');\""
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"querytmplate = querytmplate % {'table':table, 'col':col, 'x':x, 'y':x, 'name':name}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"curs = conn.cursor()\n",
"curs.execute(querytmplate)\n",
"conn.commit()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"curs = conn.cursor()\n",
"curs.execute(\"SELECT * FROM cities\")\n",
"data = curs.fetchall()\n",
"conn.commit()\n",
"print(data)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"curs = conn.cursor()\n",
"curs.execute(\"SELECT name, ST_AsText(the_geom) FROM cities\")\n",
"data = curs.fetchall()\n",
"conn.commit()\n",
"print(data)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"data[0][1]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

39
GSoC-2015/Geoprocessing with Vectors/Introduction to Geoprocessing with Vector.ipynb
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@ -1,39 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Geoprocessing with Vectors](../Geoprocessing with Vectors) - [Introduction ](../Geoprocessing with Vectors/Introduction to Geoprocessing with Vector.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* [Intro to Postgis](Intro to Postgis.ipynb)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

137
GSoC-2015/Introduction to GRASS GIS/GRASS working environment.ipynb
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@ -1,137 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Introduction to GRASS GIS](../Introduction to GRASS GIS) - [GRASS working environment](../Introduction to GRASS GIS/GRASS working environment.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the OSGeoLive, the Jupyter notebook is started by a bash script which has instructions to export the GRASS environment variables. In this way the GRASS functionalities are accessible from within the notebooks using the system command magic which consists in adding an exclamation mark as prefix to a bash command, e.g.: ```!bash-command``` "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Import GRASS script python library:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import grass.script as grass"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Direct access to GRASS commands using shell syntax:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [g.gisenv](http://localhost/grass/g.gisenv.html)\n",
"\n",
"When a user runs GRASS, certain variables are set specifying the GRASS database, location, mapset, peripheral device drivers, etc., being used in the current GRASS session. These variable name settings are recognized as long as the user is running a GRASS session. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!g.gisenv"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [g.mapset](http://localhost/grass/g.mapset.html)\n",
"\n",
"**g.mapset** is used to create new or change the current mapset."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate a new GRASS LOCATION Specifying the projection parameters using the proj-4 string syntax using [g.proj](http://localhost/grass/g.proj.html). The informations used as input to ```g.proj``` are retrieved from the gdalinfo output.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!gdalinfo /usr/local/share/data/north_carolina/rast_geotiff/basin_50K.tif"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"proj4 = '+proj=lcc +lat_1=36.1667 +lat_2=34.333 +lat_0=33.75 +lon_0=-79 +x_0=609601.22 +y_0=0 +no_defs +a=6378137 +rf=298.2572221010042 +to_meter=1'\n",
"#this will return an error if the location alreay exist (just ignore it) <-- fix me\n",
"try:\n",
" grass.run_command('g.proj', proj4=proj4, location='nc')\n",
"except:\n",
" print 'grass location nc already exist'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!g.mapset location=nc mapset=PERMANENT"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!g.proj -p"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

45
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@ -1,45 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Introduction to GRASS GIS](../Introduction to GRASS GIS) - [Introduction ](../Introduction to GRASS GIS/Introduction to GRASS GIS.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction to GRASS GIS\n",
"\n",
"* [GRASS working environment](GRASS working environment.ipynb)\n",
"* [Map display](Map display.ipynb)\n",
"\n",
"\n",
"# [python-grass-addons](python-grass-addons/00 Introduction.ipynb)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

155
GSoC-2015/Introduction to GRASS GIS/Map display.ipynb
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@ -1,155 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Introduction to GRASS GIS](../Introduction to GRASS GIS) - [Map display](../Introduction to GRASS GIS/Map display.ipynb)</center></h1>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%run grassutil.ipy"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"DATADIR='/home/user/data/north_carolina/rast_geotiff/'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!g.mapset location=nc mapset=PERMANENT"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!g.proj -p"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!r.in.gdal input={DATADIR}/elevation.tif output=elevation -e --o"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"makeImage(basemap='elevation', inputlayer='elevation', maptype='raster', \n",
" vsize=10, maptitle='elevation', region=region2dict(rast='elevation'), legend=False, outputimagename='test.png')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!r.in.gdal input={DATADIR}/basin_50K.tif output=basin_50K -e --o"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"makeImage(basemap='basin_50K', inputlayer='basin_50K', maptype='raster', \n",
" vsize=10, maptitle='Basins', region=region2dict(rast='basin_50K'), legend=False, outputimagename='test.png')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!r.blend first=elevation second=basin_50K output=basin_relief percent=30 --overwrite --quiet"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"makeImage(basemap='basin_50K', inputlayer='basin_relief', maptype='rgb', \n",
" vsize=10, maptitle='Basins', region=region2dict(rast='basin_50K'), legend=False, outputimagename='test.png')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!m.nviz.image elevation_map=elevation output=elevation position=0.5,0.5 \\\n",
" perspective=100 height=800 color_map=basin_50K \\\n",
" resolution_fine=1 resolution_coarse=1 format=tif --q"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"!convert elevation.tif elevation.png\n",
"Image(\"elevation.png\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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@ -1,127 +0,0 @@
from IPython.core.display import Image
def getLayerList(type='rast', mapset=None, verbose=None):
if mapset:
mapset = [mapset]
if not mapset:
mapset = !g.mapsets -l
mapset = mapset[1].split()
if verbose:
print type, 'layers available in mapset : ', mapset[0]
layerlist = []
for m in mapset:
llist = !g.list {type}
return llist
def list2dict(inputlist, sep="=", inverse=False):
if inverse:
dictionary = dict([(i.split(sep)[1],i.split(sep)[0]) for i in inputlist])
else :
dictionary = dict([(i.split(sep)[0],i.split(sep)[1]) for i in inputlist])
return dictionary
def vlayerInfo(map,layer=1):
hist = !v.info map={map} layer={layer} -h
map_history = {'COMMAND' : hist[0].split(':')[1],
'GISDBASE' : hist[1].split(':')[1],
'LOCATION' : hist[2].split(' ')[1],
'MAPSET' : hist[2].split(' ')[3],
'USER' : hist[2].split(' ')[5],
'DATE' : hist[2].split(' ')[7:]}
map_table = !v.info map={map} layer={layer} -c
map_table = list2dict(map_table[1:], sep='|', inverse=True)
map_region = !v.info map={map} layer={layer} -g
map_region = list2dict(map_region)
#map_title = !v.info map={map} layer={layer} -m
#try:
# map_title = map_title[0].split("=")[1].replace("(",'').replace(")",'').strip()
#except:
# 'no title found'
map_topology = !v.info map={map} layer={layer} -t
map_topology = list2dict(map_topology)
info = {'table' : map_table,
'region' : map_region,
'history' : map_history,
'topology' : map_topology,
} #'title' : map_title
return info
def rlayerInfo(map, mapset='PERMANENT'):
print 'mapset parameter not specified, using mapset PERMANENT as default'
raster_info = !r.info map={map}@{mapset} -g
print raster_info
raster_info = list2dict(raster_info)
map_range = !r.info map={map}@{mapset} -r
map_range=list2dict(map_range)
raster_info['range'] = map_range
map_history = !r.info map={map}@{mapset} -h
raster_info['history'] = '\n'.join(map_history)
return raster_info
def region2dict(rast=None, vect=None):
if rast:
region = !g.region rast={rast} -p
if vect:
region = !g.region vect={vect} -p
else :
region = !g.region -p
regiondict = {}
for i in region:
info = i.split(': ')
try:
regiondict[info[0]] = info[1].strip()
except:
print 'done'
return regiondict
def makeImage(basemap='', inputlayer='', maptype='raster', lcolor='grey', vcolor='grey', vsize=1, icon='basic/diamond',
maptitle='', region=None, grid=True, gridsize=1000, title=True, title_at=(45,95), legend=True, legend_at=(22,65,8,10), outputimagename=None):
if not outputimagename:
outputimagename=basemap
if not region:
try:
array_info = rlayerInfo(basemap)
n=array_info['north']
s=array_info['south']
w=array_info['west']
e=array_info['east']
except:
region=region2dict()
print 'no region boundary provided and unable to retrieve map layer region, using default region settings'
else:
#region=region2dict()
n=region['north']
s=region['south']
w=region['west']
e=region['east']
!rm -rf {outputimagename}.png
!g.region n={n} s={s} w={w} e={e} -a --q
#!g.region -p
!d.mon start=cairo --q output={outputimagename}.png
if maptype=='raster':
!g.region rast={inputlayer} n={n} s={s} w={w} e={e} -a --q
!d.rast map={inputlayer} --q
if legend:
!d.legend at={legend_at[0]},{legend_at[1]},{legend_at[2]},{legend_at[3]} raster={inputlayer} --q
if maptype=='vector':
!g.region vect={inputlayer} n={n} s={s} w={w} e={e} -a #p
!d.vect map={inputlayer} color={vcolor} size={vsize} icon={icon} --q
if maptype=='overlay':
for i in inputlayer['raster']:
!d.rast map={i} --q
for i in inputlayer['vector']:
!d.vect map={i} color={vcolor} size={vsize} icon={icon} --q
if maptype=='rgb':
!g.region rast={basemap} n={n} s={s} w={w} e={e} -a --q
#!d.rast map={inputlayer} --q
!d.rgb r={inputlayer}.r g={inputlayer}.g b={inputlayer}.b --q
if grid:
!d.grid size={gridsize} color=blue --q
if title:
!d.text at={title_at[0]},{title_at[1]} text={maptitle} color=red --q
!d.mon stop=cairo --q
return Image(outputimagename+'.png')

104
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@ -1,104 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction\n",
"\n",
"This set of digital notebooks was created to explore several open source solutions for geospatial data analysis, with the aim of bridging together the several software libraries already installed on OSGeo live to perform complex *geo-data-science workflows*. It was originally started as a Google Summer of Code (GSoC) project in 2015.\n",
"\n",
"The notebooks are developed in the [Jupyter notebook server](https://jupyter.org/) environment, which is heavily based on the [IPython](http://ipython.org/) project. They are written in different languages (bash, Python, R) and are organized in a series of \"topic-oriented\" geospatial notebooks.\n",
"\n",
"For a complete description of each project installed on OSGeo-Live refer to the [OSGeo-Live documentation](http://localhost/osgeolive/en/index.html). This work will focus on different aspects:\n",
" * The usage of several scientific Python libraries like [numpy](http://www.numpy.org/), [scipy](http://www.scipy.org/), [pandas](http://pandas.pydata.org/), [matplotlib](http://matplotlib.org/)\n",
" * The usage of GFOSS (Geographic Free and Open Source Software) projects like [GRASS](https://grass.osgeo.org/), [GDAL](http://www.gdal.org/), [OSSIM](https://trac.osgeo.org/ossim/), [mapserver](http://mapserver.org/) \n",
" * And finally introducing more specialized software like [R](https://www.r-project.org/) for geostatistic analyses and [postgis](http://postgis.net/) as geospatial relational database.\n",
"\n",
"\n",
"The geospatial notebook here developed will make use of the sample dataset pre-installed on OSGeo-Live:\n",
"\n",
"* [Natural Earth](http://localhost/osgeolive/en/overview/naturalearth_overview.html)\n",
"\n",
"* [OSGeo North Carolina, USA Educational dataset](http://localhost/osgeolive/en/overview/nc_dataset_overview.html)\n",
"\n",
"* [OpenStreetMap](http://localhost/osgeolive/en/overview/osm_dataset_overview.html)\n",
"\n",
"* [NetCDF Data Set](http://localhost/osgeolive/en/overview/netcdf_dataset_overview.html)\n",
"\n",
"The geospatial notebook here are composed of 6 different sections with the aim of introducing some of the several geospatial libraries installed on OSGeo-Live. The geospatial notebooks will walk the user from simple usage of command line tools such GDAL, PROJ and OSSIM to basic SQL query on how to access database information to more complex geoprocessing including raw data parsing, numerical processing and the use of complete GIS platfom like GRASS GIS.\n",
"\n",
"\n",
"# Topic Layout\n",
"\n",
"**[Access to Geospatial data](Access to Geospatial data/Introduction to Access to Geospatial data.ipynb)**\n",
"\n",
" * [GDAL-OGR Quickstart - bash](Access to Geospatial data/GDAL-OGR Quickstart.ipynb)\n",
"\n",
" * [GDAL-OGR with Python](Access to Geospatial data/GDAL-OGR with Python.ipynb)\n",
"\n",
" * [OSSIM Quickstart](Access to Geospatial data/OSSIM Quickstart.ipynb)\n",
"\n",
"**[An Introduction to Numerical Cartography](Numerical Cartography/An intro to Numerical Cartography.ipynb)**\n",
"\n",
" * [Map Projections](Numerical Cartography/Map Projections.ipynb)\n",
"\n",
" * [Spatial and Coordinate Reference System](Numerical Cartography/Spatial and Coordinate Reference System.ipynb)\n",
"\n",
" * [The Geodesic Problem](Numerical Cartography/The Geodesic Problem.ipynb)\n",
"\n",
" * [Working with coordinates](Numerical Cartography/Working with coordinates.ipynb)\n",
"\n",
" * [geometric-transformations](Numerical Cartography/geometric-transformation.ipynb)\n",
"\n",
"\n",
"**[Geoprocessing with Vectors](Geoprocessing with Vectors/Introduction to Geoprocessing with Vector.ipynb)**\n",
"\n",
" \n",
" * [Intro to Postgis](Geoprocessing with Vectors/Intro to Postgis.ipynb)\n",
" \n",
"**[Introduction to GRASS GIS](Introduction to GRASS GIS/Introduction to GRASS GIS.ipynb)**\n",
"\n",
" * [GRASS working environment](Introduction to GRASS GIS/GRASS working environment.ipynb)\n",
" \n",
" * [Map display](Introduction to GRASS GIS/Map display.ipynb)\n",
"\n",
"**[Simple web-gis products](Simple web-gis products/Introduction to Simple web-gis products.ipynb)**\n",
"\n",
" * [CESIUM](Simple web-gis products/CESIUM/cesium-introduction.ipynb)\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

