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/*!

\page gdal_vrttut GDAL Virtual Format Tutorial

\section gdal_vrttut_toc Contents

<ol>
<li> \ref gdal_vrttut_intro
<li> \ref gdal_vrttut_format
<li> \ref gdal_vrttut_overviews
<li> \ref gdal_vrttut_raw
<li> \ref gdal_vrttut_creation
<li> \ref gdal_vrttut_derived_c
<li> \ref gdal_vrttut_derived_python
<li> \ref gdal_vrttut_warped
<li> \ref gdal_vrttut_pansharpen
<li> \ref gdal_vrttut_mt
<li> \ref gdal_vrttut_perf
</ol>

\section gdal_vrttut_intro Introduction

The VRT driver is a format driver for GDAL that allows a virtual GDAL dataset
to be composed from other GDAL datasets with repositioning, and algorithms
potentially applied as well as various kinds of metadata altered or added.
VRT descriptions of datasets can be saved in an XML format normally given the
extension .vrt.<p>

The VRT format can also describe \ref gdal_vrttut_warped "warping operations"
and \ref gdal_vrttut_pansharpen "pansharpening operations".<p>

An example of a simple .vrt file referring to a 512x512 dataset with one band
loaded from utm.tif might look like this:

\code
<VRTDataset rasterXSize="512" rasterYSize="512">
  <GeoTransform>440720.0, 60.0, 0.0, 3751320.0, 0.0, -60.0</GeoTransform>
  <VRTRasterBand dataType="Byte" band="1">
    <ColorInterp>Gray</ColorInterp>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">utm.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <SrcRect xOff="0" yOff="0" xSize="512" ySize="512"/>
      <DstRect xOff="0" yOff="0" xSize="512" ySize="512"/>
    </SimpleSource>
  </VRTRasterBand>
</VRTDataset>
\endcode

Many aspects of the VRT file are a direct XML encoding of the
<a href="gdal_datamodel.html">GDAL Data Model</a> which should be reviewed
for understanding of the semantics of various elements.<p>

VRT files can be produced by translating to VRT format.  The resulting file can
then be edited to modify mappings, add metadata or other purposes.  VRT files
can also be produced programmatically by various means.<p>

This tutorial will cover the .vrt file format (suitable for users editing
.vrt files), and how .vrt files may be created and manipulated programmatically
for developers.<p>

\section gdal_vrttut_format .vrt Format

A <a href="https://raw.githubusercontent.com/OSGeo/gdal/master/gdal/data/gdalvrt.xsd">XML schema of the GDAL VRT format</a>
is available.<p>

Virtual files stored on disk are kept in an XML format with the following
elements.<p>

<b>VRTDataset</b>: This is the root element for the whole GDAL dataset.
It must have the attributes rasterXSize and rasterYSize describing the width
and height of the dataset in pixels.
It may have a subClass attributes with values VRTWarpedDataset (\ref gdal_vrttut_warped) or
VRTPansharpenedDataset (\ref gdal_vrttut_pansharpen).
It may have SRS, GeoTransform,
GCPList, Metadata, MaskBand and VRTRasterBand subelements.

\code
<VRTDataset rasterXSize="512" rasterYSize="512">
\endcode

The allowed subelements for VRTDataset are :

<ul>

<li> <b>SRS</b>: This element contains the spatial reference system (coordinate
system) in OGC WKT format.  Note that this must be appropriately escaped for
XML, so items like quotes will have the ampersand escape sequences substituted.
As as well WKT, and valid input to the SetFromUserInput() method (such as well
known GEOGCS names, and PROJ.4 format) is also allowed in the SRS element.

\code
  <SRS dataAxisToSRSAxisMapping="1,2">PROJCS[&quot;NAD27 / UTM zone 11N&quot;,GEOGCS[&quot;NAD27&quot;,DATUM[&quot;North_American_Datum_1927&quot;,SPHEROID[&quot;Clarke 1866&quot;,6378206.4,294.9786982139006,AUTHORITY[&quot;EPSG&quot;,&quot;7008&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;6267&quot;]],PRIMEM[&quot;Greenwich&quot;,0],UNIT[&quot;degree&quot;,0.0174532925199433],AUTHORITY[&quot;EPSG&quot;,&quot;4267&quot;]],PROJECTION[&quot;Transverse_Mercator&quot;],PARAMETER[&quot;latitude_of_origin&quot;,0],PARAMETER[&quot;central_meridian&quot;,-117],PARAMETER[&quot;scale_factor&quot;,0.9996],PARAMETER[&quot;false_easting&quot;,500000],PARAMETER[&quot;false_northing&quot;,0],UNIT[&quot;metre&quot;,1,AUTHORITY[&quot;EPSG&quot;,&quot;9001&quot;]],AUTHORITY[&quot;EPSG&quot;,&quot;26711&quot;]]</SRS>
\endcode

The <i>dataAxisToSRSAxisMapping</i> attribute is allowed since GDAL 3.0 to
describe the relationship between the axis indicated in the CRS definition and
the axis of the GeoTransform or GCP metadata. The value of the attribute is a comma
separated list of integers. The number of elements of this list must be the
number of axis of the CRS. Values start at 1. If m denotes the array values of
this attribute, then m[0] is the data axis number for the first axis of the CRS.
If the attribute is missing, then the OAMS_TRADITIONAL_GIS_ORDER data axis to
CRS axis mapping strategy is implied.

</li>

<li> <b>GeoTransform</b>: This element contains a six value affine
geotransformation for the dataset, mapping between pixel/line coordinates
and georeferenced coordinates.<P>

\code
  <GeoTransform>440720.0,  60,  0.0,  3751320.0,  0.0, -60.0</GeoTransform>
\endcode
</li>

<li> <b>GCPList</b>: This element contains a list of Ground Control Points for
the dataset, mapping between pixel/line coordinates and georeferenced
coordinates. The Projection attribute should contain the SRS of the
georeferenced coordinates in the same format as the SRS element.<P>

\code
<GCPList Projection="EPSG:4326">
  <GCP Id="1" Info="a" Pixel="0.5" Line="0.5" X="0.0" Y="0.0" Z="0.0" />
  <GCP Id="2" Info="b" Pixel="13.5" Line="23.5" X="1.0" Y="2.0" Z="0.0" />
</GCPList>
\endcode
</li>

<li> <b>Metadata</b>: This element contains a list of metadata name/value
pairs associated with the VRTDataset as a whole, or a VRTRasterBand.   It has
&lt;MDI&gt; (metadata item) subelements which have a "key" attribute and the value
as the data of the element. The Metadata element can be repeated multiple times,
in which case it must be accompanied with a "domain" attribute to indicate the
name of the metadata domain.

\code
  <Metadata>
    <MDI key="md_key">Metadata value</MDI>
  </Metadata>
\endcode
</li>

<li> <b>MaskBand</b>: (GDAL >= 1.8.0) This element represents a mask band that is
shared between all bands on the dataset (see GMF_PER_DATASET in RFC 15).
It must contain a single VRTRasterBand child element, that is the description of
the mask band itself.

\code
  <MaskBand>
    <VRTRasterBand dataType="Byte">
      <SimpleSource>
        <SourceFilename relativeToVRT="1">utm.tif</SourceFilename>
        <SourceBand>mask,1</SourceBand>
        <SrcRect xOff="0" yOff="0" xSize="512" ySize="512"/>
        <DstRect xOff="0" yOff="0" xSize="512" ySize="512"/>
      </SimpleSource>
    </VRTRasterBand>
  </MaskBand>
\endcode

</li>

<li> <b>VRTRasterBand</b>: This represents one band of a dataset.  It will
have a dataType attribute with the type of the pixel data associated with
this band (use names Byte, UInt16, Int16, UInt32, Int32, Float32, Float64,
CInt16, CInt32, CFloat32 or CFloat64) and the band this element represents
(1 based).  This element may have Metadata, ColorInterp, NoDataValue, HideNoDataValue,
ColorTable, GDALRasterAttributeTable, Description and MaskBand subelements as well as the various kinds of
source elements such as SimpleSource, ComplexSource, etc.  A raster band may have many "sources"
indicating where the actual raster data should be fetched from, and how it
should be mapped into the raster bands pixel space.<p>

The allowed subelements for VRTRasterBand are :

<ul>

<li> <b>ColorInterp</b>: The data of this element should be the name of
a color interpretation type.  One of Gray, Palette, Red, Green, Blue, Alpha,
Hue, Saturation, Lightness, Cyan, Magenta, Yellow, Black, or Unknown.<p>

\code
  <ColorInterp>Gray</ColorInterp>:
\endcode
</li>

<li> <b>NoDataValue</b>: If this element exists a raster band has a
nodata value associated with, of the value given as data in the element.