61
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@ -1,61 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Numerical Cartography](../numerical cartography)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# An introduction to Numerical Cartography"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* [Spatial and Coordinate Reference System](Spatial and Coordinate Reference System.ipynb)\n",
"* [Working with coordinates](Working with coordinates.ipynb)\n",
"* [The Geodesic Problem](The Geodesic Problem.ipynb)\n",
"* [Map Projections](Map Projections.ipynb)\n",
"* [Geometric transformation](geometric-transformation.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### References\n",
"\n",
"* [pyproj](https://jswhit.github.io/pyproj/)\n",
"* [Map Projections-A Working Manual](http://pubs.er.usgs.gov/publication/pp1395)\n",
"* [geographiclib](http://geographiclib.sourceforge.net/)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

266
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@ -1,266 +0,0 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting test.csv\n"
]
}
],
"source": [
"%%file test.csv\n",
"30.263888889,45.563456\n",
"23.457654,34.433425"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Latitude</th>\n",
" <th>Longitude</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>30.263889</td>\n",
" <td>45.563456</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>23.457654</td>\n",
" <td>34.433425</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"output_type": "execute_result",
"metadata": {}
}
],
"source": [
"input = pd.read_csv('test.csv', names=['Latitude', 'Longitude'])\n",
"input"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"def d2s(df,key='Latitude'):\n",
" '''convert from decimal degrees to sessagesimal degrees\n",
" take as input a pandas dataframe and a column name'''\n",
" g = df[key].values.astype(int)\n",
" p = ((( df[key].values) - df[key].values.astype(int))*60).astype(int)\n",
" s = (((df[key].values - df[key].values.astype(int)) * 60. ) - p ) * 60.\n",
" param = key\n",
" ses = pd.DataFrame(np.array([g,p,s]).T, columns=['Degree','Minute','Second'] , dtype=float)\n",
" return ses\n",
"\n",
"def s2d(df,key=['Degree','Minute','Second']):\n",
" '''convert from sessagesimal degrees to decimal degrees\n",
" take as input a pandas dataframe and a list of column names'''\n",
" deg=df[key[0]].values+(df[key[1]].values/60.+df[key[2]].values/3600.)\n",
" return deg"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"Lat = d2s(df=input,key='Latitude')\n",
"Lon = d2s(df=input,key='Longitude')"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Degree</th>\n",
" <th>Minute</th>\n",
" <th>Second</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>30</td>\n",
" <td>15</td>\n",
" <td>50.0000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>23</td>\n",
" <td>27</td>\n",
" <td>27.5544</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"output_type": "execute_result",
"metadata": {}
}
],
"source": [
"Lat"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Degree</th>\n",
" <th>Minute</th>\n",
" <th>Second</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>45</td>\n",
" <td>33</td>\n",
" <td>48.4416</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>34</td>\n",
" <td>26</td>\n",
" <td>0.3300</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"output_type": "execute_result",
"metadata": {}
}
],
"source": [
"Lon"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 30.26388889, 23.457654 ])"
]
},
"execution_count": 45,
"output_type": "execute_result",
"metadata": {}
}
],
"source": [
"s2d(Lat)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 45.563456, 34.433425])"
]
},
"execution_count": 46,
"output_type": "execute_result",
"metadata": {}
}
],
"source": [
"s2d(Lon)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.0"
}
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"nbformat": 4,
"nbformat_minor": 0
}

70
GSoC-2015/Numerical Cartography/Map Projections.ipynb
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@ -1,70 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Numerical Cartography](../numerical cartography)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Map Projections\n",
"\n",
"A map projection is a systematic representation of all or part of the surface of a round body, especially the Earth, on a plane and cannot be done without inducing distortions.\n",
"\n",
"There are several ways to project a curved surface on a plane and each way, projection, has its own particular characteristic. Depending on the purpose of the map a map maker, the cartographer, must choose the characteristic which is to be shown accurately at the expense of others, or a compromise of several characteristics.\n",
"\n",
"\n",
"The characteristics normally considered in choosing a map projection are as follows:\n",
"\n",
"* **Area** - (eg. equal-area map) on such maps the area is preserved (areas of the same size on the map represent an area f equivalent size on the earth) Shapes, angles, and scale must be distorted in most parts of such a map. Equal-area map is also called *equivalent*, *homolographic*, or *homalographic*\n",
"* **Shape** - (eg. conformal map) on those maps the relative local angles about every point on the map are shown correctly. Because local angles are correct, meridians intersect parallels at right ($90^\\circ$) angles on a conformal projection.\n",
"* **Scale** (eg. equidistant projections) No map projection shows scale correctly throughout the map, but there are usually one or more lines on the map along which the scale remains true. An equidistant projection shows true scale between one or two points and every other point on the map, or along every meridian.\n",
"* **Direction** - While conformal maps give the relative local directions correctly at any given point, there is one frequently used group of map projections, called azimuthal (or zenithal), on which the directions or azimuths of all points on the map are shown correctly with respect to the center. Some projection of this kind can be *equal-area* others can be *conformal* or *equidistant* \n",
"* **Special characteristic** - Several map projections provide special characteristics that no other projection provides. eg. On the *Mercator projection*, the lines of constant direction (rhumb lines) are shown as straight lines. On the *Gnomonic projection*, all great circle paths are shown as straight lines. On the *Stereographic*, all small circles, as well as great circles, are shown as circles on the map. \n",
"\n",
"Source: [Map Projections](http://pubs.usgs.gov/pp/1395/report.pdf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are several tools that can handle map projections right an easy and powerful tool to explore map projections is the cartopy python library. For several examples see the relative example [notebooks](../../Projects/CARTOPY/)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"[top](#Notebooks---Numerical-Cartography)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
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106
GSoC-2015/Numerical Cartography/Spatial and Coordinate Reference System.ipynb
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@ -1,106 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Numerical Cartography](../numerical cartography)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Spatial and Coordinate Reference System\n",
"\n",
"A **spatial reference system** (SRS) or **coordinate reference system** (CRS) is a [coordinate-based](https://en.wikipedia.org/wiki/Coordinate_system) local, regional or global system used to locate geographical entities. A spatial reference system defines a specific [map projection](https://en.wikipedia.org/wiki/Map_projection), as well as transformations between different spatial reference systems. Spatial reference systems are defined by the [OGC](https://en.wikipedia.org/wiki/Open_Geospatial_Consortium)'s [Simple feature access](https://en.wikipedia.org/wiki/Simple_feature_access) using [well-known text](https://en.wikipedia.org/wiki/Well-known_text), and support has been implemented by several [standards-based](https://en.wikipedia.org/wiki/Technical_standard) [geographic information systems](https://en.wikipedia.org/wiki/Geographic_information_system). Spatial reference systems can be referred to using an [SRID](https://en.wikipedia.org/wiki/SRID) integer, including EPSG codes defined by the [International Association of Oil and Gas Producers](https://en.wikipedia.org/wiki/International_Association_of_Oil_and_Gas_Producers).\n",
"\n",
"**source:** \n",
"\n",
"**[Wikipedia: Spatial reference system](https://en.wikipedia.org/wiki/Spatial_reference_system)**\n",
"\n",
"**[Wikipedia: Geographic coordinate system](https://en.wikipedia.org/wiki/Geographic_coordinate_system)**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Coordinate Reference System (CRS):\n",
"A position refers to the spatial location of an entity and it is determined by its spatial coordinates relative to a spatial reference system (SRS).\n",
"The most common choices of coordinates are ** *Geographic coordinates* ** and ** *UTM coordinates* **.\n",
"\n",
"\n",
"### Geographic latitude and longitude:\n",
" \n",
" A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers or letters.A common choice of coordinates is latitude, longitude, and elevation.\n",
" \n",
" * **Latitude** (angle between the equatorial plane and the straight line that passes through that point and through, or close to, the center of the Earth)\n",
" * **Longitude** (the angle east or west from a reference meridian to another meridian that passes through that position). \n",
"\n",
"The combination of these two components specifies the position of any location on the surface of the Earth, without consideration of altitude or depth. \n",
"\n",
"<img src=\"../images/ECEF.svg\">"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Universal Transverse Mercator (UTM) coordinate system:\n",
"\n",
" The UTM coordinate system uses a metric-based cartesian grid laid out on a conformally projected surface. The UTM system is not a single map projection but a series of sixty, each covering 6-degree bands of longitude.\n",
" \n",
" \n",
"<img src=\"../images/utmzone.svg\">"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Geodetic Coordinates:\n",
" \n",
" To completely specify a location of a topographical feature on, in, or above the Earth, one has to also specify the vertical distance from the center of the Earth, or from the surface of the Earth.\n",
" \n",
" In order to be unambiguous about the direction of \"vertical\" and the \"surface\" above which they are measuring, map-makers choose a reference ellipsoid with a given origin and orientation that best fits their need for the area they are mapping. They then choose the most appropriate mapping of the spherical coordinate system onto that ellipsoid, called a terrestrial reference system or geodetic datum. Datums may be global, meaning that they represent the whole earth, or they may be local, meaning that they represent a best-fit ellipsoid to only a portion of the earth.\n",
" \n",
" The choice of which layer to use for defining height is arbitrary. Common height baselines include:\n",
" * The surface of the datum ellipsoid, resulting in an ellipsoidal height\n",
" * The mean sea level as described by the gravity geoid, yielding the orthometric height\n",
" * A vertical datum, yielding a dynamic height relative to a known reference height.\n",
"Along with the latitude $\\phi$ and longitude $\\lambda$, the height $h$ provides the three-dimensional *geodetic coordinates* or *geographic coordinates* for a location."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"[top](#Notebooks---Numerical-Cartography)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

362
GSoC-2015/Numerical Cartography/The Geodesic Problem.ipynb
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@ -1,362 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Numerical Cartography](../numerical cartography)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The Geodesic Problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"##Distances and angles \n",
"\n",
"The distances between two points can be axpressesd as the shortest path between the points themselves. For a plane such distance will coincide with a straight line and is expressed by the eucidean distance (eq. 1).\n",
"\n",
"<center><it>euclidean distance</it></center>\n",
"<br>\n",
"$$\n",
"d = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\quad (1) \n",
"$$\n",
"\n",
"On the earth surface the distances between 2 points can't be expressed as a straight line and a more relatively complex geometry has to be adopted. In the simplest case we can approssimate the shape of the earth to a sphere and perform distance calculations on the basis of a spherical trigonometry (ignoring ellipsoidal effects). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Distance on a sphere\n",
"[source](https://www.math.ksu.edu/~dbski/writings/haversine.pdf)\n",
"\n",
"Given 2 Points $P_1(\\theta_1,\\phi_1)$ and $P_2(\\theta_2,\\phi_2)$ on the Earth’s Surface in polar coordinates, which coincide with $P_1(x_1,y_1,z_1)$ and $P_2(x_2,y_2,z_2)$ in cartesian coordinates. The distance $d$ on the surface of a sphere is computed in two stages:\n",
"* Compute the euclidean distance as a straight line\n",
"* Convert the measurments to spherical coordinates\n",
"\n",
"The conversion from polar coordinates $(\\theta, \\phi)$ to cartesian $(X,Y,Z)$ is given by the relation:\n",
"\n",
"$$\n",
"X = R \\cdot \\cos(\\theta) \\cdot \\cos(\\phi) \\\\\n",
"Y = R \\cdot \\cos(\\theta) \\cdot \\sin(\\phi) \\\\\n",
"Z = R \\cdot sin(\\theta) \n",
"$$\n",
"\n",
"and the three-dimensional euclidean distance $d$ is given by:\n",
"\n",
"$$\n",
"d = \\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2} \n",
"$$\n",
"\n",
"\n",
"\n",
"Converting the cartesian coordinates to spherical coordinates, the distance $d$ on a sphere is found by:\n",
"\n",
"$$\n",
"d^2 = 2 - 2 \\cos(\\theta_1) \\cdot cos(\\theta_2) \\cdot cos(\\phi_1 - \\phi_2) - 2\\sin(\\theta_1) \\cdot sin(\\theta_2)\n",
"$$\n",
"\n",
"\n",
"Now from figure 1 we have that:\n",
"\n",
"$$\n",
"\\sin{\\frac{\\alpha}{2}} = \\frac{d}{2R}\n",
"$$\n",
"\n",
"which gives:\n",
"\n",
"$$\n",
"\\sin(\\alpha) = \\frac{d}{R} \\cdot \\sqrt{1-(\\frac{d}{2R})^2} = \\frac{d}{2R^2} \\cdot \\sqrt{4R^2-d^2}\n",
"$$\n",
"\n",
"and in therms of $d$ and $R$ the distance $D$ is given by:\n",
"\n",
"$$\n",
"D = R \\alpha = R \\sin^{-1}{(\\frac{d}{2R^2}\\cdot \\sqrt{4R^2-d^2})}\n",
"$$\n",
"\n",
"<img src=\"../images/sc1.svg\" width=\"80%\">\n",
"<center>Figure 1</center>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Distance on curved surface\n",
"\n",
"The shortest path between two points on a curved surface is colled *geodesic* which in case of a spheroid is also colled *Great Circle*.\n",
"Considering two points: $P_1(\\lambda_1,\\phi_1), P_2(\\lambda_2,\\phi_2)$, The great circle distance $d$ between $P_1$ and $P_2$ is given by eq.2: \n",
"\n",
"$$\n",
"d = 2 \\cdot \\arcsin(\\sqrt{\\sin{(\\frac{\\phi_1-\\phi_2}{2})}^2 + \\cos(\\phi_1) \\cdot \\cos(\\phi_2) \\cdot (\\sin{\\frac{\\lambda_1-\\lambda_2}{2}})^2} \\quad (2)\n",
"$$\n",
"\n",
"This approach is good enough for most purposes but for more accurate results, the computation needs to be performed on an ellipsoid of revolution. \n",
"\n",
"The shortes distance between two points on the ellipse surface is also known as *Geodesics on an ellipsoid* and can be computed by the algorithms given in [*Algorithms for geodesics* Karney (2013)](http://link.springer.com/article/10.1007%2Fs00190-012-0578-z) which is implemented in the [geographiclib](http://geographiclib.sourceforge.net/) software, internally adopted by the proj library.\n",
"\n",
"\n",
"---\n",
"\n",
"## The direct and Inverse Geodesic Problems on a Ellipsoid of revolution\n",
"\n",
"\n",
"The problems in geodesy are usually reduced to two main cases: the direct problem, given a starting point and an initial heading, find the position after traveling a certain distance along the geodesic; and the inverse problem, given two points on the ellipsoid find the connecting geodesic and hence the shortest distance between them. Because the flattening of the Earth is small, the geodesic distance between two points on the Earth is well approximated by the great-circle distance using the mean Earth radius - the relative error is less than 1%. However, the course of the geodesic can differ dramatically from that of the great circle. As an extreme example, consider two points on the equator with a longitude difference of $179^\\circ59'$; while the connecting great circle follows the equator, the shortest geodesics pass within 180 km of either pole (the flattening makes two symmetric paths passing close to the poles shorter than the route along the equator).\n",
"\n",
" It is possible to reduce the various geodesic problems into one of two types. Consider two points: $A$ at latitude $\\phi_1$ and longitude $\\lambda_1$ and $B$ at latitude $\\phi_2$ and longitude $\\lambda_2$ (see Fig. 3). The connecting geodesic (from $A$ to $B$) is $AB$, of length $s_{12}$, which has azimuths $\\alpha_1$ and $\\alpha_2$ at the two endpoints. \n",
"\n",
" The two geodesic problems usually considered are:\n",
"\n",
" * the **direct geodesic problem** or first geodesic problem, determine $\\phi_{2}$, $\\lambda_{12}$, and $\\alpha_2$, given $\\phi_1$, $\\alpha_1$ and $s_{12}$; \n",
"\n",
" * the **inverse geodesic problem** or second geodesic problem, determine $s_{12}$, $\\alpha_1$ and $\\alpha_2$ given $\\phi_1$, $\\phi_2$, and $\\lambda_{12}$. \n",
"\n",
"\n",
"<img src=\"../images/Geodesic_problem_on_an_ellipsoid.svg\" width=\"50%\">\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"FIG. 2 The ellipsoidal triangle $NAB$. $N$ is the north pole, $NA$ and\n",
"$NB$ are *meridians*, and $AB$ is a *geodesic* of length $s_{12}$. The longitude\n",
"of $B$ relative to $A$ is $\\lambda_{12}$; the latitudes of $A$ and $B$ are $\\phi_1$ and\n",
"$\\phi_2$. $EFH$ is the *equator* with $E$ also lying on the extension of the\n",
"geodesic $AB$; and $\\alpha_0$, $\\alpha_1$, and $\\alpha_2$ are the azimuths of the geodesic\n",
"at $E$, $A$, and $B$. \n",
"\n",
"[source](https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"### The inverse geodesic problem\n",
"\n",
"**Example:**\n",
"\n",
"Calculate the distance between two points, as well as the local heading:\n",
"\n",
"* First we import the class [```Geod```](http://jswhit.github.io/pyproj/pyproj.Geod-class.html) then we define a reference ellipsoid where ```ellps='WGS84'``` selects WGS84 reference ellipsoid. ```help(Geod.__new__)``` gives a list of possible ellipsoids."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from pyproj import Geod\n",
"g = Geod(ellps='WGS84')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Set two location for which we want compute the measurments, in this example $P_1$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"lat1,lon1 = (40.7143528, -74.0059731) # New York, NY\n",
"lat2,lon2 = (1.359, 103.989) # Delhi, India\n",
"az12,az21,dist = g.inv(lon1,lat1,lon2,lat2)\n",
"az12,az21,dist"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# using geograhiclib:\n",
"# Compute path from 1 to 2\n",
"from geographiclib.geodesic import Geodesic\n",
"g = Geodesic.WGS84.Inverse(lat1, lon1, lat2, lon2)\n",
"g"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note: \n",
"* pyproj takes as input longitude first then latitude\n",
"* the output of geographiclib and pyproj for the backward azimuth are complementary of 180^{\\circ}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The direct geodesic problem:\n",
"\n",
"**Example:**\n",
"\n",
"Compute the midpoint on the path from 1 to 2 starting at 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"h = Geodesic.WGS84.Direct(lat1, lon1, g['azi1'], g['s12']/2)\n",
"print(h['lat2'], h['lon2']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Geodetic curve\n",
"\n",
"**Example:**\n",
"\n",
"Compute a list of points along the $geodesic \\ curve$ with a fixed distance of $100000m$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"gc = [Geodesic.WGS84.Direct(lat1, lon1, g['azi1'], i) for i in range(0,int(g['s12']),100000)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Extract *Latitude* and *Longitude* from and add the destination point which is missed in the previous list"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"lat = [i['lat2'] for i in gc]\n",
"lat.append(lat2)\n",
"lon = [i['lon2'] for i in gc]\n",
"lon.append(lon2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can plot the resulting geodesic with:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.plot(lon,lat,'-');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"### Surface's area on the ellipsoid\n",
"The Geodesic class in geographiclib can be also used to compute the area on an ellipsoidal surface, see example:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Computing the area of a geodesic polygon\n",
"def p(lat,lon): return {'lat': lat, 'lon': lon}\n",
"Geodesic.WGS84.Area([p(0, 0), p(0, 90), p(90, 0)])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"[top](#Notebooks---Numerical-Cartography)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
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"nbformat_minor": 0
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446
GSoC-2015/Numerical Cartography/Working with coordinates.ipynb
View File