\code
  <NoDataValue>-100.0</NoDataValue>
\endcode
</li>

<li> <b>HideNoDataValue</b>: If this value is 1, the nodata value will not be
reported.  Essentially, the caller will not be aware of a nodata pixel when it
reads one.  Any datasets copied/translated from this will not have a nodata
value.  This is useful when you want to specify a fixed background value for
the dataset.  The background will be the value specified by the NoDataValue
element.

Default value is 0 when this element is absent.

\code
  <HideNoDataValue>1</HideNoDataValue>
\endcode
</li>

<li> <b>ColorTable</b>: This element is parent to a set of Entry
elements defining the entries in a color table.  Currently only RGBA
color tables are supported with c1 being red, c2 being green, c3 being
blue and c4 being alpha.  The entries are ordered and will be assumed
to start from color table entry 0.

\code
    <ColorTable>
      <Entry c1="0" c2="0" c3="0" c4="255"/>
      <Entry c1="145" c2="78" c3="224" c4="255"/>
    </ColorTable>
\endcode
</li>

<li> <b>GDALRasterAttributeTable</b>: (GDAL &gt;=2.3) This element is parent
to a set of FieldDefn elements defining the columns of a raster attribute table,
followed by a set of Row element defining the values of the columns of each
row.
\code
    <GDALRasterAttributeTable>
      <FieldDefn index="0">
        <Name>Value</Name>
        <Type>0</Type>
        <Usage>0</Usage>
      </FieldDefn>
      <FieldDefn index="1">
        <Name>Red</Name>
        <Type>0</Type>
        <Usage>6</Usage>
      </FieldDefn>
      <FieldDefn index="2">
        <Name>Green</Name>
        <Type>0</Type>
        <Usage>7</Usage>
      </FieldDefn>
      <FieldDefn index="3">
        <Name>Blue</Name>
        <Type>0</Type>
        <Usage>8</Usage>
      </FieldDefn>
      <Row index="0">
        <F>-500</F>
        <F>127</F>
        <F>40</F>
        <F>65</F>
      </Row>
      <Row index="1">
        <F>-400</F>
        <F>154</F>
        <F>168</F>
        <F>118</F>
      </Row>
    </GDALRasterAttributeTable>
\endcode
</li>

<li> <b>Description</b>: This element contains the optional description
of a raster band as its text value.

\code
  <Description>Crop Classification Layer</Description>
\endcode
</li>

<li> <b>UnitType</b>: This optional element contains the vertical units for
elevation band data.  One of "m" for meters or "ft" for feet. Default
assumption is meters.<p>

\code
  <UnitType>ft</UnitType>
\endcode
</li>

<li> <b>Offset</b>: This optional element contains the offset that should be
applied when computing "real" pixel values from scaled pixel values on
a raster band.   The default is 0.0.<p>

\code
  <Offset>0.0</Offset>
\endcode
</li>

<li> <b>Scale</b>: This optional element contains the scale that should be
applied when computing "real" pixel values from scaled pixel values on a
raster band.   The default is 1.0.<p>

\code
  <Scale>0.0</Scale>
\endcode
</li>

<li> <b>Overview</b>: This optional element describes one overview level for
the band.  It should have a child SourceFilename and SourceBand element.  The
SourceFilename may have a relativeToVRT boolean attribute.  Multiple elements
may be used to describe multiple overviews. <p>

\code
    <Overview>
      <SourceFilename relativeToVRT="1">yellowstone_2.1.ntf.r2</SourceFilename>
      <SourceBand>1</SourceBand>
    </Overview>
\endcode
</li>

<li> <b>CategoryNames</b>: This optional element contains a list of Category
subelements with the names of the categories for classified raster band. <p>

\code
  <CategoryNames>
    <Category>Missing</Category>
    <Category>Non-Crop</Category>
    <Category>Wheat</Category>
    <Category>Corn</Category>
    <Category>Soybeans</Category>
  </CategoryNames>
\endcode
</li>

<li> <b>SimpleSource</b>: The SimpleSource indicates that raster data
should be read from a separate dataset, indicating the dataset, and band to be
read from, and how the data should map into this bands raster space.
The SimpleSource may have the SourceFilename, SourceBand, SrcRect, and DstRect
subelements.  The SrcRect element will indicate what rectangle on the indicated
source file should be read, and the DstRect element indicates how that
rectangle of source data should be mapped into the VRTRasterBands space.

The relativeToVRT attribute on the SourceFilename indicates whether the
filename should be interpreted as relative to the .vrt file (value is 1)
or not relative to the .vrt file (value is 0).  The default is 0.

The shared attribute, added in GDAL 2.0.0, on the SourceFilename indicates whether the
dataset should be shared (value is 1) or not (value is 0). The default is 1.
If several VRT datasets referring to the same underlying sources are used in a multithreaded context,
shared should be set to 0. Alternatively, the VRT_SHARED_SOURCE configuration
option can be set to 0 to force non-shared mode.

Some characteristics of the source band can be specified in the optional
SourceProperties tag to enable the VRT driver to differ the opening of the source
dataset until it really needs to read data from it. This is particularly useful
when building VRTs with a big number of source datasets. The needed parameters are the
raster dimensions, the size of the blocks and the data type. If the SourceProperties
tag is not present, the source dataset will be opened at the same time as the VRT itself.

Starting with GDAL 1.8.0, the content of the SourceBand subelement can refer to
a mask band. For example mask,1 means the mask band of the first band of the source.

\code
    <SimpleSource>
      <SourceFilename relativeToVRT="1">utm.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <SourceProperties RasterXSize="512" RasterYSize="512" DataType="Byte" BlockXSize="128" BlockYSize="128"/>
      <SrcRect xOff="0" yOff="0" xSize="512" ySize="512"/>
      <DstRect xOff="0" yOff="0" xSize="512" ySize="512"/>
    </SimpleSource>
\endcode

Starting with GDAL 2.0, a OpenOptions subelement can be added to specify
the open options to apply when opening the source dataset. It has &lt;OOI&gt; (open option item)
subelements which have a "key" attribute and the value as the data of the element.

\code
    <SimpleSource>
      <SourceFilename relativeToVRT="1">utm.tif</SourceFilename>
      <OpenOptions>
          <OOI key="OVERVIEW_LEVEL">0</OOI>
      </OpenOptions>
      <SourceBand>1</SourceBand>
      <SourceProperties RasterXSize="256" RasterYSize="256" DataType="Byte" BlockXSize="128" BlockYSize="128"/>
      <SrcRect xOff="0" yOff="0" xSize="256" ySize="256"/>
      <DstRect xOff="0" yOff="0" xSize="256" ySize="256"/>
    </SimpleSource>
\endcode

Starting with GDAL 2.0, a resampling attribute can be specified on a SimpleSource
or ComplexSource element to specified the resampling algorithm used when the
size of the destination rectangle is not the same as the size of the source
rectangle. The values allowed for that attribute are : nearest,bilinear,cubic,
cubicspline,lanczos,average,mode.

\code
    <SimpleSource resampling="cubic">
      <SourceFilename relativeToVRT="1">utm.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <SourceProperties RasterXSize="256" RasterYSize="256" DataType="Byte" BlockXSize="128" BlockYSize="128"/>
      <SrcRect xOff="0" yOff="0" xSize="256" ySize="256"/>
      <DstRect xOff="0" yOff="0" xSize="128" ySize="128"/>
    </SimpleSource>
\endcode

</li>

<li> <b>AveragedSource</b>: The AveragedSource is derived from the
SimpleSource and shares the same properties except that it uses an averaging
resampling instead of a nearest neighbour algorithm as in SimpleSource, when
the size of the destination rectangle is not the same as the size of the source
rectangle. Note: starting with GDAL 2.0, a more general mechanism to specify
resampling algorithms can be used. See above paragraph about the 'resampling' attribute.

<li> <b>ComplexSource</b>: The ComplexSource is derived from the
SimpleSource (so it shares the SourceFilename, SourceBand, SrcRect and
DestRect elements), but it provides support to rescale and offset
the range of the source values. Certain regions of the source
can be masked by specifying the NODATA value.

Starting with GDAL 1.11, alternatively to linear scaling, non-linear
scaling using a power function can be used by specifying the Exponent,
SrcMin, SrcMax, DstMin and DstMax elements. If SrcMin and SrcMax are
not specified, they are computed from the source minimum and maximum
value (which might require analyzing the whole source dataset). Exponent
must be positive. (Those 5 values can be set with the -exponent and -scale
options of gdal_translate.)

The ComplexSource supports adding a custom lookup table to transform
the source values to the destination. The LUT can be specified using
the following form:

\code
    <LUT>[src value 1]:[dest value 1],[src value 2]:[dest value 2],...</LUT>
\endcode

The intermediary values are calculated using a linear interpolation
between the bounding destination values of the corresponding range.

The ComplexSource supports fetching a color component from a source raster
band that has a color table. The ColorTableComponent value is the index of the
color component to extract : 1 for the red band, 2 for the green band, 3 for
the blue band or 4 for the alpha band.