@ -1,446 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Numerical Cartography](../numerical cartography)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Working with Coordinates\n",
"\n",
"* [Coordinate notation](#Coordinate-notation)\n",
"* [Coordinate conversion](#Coordinate-conversion)\n",
"* [Datum transformation](#Datum-transformation)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Coordinate notation\n",
"To express the values for the geographic longitude and latitude there are different notations, the most used are:\n",
" * **degimal degrees** (eg: $30.263888889^{\\circ}$)\n",
" * **sessagesimal degrees** (eg: $ 30^{\\circ} 15^{'} 50^{\"}$)\n",
"\n",
"A simple example to convert back and forward those 2 different notations is shown below:\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's use the IPython magic funcion ```%%file``` to make a simple comma separated value (CSV) file'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%%file test.csv\n",
"30.263888889,45.563456\n",
"23.457654,34.433425"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"now read the CSV using [pandas](), we'll create a [pandas.dataframe]() using the [pandas.read_csv]() method:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"input = pd.read_csv('test.csv', names=['Latitude', 'Longitude'])\n",
"input"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Simple code to convert between the two notations:\n",
"\n",
"* d2s: convert from decimal degrees to sessagesimal degrees\n",
"* s2d: convert from sessagesimal degrees to decimal degrees"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"def d2s(df,key='Latitude'):\n",
" '''convert from decimal degrees to sessagesimal degrees\n",
" take as input a pandas dataframe and a column name'''\n",
" g = df[key].values.astype(int)\n",
" p = ((( df[key].values) - df[key].values.astype(int))*60).astype(int)\n",
" s = (((df[key].values - df[key].values.astype(int)) * 60. ) - p ) * 60.\n",
" param = key\n",
" ses = pd.DataFrame(np.array([g,p,s]).T, columns=['Degree','Minute','Second'] , dtype=float)\n",
" return ses\n",
"\n",
"def s2d(df,key=['Degree','Minute','Second']):\n",
" '''convert from sessagesimal degrees to decimal degrees\n",
" take as input a pandas dataframe and a list of column names'''\n",
" deg=df[key[0]].values+(df[key[1]].values/60.+df[key[2]].values/3600.)\n",
" return deg"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# convert from decimal degrees to sessagesimal degree"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"Lat = d2s(df=input,key='Latitude')\n",
"Lon = d2s(df=input,key='Longitude')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Lat"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Lon"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# convert from sessagesimal degree to decimal degree"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"s2d(Lat)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"s2d(Lon)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Coordinate conversion\n",
"\n",
"Common task when working with points is to convert their coordinates from Latitude and Longitude to UTM and viceversa. \n",
"Common example is the position reported by a GPS receiver which usually report the position latitude and longitude expressed in decimal degrees and referred to the WGS84 ellipsoid. In this case we have a two way conversion:\n",
" * from Geographic to UTM\n",
" * from UTM to Geographic\n",
"Note: this is an exact conversion, it is not a transformation of coordinates. The point is located on the same ellipsoid *WGS84* and the conversion between the two different notation does not involve any approssimation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Example:**\n",
"\n",
"We want find the UTM coordinates for the point. For the purpose of this excercize we will use the [pyproj](http://jswhit.github.io/pyproj/) module (python wrapper of the widely used Cartographic Projections Library: [PROJ](https://github.com/OSGeo/proj.4/wiki).\n",
"\n",
"\n",
"$$P(longitude,latitude) :\\quad -70.9393^{\\circ}, 43.1356^{\\circ}$$\n",
"\n",
"The UTM coordinate system is divided in 60 different zones, each zone has its own definition and can be easly identified by an unic ID using its [EPSG code](). \n",
"Our point P falls in the state of New Hampshire (US) which is included in the 19th fuse of the UTM system.\n",
"To find out which EPSG code is assigned to the UTM zone 19th on the WGS84 ellipsoid, we can use services like [EPSG.io](http://epsg.io/) which are based on the [EPSG API](http://www.ogp.org.uk/pubs/373-07-3.pdf) and look for: \n",
"\n",
"```WGS 84 / UTM zone 19N```\n",
"\n",
"\n",
"Which will return : \n",
"\n",
"[```EPSG:32619```](http://epsg.io/32619)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Longitude Latitude WGS84 -> UTM 19N / WGS 84"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#import the pyproj library\n",
"import pyproj\n",
"\n",
"# set point P coordinates: \n",
"P = (-70.93931369842528, 43.13567095719326)\n",
"\n",
"# define projection UTM 19 N: \n",
"# UTM zone 19, WGS84 ellipse, WGS84 datum, defined by epsg code 32619\n",
"p1 = pyproj.Proj(init='epsg:32619')\n",
"\n",
"#Find UTM coordinates for the point P(-70.93931369842528,43.13567095719326)\n",
"x1, y1 = p1(P[0],P[1])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x1, y1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"You can easly verify the results of the conversion using the [epsg.io map widget](http://epsg.io/32619/map) on and look for:\n",
"\n",
"```Jere A. Chase Ocean Engineering Laboratory\n",
"24 Colovos Road, Durham, NH 03824, United States```\n",
"\n",
"which will show the coordinated of the point $P$ in longitude and lattude on the upper right and in UTM on the center bottom.\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Datum transformation \n",
"(Change in reference system)\n",
"\n",
"\n",
"A reference system is a set of rules and measurments to establish the spatio-temporal position of a point location, regardless off the coordinate system. This system of rules and measurments must lock the degrees of freedom left free from the relative measurments. A coordinate system can be referenced to celestial bodies (quasi-inertial-reference-frame) or the more practical systems referenced to the earth. In the case of earth referenced system a SRS is defined by:\n",
"\n",
"* A Reference Surface (Ellipsoid)\n",
"* Its Localization, where the ellipsoid can be earth-centered (WGS84) or oriented locally (eg. Gauss Boaga Roma 1940)\n",
"\n",
"A change in reference system can not be confused with coordinate transformation, which are pure mathematical transformations. Those problems can be separted in :\n",
"\n",
"* Coordinate Transformation\n",
"* Change in Reference System (or DATUM change)\n",
"\n",
"\n",
"\n",
"A Change in reference System is a tranformation which involve the estimation of a set of transformation parameteres. there are different methods which can be used to estimate those parameters besed on a set of reference points which coodinates are know in different reference systems. The proj library can be used to perform DATUM changes, see examples below: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Example** \n",
"\n",
"* UTM 19N / WGS 84 -> UTM 19N NAD 83 "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# define projection 1: \n",
"# UTM zone 19, WGS84 ellipse, WGS84 datum, defined by epsg code 32619\n",
"p1 = pyproj.Proj(init='epsg:32619')\n",
"\n",
"# define projection 2: UTM zone 19, GRS 1980 ellipse, NAD83 datum\n",
"p2 = pyproj.Proj(init='epsg:26919')\n",
"\n",
"# transform the UTM coordinates for the point P to projection 2 coordinates.\n",
"x2, y2 = pyproj.transform(p1,p2,x1,y1)\n",
"\n",
"x2, y2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* UTM 19N / WGS 84 -> UTM 19N NAD 27 "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# define projection: UTM zone 19, Clarke 1866, NAD27 datum\n",
"p3 = pyproj.Proj(init='epsg:26719')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# transform the UTM coordinates for the point P to projection 3 coordinates.\n",
"x3, y3 = pyproj.transform(p1,p3,x1,y1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x3, y3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note: \n",
"\n",
"The earth is in constant movment (Plate tectonics theory). Geodesist costantly redefine the specification of ellipsoid used as reference for the various CRS. The initial definition of NAD83(1986) was intended to match GRS80 and WGS84. In this example we are considering the *original* CRS means the WGS84 with ellipsoid epoc:1984 and the NAD 83 as defined in the 1986.\n",
"\n",
"This explain how close are the coordinates for the two CRS *UTM 19 N / WGS 84* and *UTM 19 N / NAD 83* which for the epoc of their definition are almost identical.\n",
"To perform a more accurate transformation it is possible to specify the projection parameters esplicitly using the proj format string.\n",
"read more: [WGS84 and NAD83](http://www.ngs.noaa.gov/CORS/Articles/WGS84NAD83.pdf), [North American Datum](https://en.wikipedia.org/wiki/North_American_Datum)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"The problem of parameter estimation is developed on a dedicated in the [geometric transformations notebook](geometric-transformation.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"[top](#Notebooks---Numerical-Cartography)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
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"name": "ipython",
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"file_extension": ".py",
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11
GSoC-2015/Numerical Cartography/d1s.csv
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GSoC-2015/Numerical Cartography/d2.csv
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11
GSoC-2015/Numerical Cartography/d2s.csv
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GSoC-2015/Numerical Cartography/geometric-transformation.ipynb
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@ -1,450 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Numerical Cartography](../numerical cartography)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Geodetic datum transformations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Is common practice in Geospatial data science to work with datasets collected at different epoch and or referenced to different reference systems. In this context, the transformation parameters needed to convert data accurately into a more up-to-date reference system are often missed or, when available, are valid for wide areas affecting the accuracy of the transformation. In this briefing notes a simplified approach to derive datum transformation parameters is introduced.\n",
"\n",
"A Datum transformations can be defined as a geometric transformation between two three-dimensional coordinate reference systems. A common method consists of applying a *linear transformation* in the three-dimensional space (x,y,z).\n",
"A general linear transformation of a vector $x$ to another vector $y$ takes the form\n",
"\n",
"$$y=Mx+t \\quad (1)$$\n",
"\n",
"Each element of the $y$ vector is a combination of the element of $x$ plus a translation or shift represented by an element of the $t$ vector. The matrix **M** is called *transformation matrix* and **t** is called *translation vector*. With **M** being square nonsingular, the inverse relation exists (eq. 2)\n",
"\n",
"$$x = M^{-1}(y-t) \\quad (2)$$\n",
"\n",
"in which case is called *affine transformation*.\n",
"\n",
"Limited to the two- and three- dimensional space, six *elementary* transformations are identified, each representing a single effect. They are geometrically described as *Translation, Uniform scale, Rotation, Reflection, Stretch (Nonuniform scale factors) and Skew (Shear)*. \n",
"\n",
"<img src=\"../images/linear-transformation.svg\", width=\"80%\">\n",
"\n",
"<center>Figure 1: Elementary transformations</center>\n",
"\n",
"\n",
"---\n",
"\n",
"## The Helmert 7-parameter transformation\n",
"\n",
"<img src=\"../images/helmert.svg\", width=\"80%\">\n",
"\n",
"<center>Figure 2: Roto-Traslation and scaling in three- dimensional space</center>\n",
"\n",
"\n",
"The Helmert 7-parameter transformation, which is an affine (distortion-free) transformation in three dimensions, is extensively used in geodesy to perform Datum transformations. It is applied to geocentric coordinates and can be factored into seven elementary transformations: one uniform scale change, three translations, and three rotations.\n",
"\n",
"\n",
"\n",
"Considering a generic point $P$ represented in two orthogonal three dimensional Cartesian spatial reference frames $D_1 (x,y,z)$ and $D_2 (x',y',z')$. For small rotation the direct transformation $P_{D_1} \\to P_{D_2}$, is given by\n",
"\n",
"$$\n",
" {\\begin{pmatrix}\n",
"x_p \\\\\n",
"y_p \\\\\n",
"z_p \n",
"\\end{pmatrix}}_{{D}_2} = \\begin{pmatrix}\n",
"x^{\\prime}_0 \\\\\n",
"y^{\\prime}_0 \\\\\n",
"z^{\\prime}_0 \n",
"\\end{pmatrix} + (1+k) \\begin{pmatrix}\n",
"1 & R_z & -R_y \\\\\n",
"-R_z & 1 & R_x \\\\\n",
"R_y & -R_x & 1\n",
"\\end{pmatrix} \\begin{pmatrix}\n",
"x^{\\prime}_p \\\\\n",
"y^{\\prime}_p \\\\\n",
"z^{\\prime}_p\n",
"\\end{pmatrix}_{{D}_1} \\quad (3)\n",
"$$\n",
"\n",
"\n",
"## Horizontal geodetic datum transformations\n",
"\n",
"\n",
"\n",
"It is common in Geodesy to separate altimetry from planimetry, in this scenario the affine transformation (eq. 3) can be simplified to a *plane roto-translation with isotropic scale variation* which requires only four parameters: one scale factor $(\\lambda)$, one rotation $(\\alpha)$, two translations $(x'_0, y'_0)$. The direct (eq. 4) and inverse (eq. 5) transformations are expressed by:\n",
"\n",
"\n",
"<img src=\"../images/plane.svg\", width=\"80%\">\n",
"\n",
"<center>Figure 3: Roto-Traslation and scaling in two- dimensional space</center>\n",
"\n",
"$$\n",
" \\begin{pmatrix}\n",
"x_p \\\\\n",
"y_p\n",
"\\end{pmatrix}_{{D}_2} = \\begin{pmatrix}\n",
"T_x \\\\\n",
"T_y\n",
"\\end{pmatrix} + \\lambda \\begin{pmatrix}\n",
"\\cos \\alpha & \\sin \\alpha \\\\\n",
"- \\sin \\alpha & \\cos \\alpha\n",
"\\end{pmatrix} \\begin{pmatrix}\n",
"x'_p \\\\\n",
"y'_p\n",
"\\end{pmatrix}_{{D}_1} \\quad (4)\n",
"$$\n",
"\n",
"$$\n",
" \\begin{pmatrix}\n",
"x'_p \\\\\n",
"y'_p\n",
"\\end{pmatrix}_{{D}_2} = \\lambda^{-1} \\begin{pmatrix}\n",
"\\cos \\alpha & -\\sin \\alpha \\\\\n",
"\\sin \\alpha & \\cos \\alpha\n",
"\\end{pmatrix} \\begin{pmatrix}\n",
"x_p - T_x \\\\\n",
"y_p - T_y\n",
"\\end{pmatrix}_{{D}_1} \\quad (5)\n",
"$$\n",
"\n",
"To estimate the four parameters $(\\lambda, \\alpha, x_0, y_0)$ at least two planimetric coordinates in the two systems are needed. However, if more positions are available a least square method (*Fitting*) can be used solving the linear system:\n",
"\n",
"$$\n",
"\\left\\{ \n",
" \\begin{array}{l l}\n",
"x'_0 + a x'_p + b y'_p - x_p = 0 \\\\\n",
"y'_0 + a y'_p - b x'_p - y_p = 0 \n",
"\\end{array} \\right. \\quad (6)\n",
"$$\n",
"\n",
"with:\n",
"\n",
"$$\n",
"a = \\lambda \\cos \\alpha\n",
"$$\n",
"$$\n",
"b = \\lambda \\sin \\alpha\n",
"$$\n",
"\n",
"The linear system (6) can be solved knowing, at least, two points in $(D_1,D_2)$ once estimated the four unknown parameters $(a,b,{x'}_0,{y'}_0)$ it is possible to derive the rotation angle $\\alpha$ and the scale factor $\\lambda$ by:\n",
"\n",
"$$\n",
"\\left\\{ \n",
" \\begin{array}{l l}\n",
" \\lambda = \\sqrt{a^2 + b^2} \\\\\n",
" \\alpha = \\arctan \\frac{b}{a}\n",
" \\end{array} \\right. \\quad (7)\n",
"$$\n",
"\n",
"The relation expressed in (eq. 6) can be used in two different ways: \n",
"\n",
"\n",
"1. Knowing the four parameters it is possible to transform the coordinates of $P$ from $D_1 \\to D_2$; \n",
"2. Knowing the position of at least 2 points in both systems $(D_1, D_2)$ it is possible to estimate the four parameters by the *Least Square Method*.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Implementation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* [Conforme 2D](#Conforme-2D) \n",
"* [Affine 2D](#Affine-2D)\n",
"* [Helmert-7-Parameters (3D)](#Helmert-7-Parameters)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Firs we need to generate a proper test dataset, to do so we'll use a combination of pyproj and numpy.\n",
"Starting from the data used in the [Working with coordinates - Datum-transformation](../numerical cartography/Working with coordinates.ipynb#Datum-transformation) example, we generate a series of 50 random points in two different DATUM:\n",
"\n",
"* UTM zone 19, WGS84 ellipse, WGS84\n",
"* UTM zone 19, Clarke 1866, NAD27"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#import the pyproj and numpy library\n",
"import pyproj\n",
"import numpy as np\n",
"\n",
"# set a reference point P with coordinates: \n",
"P = (-70.93931369842528, 43.13567095719326)\n",
"\n",
"# define projection UTM 19 N: \n",
"# UTM zone 19, WGS84 ellipse, WGS84 datum, defined by epsg code 32619\n",
"p1 = pyproj.Proj(init='epsg:32619')\n",
"\n",
"#Find UTM coordinates for the point P(-70.93931369842528,43.13567095719326)\n",
"x1, y1 = p1(P[0],P[1])\n",
"\n",
"# define projection: UTM zone 19, Clarke 1866, NAD27 datum\n",
"p3 = pyproj.Proj(init='epsg:26719')\n",
"\n",
"# transform the UTM coordinates for the point P to projection 3 coordinates.\n",
"x3, y3 = pyproj.transform(p1,p3,x1,y1)\n",
"\n",
"# generate a set of random points in the range of 100 meters from P1 \n",
"# note: we use a fake altitude to perform a 3D transformation\n",
"# the value of 6371 is the ray of the spheroid in km\n",
"\n",
"xrand = (np.random.random_sample((50,))*100)+x1\n",
"yrand = (np.random.random_sample((50,))*100)+y1\n",
"zrand = (np.random.random_sample((50,))*10)+(6371*1000)\n",
"xrand,yrand,zrand\n",
"\n",
"# transform the UTM coordinates for the points [xrand, yrand] to the projection 3 coordinates.\n",
"x, y = pyproj.transform(p1,p3,xrand[:],yrand[:])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# now generate 2 dataframes to store the x,y,z coordinates in the two different DATUM \n",
"# and save the reults in a space delimited text file\n",
"import pandas as pd\n",
"d1 = pd.DataFrame(np.array([xrand,yrand,zrand],dtype=np.float).T, columns=['x','y','z'])\n",
"d2 = pd.DataFrame(np.array([x,y,zrand],dtype=np.float).T, columns=['x','y','z'])\n",
"d1.to_csv('d1.csv', index=False, header=False, sep=\" \")\n",
"d2.to_csv('d2.csv', index=False, header=False, sep=\" \")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Random points in DATUM 1**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"d1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Random points in Datum 2**\n",
"\n",
"(transformation performed using pyproj)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"d2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* testing dataset:\n",
"\n",
"We'll first select the first 10 points in both data frame and use them to estimate the transformation parameters. Then we'll use the other 40 points in $d1$ as input for the transformation. Finally, compare the results with the output of pyproj."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#d1,d2 subsample\n",
"d1s=d1[:11]\n",
"d2s=d1[:11]\n",
"d=d1[11:]\n",
"# save to file\n",
"d1s.to_csv('d1s.csv', index=False, header=False, sep=\" \")\n",
"d2s.to_csv('d2s.csv', index=False, header=False, sep=\" \")\n",
"d.to_csv('d.csv', index=False, header=False, sep=\" \")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Conforme 2D"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from transform import conforme"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"res_conforme = conforme(gcpD1='d1s.csv', gcpD2='d2s.csv', knowD1='d.csv', output='conforme.csv')\n",
"res_conforme"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Affine 2D"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from transform import affine"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"res_affine = affine(gcpD1='d1s.csv', gcpD2='d2s.csv', knowD1='d.csv', output='affine.csv')\n",
"res_affine"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Helmert 7 Parameters"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from transform import helmert"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"res_helmert = helmert(gcp1='d1s.csv', gcp2='d2s.csv', inputf='d.csv', output='helmert.txt')\n",
"res_helmert"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"d2[11:][['x','y']]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"delta_conforme = (d2[11:]['x'].values - res_conforme[:,0], d2[11:]['y'].values - res_conforme[:,1])\n",
"delta_conforme"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"delta_affine = (d2[11:]['x'].values - res_affine[:,0], d2[11:]['y'].values - res_affine[:,1])\n",
"delta_affine"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"delta_helmert = (d2[11:]['x'].values - res_helmert[:,0], d2[11:]['y'].values - res_helmert[:,1])\n",
"delta_helmert"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"[top](#Notebooks---Numerical-Cartography)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### References\n",
"\n",
"GPS. Principi, modalita' e tecniche di posizionamento - Alberto Cina (2000) - ISBN: 8876614176"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2.0
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

39
GSoC-2015/Numerical Cartography/helmert.txt
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@ -1,39 +0,0 @@
3.422910531172005576e+05 4.777740363479495049e+06 6.371005418482345529e+06
3.422780525059666834e+05 4.777751609494659118e+06 6.371000550520975143e+06
3.423544274841793813e+05 4.777718690010458231e+06 6.371002766752424650e+06
3.423292157290527830e+05 4.777784671567500569e+06 6.371004462662098929e+06
3.423604034956423566e+05 4.777781803438861854e+06 6.371004265624630265e+06
3.423284602034637355e+05 4.777790233755520545e+06 6.371002675618864596e+06
3.422919469853131450e+05 4.777712539965643547e+06 6.371001032911824062e+06
3.423082369248265168e+05 4.777747347229405306e+06 6.371001303604850546e+06
3.423139665708763059e+05 4.777742206223327667e+06 6.371009724931769073e+06
3.423629655590662151e+05 4.777771211742747575e+06 6.371000423834800720e+06
3.423615139199149562e+05 4.777707336521958001e+06 6.371005347219641320e+06
3.423314114728729473e+05 4.777787557462602854e+06 6.371005661907915026e+06
3.422984944834707421e+05 4.777786426113739610e+06 6.371005715945014730e+06
3.423086088819543947e+05 4.777806424985138699e+06 6.371000123961099423e+06
3.423591765592533629e+05 4.777799298533591442e+06 6.371005528996963985e+06
3.423435574773782864e+05 4.777796740105740726e+06 6.371003938704710454e+06
3.423123570766042685e+05 4.777783368158218451e+06 6.371003696283833124e+06
3.423176263008305687e+05 4.777804078216431662e+06 6.371005768622835167e+06
3.423728023016868392e+05 4.777709045514377765e+06 6.371000675273722969e+06
3.422923084668048541e+05 4.777770123743905686e+06 6.371007363129526377e+06
3.422814302514794981e+05 4.777787441929566674e+06 6.371008915446749888e+06
3.422967017101223464e+05 4.777790021469592117e+06 6.371009537946073338e+06
3.422916888997707283e+05 4.777734369702809490e+06 6.371009633000481874e+06
3.423216866985324887e+05 4.777775188259245828e+06 6.371000731247326359e+06
3.423526324396999553e+05 4.777768645840060897e+06 6.371000981828987598e+06
3.423218758604582399e+05 4.777761765366605483e+06 6.371000672535302117e+06
3.423020888135355781e+05 4.777755227641544305e+06 6.371006185327406041e+06
3.422941201462723548e+05 4.777773083191342652e+06 6.371002732519299723e+06
3.423731302605434903e+05 4.777723814718367532e+06 6.371007242484644987e+06
3.423591411253153346e+05 4.777710822556014173e+06 6.371009191004937515e+06
3.423140703031602316e+05 4.777710084696033970e+06 6.371006937534978613e+06
3.423597842652014806e+05 4.777749610747885890e+06 6.371001560979159549e+06
3.423012843319001840e+05 4.777756469547622837e+06 6.371008458509415388e+06
3.423272170942250523e+05 4.777789717194980942e+06 6.371003352428907529e+06
3.423181228947083000e+05 4.777708338737960905e+06 6.371001168572855182e+06
3.422847886936801369e+05 4.777804453777041286e+06 6.371005632761033252e+06
3.423329211885412224e+05 4.777710391670132056e+06 6.371009397662129253e+06
3.423033878647821839e+05 4.777763407477849163e+06 6.371009832818288356e+06
3.423499323941044277e+05 4.777746946433324367e+06 6.371000875813973136e+06