When transforming the source values the operations are executed
in the following order:

<ol>
<li>Nodata masking</li>
<li>Color table expansion</li>
<li>For linear scaling, applying the scale ratio, then scale offset</li>
<li>For non-linear scaling, apply (DstMax-DstMin) * pow( (SrcValue-SrcMin) / (SrcMax-SrcMin), Exponent) + DstMin</li>
<li>Table lookup</li>
</ol>

\code
    <ComplexSource>
      <SourceFilename relativeToVRT="1">utm.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <ScaleOffset>0</ScaleOffset>
      <ScaleRatio>1</ScaleRatio>
      <ColorTableComponent>1</ColorTableComponent>
      <LUT>0:0,2345.12:64,56789.5:128,2364753.02:255</LUT>
      <NODATA>0</NODATA>
      <SrcRect xOff="0" yOff="0" xSize="512" ySize="512"/>
      <DstRect xOff="0" yOff="0" xSize="512" ySize="512"/>
    </ComplexSource>
\endcode

Non-linear scaling:

\code
    <ComplexSource>
      <SourceFilename relativeToVRT="1">16bit.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <Exponent>0.75</Exponent>
      <SrcMin>0</SrcMin>
      <SrcMax>65535</SrcMax>
      <DstMin>0</DstMin>
      <DstMax>255</DstMax>
      <SrcRect xOff="0" yOff="0" xSize="512" ySize="512"/>
      <DstRect xOff="0" yOff="0" xSize="512" ySize="512"/>
    </ComplexSource>
\endcode

</li>

<li> <b>KernelFilteredSource</b>: This is a pixel source derived from the
Simple Source (so it shares the SourceFilename, SourceBand, SrcRect and
DestRect elements, but it also passes the data through a simple filtering
kernel specified with the Kernel element.  The Kernel element should have
two child elements, Size and Coefs and optionally the boolean attribute
normalized (defaults to false=0).  The size must always be an odd number,
and the Coefs must have Size * Size entries separated by spaces.  For now
kernel is not applied to sub-sampled or over-sampled data.

\code
    <KernelFilteredSource>
      <SourceFilename>/debian/home/warmerda/openev/utm.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <Kernel normalized="1">
        <Size>3</Size>
        <Coefs>0.11111111 0.11111111 0.11111111 0.11111111 0.11111111 0.11111111 0.11111111 0.11111111 0.11111111</Coefs>
      </Kernel>
    </KernelFilteredSource>
\endcode

Starting with GDAL 2.3, a separable kernel may also be used.  In this case the
number of Coefs entries should correspond to the Size.  The Coefs specify a
one-dimensional kernel which is applied along each axis in succession, resulting
in far quicker execution. Many common image-processing filters are separable.
For example, a Gaussian blur:

\code
    <KernelFilteredSource>
      <SourceFilename>/debian/home/warmerda/openev/utm.tif</SourceFilename>
      <SourceBand>1</SourceBand>
      <Kernel normalized="1">
        <Size>13</Size>
        <Coefs>0.01111 0.04394 0.13534 0.32465 0.60653 0.8825 1.0 0.8825 0.60653 0.32465 0.13534 0.04394 0.01111</Coefs>
      </Kernel>
    </KernelFilteredSource>
\endcode
</li>

<li> <b>MaskBand</b>: (GDAL >= 1.8.0) This element represents a mask band that is
specific to the VRTRasterBand it contains. It must contain a single VRTRasterBand
child element, that is the description of the mask band itself.
</li>

</ul>

</ul>

\section gdal_vrttut_overviews Overviews

GDAL can make efficient use of overviews available in the sources that compose
the bands when dealing with RasterIO() requests that involve downsampling.
But in the general case, the VRT bands themselves will not expose overviews.

Except if (from top priority to lesser priority) :
<ol>
<li>The <b>Overview</b> element is present in the VRTRasterBand element. See above.
</li>
<li>or external .vrt.ovr overviews are built</li>
<li>(starting with GDAL 2.1) if the VRTRasterBand are made of a single SimpleSource
or ComplexSource that has overviews. Those "virtual" overviews will be hidden
by external .vrt.ovr overviews that might be built later.</li>
</ol>

\section gdal_vrttut_raw .vrt Descriptions for Raw Files

So far we have described how to derive new virtual datasets from existing
files supports by GDAL.  However, it is also common to need to utilize
raw binary raster files for which the regular layout of the data is known
but for which no format specific driver exists.  This can be accomplished
by writing a .vrt file describing the raw file.

For example, the following .vrt describes a raw raster file containing
floating point complex pixels in a file called <i>l2p3hhsso.img</i>.  The
image data starts from the first byte (ImageOffset=0).  The byte offset
between pixels is 8 (PixelOffset=8), the size of a CFloat32.  The byte offset
from the start of one line to the start of the next is 9376 bytes
(LineOffset=9376) which is the width (1172) times the size of a pixel (8).

\code
<VRTDataset rasterXSize="1172" rasterYSize="1864">
  <VRTRasterBand dataType="CFloat32" band="1" subClass="VRTRawRasterBand">
    <SourceFilename relativetoVRT="1">l2p3hhsso.img</SourceFilename>
    <ImageOffset>0</ImageOffset>
    <PixelOffset>8</PixelOffset>
    <LineOffset>9376</LineOffset>
    <ByteOrder>MSB</ByteOrder>
  </VRTRasterBand>
</VRTDataset>
\endcode

Some things to note are that the VRTRasterBand has a subClass specifier
of "VRTRawRasterBand".  Also, the VRTRawRasterBand contains a number of
previously unseen elements but no "source" information.  VRTRawRasterBands
may never have sources (i.e. SimpleSource), but should contain the following
elements in addition to all the normal "metadata" elements previously
described which are still supported.

<ul>

<li> <b>SourceFilename</b>: The name of the raw file containing the
data for this band.  The relativeToVRT attribute can be used to indicate
if the SourceFilename is relative to the .vrt file (1) or not (0).

<li> <b>ImageOffset</b>: The offset in bytes to the beginning of the first
pixel of data of this image band.   Defaults to zero.

<li> <b>PixelOffset</b>: The offset in bytes from the beginning of one
pixel and the next on the same line.  In packed single band data this will
be the size of the <b>dataType</b> in bytes.

<li> <b>LineOffset</b>: The offset in bytes from the beginning of one
scanline of data and the next scanline of data.  In packed single band
data this will be PixelOffset * rasterXSize.

<li> <b>ByteOrder</b>: Defines the byte order of the data on disk.
Either LSB (Least Significant Byte first) such as the natural byte order
on Intel x86 systems or MSB (Most Significant Byte first) such as the natural
byte order on Motorola or Sparc systems.  Defaults to being the local machine
order.

</ul>

A few other notes:

<ul>

<li> The image data on disk is assumed to be of the same data type as
the band <b>dataType</b> of the VRTRawRasterBand.

<li> All the non-source attributes of the VRTRasterBand are supported,
including color tables, metadata, nodata values, and color interpretation.

<li> The VRTRawRasterBand supports in place update of the raster, whereas
the source based VRTRasterBand is always read-only.

<li> The OpenEV tool includes a File menu option to input parameters
describing a raw raster file in a GUI and create the corresponding .vrt
file.

<li> Multiple bands in the one .vrt file can come from the same raw file.
Just ensure that the ImageOffset, PixelOffset, and LineOffset definition
for each band is appropriate for the pixels of that particular band.

</ul>

Another example, in this case a 400x300 RGB pixel interleaved image.

\code
<VRTDataset rasterXSize="400" rasterYSize="300">
  <VRTRasterBand dataType="Byte" band="1" subClass="VRTRawRasterBand">
    <ColorInterp>Red</ColorInterp>
    <SourceFilename relativetoVRT="1">rgb.raw</SourceFilename>
    <ImageOffset>0</ImageOffset>
    <PixelOffset>3</PixelOffset>
    <LineOffset>1200</LineOffset>
  </VRTRasterBand>
  <VRTRasterBand dataType="Byte" band="2" subClass="VRTRawRasterBand">
    <ColorInterp>Green</ColorInterp>
    <SourceFilename relativetoVRT="1">rgb.raw</SourceFilename>
    <ImageOffset>1</ImageOffset>
    <PixelOffset>3</PixelOffset>
    <LineOffset>1200</LineOffset>
  </VRTRasterBand>
  <VRTRasterBand dataType="Byte" band="3" subClass="VRTRawRasterBand">
    <ColorInterp>Blue</ColorInterp>
    <SourceFilename relativetoVRT="1">rgb.raw</SourceFilename>
    <ImageOffset>2</ImageOffset>
    <PixelOffset>3</PixelOffset>
    <LineOffset>1200</LineOffset>
  </VRTRasterBand>
</VRTDataset>
\endcode

\section gdal_vrttut_creation Programmatic Creation of VRT Datasets

The VRT driver supports several methods of creating VRT datasets.  As of
GDAL 1.2.0 the vrtdataset.h include file should be installed with the core
GDAL include files, allowing direct access to the VRT classes.  However,
even without that most capabilities remain available through standard GDAL
interfaces.<p>

To create a VRT dataset that is a clone of an existing dataset use the
CreateCopy() method.  For example to clone utm.tif into a wrk.vrt file in
C++ the following could be used:

\code
  GDALDriver *poDriver = (GDALDriver *) GDALGetDriverByName( "VRT" );
  GDALDataset *poSrcDS, *poVRTDS;

  poSrcDS = (GDALDataset *) GDALOpenShared( "utm.tif", GA_ReadOnly );

  poVRTDS = poDriver->CreateCopy( "wrk.vrt", poSrcDS, FALSE, NULL, NULL, NULL );

  GDALClose((GDALDatasetH) poVRTDS);
  GDALClose((GDALDatasetH) poSrcDS);
\endcode

Note the use of GDALOpenShared() when opening the source dataset. It is advised
to use GDALOpenShared() in this situation so that you are able to release
the explicit reference to it before closing the VRT dataset itself. In other
words, in the previous example, you could also invert the 2 last lines, whereas
if you open the source dataset with GDALOpen(), you'd need to close the VRT dataset
before closing the source dataset.

To create a virtual copy of a dataset with some attributes added or changed
such as metadata or coordinate system that are often hard to change on other
formats, you might do the following.  In this case, the virtual dataset is
created "in memory" only by virtual of creating it with an empty filename, and
then used as a modified source to pass to a CreateCopy() written out in TIFF
format.

\code
  poVRTDS = poDriver->CreateCopy( "", poSrcDS, FALSE, NULL, NULL, NULL );

  poVRTDS->SetMetadataItem( "SourceAgency", "United States Geological Survey");
  poVRTDS->SetMetadataItem( "SourceDate", "July 21, 2003" );

  poVRTDS->GetRasterBand( 1 )->SetNoDataValue( -999.0 );

  GDALDriver *poTIFFDriver = (GDALDriver *) GDALGetDriverByName( "GTiff" );
  GDALDataset *poTiffDS;

  poTiffDS = poTIFFDriver->CreateCopy( "wrk.tif", poVRTDS, FALSE, NULL, NULL, NULL );

  GDALClose((GDALDatasetH) poTiffDS);
\endcode

In the above example the nodata value is set as -999. You can set the
HideNoDataValue element in the VRT dataset's band using SetMetadataItem() on
that band.

\code
  poVRTDS->GetRasterBand( 1 )->SetMetadataItem( "HideNoDataValue" , "1" );
\endcode

In this example a virtual dataset is created with the Create() method, and
adding bands and sources programmatically, but still via the "generic" API.
A special attribute of VRT datasets is that sources can be added to the VRTRasterBand
(but not to VRTRawRasterBand) by passing the XML describing the source into SetMetadata() on the special
domain target "new_vrt_sources".  The domain target "vrt_sources" may also be
used, in which case any existing sources will be discarded before adding the
new ones.  In this example we construct a simple averaging filter source
instead of using the simple source.

\code
  // construct XML for simple 3x3 average filter kernel source.
  const char *pszFilterSourceXML  =
"<KernelFilteredSource>"
"  <SourceFilename>utm.tif</SourceFilename><SourceBand>1</SourceBand>"
"  <Kernel>"
"    <Size>3</Size>"
"    <Coefs>0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111</Coefs>"
"  </Kernel>"
"</KernelFilteredSource>";

  // Create the virtual dataset.
  poVRTDS = poDriver->Create( "", 512, 512, 1, GDT_Byte, NULL );
  poVRTDS->GetRasterBand(1)->SetMetadataItem("source_0",pszFilterSourceXML,
                                             "new_vrt_sources");
\endcode

A more general form of this that will produce a 3x3 average filtered clone
of any input datasource might look like the following.  In this case we
deliberately set the filtered datasource as in the "vrt_sources" domain
to override the SimpleSource created by the CreateCopy() method.  The fact
that we used CreateCopy() ensures that all the other metadata, georeferencing
and so forth is preserved from the source dataset ... the only thing we are
changing is the data source for each band.

\code
  int   nBand;
  GDALDriver *poDriver = (GDALDriver *) GDALGetDriverByName( "VRT" );
  GDALDataset *poSrcDS, *poVRTDS;

  poSrcDS = (GDALDataset *) GDALOpenShared( pszSourceFilename, GA_ReadOnly );

  poVRTDS = poDriver->CreateCopy( "", poSrcDS, FALSE, NULL, NULL, NULL );

  for( nBand = 1; nBand <= poVRTDS->GetRasterCount(); nBand++ )
  {
      char szFilterSourceXML[10000];

      GDALRasterBand *poBand = poVRTDS->GetRasterBand( nBand );

      sprintf( szFilterSourceXML,
	"<KernelFilteredSource>"
	"  <SourceFilename>%s</SourceFilename><SourceBand>%d</SourceBand>"
	"  <Kernel>"
	"    <Size>3</Size>"
	"    <Coefs>0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111</Coefs>"
	"  </Kernel>"
	"</KernelFilteredSource>",
	pszSourceFilename, nBand );

      poBand->SetMetadataItem( "source_0", szFilterSourceXML, "vrt_sources" );
  }
\endcode

The VRTDataset class is one of the few dataset implementations that supports the AddBand()
method. The options passed to the AddBand() method can be used to control the type of the
band created (VRTRasterBand, VRTRawRasterBand, VRTDerivedRasterBand), and in the case of
the VRTRawRasterBand to set its various parameters. For standard VRTRasterBand, sources
should be specified with the above SetMetadata() / SetMetadataItem() examples.

\code
  GDALDriver *poDriver = (GDALDriver *) GDALGetDriverByName( "VRT" );
  GDALDataset *poVRTDS;

  poVRTDS = poDriver->Create( "out.vrt", 512, 512, 0, GDT_Byte, NULL );
  char** papszOptions = NULL;
  papszOptions = CSLAddNameValue(papszOptions, "subclass", "VRTRawRasterBand"); // if not specified, default to VRTRasterBand
  papszOptions = CSLAddNameValue(papszOptions, "SourceFilename", "src.tif"); // mandatory
  papszOptions = CSLAddNameValue(papszOptions, "ImageOffset", "156"); // optional. default = 0
  papszOptions = CSLAddNameValue(papszOptions, "PixelOffset", "2"); // optional. default = size of band type
  papszOptions = CSLAddNameValue(papszOptions, "LineOffset", "1024"); // optional. default = size of band type * width
  papszOptions = CSLAddNameValue(papszOptions, "ByteOrder", "LSB"); // optional. default = machine order
  papszOptions = CSLAddNameValue(papszOptions, "relativeToVRT", "true"); // optional. default = false
  poVRTDS->AddBand(GDT_Byte, papszOptions);
  CSLDestroy(papszOptions);

  delete poVRTDS;
\endcode

\section gdal_vrttut_derived_c Using Derived Bands (with pixel functions in C/C++)

A specialized type of band is a 'derived' band which derives its pixel
information from its source bands.  With this type of band you must also
specify a pixel function, which has the responsibility of generating the
output raster.  Pixel functions are created by an application and then
registered with GDAL using a unique key.

Using derived bands you can create VRT datasets that manipulate bands on
the fly without having to create new band files on disk.  For example, you
might want to generate a band using four source bands from a nine band input
dataset (x0, x3, x4, and x8):

\code
  band_value = sqrt((x3*x3+x4*x4)/(x0*x8));
\endcode

You could write the pixel function to compute this value and then register
it with GDAL with the name "MyFirstFunction".  Then, the following VRT XML
could be used to display this derived band:

\code
<VRTDataset rasterXSize="1000" rasterYSize="1000">
  <VRTRasterBand dataType="Float32" band="1" subClass="VRTDerivedRasterBand">
    <Description>Magnitude</Description>
    <PixelFunctionType>MyFirstFunction</PixelFunctionType>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">nine_band.dat</SourceFilename>
      <SourceBand>1</SourceBand>
      <SrcRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
      <DstRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
    </SimpleSource>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">nine_band.dat</SourceFilename>
      <SourceBand>4</SourceBand>
      <SrcRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
      <DstRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
    </SimpleSource>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">nine_band.dat</SourceFilename>
      <SourceBand>5</SourceBand>
      <SrcRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
      <DstRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
    </SimpleSource>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">nine_band.dat</SourceFilename>
      <SourceBand>9</SourceBand>
      <SrcRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
      <DstRect xOff="0" yOff="0" xSize="1000" ySize="1000"/>
    </SimpleSource>
  </VRTRasterBand>
</VRTDataset>
\endcode

In addition to the subclass specification (VRTDerivedRasterBand) and
the PixelFunctionType value, there is another new parameter that can come
in handy: SourceTransferType.  Typically the source rasters are obtained
using the data type of the derived band.  There might be times,
however, when you want the pixel function to have access to
higher resolution source data than the data type being generated.
For example, you might have a derived band of type "Float", which takes
a single source of type "CFloat32" or "CFloat64", and returns the imaginary
portion.  To accomplish this, set the SourceTransferType to "CFloat64".
Otherwise the source would be converted to "Float" prior to
calling the pixel function, and the imaginary portion would be lost.