2
GSoC-2015/Numerical Cartography/test.csv
View File

@ -1,2 +0,0 @@
30.263888889,45.563456
23.457654,34.433425
1 30.263888889 45.563456
2 23.457654 34.433425

260
GSoC-2015/Numerical Cartography/transform.py
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@ -1,260 +0,0 @@
import numpy as np
from scipy import linalg
import math
def conforme(gcpD1, gcpD2, knowD1, output, verbose=False):
L = np.loadtxt(str(gcpD1))
A = np.zeros((2*L.shape[0],4),float)
A[ ::2, 0] = 1.0
A[1::2, 1] = 1.0
A[ ::2, 2] = L[:,0]
A[1::2, 2] = L[:,1]
A[ ::2, 3] = L[:,1]
A[1::2, 3] = -L[:,0]
G = np.loadtxt(str(gcpD2))
Y = np.zeros((2*G.shape[0],1),float)
Y[ ::2, 0] = G[:,0]
Y[1::2, 0] = G[:,1]
N = np.dot(A.T.conj(), A)
T = np.dot(A.T.conj(), Y)
C = np.dot(linalg.inv(N), T)
Lambda = abs(C[2]+C[3]*1j)
Alpha = np.angle(C[2]+C[3]*1j)
E0 = C[0]
N0 = C[1]
LX = np.loadtxt(str(knowD1))
ss = LX.shape[0]
pq = G.shape[0]
ENglob = np.zeros((ss,2),float)
lam = math.sqrt(C[2]** + C[3]**2)
alp = np.arctan(C[3] / C[2]) / (math.pi / 180.)
for i in np.arange(ss):
E2 = E0+LX[i,0]*C[2]+LX[i,1]*C[3]
N2 = N0+LX[i,1]*C[2]-LX[i,0]*C[3]
ENglob[i,:] = np.hstack((E2,N2))
np.savetxt(output, ENglob)
sq = LX.shape[0]
sqx = np.zeros((G.shape[0],1),float)
sqy = np.zeros((G.shape[0],1),float)
sqx[ ::1, 0] = G[:,0]
sqy[::1, 0] = G[:,1]
sizeq = sqx.shape[0]
scartix = np.zeros((sizeq,1),float)
scartiy = np.zeros((sizeq,1),float)
scartiqx = np.zeros((sizeq,1),float)
scartiqy = np.zeros((sizeq,1),float)
sqm = np.zeros((sizeq,1),float)
for i in np.arange(sizeq):
Vx = E0 + LX[i,0] * C[2,0] + LX[i,1] * C[3,0] - sqx[i,0]
Vy = N0 + LX[i,1] * C[2,0] - LX[i,0] * C[3,0] - sqy[i,0]
sqmr = math.sqrt(Vx**2 + Vy**2)
sqm[i,:] = sqmr
scartiqx[i,0] = Vx**2
scartiqy[i,0] = Vy**2
scartix[i,0] = Vx
scartiy[i,0] = Vy
scartiq = np.concatenate((scartiqx,scartiqy))
scarti = np.concatenate((scartix,scartiy))
scartixy = np.concatenate((scartiqx,scartiqy),1)
scartiqxy = np.concatenate((scartix,scartiy),1)
sumscarti = sum(scartiq)
varqp = sumscarti / ((2 * sizeq) - 4)
varp = math.sqrt(varqp)
varianzaq = varqp * linalg.inv(N)
varianza = varp * linalg.inv(N)
varqunitp = np.diag(varianzaq)
varunitp = np.diag(varianza)
prec = np.zeros((sq,2),float)
for i in np.arange(sq):
xx = math.sqrt((LX[i,0]**2) * (varqunitp[2]) + (LX[i,1]**2) * (varqunitp[3]) + varqunitp[0])
yy = math.sqrt((LX[i,1]**2) * (varqunitp[2]) + (LX[i,0]**2) * (varqunitp[3]) + varqunitp[1])
prec[i,:] = np.hstack((xx,yy))
errore = np.concatenate((scartixy,scartiqxy,sqm),1)
np.savetxt(output+str('_precision'), prec)
np.savetxt(output+str('_error'), errore)
err_med = sum(sqm) / pq
a = C[2,0]
b = C[3,0]
lamvar = math.sqrt(((((2 * a) / math.sqrt(a**2 + b**2))**2) * varqunitp[2]) + ((((2 * b) / math.sqrt(a**2 + b**2))**2) * varqunitp[3]))
alphavar = math.sqrt(((((-b / a**2) / (1 + (b / a)**2))**2) * varqunitp[2]) + (((1 / a) / (1 + (b / a)**2))**2 * varqunitp[3])) / (math.pi / 180.)
results = str('Trasformation Parameters :\n')
results += str("\n")
results += str('Tx : ')+str(C[0,0])+'\n'
results += str('Ty : ')+str(C[1,0])+'\n'
results += str('Rigid Rotation : ')+str(alp)+'\n'
results += str('Scale Factor : ')+str(lam)+'\n'
results += str("\n")
results += str('Trasformation Parameters Variance :\n')
results += str("\n")
results += str('Sigma quadro Rigid Rotation :')+str(alphavar)+'\n'
results += str('Sigma quadro Scale Factor:')+str(lamvar)+'\n'
results += str("\n")
results += str('Results : ')+str("\n")
results += str(ENglob)
results += '\n'
results += str('Mean Error : ')+'\n'
results += str(err_med)+'\n'
results += '\n'
results += str('Precision : ')+'\n'
results += str(prec)
results += '\n'
results += str('Error : ')+str("\n")
results += str(errore)
results = results.replace('[','').replace(']','')
if verbose:
print(results)
return ENglob
def affine(gcpD1, gcpD2, knowD1, output, verbose=False):
L = np.loadtxt(str(gcpD1))
A = np.zeros((2*L.shape[0],6),float)
A[ ::2, 2] = 1.0
A[1::2, 5] = 1.0
A[ ::2, 0] = L[:,0]
A[1::2, 4] = L[:,1]
A[ ::2, 1] = L[:,1]
A[1::2, 3] = L[:,0]
G = np.loadtxt(str(gcpD2))
Y = np.zeros((2*G.shape[0],1),float)
Y[ ::2, 0] = G[:,0]
Y[1::2, 0] = G[:,1]
N = np.dot(A.T.conj(), A)
T = np.dot(A.T.conj(), Y)
C = np.dot(linalg.inv(N), T)
E0 = C[2]
N0 = C[5]
LX = np.loadtxt(str(knowD1))
ss = LX.shape[0]
ENglob = np.zeros((ss,2),float)
for i in np.arange(ss):
E2 = E0+LX[i,0]*C[0]+LX[i,1]*C[1]
N2 = N0+LX[i,0]*C[3]+LX[i,1]*C[4]
ENglob[i,:] = np.hstack((E2,N2))
np.savetxt(output,ENglob)
sq = LX.shape[0]
sqx = np.zeros((G.shape[0],1),float)
sqy = np.zeros((G.shape[0],1),float)
sqx[ ::1, 0] = G[:,0]
sqy[::1, 0] = G[:,1]
sizeq = sqx.shape[0]
scartix = np.zeros((sizeq,1),float)
scartiy = np.zeros((sizeq,1),float)
scartiqx = np.zeros((sizeq,1),float)
scartiqy = np.zeros((sizeq,1),float)
sqm = np.zeros((sizeq,1),float)
for i in np.arange(sizeq):
Vx = E0 + LX[i,0] * C[0,0] + LX[i,1] * C[1,0] - sqx[i,0]
Vy = N0 + LX[i,0] * C[3,0] + LX[i,1] * C[4,0] - sqy[i,0]
sqmr = math.sqrt(Vx**2 + Vy**2)
sqm[i,:] = sqmr
scartiqx[i,0] = Vx**2
scartiqy[i,0] = Vy**2
scartix[i,0] = Vx
scartiy[i,0] = Vx
scartiq = np.concatenate((scartiqx,scartiqy))
scarti = np.concatenate((scartix,scartiy))
scartixy = np.concatenate((scartiqx,scartiqy),1)
scartiqxy = np.concatenate((scartix,scartiy),1)
sumscarti = sum(scartiq)
varqp = sumscarti / ((2 * ss) - 4)
varp = math.sqrt(varqp)
varianzaq = varqp * linalg.inv(N)
varianza = varp * linalg.inv(N)
varqunitp = np.diag(varianzaq)
varunitp = np.diag(varianza)
prec = np.zeros((sq,2),float)
for i in np.arange(sq):
xx = math.sqrt((LX[i,0]**2) * (varqunitp[0]) + (LX[i,1]**2) * (varqunitp[1]) + varqunitp[2])
yy = math.sqrt((LX[i,1]**2) * (varqunitp[0]) + (LX[i,0]**2) * (varqunitp[1]) + varqunitp[5])
prec[i,:] = np.hstack((xx,yy))
errore = np.concatenate((scartixy,scartiqxy,sqm),1)
np.savetxt(output+str('_precision'), prec)
np.savetxt(output+str('_error'), errore)
err_med = sum(sqm) / sq
results = str('Trasformation Parameters :\n')
results += str('Tx : ')+str(C[2,0])+'\n'
results += str('Ty : ')+str(C[5,0])+'\n'
results += str('Rigid Rotation X : ')+str(C[1,0])+'\n'
results += str('Rigid Rotation Y : ')+str(C[3,0])+'\n'
results += str('Scale Factor X : ')+str(C[0,0])+'\n'
results += str('Scale Factor Y : ')+str(C[4,0])+'\n'
results += '\n'
results += str('Results : ')+'\n'
results += str(ENglob)
results += str("\n")
results += str('Mean Error : ')+'\n'
results += str(err_med)+'\n'
results += '\n'
results += str('Precision : ')+'\n'
results += str(prec)+'\n'
results += '\n'
results += str('Error : ')+'\n'
results += str(errore)
results = results.replace('[','').replace(']','')
if verbose:
print(results)
return ENglob
def vcross(v):
x, y, z = v
mat = np.zeros((3,3))
mat[0] = [ 0, -z, y]
mat[1] = [ z, 0, -x]
mat[2] = [-y, x, 0]
return mat
def block(v):
return np.hstack((np.eye(3), -vcross(v), v[:, np.newaxis]))
def helmert(gcp1, gcp2, inputf, output, verbose=False):
pt1 = np.loadtxt(str(gcp1))
pt2 = np.loadtxt(str(gcp2))
A = []
rhs = []
for i in range(3):
A.append(block(pt1[i]))
rhs.append((pt2[i] - pt1[i])[:, np.newaxis])
A = np.vstack(A)
rhs = np.vstack(rhs)
sol = np.linalg.lstsq(A, rhs)[0]
res = rhs - np.dot(A, sol)
XYZ = np.loadtxt(str(inputf))
XYZsize = XYZ.shape[0]
ENZglob = np.zeros((XYZsize,3),float)
for i in np.arange(XYZsize):
X = sol[0] + (1 + sol[6]) * ( XYZ[i,0] - sol[5] * XYZ[i,1] + sol[4] * XYZ[i,2] )
Y = sol[1] + (1 + sol[6]) * ( sol[5] * XYZ[i,0] + XYZ[i,1] - sol[3] * XYZ[i,2] )
Z = sol[2] + (1 + sol[6]) * ( -sol[4] * XYZ[i,0] + sol[3] * XYZ[i,1] + XYZ[i,2] )
ENZglob[i,:] = np.hstack((X,Y,Z))
np.savetxt(output,ENZglob)
hresults = str('Trasformation Parameters :\n')
hresults += str("\n")
hresults = str('Traslation :\n')
hresults += str("\n")
hresults += str('Tx : ')+str(sol[0])+'\n'
hresults += str('Ty : ')+str(sol[1])+'\n'
hresults += str('Tz : ')+str(sol[2])+'\n'
hresults += str("\n")
hresults += str('Rotation :\n ')
hresults += str("\n")
hresults += str('Rx : ')+str(sol[3])+'\n'
hresults += str('Ry : ')+str(sol[4])+'\n'
hresults += str('Rz : ')+str(sol[5])+'\n'
hresults += str("\n")
hresults += str('Scale Factor :\n ')
hresults += str("\n")
hresults += str("S : ")+str(sol[6])+'\n'
hresults += str("\n")
hresults += str('Trasformation Residuals :\n')
hresults += str("\n")
hresults += str(res)+'\n'
hresults += str('Results : \n')
hresults += str("\n")
hresults += str(ENZglob)
hresults += '\n'
hresults = hresults.replace('[','').replace(']','')
if verbose:
print(hresults)
return ENZglob

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1
GSoC-2015/OUTPUT/readme.md
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# Directory to host output data