\code
<VRTDataset rasterXSize="1000" rasterYSize="1000">
  <VRTRasterBand dataType="Float32" band="1" subClass="VRTDerivedRasterBand">
    <Description>Magnitude</Description>
    <PixelFunctionType>MyFirstFunction</PixelFunctionType>
    <SourceTransferType>CFloat64</SourceTransferType>
    ...
\endcode

\subsection gdal_vrttut_derived_default_c_pixel_functions Default Pixel Functions

Starting with GDAL 2.2, GDAL provides a set of default pixel functions that can be used without writing new code:

<ul>
<li><b>"real": </b> extract real part from a single raster band (just a copy if the input is non-complex)
<li><b>"imag": </b>
    extract imaginary part from a single raster band (0 for non-complex)
<li><b> "complex":   </b> make a complex band merging two bands used as real and imag values
<li><b> "mod":       </b> extract module from a single raster band (real or complex)
<li><b> "phase":     </b> extract phase from a single raster band [-PI,PI] (0 or PI for non-complex)
<li><b> "conj":      </b> computes the complex conjugate of a single raster band (just a copy if the input is non-complex)
<li><b> "sum":       </b> sum 2 or more raster bands
<li><b> "diff":      </b> computes the difference between 2 raster bands (b1 - b2)
<li><b> "mul":       </b> multiply 2 or more raster bands
<li><b> "cmul":      </b> multiply the first band for the complex conjugate of the second
<li><b> "inv":       </b>  inverse (1./x). Note: no check is performed on zero division
<li><b> "intensity": </b> computes the intensity Re(x*conj(x)) of a single raster band (real or complex)
<li><b> "sqrt":      </b> perform the square root of a single raster band (real only)
<li><b> "log10":     </b> compute the logarithm (base 10) of the abs of a single raster band (real or complex): log10( abs( x ) )
<li><b> "dB":        </b> perform conversion to dB of the abs of a single raster band (real or complex): 20. * log10( abs( x ) )
<li><b> "dB2amp":    </b> perform scale conversion from logarithmic to linear (amplitude) (i.e. 10 ^ ( x / 20 ) ) of a single raster band (real only)
<li><b> "dB2pow":    </b> perform scale conversion from logarithmic to linear (power) (i.e. 10 ^ ( x / 10 ) ) of a single raster band (real only)
</ul>

\subsection gdal_vrttut_derived_c_pixel_functions Writing Pixel Functions

To register this function with GDAL (prior to accessing any VRT datasets
with derived bands that use this function), an application calls
GDALAddDerivedBandPixelFunc with a key and a GDALDerivedPixelFunc:

\code
    GDALAddDerivedBandPixelFunc("MyFirstFunction", TestFunction);
\endcode

A good time to do this is at the beginning of an application when the
GDAL drivers are registered.

GDALDerivedPixelFunc is defined with a signature similar to IRasterIO:

@param papoSources A pointer to packed rasters; one per source.  The
datatype of all will be the same, specified in the eSrcType parameter.

@param nSources The number of source rasters.

@param pData The buffer into which the data should be read, or from which
it should be written.  This buffer must contain at least nBufXSize *
nBufYSize words of type eBufType.  It is organized in left to right,
top to bottom pixel order.  Spacing is controlled by the nPixelSpace,
and nLineSpace parameters.

@param nBufXSize The width of the buffer image into which the desired
region is to be read, or from which it is to be written.

@param nBufYSize The height of the buffer image into which the desired
region is to be read, or from which it is to be written.

@param eSrcType The type of the pixel values in the papoSources raster
array.

@param eBufType The type of the pixel values that the pixel function must
generate in the pData data buffer.

@param nPixelSpace The byte offset from the start of one pixel value in
pData to the start of the next pixel value within a scanline.  If
defaulted (0) the size of the datatype eBufType is used.

@param nLineSpace The byte offset from the start of one scanline in
pData to the start of the next.

@return CE_Failure on failure, otherwise CE_None.

\code
typedef CPLErr
(*GDALDerivedPixelFunc)(void **papoSources, int nSources, void *pData,
			int nXSize, int nYSize,
			GDALDataType eSrcType, GDALDataType eBufType,
                        int nPixelSpace, int nLineSpace);
\endcode

The following is an implementation of the pixel function:

\code
#include "gdal.h"

CPLErr TestFunction(void **papoSources, int nSources, void *pData,
		    int nXSize, int nYSize,
		    GDALDataType eSrcType, GDALDataType eBufType,
		    int nPixelSpace, int nLineSpace)
{
    int ii, iLine, iCol;
    double pix_val;
    double x0, x3, x4, x8;

    // ---- Init ----
    if (nSources != 4) return CE_Failure;

    // ---- Set pixels ----
    for( iLine = 0; iLine < nYSize; iLine++ )
    {
        for( iCol = 0; iCol < nXSize; iCol++ )
        {
            ii = iLine * nXSize + iCol;
            /* Source raster pixels may be obtained with SRCVAL macro */
            x0 = SRCVAL(papoSources[0], eSrcType, ii);
            x3 = SRCVAL(papoSources[1], eSrcType, ii);
            x4 = SRCVAL(papoSources[2], eSrcType, ii);
            x8 = SRCVAL(papoSources[3], eSrcType, ii);

            pix_val = sqrt((x3*x3+x4*x4)/(x0*x8));

            GDALCopyWords(&pix_val, GDT_Float64, 0,
                          ((GByte *)pData) + nLineSpace * iLine + iCol * nPixelSpace,
                          eBufType, nPixelSpace, 1);
        }
    }

    // ---- Return success ----
    return CE_None;
}
\endcode

\section gdal_vrttut_derived_python Using Derived Bands (with pixel functions in Python)

Starting with GDAL 2.2, in addition to pixel functions written in C/C++ as
documented in the \ref gdal_vrttut_derived_c section, it is possible to use
pixel functions written in Python. Both
<a href="https://www.python.org/">CPython</a>
and <a href="http://www.numpy.org/">NumPy</a> are requirements at run-time.

The subelements for VRTRasterBand (whose subclass specification must be
set to VRTDerivedRasterBand) are :
<ul>

<li> <i>PixelFunctionType</i> (required): Must be set to a function
name that will be defined as a inline Python module in PixelFunctionCode
element or as the form "module_name.function_name" to refer to a function in an
external Python module</li>

<li> <i>PixelFunctionLanguage</i> (required): Must be set to Python.</li>

<li> <i>PixelFunctionArguments</i> (optional): It is possible to pass
arguments to the Python pixel function by defining attributes in the
PixelFunctionArguments element.</li>

<li> <i>PixelFunctionCode</i> (required if PixelFunctionType is of the form
"function_name", ignored otherwise). The in-lined code of a Python module, that
must be at least have a function whose name is given by PixelFunctionType.</li>

<li> <i>BufferRadius</i> (optional, defaults to 0): Amount of extra pixels, with
respect to the original RasterIO() request to satisfy, that are fetched at the
left, right, bottom and top of the input and output buffers passed to the pixel
function. Note that the values of the output buffer in this buffer zone will
be ignored.</li>

</ul>

The signature of the Python pixel function must have the following arguments:
<ol>
<li> <i>in_ar</i>: list of input NumPy arrays (one NumPy array for each
source)</li>
<li> <i>out_ar</i>: output NumPy array to fill. The array is initialized at the
right dimensions and with the VRTRasterBand.dataType.</li>
<li> <i>xoff</i>: pixel offset to the top left corner of the accessed region
of the band. Generally not needed except if the processing depends on the
pixel position in the raster.</li>
<li> <i>yoff</i> line offset to the top left corner of the accessed region of
the band. Generally not needed.</li>
<li> <i>xsize</i>: width of the region of the accessed region of the band.
Can be used together with out_ar.shape[1] to determine the horizontal
resampling ratio of the request.</li>
<li> <i>ysize</i>: height of the region of the accessed region of the band.
Can be used together with out_ar.shape[0] to determine the vertical
resampling ratio of the request.</li>
<li> <i>raster_xsize</i>: total with of the raster band. Generally not
needed.</li>
<li> <i>raster_ysize</i>: total with of the raster band. Generally not
needed.</li>
<li> <i>buf_radius</i>: radius of the buffer (in pixels) added to the left,
right, top and bottom of in_ar / out_ar. This is the value of the optional
BufferRadius element that can be set so that the original pixel request is
extended by a given amount of pixels.</li>
<li> <i>gt</i>: geotransform. Array of 6 double values.</li>
<li> <i>kwargs</i>: dictionary with user arguments defined in
PixelFunctionArguments</li>
</ol>

\subsection gdal_vrttut_derived_python_examples Examples

<ul>

<li>VRT that multiplies the values of the source file by a factor of 1.5

\code
<VRTDataset rasterXSize="20" rasterYSize="20">
  <SRS>EPSG:26711</SRS>
  <GeoTransform>440720,60,0,3751320,0,-60</GeoTransform>
  <VRTRasterBand dataType="Byte" band="1" subClass="VRTDerivedRasterBand">
    <PixelFunctionType>multiply</PixelFunctionType>
    <PixelFunctionLanguage>Python</PixelFunctionLanguage>
    <PixelFunctionArguments factor="1.5"/>
    <PixelFunctionCode><![CDATA[
import numpy as np
def multiply(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize,
                   raster_ysize, buf_radius, gt, **kwargs):
    factor = float(kwargs['factor'])
    out_ar[:] = np.round_(np.clip(in_ar[0] * factor,0,255))
]]>
    </PixelFunctionCode>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">byte.tif</SourceFilename>
    </SimpleSource>
  </VRTRasterBand>
</VRTDataset>
\endcode

</li>

<li>VRT that adds 2 (or more) rasters

\code
<VRTDataset rasterXSize="20" rasterYSize="20">
  <SRS>EPSG:26711</SRS>
  <GeoTransform>440720,60,0,3751320,0,-60</GeoTransform>
  <VRTRasterBand dataType="Byte" band="1" subClass="VRTDerivedRasterBand">
    <PixelFunctionType>add</PixelFunctionType>
    <PixelFunctionLanguage>Python</PixelFunctionLanguage>
    <PixelFunctionCode><![CDATA[
import numpy as np
def add(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize,
                   raster_ysize, buf_radius, gt, **kwargs):
    np.round_(np.clip(np.sum(in_ar, axis = 0, dtype = 'uint16'),0,255),
              out = out_ar)
]]>
    </PixelFunctionCode>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">byte.tif</SourceFilename>
    </SimpleSource>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">byte2.tif</SourceFilename>
    </SimpleSource>
  </VRTRasterBand>
</VRTDataset>
\endcode

</li>

<li>VRT that computes hillshading using an external library

\code
<VRTDataset rasterXSize="121" rasterYSize="121">
  <SRS>EPSG:4326</SRS>
  <GeoTransform>-80.004166666666663,0.008333333333333,0,
44.004166666666663,0,-0.008333333333333</GeoTransform>
  <VRTRasterBand dataType="Byte" band="1" subClass="VRTDerivedRasterBand">
    <ColorInterp>Gray</ColorInterp>
    <SimpleSource>
      <SourceFilename relativeToVRT="1">n43.dt0</SourceFilename>
    </SimpleSource>
    <PixelFunctionLanguage>Python</PixelFunctionLanguage>
    <PixelFunctionType>hillshading.hillshade</PixelFunctionType>
    <PixelFunctionArguments scale="111120" z_factor="30" />
    <BufferRadius>1</BufferRadius>
    <SourceTransferType>Int16</SourceTransferType>
  </VRTRasterBand>
</VRTDataset>
\endcode

with hillshading.py:

\code
# Licence: X/MIT
# Copyright 2016, Even Rouault
import math

def hillshade_int(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize,
                         raster_ysize, radius, gt, z, scale):
    ovr_scale_x = float(out_ar.shape[1] - 2 * radius) / xsize
    ovr_scale_y = float(out_ar.shape[0] - 2 * radius) / ysize
    ewres = gt[1] / ovr_scale_x
    nsres = gt[5] / ovr_scale_y
    inv_nsres = 1.0 / nsres
    inv_ewres = 1.0 / ewres

    az = 315
    alt = 45
    degreesToRadians = math.pi / 180

    sin_alt = math.sin(alt * degreesToRadians)
    azRadians = az * degreesToRadians
    z_scale_factor = z / (8 * scale)
    cos_alt_mul_z_scale_factor = \
              math.cos(alt * degreesToRadians) * z_scale_factor
    cos_az_mul_cos_alt_mul_z_scale_factor_mul_254 = \
                254 * math.cos(azRadians) * cos_alt_mul_z_scale_factor
    sin_az_mul_cos_alt_mul_z_scale_factor_mul_254 = \
                254 * math.sin(azRadians) * cos_alt_mul_z_scale_factor
    square_z_scale_factor = z_scale_factor * z_scale_factor
    sin_alt_mul_254 = 254.0 * sin_alt

    for j in range(radius, out_ar.shape[0]-radius):
        win_line = in_ar[0][j-radius:j+radius+1,:]
        for i in range(radius, out_ar.shape[1]-radius):
            win = win_line[:,i-radius:i+radius+1].tolist()
            x = inv_ewres * ((win[0][0] + win[1][0] + win[1][0] + win[2][0])-\
                             (win[0][2] + win[1][2] + win[1][2] + win[2][2])) 
            y = inv_nsres * ((win[2][0] + win[2][1] + win[2][1] + win[2][2])-\
                             (win[0][0] + win[0][1] + win[0][1] + win[0][2]))
            xx_plus_yy = x * x + y * y
            cang_mul_254 = (sin_alt_mul_254 - \
                (y * cos_az_mul_cos_alt_mul_z_scale_factor_mul_254 - \
                    x * sin_az_mul_cos_alt_mul_z_scale_factor_mul_254)) / \
                math.sqrt(1 + square_z_scale_factor * xx_plus_yy)
            if cang_mul_254 < 0:
                out_ar[j,i] = 1
            else:
                out_ar[j,i] = 1 + round(cang_mul_254)

def hillshade(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize, 
              raster_ysize, radius, gt, **kwargs):
    z = float(kwargs['z_factor'])
    scale= float(kwargs['scale'])
    hillshade_int(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize,
                  raster_ysize, radius, gt, z, scale)
\endcode

</li>

\subsection gdal_vrttut_derived_python_python_module_path Python module path

When importing modules from inline Python code or when relying on out-of-line
code (PixelFunctionType of the form "module_name.function_name"), you need
to make sure the modules are accessible through the python path. Note that
contrary to the Python interactive interpreter, the current path is not
automatically added when used from GDAL. So you may need to define the
PYTHONPATH environment variable if you get ModuleNotFoundError exceptions.

\subsection gdal_vrttut_derived_python_security Security implications

The ability to run Python code potentially opens the door to many potential
vulnerabilities if the user of GDAL may process untrusted datasets. To avoid
such issues, by default, execution of Python pixel function will be disabled.
The execution policy can be controlled with the GDAL_VRT_ENABLE_PYTHON
configuration option, which can accept 3 values:
<ul>
<li>YES: all VRT scripts are considered as trusted and their Python pixel
functions will be run when pixel operations are involved.</li>
<li>NO: all VRT scripts are considered untrusted, and none Python pixel
function will be run.</li>
<li>TRUSTED_MODULES (default setting): all VRT scripts with inline Python
code in their PixelFunctionCode elements will be considered untrusted and will
not be run. VRT scripts that use a PixelFunctionType of the form
"module_name.function_name" will be considered as trusted, only if "module_name"
is allowed in the GDAL_VRT_TRUSTED_MODULES configuration option. The value of
this configuration option is a comma separated listed of trusted module names.
The '*' wildcard can be used at the name of a string to match all strings beginning
with the substring before the '*' character. For example 'every*' will make
'every.thing' or 'everything' module trusted. '*' can also be used to make all
modules to be trusted.
The ".*" wildcard can also be used to match exact modules or submodules names.
For example 'every.*' will make 'every' and 'every.thing' modules trusted, but
not 'everything'.</li>
</ul>

\subsection gdal_vrttut_derived_python_interpreter Linking mechanism to a Python interpreter.

Currently only CPython - 2.6, 2.7 and 3.x - is supported. The GDAL shared object
is not explicitly linked at build time to any of the CPython library. When GDAL
will need to run Python code, it will first determine if the Python interpreter
is loaded in the current process (which is the case if the program is a Python
interpreter itself, or if another program, e.g. QGIS, has already loaded the
CPython library). Otherwise it will look if the PYTHONSO configuration option is
defined. This option can be set to point to the name of the Python library to
use, either as a shortname like "libpython2.7.so" if it is accessible through
the Linux dynamic loader (so typically in one of the paths in /etc/ld.so.conf or
LD_LIBRARY_PATH) or as a full path name like "/usr/lib/x86_64-linux-gnu/libpython2.7.so".
The same holds on Windows will shortnames like "python27.dll" if accessible through
the PATH or full path names like "c:\python27\python27.dll". If the PYTHONSO
configuration option is not defined, it will look for a "python" binary in the
directories of the PATH and will try to determine the related shared object
(it will retry with "python3" if no "python" has been found). If the above
was not successful, then a predefined list of shared objects names
will be tried. At the time of writing, the order of versions searched is 2.7,
2.6, 3.4, 3.5, 3.6, 3.3, 3.2. Enabling debug information (CPL_DEBUG=VRT) will
show which Python version is used.