167
GSoC-2015/Simple web-gis products/CESIUM/CesiumWidget Example KML.ipynb
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@ -1,167 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cesium Widget Example KML\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the installation of Cesiumjs is ok, it should be reachable here:\n",
"http://localhost:8888/nbextensions/CesiumWidget/cesium/index.html"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from CesiumWidget import CesiumWidget\n",
"from IPython import display\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create widget object"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesium = CesiumWidget()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Display the widget:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesium"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cesium is packed with example data. Let's look at some GDP per captia data from 2008. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesium.kml_url = '/nbextensions/CesiumWidget/cesium/Apps/SampleData/kml/gdpPerCapita2008.kmz'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example zoomto"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"for lon in np.arange(0, 360, 0.5):\n",
" cesium.zoom_to(lon, 0, 36000000, 0 ,-90, 0)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cesium._zoomto"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example flyto"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesium.fly_to(14, 90, 20000001)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cesium._flyto"
]
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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@ -1,176 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# CesiumWidget together with CZML library\n",
"This notebook shows how to use the CesiumWidget together with the CZML library from https://github.com/cleder/czml"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the CesiumWidget is installed correctly, Cesium should be accessable at:\n",
"http://localhost:8888/nbextensions/CesiumWidget/cesium/index.html\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import collections\n",
"from CesiumWidget import CesiumWidget\n",
"import czml"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"points = collections.OrderedDict()\n",
"points['p1'] = [18.07,59.33, 20]\n",
"points['p2'] = [19.07,59.33, 20]\n",
"points['p3'] = [20.07,59.33, 20]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"points"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"doc = czml.CZML()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"packet1 = czml.CZMLPacket(id='document',version='1.0')\n",
"doc.packets.append(packet1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"for i,v in enumerate(points):\n",
" print(i,v)\n",
" p = czml.CZMLPacket(id=i)\n",
" p.position = czml.Position(cartographicDegrees = points[v])\n",
" point = czml.Point(pixelSize=20, show=True)\n",
" point.color = czml.Color(rgba=(223, 150, 47, 128))\n",
" point.show = True\n",
" p.point = point\n",
" l = czml.Label(show=True, text=v)\n",
" l.scale = 0.5\n",
" p.label = l\n",
" doc.packets.append(p)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesiumExample = CesiumWidget(width=\"100%\", czml=tuple(doc.data()))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesiumExample"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cesiumExample.zoom_to(points['p1'][0], points['p1'][1], 360000, 0 ,-90, 0)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"doc.dumps()"
]
}
],
"metadata": {
"hide_input": true,
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
},
"latex_envs": {
"bibliofile": "biblio.bib",
"cite_by": "apalike",
"current_citInitial": 1,
"eqLabelWithNumbers": true,
"eqNumInitial": 0
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cesium Widget Example\n",
"This is an example notebook accessing the CesiumWidget, in the way it should be accessed."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import json\n",
"from IPython import display\n",
"from CesiumWidget import CesiumWidget"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the installation of Cesiumjs is ok, it should be reachable [here](http://localhost:8888/nbextensions/CesiumWidget/cesium/index.html)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great, let's create a `CesiumWidget`!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cesium = CesiumWidget()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Display the widget:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesium"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can change many settings of the widget:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cesium.class_own_traits()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's turn on lighting: let there be light!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesium.enable_lighting = True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load data for the viewer to display in the [CZML](https://github.com/AnalyticalGraphicsInc/cesium/wiki/CZML-Guide) format, which is based on JSON. It always expects a list of Packet objects."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from CesiumWidget.examples.iss import ISS\n",
"cesium.czml = ISS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can also use the excellent `czml` module to generate valid CZML: see an [example here](./CesiumWidget Example with CZML library.ipynb)."
]
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cesium Widget Example\n",
"This is an example notebook to sow how to *bind* the [Cesiumjs](http://cesiumjs.org/index.html) with the [IPython interactive widget system](https://github.com/ipython/ipywidgets)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from CesiumWidget import CesiumWidget\n",
"from IPython import display\n",
"from czml_example import simple_czml, complex_czml"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The code:\n",
"\n",
"```from czml_example import simple_czml, complex_czml```\n",
"\n",
"Simply import some [CZML]() data for the viewer to display."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Create widget object**"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cesiumExample = CesiumWidget(width=\"100%\", enable_lighting=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Display the widget:**"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesiumExample"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Add some data to the viewer**\n",
"\n",
"* A simple czml"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesiumExample.czml = simple_czml"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* A more complex CZML example"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesiumExample.czml = complex_czml"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's make some interactive widget:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"from ipywidgets import interact, interactive, fixed\n",
"from ipywidgets import widgets"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* store the CZML objet in a dictionary and use their name as ```keys```\n",
"* define a function to switch between CZML\n",
"* bind the IPython intercat class to the function"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"myczml = {'simple_czml':simple_czml, 'complex_czml':complex_czml}"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"myplace = {'Eboli, IT':'', 'Woods Hole, MA':'', 'Durham, NH':''}"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "ImportError",
"evalue": "No module named geocoder",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mImportError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-9-45ff9bcce4a8>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mgeocoder\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mtime\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mmyplace\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[0mg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgeocoder\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgoogle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlatlng\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mImportError\u001b[0m: No module named geocoder"
]
}
],
"source": [
"import geocoder\n",
"import time\n",
"for i in myplace.keys():\n",
" g = geocoder.google(i)\n",
" print(g.latlng)\n",
" myplace[i]=g.latlng"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"myplace"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"@interact(z=(0,20000000), heading=(-180,180), pitch=(-90,90), roll=(-360,360), \n",
" Location=('Eboli, IT','Woods Hole, MA','Durham, NH'))\n",
"def f(z=1000000, heading=0, pitch=-90, roll=0, Location='Eboli, IT'):\n",
" cesiumExample.zoom_to(myplace[Location][1], myplace[Location][0], z, heading, pitch, roll)\n",
"@interact(CZML=('simple_czml','complex_czml'))\n",
"def c(CZML=None):\n",
" cesiumExample.czml = myczml[CZML]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cesiumExample"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"hide_input": true,
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
},
"latex_envs": {
"bibliofile": "biblio.bib",
"cite_by": "apalike",
"current_citInitial": 1,
"eqLabelWithNumbers": true,
"eqNumInitial": 0
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../../) - [Simple web-gis products](../) - [CESIUM](../CESIUM/)- [Introduction](../CESIUM/cesium-introduction.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## CesiumWidget\n",
"\n",
"CesiumWidget is an IPython/Jupyter notebook widget based on [Cesiumjs](http://cesiumjs.org/), a javascript\n",
"world globe widget.\n",
"\n",
"For license on Cesiumjs see http://cesiumjs.org/index.html\n",
"\n",
"CesiumWidget part of code is under Apache license\n",
"\n",
"\n",
"\n",
"## Features\n",
"\n",
"The widget is in development and has currently basic features such as load CZML, KML, GeoJson and camera functionalities like go-to, zoom-to, zoom-ti-region.\n",
"\n",
"The vision is to have a widget for representing orbits,\n",
"geo-related informations in an efficient way directly in the browser. By using the full\n",
"screen button, the widget can be expanded to provide a larger view.\n",
"\n",
"Roadmap still to be written but visioned features are:\n",
"* Time readout and control of widget from python\n",
"* Better interface with czml\n",
"* Pyplot-like interface to quickly plot stuff\n",
"\n",
"\n",
"## Examples\n",
"\n",
"* [CesiumWidget Example](CesiumWidget Example.ipynb)\n",
"* [CesiumWidget Example KML](CesiumWidget Example KML.ipynb)\n",
"* [CesiumWidget Example with CZML library](CesiumWidget Example with CZML library.ipynb)\n",
"* [CesiumWidget Interact-Example](CesiumWidget Interact-Example.ipynb)\n",
"\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>[Notebooks](../) - [Simple web-gis products](../Simple web-gis products) - [Introduction ](../Simple web-gis products/Introduction to Simple web-gis products.ipynb)</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The intent of this set of notebooks is to provide some examoples on how to build simple ```HTML``` and ```JavaScrpt``` web based tools, using templates based on *cesiumJS*, *Openlayers*, *Leaflets*.\n",
"\n",
"The ability of the notebook to work on very diverse and heterogeneous data and information sources, provides an effective way to document the processes involved in generating a data product as well as a way to share the source code used to generate those products and associated metadata. Those features enable the ability to track the workflow provenance to allow the reproducibility of a data product."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"**[CESIUM](CESIUM/cesium-introduction.ipynb)**\n",
"\n",
"\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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<?xml version='1.0'?>
<!-- This file was generated by dvisvgm 1.6 -->
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course_content/simple.svg
.ipynb_checkpoints
.project
.pydevproject

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# The language in this case has no bearing - we are going to be making use of conda for a
# python distribution for the scientific python stack.
language: python
sudo: false
env:
global:
- CONDA_INSTALL_LOCN="${HOME}/conda"
# Generated with `$ travis encrypt GH_TOKEN=<auth_token>` for SciTools/courses.
- secure: "IGrdEKM5CH5OCus7pCCrzSWV9WOEuY9QKvWFbNBkBLa3MNszvZop3oioB3QVvygHvMV2HvcOBEx4KaQvUt6UanNb8j+C1zrPGWBuDeuWVDC3pCfqCsXRGXJU1TJp0alRByxaSoenvSjEBJi/GpF9zsAosS/wJIX1rBCbLsjKrhU="
matrix:
- PYTHON=3.4
install:
- wget https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O ${HOME}/miniconda.sh
- bash ${HOME}/miniconda.sh -b -p ${CONDA_INSTALL_LOCN} && export PATH=${CONDA_INSTALL_LOCN}/bin:$PATH
- git config --global user.name "Travis user"
- git config --global user.email travis-tests@example.com
# Now do the things we need to do to install it.
- conda install notebook nbconvert python=${PYTHON} --yes --quiet
- rm -rf build
- git clone https://dkillick:${GH_TOKEN}@github.com/SciTools/courses.git --branch build build
script:
- ./make.sh
- cd build
- git add -A --ignore-removal .
- git status
# This will only fail if there's nothing to commit, so we can safely skip over this failure.
- git commit -am "Build of ${TRAVIS_COMMIT}" || true
- if [ ! -z "$GH_TOKEN" ]; then
git push origin build > /dev/null;
fi

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GNU GENERAL PUBLIC LICENSE
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Also add information on how to contact you by electronic and paper mail.
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This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
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{http://www.gnu.org/philosophy/why-not-lgpl.html}.

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Python courses for the scientific researcher
============================================
This repository contains several courses for the benefit of scientific researchers,
particularly in the fields of oceanography and meteorology.
There are currently four courses:
### An introduction to numpy
3.5 hours &mdash; depends on a basic Python background
http://nbviewer.ipython.org/github/SciTools/courses/blob/master/course_content/notebooks/numpy_intro.ipynb?create=1
### An introduction to matplotlib
3 hours &mdash; depends on "An introduction to numpy"
http://nbviewer.ipython.org/github/SciTools/courses/blob/master/course_content/notebooks/matplotlib_intro.ipynb?create=1
### Cartopy in a nutshell (for Iris)
0.5 hours &mdash; depends on "An introduction to matplotlib"
http://nbviewer.ipython.org/github/SciTools/courses/blob/master/course_content/notebooks/cartopy_intro.ipynb?create=1
### An introduction to Iris
6 hours &mdash; depends on "Cartopy in a nutshell"
http://nbviewer.ipython.org/github/SciTools/courses/blob/master/course_content/notebooks/iris_intro.ipynb?create=1