\subsection gdal_vrttut_derived_python_jit Just-in-time compilation

The use of a just-in-time compiler may significantly speed up execution times.
<a href="http://numba.pydata.org/">Numba</a> has been successfully tested. For
better performance, it is recommended to use a offline pixel function so that
the just-in-time compiler may cache its compilation.

Given the following mandelbrot.py file :

\code
# Trick for compatibility with and without numba
try:
    from numba import jit
    #print('Using numba')
    g_max_iterations = 100
except:
    class jit(object):
        def __init__(self, nopython = True, nogil = True):
            pass

        def __call__(self, f):
            return f

    #print('Using non-JIT version')
    g_max_iterations = 25

# Use a wrapper for the entry point regarding GDAL, since GDAL cannot access
# the jit decorated function with the expected signature.
def mandelbrot(in_ar, out_ar, xoff, yoff, xsize, ysize, raster_xsize,
                        raster_ysize, r, gt, **kwargs):
    mandelbrot_jit(out_ar, xoff, yoff, xsize, ysize, raster_xsize, raster_ysize, 
g_max_iterations)

# Will make sure that the code is compiled to pure native code without Python
# fallback.
@jit(nopython=True, nogil=True, cache=True)
def mandelbrot_jit(out_ar, xoff, yoff, xsize, ysize, raster_xsize,
                        raster_ysize, max_iterations):
    ovr_factor_y = float(out_ar.shape[0]) / ysize
    ovr_factor_x = float(out_ar.shape[1]) / xsize
    for j in range( out_ar.shape[0]):
        y0 = 2.0 * (yoff + j / ovr_factor_y) / raster_ysize - 1
        for i in range(out_ar.shape[1]):
            x0 = 3.5 * (xoff + i / ovr_factor_x) / raster_xsize - 2.5
            x = 0.0
            y = 0.0
            x2 = 0.0
            y2 = 0.0
            iteration = 0
            while x2 + y2 < 4 and iteration < max_iterations:
                y = 2*x*y + y0
                x = x2 - y2 + x0
                x2 = x * x
                y2 = y * y
                iteration += 1

            out_ar[j][i] = iteration * 255 / max_iterations
\endcode

the following VRT file can be used (to be opened with QGIS for example)

\code

<VRTDataset rasterXSize="100000000" rasterYSize="100000000">
  <VRTRasterBand dataType="Byte" band="1" subClass="VRTDerivedRasterBand">
    <PixelFunctionLanguage>Python</PixelFunctionLanguage>
    <PixelFunctionType>mandelbrot.mandelbrot</PixelFunctionType>
    <Metadata>
      <MDI key="STATISTICS_MAXIMUM">255</MDI>
      <MDI key="STATISTICS_MEAN">127</MDI>
      <MDI key="STATISTICS_MINIMUM">0</MDI>
      <MDI key="STATISTICS_STDDEV">127</MDI>
    </Metadata>
    <ColorInterp>Gray</ColorInterp>
    <Histograms>
      <HistItem>
        <HistMin>-0.5</HistMin>
        <HistMax>255.5</HistMax>
        <BucketCount>256</BucketCount>
        <IncludeOutOfRange>0</IncludeOutOfRange>
        <Approximate>1</Approximate>
        <HistCounts>0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|
0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|
0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|
0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|
0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|
0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|
0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0</HistCounts>
      </HistItem>
    </Histograms>
  </VRTRasterBand>
</VRTDataset>
\endcode

\section gdal_vrttut_warped Warped VRT

A warped VRT is a VRTDataset with subClass="VRTWarpedDataset". It has a
GDALWarpOptions element which describe the warping options.

\code
<VRTDataset rasterXSize="20" rasterYSize="20" subClass="VRTWarpedDataset">
  <SRS>PROJCS["NAD27 / UTM zone 11N",GEOGCS["NAD27",DATUM["North_American_Datum_1927",SPHEROID["Clarke 1866",6378206.4,294.9786982138982,AUTHORITY["EPSG","7008"]],AUTHORITY["EPSG","6267"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4267"]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",0],PARAMETER["central_meridian",-117],PARAMETER["scale_factor",0.9996],PARAMETER["false_easting",500000],PARAMETER["false_northing",0],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Easting",EAST],AXIS["Northing",NORTH],AUTHORITY["EPSG","26711"]]</SRS>
  <GeoTransform>  4.4072000000000000e+05,  6.0000000000000000e+01,  0.0000000000000000e+00,  3.7513200000000000e+06,  0.0000000000000000e+00, -6.0000000000000000e+01</GeoTransform>
  <Metadata>
    <MDI key="AREA_OR_POINT">Area</MDI>
  </Metadata>
  <VRTRasterBand dataType="Byte" band="1" subClass="VRTWarpedRasterBand">
    <ColorInterp>Gray</ColorInterp>
  </VRTRasterBand>
  <BlockXSize>20</BlockXSize>
  <BlockYSize>20</BlockYSize>
  <GDALWarpOptions>
    <WarpMemoryLimit>6.71089e+07</WarpMemoryLimit>
    <ResampleAlg>NearestNeighbour</ResampleAlg>
    <WorkingDataType>Byte</WorkingDataType>
    <Option name="INIT_DEST">0</Option>
    <SourceDataset relativeToVRT="1">byte.vrt</SourceDataset>
    <Transformer>
      <ApproxTransformer>
        <MaxError>0.125</MaxError>
        <BaseTransformer>
          <GenImgProjTransformer>
            <SrcGeoTransform>440720,60,0,3751320,0,-60</SrcGeoTransform>
            <SrcInvGeoTransform>-7345.33333333333303,0.0166666666666666664,0,62522,0,-0.0166666666666666664</SrcInvGeoTransform>
            <DstGeoTransform>440720,60,0,3751320,0,-60</DstGeoTransform>
            <DstInvGeoTransform>-7345.33333333333303,0.0166666666666666664,0,62522,0,-0.0166666666666666664</DstInvGeoTransform>
          </GenImgProjTransformer>
        </BaseTransformer>
      </ApproxTransformer>
    </Transformer>
    <BandList>
      <BandMapping src="1" dst="1" />
    </BandList>
  </GDALWarpOptions>
</VRTDataset>
\endcode

\section gdal_vrttut_pansharpen Pansharpened VRT

(Since GDAL 2.1)

A VRT can describe a dataset resulting from a
<a href="https://en.wikipedia.org/wiki/Pansharpened_image">pansharpening operation</a>.
The pansharpening VRT combines a panchromatic band with several spectral bands
of lower resolution to generate output spectral bands of the same resolution as
the panchromatic band.

VRT pansharpening assumes that the panchromatic and spectral bands have the same
projection (or no projection). If that is not the case, reprojection must be done in a prior step.
Bands might have different geotransform matrices, in which case, by default, the
resulting dataset will have as extent the union of all extents.

Currently the only supported pansharpening algorithm is a "weighted" Brovey algorithm.
The general principle of this algorithm is that, after resampling the spectral bands
to the resolution of the panchromatic band, a pseudo panchromatic intensity is computed
from a weighted average of the spectral bands. Then the output value of the spectral
band is its input value multiplied by the ratio of the real panchromatic intensity
over the pseudo panchromatic intensity.

Corresponding pseudo code:
\code
pseudo_panchro[pixel] = sum(weight[i] * spectral[pixel][i] for i=0 to nb_spectral_bands-1)
ratio = panchro[pixel] / pseudo_panchro[pixel]
for i=0 to nb_spectral_bands-1:
    output_value[pixel][i] = input_value[pixel][i] * ratio
\endcode

A valid pansharpened VRT must declare subClass="VRTPansharpenedDataset" as an
attribute of the VRTDataset top element. The VRTDataset element must have a
child <b>PansharpeningOptions</b> element. This PansharpeningOptions element must have
a <b>PanchroBand</b> child element and one of several <b>SpectralBand</b> elements.
PanchroBand and SpectralBand elements must have at least a <b>SourceFilename</b> child
element to specify the name of the dataset. They may also have a <b>SourceBand</b> child
element to specify the number of the band in the dataset (starting with 1). If not
specify, the first band will be assumed.

The SpectralBand element must generally have a <b>dstBand</b> attribute to specify the
number of the output band (starting with 1) to which the input spectral band must be mapped.
If the attribute is not specified, the spectral band will be taken into account
in the computation of the pansharpening, but not exposed as an output band.