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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cartopy in a nutshell\n",
"\n",
"Cartopy is a Python package that provides easy creation of maps, using matplotlib, for the analysis and visualisation of geospatial data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to create a map with cartopy and matplotlib, we typically need to import pyplot from matplotlib and cartopy's crs (coordinate reference system) submodule. These are typically imported as follows:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import cartopy.crs as ccrs"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cartopy's matplotlib interface is set up via the `projection` keyword when constructing a matplotlib `Axes` / `SubAxes` instance. The resulting axes instance has new methods, such as the **``coastlines()``** method, which are specific to drawing cartographic data:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ax = plt.axes(projection=ccrs.PlateCarree())\n",
"ax.coastlines()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A full list of Cartopy projections is available at http://scitools.org.uk/cartopy/docs/latest/crs/projections.html."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To draw cartographic data, we use the the standard matplotlib plotting routines with an additional **transform** keyword argument. The value of the **transform** argument should be the cartopy coordinate reference system *of the data being plotted*:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ax = plt.axes(projection=ccrs.PlateCarree())\n",
"ax.coastlines()\n",
"ax.set_global()\n",
"plt.plot([-100, 50], [25, 25], linewidth=4, transform=ccrs.Geodetic())\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that unless we specify a map extent (we did so via the **``set_global``** method in this case) the map will zoom into the range of the plotted data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can add graticule lines and tick labels to the map using the gridlines method (this currently is limited to just a few coordinate reference systems):"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ax = plt.axes(projection=ccrs.Mercator())\n",
"ax.coastlines()\n",
"gl = ax.gridlines(draw_labels=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can control the specific tick values by using matplotlib's locator object, and the formatting can be controlled with matplotlib formatters:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.ticker as mticker\n",
"from cartopy.mpl.gridliner import LATITUDE_FORMATTER\n",
"\n",
"ax = plt.axes(projection=ccrs.PlateCarree())\n",
"ax.coastlines()\n",
"gl = ax.gridlines(draw_labels=True)\n",
"\n",
"gl.xlocator = mticker.FixedLocator([-180, -45, 0, 45, 180])\n",
"gl.yformatter = LATITUDE_FORMATTER\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cartopy cannot currently label all types of projection, though more work is intended on this functionality in the future."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 1\n",
"\n",
"The following snippet of code produces coordinate arrays and some data in a rotated pole coordinate system. The coordinate system for the `x` and `y` values, which is similar to that found in the some limited area models of Europe, has a projection \"north pole\" at 177.5 longitude and 37.5 latitude."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import cartopy.crs as ccrs\n",
"\n",
"x = np.linspace(310, 390, 25)\n",
"y = np.linspace(-24, 25, 35)\n",
"x2d, y2d = np.meshgrid(x, y)\n",
"\n",
"data = np.cos(np.deg2rad(y2d) * 4) + np.sin(np.deg2rad(x2d) * 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Part 1**\n",
"\n",
"Define a cartopy coordinate reference system which represents a rotated pole with a pole latitude of 37.5 and a pole longitude of 177.5."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Part 2**\n",
"\n",
"Produce a map, with coastlines, using the coordinate reference system created in Part 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Part 3**\n",
"\n",
"Produce a map, with coastlines, in a Plate Carree projection with a pcolormesh of the data generated by the code snippet provided at the beginning of the exercise. Remember that the data is supplied in the rotated coordinate system defined in Part 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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@ -1,618 +0,0 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# An introduction to matplotlib\n",
"\n",
"Matplotlib is a Python package used widely throughout the scientific Python community to produce high quality 2D publication graphics. It transparently supports a wide range of output formats including PNG (and other raster formats), PostScript/EPS, PDF and SVG and has interfaces for all of the major desktop GUI (Graphical User Interface) toolkits.\n",
"\n",
"Matplotlib comes with a convenience sub-package called ``pyplot``. For consistency with the wider maptlotlib community, this should always be imported as ``plt``:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The matplotlib Figure\n",
"\n",
"At the heart of every matplotlib plot is the \"Figure\". The Figure is the top level concept that can be drawn to one of the many output formats, or simply just to screen.\n",
"\n",
"Let's create our first Figure using pyplot, and then show it:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"fig = plt.figure()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On its own, drawing the Figure is uninteresting and will result in an empty piece of paper (that's why we didn't see anything above). \n",
"Other visible elements are added to a Figure to make a plot. All visible items in Matplotlib are instances of the [Artist](http://matplotlib.org/api/artist_api.html#artist-class) class : The Figure and Axes are both types of Artist.\n",
"\n",
"To start with we can draw an [Axes](http://matplotlib.org/api/axes_api.html) artist in the Figure, to represent our data space. The most basic Axes is rectangular and has tick labels and tick marks. Multiple Axes artists can be placed on a Figure.\n",
"\n",
"Let's go ahead and create a Figure with a single Axes, and show it using pyplot:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ax = plt.axes()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Matplotlib's ``pyplot`` module makes the process of creating graphics easier by allowing us to skip some of the tedious object construction. For example, we did not need to manually create the Figure with ``plt.figure`` because it was implicit that we needed a Figure when we created the Axes.\n",
"\n",
"Under the hood matplotlib still had to create a Figure; we just didn't need to capture it into a variable. We can access the created object with the \"state\" functions found in pyplot called **``gcf``** and **``gca``**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 1\n",
"\n",
"Go to matplotlib.org and search for what these strangely named functions do.\n",
"\n",
"Hint: you will find multiple results so remember we are looking for the ``pyplot`` versions of these functions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Working with the Axes\n",
"\n",
"As has already been mentioned, most of your time building a graphic in matplotlib will be spent on the Axes. Whilst the matplotlib documentation for the Axes is very detailed, it is also rather difficult to navigate (though this is an area of ongoing improvement).\n",
"\n",
"As a result, it is often easier to find new plot types by looking at the pyplot module's documentation.\n",
"\n",
"The first and most common Axes method is ``plot``. Go ahead and look at the ``plot`` documentation from the following sources:\n",
"\n",
" * http://matplotlib.org/api/pyplot_summary.html\n",
" * http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.plot\n",
" * http://matplotlib.org/api/axes_api.html?#matplotlib.axes.Axes.plot\n",
" \n",
"Plot can be used to draw one or more lines in axes data space:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ax = plt.axes()\n",
"line1, = ax.plot([0, 1, 2, 1.5], [3, 1, 2, 4])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice how the Axes view limits (``ax.viewLim``) have been updated to include the whole of the line.\n",
"Should we want to add some spacing around the edges of our Axes we can set a margin using the [``margins``](http://matplotlib.org/api/axes_api.html?highlight=axes#matplotlib.axes.Axes.margins) method. Alternatively, we can manually set the limits with the [``set_xlim``](http://matplotlib.org/api/axes_api.html?#matplotlib.axes.Axes.set_xlim) and [``set_ylim``](http://matplotlib.org/api/axes_api.html?#matplotlib.axes.Axes.set_ylim) methods."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 2\n",
"\n",
"Modify the previous example to produce three different Figures that control the limits of the Axes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1\\. Manually set the x and y limits to $[0.5, 2]$ and $[1, 5]$ respectively."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" 2\\. Define a margin such that there is 10% whitespace inside the axes around the drawn line (Hint: numbers to margins are normalised such that 0% is 0.0 and 100% is 1.0)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3\\. Set a 10% margin on the Axes with the lower y limit set to 0. (Note: order is important here)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"--------------\n",
"\n",
"If we want to create a plot in its simplest form, without any modifications to the Figure or Axes, we can leave out the creation of artist variables. Our simple line example then becomes:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.plot([0, 1, 2, 1.5], [3, 1, 2, 4])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The simplicity of this example shows how visualisations can be produced quickly and easily with matplotlib, but it is worth remembering that for full control of the Figure and Axes artists we can mix the convenience of ``pyplot`` with the power of matplotlib's object oriented design."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 3\n",
"\n",
"By calling ``plot`` multiple times, create a single Axes showing the line plots of $y=sin(x)$ and $y=cos(x)$ in the interval $[0, 2\\pi]$ with 200 linearly spaced $x$ samples."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"--------\n",
"\n",
"## Multiple Axes on the same Figure (aka subplot)\n",
"\n",
"Matplotlib makes it relatively easy to add more than one Axes object to a Figure. The ``Figure.add_subplot()`` method, which is wrapped by the ``pyplot.subplot()`` function, adds an Axes in the grid position specified. To compute the position, we tell matplotlib the number of rows and columns (respectively) to divide the figure into, followed by the index of the axes to be created (1 based). \n",
"\n",
"For example, to create an axes grid with two columns, the grid specification would be ``plt.subplot(1, 2, <plot_number>)``. \n",
"The left-hand Axes is plot number 1, created with ``subplot(1, 2, 1)``, and the right-hand one is number 2, ``subplot(1, 2, 2)`` :"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ax_left = plt.subplot(1, 2, 1)\n",
"plt.plot([2,1,3,4])\n",
"plt.title('left = #1')\n",
"\n",
"ax_left = plt.subplot(1, 2, 2)\n",
"plt.plot([4,1,3,2])\n",
"plt.title('right = #2')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Likewise, for plots above + below one another we would use *two* rows and *one* column, as in ``subplot(2, 1, <plot_number>)``."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's expand our grid to two rows and three columns, and place one set of axes on the top right (grid specification ``(2, 3, 3)``) and another on the bottom left (grid specification ``(2, 3, 4)``)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"top_right_ax = plt.subplot(2, 3, 3, title='#3 = top-right')\n",
"bottom_left_ax = plt.subplot(2, 3, 4, title='#4 = bottom-left')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"--------\n",
"\n",
"**Exercise 3 continued:** Copy the answer from the previous task (plotting $y=sin(x)$ and $y=cos(x)$) and add the appropriate ``plt.subplot`` calls to create a Figure with two rows of Axes, one showing $y=sin(x)$ and the other showing $y=cos(x)$."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"--------\n",
"\n",
"## Further plot types\n",
"\n",
"Matplotlib comes with a huge variety of different plot types. Here is a quick demonstration of the more common ones."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = np.linspace(-180, 180, 60)\n",
"y = np.linspace(-90, 90, 30)\n",
"x2d, y2d = np.meshgrid(x, y)\n",
"data = np.cos(3 * np.deg2rad(x2d)) + np.sin(2 * np.deg2rad(y2d))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.contourf(x, y, data)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.imshow(data, extent=[-180, 180, -90, 90],\n",
" interpolation='nearest', origin='lower')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.pcolormesh(x, y, data)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.scatter(x2d, y2d, c=data, s=15)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.bar(x, data.sum(axis=0), width=np.diff(x)[0])\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.plot(x, data.sum(axis=0), linestyle='--',\n",
" marker='d', markersize=10, color='red')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Titles, legends, colorbars and annotations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Matplotlib has convenience functions for the addition of plot elements such as titles, legends, colorbars and text based annotation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ``suptitle`` pyplot function allows us to set the title of a Figure, and the ``set_title`` method on an Axes allows us to set the title of an individual Axes. Additionally, an Axes has methods named ``set_xlabel`` and ``set_ylabel`` to label the respective x and y axes. Finally, we can add text, located by data coordinates, with the Axes ``text`` method:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"fig = plt.figure()\n",
"ax = plt.axes()\n",
"# Adjust the created axes so its topmost extent is 0.8 of the figure.\n",
"fig.subplots_adjust(top=0.8)\n",
"\n",
"fig.suptitle('Figure title', fontsize=18, fontweight='bold')\n",
"ax.set_title('Axes title', fontsize=16)\n",
"\n",
"ax.set_xlabel('The X axis')\n",
"ax.set_ylabel('The Y axis $y=f(x)$', fontsize=16)\n",
"\n",
"ax.text(0.5, 0.5, 'Text centered at (0.5, 0.5)\\nin data coordinates.',\n",
" horizontalalignment='center', fontsize=14)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The creation of a legend is as simple as adding a \"label\" to lines of interest. This can be done in the call to ``plt.plot`` and then followed up with a call to ``plt.legend``:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = np.linspace(-3, 7, 200)\n",
"plt.plot(x, 0.5*x**3 - 3*x**2, linewidth=2,\n",
" label='$f(x)=0.5x^3-3x^2$')\n",
"plt.plot(x, 1.5*x**2 - 6*x, linewidth=2, linestyle='--',\n",
" label='Gradient of $f(x)$', )\n",
"plt.legend(loc='lower right')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Colorbars are created with the ``plt.colorbar`` function:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = np.linspace(-180, 180, 60)\n",
"y = np.linspace(-90, 90, 30)\n",
"x2d, y2d = np.meshgrid(x, y)\n",
"data = np.cos(3 * np.deg2rad(x2d)) + np.sin(2 * np.deg2rad(y2d))\n",
"\n",
"plt.contourf(x, y, data)\n",
"plt.colorbar(orientation='horizontal')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Matplotlib comes with powerful annotation capabilities, which are described in detail at http://matplotlib.org/users/annotations_intro.html.\n",
"\n",
"The annotation's power can mean that the syntax is a little harder to read, which is demonstrated by one of the simplest examples of using annotate:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = np.linspace(-3, 7, 200)\n",
"plt.plot(x, 0.5*x**3 - 3*x**2, linewidth=2)\n",
"plt.annotate('Local minimum',\n",
" xy=(4, -18),\n",
" xytext=(-2, -40), fontsize=15,\n",
" arrowprops={'facecolor': 'black', 'frac': 0.3})\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Savefig & backends\n",
"\n",
"Matplotlib allows you to specify a \"backend\" to drive rendering the Figure. The backend includes the graphical user interface (GUI) library to use, and the most used backend (as it is normally the default one) is the \"TkAgg\" backend. When ``plt.show()`` is called, this backend pops up a Figure in a new TkInter window, which is rendered by the anti-grain graphics library (also known as \"agg\"). Generally, the most common reason to want to change backends is for automated Figure production on a headless server. In this situation, the \"agg\" backend can be used:\n",
"\n",
" import matplotlib\n",
" matplotlib.use('agg')\n",
" import matplotlib.pyplot as plt\n",
" \n",
"Note: The backend must be chosen before importing pyplot for the first time, unless the ``force`` keyword is added.\n",
"\n",
"Non-interactive backends such as the \"agg\" backend will do nothing when **``plt.show()``** is called - this is because there is nowhere (no graphical display) specified for a Figure to be displayed.\n",
"\n",
"To save a Figure programmatically the ``savefig`` function can be used from _any_ backend:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.plot(range(10))\n",
"plt.savefig('simple.svg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For graphical backends, showing and subsequently closing the window of a Figure results in the Figure being cleared from the matplotlib system. This is not the case for ``plt.savefig``, which typically should be called before ``plt.show``.\n",
"\n",
"It is also possible to manually close Figures without showing them by using the ``plt.close`` function. This could be called to remove the current Figure after saving it with ``plt.savefig`` on the occasion where not clearing the Figure might interfere with subsequent plots to be created."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
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"nbformat_minor": 0
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"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 1:\n",
"\n",
"1\\. Using the file in ``iris.sample_data_path('atlantic_profiles.nc')`` load the data and print the cube list. Store these cubes in a variable called cubes.\n",
"\n",
"2\\. Print a sorted list of unique names for the cubes.\n",
"\n",
"3\\. Extract the \"sea_water_potential_temperature\" cube. Print the minimum, maximum, mean and standard deviation of the cube's data.\n",
"\n",
"4\\. Print the attributes of the cube.\n",
"\n",
"5\\. Print the names of all coordinates on the cube. (Hint: Remember the cube.coords method)\n",
"\n",
"6\\. Get hold of the \"latitude\" coordinate on the cube. Identify whether the cube has bounds. Print the minimum and maximum latitude points in this cube."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
}
],
"metadata": {}
}
]
}

80
SciTools-courses/course_content/solutions/iris_exercise_2.ipynb
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"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise 2:**\n",
"Print the result of ``iris.sample_data_path('uk_hires.pp')`` to verify that it returns a string pointing to a file on your system. Use this string directly in the call to ``iris.load`` and confirm the result is the same as in the previous example e.g.:\n",
"\n",
" print iris.load('/path/to/iris/sampledata/uk_hires.pp', 'air_potential_temperature')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise 2 continued:** Read in the files found at ``iris.sample_data_path('GloSea4', 'ensemble_010.pp')`` and ``iris.sample_data_path('GloSea4', 'ensemble_011.pp')`` using a single load call. Do this by:\n",
"\n",
"1\\. Providing a list of the two filenames."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import iris\n",
"print iris.load([iris.sample_data_path('GloSea4', 'ensemble_010.pp'),\n",
" iris.sample_data_path('GloSea4', 'ensemble_011.pp')])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0: surface_temperature / (K) (realization: 2; time: 6; latitude: 145; longitude: 192)\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2\\. Providing a suitable glob pattern."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print iris.load(iris.sample_data_path('GloSea4', 'ensemble_01[12].pp'))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0: surface_temperature / (K) (time: 6; forecast_reference_time: 2; latitude: 145; longitude: 192)\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}