Panchromatic and spectral bands should generally come from different datasets,
since bands of a GDAL dataset are assumed to have all the same dimensions.
Spectral bands themselves can come from one or several datasets. The only
constraint is that they have all the same dimensions.

An example of a minimalist working VRT is the following. It will generates a dataset with 3 output
bands corresponding to the 3 input spectral bands of multispectral.tif, pansharpened
with panchromatic.tif.

\code
<VRTDataset subClass="VRTPansharpenedDataset">
  <PansharpeningOptions>
    <PanchroBand>
      <SourceFilename relativeToVRT="1">panchromatic.tif</SourceFilename>
      <SourceBand>1</SourceBand>
    </PanchroBand>
    <SpectralBand dstBand="1">
      <SourceFilename relativeToVRT="1">multispectral.tif</SourceFilename>
      <SourceBand>1</SourceBand>
    </SpectralBand>
    <SpectralBand dstBand="2">
      <SourceFilename relativeToVRT="1">multispectral.tif</SourceFilename>
      <SourceBand>2</SourceBand>
    </SpectralBand>
    <SpectralBand dstBand="3">
      <SourceFilename relativeToVRT="1">multispectral.tif</SourceFilename>
      <SourceBand>3</SourceBand>
    </SpectralBand>
  </PansharpeningOptions>
</VRTDataset>
\endcode

In the above example, 3 output pansharpend bands will be created from the 3 declared
input spectral bands. The weights will be 1/3. Cubic resampling will be used. The
projection and geotransform from the panchromatic band will be reused for the VRT
dataset.

It is possible to create more explicit and declarative pansharpened VRT, allowing
for example to only output part of the input spectral bands (e.g. only RGB when
the input multispectral dataset is RGBNir). It is also possible to add "classic"
VRTRasterBands, in addition to the pansharpened bands.

In addition to the above mentioned required PanchroBand and SpectralBand elements,
the PansharpeningOptions element may have the following children elements :
<ul>
<li> <b>Algorithm</b>: to specify the pansharpening algorithm. Currently, only
WeightedBrovey is supported.</li>
<li> <b>AlgorithmOptions</b>: to specify the options of the pansharpening algorithm.
With WeightedBrovey algorithm, the only supported option is a <b>Weights</b> child
element whose content must be a comma separated list of real values assigning the
weight of each of the declared input spectral bands. There must be as many values
as declared input spectral bands.</li>
<li> <b>Resampling</b>: the resampling kernel used to resample the spectral bands
to the resolution of the panchromatic band. Can be one of Cubic (default), Average,
Near, CubicSpline, Bilinear, Lanczos.</li>
<li> <b>NumThreads</b>: Number of worker threads. Integer number or ALL_CPUS.
If this option is not set, the GDAL_NUM_THREADS configuration option will be queried
(its value can also be set to an integer or ALL_CPUS)</li>
<li> <b>BitDepth</b>: Can be used to specify the bit depth of the panchromatic and
spectral bands (e.g. 12). If not specified, the NBITS metadata item from the
panchromatic band will be used if it exists.</li>
<li> <b>NoData</b>: Nodata value to take into account for panchromatic and
spectral bands. It will be also used as the output nodata value. If not specified and
all input bands have the same nodata value, it will be implicitly used (unless
the special None value is put in NoData to prevent that).</li>
<li> <b>SpatialExtentAdjustment</b>: Can be one of <i>Union</i> (default), <i>Intersection</i>,
<i>None</i> or <i>NoneWithoutWarning</i>. Controls the behaviour when panchromatic
and spectral bands have not the same geospatial extent. By default, Union will take
the union of all spatial extents. Intersection the intersection of all spatial extents.
None will not proceed to any adjustment at all (might be useful if the geotransform are
somehow dummy, and the top-left and bottom-right corners of all bands match), but will
emit a warning. NoneWithoutWarning is the same as None, but in a silent way.</li>
</li>
</ul>


The below examples creates a VRT dataset with 4 bands. The first band is the
panchromatic band. The 3 following bands are than red, green, blue pansharpened
bands computed from a multispectral raster with red, green, blue and near-infrared
bands. The near-infrared bands is taken into account for the computation of the
pseudo panchromatic intensity, but not bound to an output band.

\code
<VRTDataset rasterXSize="800" rasterYSize="400" subClass="VRTPansharpenedDataset">
  <SRS>WGS84</SRS>
  <GeoTransform>-180, 0.45, 0, 90, 0, -0.45</GeoTransform>
  <Metadata>
    <MDI key="DESCRIPTION">Panchromatic band + pan-sharpened red, green and blue bands</MDI>
  </Metadata>
  <VRTRasterBand dataType="Byte" band="1" >
    <SimpleSource>
      <SourceFilename relativeToVRT="1">world_pan.tif</SourceFilename>
      <SourceBand>1</SourceBand>
    </SimpleSource>
  </VRTRasterBand>
  <VRTRasterBand dataType="Byte" band="2" subClass="VRTPansharpenedRasterBand">
      <ColorInterp>Red</ColorInterp>
  </VRTRasterBand>
  <VRTRasterBand dataType="Byte" band="3" subClass="VRTPansharpenedRasterBand">
      <ColorInterp>Green</ColorInterp>
  </VRTRasterBand>
  <VRTRasterBand dataType="Byte" band="4" subClass="VRTPansharpenedRasterBand">
      <ColorInterp>Blue</ColorInterp>
  </VRTRasterBand>
  <BlockXSize>256</BlockXSize>
  <BlockYSize>256</BlockYSize>
  <PansharpeningOptions>
    <Algorithm>WeightedBrovey</Algorithm>
    <AlgorithmOptions>
      <Weights>0.25,0.25,0.25,0.25</Weights>
    </AlgorithmOptions>
    <Resampling>Cubic</Resampling>
    <NumThreads>ALL_CPUS</NumThreads>
    <BitDepth>8</BitDepth>
    <NoData>0</NoData>
    <SpatialExtentAdjustment>Union</SpatialExtentAdjustment>
    <PanchroBand>
      <SourceFilename relativeToVRT="1">world_pan.tif</SourceFilename>
     <SourceBand>1</SourceBand>
    </PanchroBand>
    <SpectralBand dstBand="2">
      <SourceFilename relativeToVRT="1">world_rgbnir.tif</SourceFilename>
      <SourceBand>1</SourceBand>
    </SpectralBand>
    <SpectralBand dstBand="3">
      <SourceFilename relativeToVRT="1">world_rgbnir.tif</SourceFilename>
      <SourceBand>2</SourceBand>
    </SpectralBand>
    <SpectralBand dstBand="4">
      <SourceFilename relativeToVRT="1">world_rgbnir.tif</SourceFilename>
      <SourceBand>3</SourceBand>
    </SpectralBand>
    <SpectralBand> <!-- note the absence of the dstBand attribute, to indicate
                        that the NIR band is not bound to any output band -->
      <SourceFilename relativeToVRT="1">world_rgbnir.tif</SourceFilename>
      <SourceBand>4</SourceBand>
    </SpectralBand>
  </PansharpeningOptions>
</VRTDataset>
\endcode

\section gdal_vrttut_mt Multi-threading issues

The below section applies to GDAL &lt;= 2.2. Starting with GDAL 2.3, the use
of VRT datasets is subject to the standard GDAL dataset multi-threaded rules
(that is a VRT dataset handle may only be used by a same thread at a time,
but you may open several dataset handles on the same VRT file and use them
in different threads)

When using VRT datasets in a multi-threading environment, you should be
careful to open the VRT dataset by the thread that will use it afterwards. The
reason for that is that the VRT dataset uses GDALOpenShared when opening the
underlying datasets. So, if you open twice the same VRT dataset by the same
thread, both VRT datasets will share the same handles to the underlying
datasets.

The shared attribute, added in GDAL 2.0.0, on the SourceFilename indicates whether the
dataset should be shared (value is 1) or not (value is 0). The default is 1.
If several VRT datasets referring to the same underlying sources are used in a multithreaded context,
shared should be set to 0. Alternatively, the VRT_SHARED_SOURCE configuration
option can be set to 0 to force non-shared mode.

\section gdal_vrttut_perf Performance considerations

A VRT can reference many (hundreds, thousands, or more) datasets. Due to
operating system limitations, and for performance at opening time, it is
not reasonable/possible to open them all at the same time. GDAL has a "pool"
of datasets opened by VRT files whose maximum limit is 100 by default. When it
needs to access a dataset referenced by a VRT, it checks if it is already in
the pool of open datasets. If not, when the pool has reached its limit, it closes
the least recently used dataset to be able to open the new one. This maximum
limit of the pool can be increased by setting the GDAL_MAX_DATASET_POOL_SIZE
 configuration option to a bigger value. Note that a typical user process on
Linux is limited to 1024 simultaneously opened files, and you should let some
margin for shared libraries, etc...
As of GDAL 2.0, gdal_translate and gdalwarp, by default, increase the pool size
to 450.

*/