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SciTools-courses/course_content/solutions/iris_exercise_3.ipynb
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"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise 3:**\n",
"\n",
"1. Write a function, which when given a cube, returns True or False depending on whether a cell method exists.\n",
"2. Use this function as a value for the ``iris.Constraint`` **cube_func** keyword, and load the file in ``iris.sample_data_path('A1B_north_america.nc')`` such that only cubes with cell methods are loaded (note: in this case, that is all that exists in the file)."
]
}
],
"metadata": {}
}
]
}

43
SciTools-courses/course_content/solutions/iris_exercise_4.ipynb
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@ -1,43 +0,0 @@
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 4\n",
"\n",
"The following exercise is designed to give you experience of identifying why two cubes are not merging. Work is underway to make this identification process more automatic, but the resolution of the identified differences will still be a necessary process.\n",
"\n",
"There are 6 problems, each of which are not merging into a single cube as desired. In no particular order the problems are:\n",
"\n",
" 1. one of the cubes has a history attribute, but the other doesn't\n",
" 2. one of the cubes has bounds on the spatial coordinates, but the other doesn't\n",
" 3. the two cubes have different time coordinate units\n",
" 4. the two cubes have different data dtypes\n",
" 5. the two cubes have different long names\n",
" 6. the two cubes have different shapes (the data must currently be loaded to correct this)\n",
" \n",
"The files can be found in the repository along with this course in ```exercises/iris/merge/```. There are two files to be loaded for each exercise: ```merge_exercise.{problem_number}.f1.nc``` and ```merge_exercise.{problem_number}.f2.nc```.\n",
"\n",
"Identify, and correct, the reason that the two cubes are not merging for all 6 sets of files."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 1"
]
}
],
"metadata": {}
}
]
}

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"input": [
"import iris.analysis.cartography\n",
"cube.coord('grid_latitude').guess_bounds()\n",
"cube.coord('grid_longitude').guess_bounds()\n",
"grid_areas = iris.analysis.cartography.area_weights(cube)\n",
"\n",
"area_avg = cube.collapsed(['grid_longitude', 'grid_latitude'], iris.analysis.MEAN, weights=grid_areas)"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exercise 5:** What other aggregators are available? Calculate the potential temperature variance with time for the area averaged cube (hint: We want to reduce the vertical dimension, and end up with a cube of length 3). Print the data values of the resulting cube."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}

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SciTools-courses/course_content/solutions/iris_exercise_6.ipynb
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SciTools-courses/course_content/solutions/iris_exercise_7.ipynb
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{
"metadata": {
"name": "iris_exercise_7"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Graduation exercise\n",
"\n",
"1\\. Load 'A1B_north_america.nc' from the iris sample data"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import iris\n",
"filename = iris.sample_data_path(\"A1B_north_america.nc\")\n",
"cube = iris.load_cube(filename)\n",
"print cube"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"air_temperature / (K) (time: 240; latitude: 37; longitude: 49)\n",
" Dimension coordinates:\n",
" time x - -\n",
" latitude - x -\n",
" longitude - - x\n",
" Auxiliary coordinates:\n",
" forecast_period x - -\n",
" Scalar coordinates:\n",
" forecast_reference_time: 1859-09-01 06:00:00\n",
" height: 1.5 m\n",
" Attributes:\n",
" Conventions: CF-1.5\n",
" Model scenario: A1B\n",
" STASH: m01s03i236\n",
" source: Data from Met Office Unified Model 6.05\n",
" Cell methods:\n",
" mean: time (6 hour)\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2\\. Extract just data from the year 1980 and beyond from the loaded cube"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"tcoord = cube.coord('time')\n",
"def since_1980(cell):\n",
" return tcoord.units.num2date(cell.point).year >= 1980\n",
"\n",
"tcon = iris.Constraint(time=since_1980)\n",
"cube = cube.extract(tcon)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"tcoord = cube.coord('time')\n",
"\n",
"print tcoord.units.num2date(tcoord.points.min())\n",
"print tcoord.units.num2date(tcoord.points.max())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"1980-06-01 00:00:00\n",
"2099-06-01 00:00:00\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3\\. Define a function which takes a coordinate and a single time point as arguments, and returns the decade. For example, your function should return 2010 for the following:\n",
"\n",
" time = iris.coords.DimCoord([10], 'time', units='days since 2018-01-01')\n",
" print your_decade_function(time, time.points[0])"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def get_decade(coord, point):\n",
" year = coord.units.num2date(point).year\n",
" return (year/10)*10\n",
"time = iris.coords.DimCoord([10], 'time', units='days since 2018-01-01')\n",
"print get_decade(time, time.points[0])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2010\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"4\\. Add a \"decade\" coordinate to the loaded cube using your function and the coord categorisation module"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import iris.coord_categorisation as coord_cat\n",
"coord_cat.add_categorised_coord(cube, 'decade', 'time', get_decade)\n",
"print cube.coord('decade')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"AuxCoord(array([1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1990,\n",
" 1990, 1990, 1990, 1990, 1990, 1990, 1990, 1990, 1990, 2000, 2000,\n",
" 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2010, 2010, 2010,\n",
" 2010, 2010, 2010, 2010, 2010, 2010, 2010, 2020, 2020, 2020, 2020,\n",
" 2020, 2020, 2020, 2020, 2020, 2020, 2030, 2030, 2030, 2030, 2030,\n",
" 2030, 2030, 2030, 2030, 2030, 2040, 2040, 2040, 2040, 2040, 2040,\n",
" 2040, 2040, 2040, 2040, 2050, 2050, 2050, 2050, 2050, 2050, 2050,\n",
" 2050, 2050, 2050, 2060, 2060, 2060, 2060, 2060, 2060, 2060, 2060,\n",
" 2060, 2060, 2070, 2070, 2070, 2070, 2070, 2070, 2070, 2070, 2070,\n",
" 2070, 2080, 2080, 2080, 2080, 2080, 2080, 2080, 2080, 2080, 2080,\n",
" 2090, 2090, 2090, 2090, 2090, 2090, 2090, 2090, 2090, 2090]), standard_name=None, units=Unit('1'), long_name=u'decade')\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"5\\. Calculate the decadal means cube for this scenario"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import iris.analysis\n",
"cube = cube.aggregated_by('decade', iris.analysis.MEAN)\n",
"print cube"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"air_temperature / (K) (time: 12; latitude: 37; longitude: 49)\n",
" Dimension coordinates:\n",
" time x - -\n",
" latitude - x -\n",
" longitude - - x\n",
" Auxiliary coordinates:\n",
" decade x - -\n",
" forecast_period x - -\n",
" Scalar coordinates:\n",
" forecast_reference_time: 1859-09-01 06:00:00\n",
" height: 1.5 m\n",
" Attributes:\n",
" Conventions: CF-1.5\n",
" Model scenario: A1B\n",
" STASH: m01s03i236\n",
" history: Mean of air_temperature aggregated over decade\n",
" source: Data from Met Office Unified Model 6.05\n",
" Cell methods:\n",
" mean: time (6 hour)\n",
" mean: decade\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"6\\. Create a figure with 3 rows and 4 columns displaying the decadal means, with the decade displayed prominently in each axes' title"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"import iris.plot as iplt\n",
"\n",
"plt.figure(figsize=(12, 6))\n",
"\n",
"plt.suptitle('Decadal means for the A1B scenario')\n",
"for i, decade_cube in enumerate(cube.slices(['latitude', 'longitude'])):\n",
" plt.subplot(3, 4, i+1)\n",
" iplt.contourf(decade_cube, 20)\n",
" plt.title('{}'.format(decade_cube.coord('decade').points[0]))\n",
" plt.gca().coastlines()\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
}
],
"metadata": {}
}
]
}

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SciTools-courses/course_content/solutions/matplotlib_exercise_3.ipynb
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SciTools-courses/course_content/solutions/numpy_exercise_1.ipynb
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{
"metadata": {
"name": "",
"signature": "sha256:848ef38126532012d51f85fda6138dfe097a4c6c37850c846063ebee9d3928bb"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 1\n",
"\n",
"Use ``np.arange`` and ``reshape`` to create the array\n",
"\n",
" A = [[1 2 3 4]\n",
" [5 6 7 8]]"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"A = np.arange(1, 9).reshape(2, -1)\n",
"print A"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[1 2 3 4]\n",
" [5 6 7 8]]\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Use ``np.array`` to create the array\n",
"\n",
" B = [1 2]"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"B = np.array([1, 2])\n",
"print B"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[1 2]\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use broadcasting to add ``B`` to ``A`` to create the final array\n",
"\n",
" A + B = [[2 3 4 5]\n",
" [7 8 9 10]\n",
"\n",
"Hint: what shape does ``B`` have to be changed to?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print A + B.reshape(2, 1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[ 2 3 4 5]\n",
" [ 7 8 9 10]]\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}

305
SciTools-courses/course_content/solutions/numpy_exercise_2.ipynb
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@ -1,305 +0,0 @@
{
"metadata": {
"name": "",
"signature": "sha256:e3e7c1608702d0a84f35e6fa63112daab968fe74a96ae1f6ee9f39993826a343"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Exercise: trapezoidal integration\n",
"\n",
"In this exercise, you are tasked with implementing the simple trapezoid rule\n",
"formula for numerical integration. If we want to compute the definite integral\n",
"\n",
"$$\n",
" \\int_{a}^{b}f(x)dx\n",
"$$\n",
"\n",
"we can partition the integration interval $[a,b]$ into smaller subintervals. We then approximate the area under the curve for each subinterval by calculating the area of the trapezoid created by linearly interpolating between the two function values at each end of the subinterval:\n",
"\n",
"![Illustration of the trapezoidal rule](../images/trapezoidal_rule.png)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"For a pre-computed $y$ array (where $y = f(x)$ at discrete samples) the trapezoidal rule equation is:\n",
"\n",
"$$\n",
" \\int_{a}^{b}f(x)dx\\approx\\frac{1}{2}\\sum_{i=1}^{n}\\left(x_{i}-x_{i-1}\\right)\\left(y_{i}+y_{i-1}\\right).\n",
"$$\n",
"\n",
"In pure python, this can be written as:\n",
"\n",
" def trapz_slow(x, y):\n",
" area = 0.\n",
" for i in range(1, len(x)):\n",
" area += (x[i] - x[i-1]) * (y[i] + y[i-1])\n",
" return area / 2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Exercise 2\n",
"\n",
"#### Part 1\n",
"\n",
"Create two arrays $x$ and $y$, where $x$ is a linearly spaced array in the interval $[0, 3]$ of length 10, and $y$ represents the function $f(x) = x^2$ sampled at $x$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"\n",
"x = np.linspace(0, 3, 10)\n",
"y = x ** 2\n",
"\n",
"print x\n",
"print y"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0. 0.33333333 0.66666667 1. 1.33333333 1.66666667\n",
" 2. 2.33333333 2.66666667 3. ]\n",
"[ 0. 0.11111111 0.44444444 1. 1.77777778 2.77777778\n",
" 4. 5.44444444 7.11111111 9. ]\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"#### Part 2\n",
"\n",
"Use indexing (not a for loop) to find the 9 values representing $y_{i}+y_{i-1}$ for $i$ between 1 and 10.\n",
"\n",
"Hint: What indexing would be needed to get all but the last element of the 1d array **``y``**. Similarly what indexing would be needed to get all but the first element of a 1d array."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"y_roll_sum = y[:-1] + y[1:]\n",
"print y_roll_sum"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0.11111111 0.55555556 1.44444444 2.77777778 4.55555556\n",
" 6.77777778 9.44444444 12.55555556 16.11111111]\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"#### Part 3\n",
"\n",
"Write a function `trapz(x, y)`, that applies the trapezoid formula to pre-computed values, where `x` and `y` are 1-d arrays. The function should not use a for loop."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def trapz(x, y):\n",
" return 0.5 * np.sum((x[1:] - x[:-1]) * (y[:-1] + y[1:]))"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"#### Part 4\n",
"\n",
"Verify that your function is correct by using the arrays created in #1 as input to ``trapz``. Your answer should be a close approximation of $\\int_0^3 x^2$ which is $9$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"trapz(x, y)"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"9.0555555555555554"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"#### Part 5 (extension)\n",
"\n",
"``numpy`` and ``scipy.integrate`` provides many common integration schemes. Find the documentation for NumPy's own version of the trapezoidal integration scheme and check its result with your own:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print np.trapz(y, x)"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"9.05555555556\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"#### Part 6 (extension)\n",
"\n",
"Write a function `trapzf(f, a, b, npts=100)` that accepts a function `f`, the endpoints `a` and `b` and the number of samples to take `npts`. Sample the function uniformly at these\n",
"points and return the value of the integral.\n",
"\n",
"Use the trapzf function to identify the minimum number of sampling points needed to approximate the integral $\\int_0^3 x^2$ with an absolute error of $<=0.0001$. (A loop is necessary here)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def trapzf(f, a, b, npts=100):\n",
" x = np.linspace(a, b, npts)\n",
" y = f(x)\n",
" return trapz(x, y)\n",
"\n",
"def x_squared(x):\n",
" return x ** 2\n",
"\n",
"abs_err = 1.0\n",
"n_samples = 0\n",
"expected = 9\n",
"while abs_err > 0.0001:\n",
" n_samples += 1\n",
" integral = trapzf(x_squared, 0, 3, npts=n_samples)\n",
" abs_err = np.abs(integral - 9)\n",
"\n",
"print 'Minimum samples for absolute error less than or equal to 0.0001:', n_samples\n",
" "
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Minimum samples for absolute error less than or equal to 0.0001: 214\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}

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../resources

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#!/usr/bin/env bash
# Fail on first exception.
set -e
# Clean out the build folder then replace the files we need to keep.
rm -rf build/*
cp .gitignore LICENSE README.md build
# Set up the folders we will need.
mkdir -p build/html
mkdir -p build/notebooks
mkdir -p build/solutions
cd build
cp -rf ../course_content/images images
cp -rf ../course_content/resources resources
for name in "numpy_intro" "matplotlib_intro" "cartopy_intro" "iris_intro"
do
#ipython nbconvert --to slides ../../course_content/${name}.ipynb
# Build static (html) copies of the course content.
jupyter nbconvert --to html ../course_content/notebooks/${name}.ipynb
mv ../course_content/notebooks/*.html ./html/
done
#.reveal aside.notes {
# visibility: inline;
#}

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