XDMF

https://www.xdmf.org/index.php/XDMF_Model_and_Format
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XDMF (eXtensible Data Model and Format) is a standardized format for exchanging scientific data...
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### XPath Examples for Referencing XML Elements

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Provides examples of XPath expressions used to navigate and select specific elements within an XML document. This is crucial for the XDMF API to access data.

```xpath
/Xdmf/Domain/Grid

```

```xpath
/Xdmf/Domain/Grid[10]

```

```xpath
/Xdmf/Domain/Grid[@Name="Copper Plate"]

```

--------------------------------

### Grid Structure Examples in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Illustrates the hierarchical structure of the Grid element in XDMF, which serves as a container for 2D and 3D spatial data. Examples show the 'Tree' and 'Collection' GridTypes, demonstrating how Uniform grids can be nested within them. Uniform grids require 'Topology' and 'Geometry' elements.

```xml
<Grid Name="Car Wheel" GridType="Tree">
    <Grid Name="Tire" GridType="Uniform">
        <Topology> ... </Topology>
        <Geometry> ... </Geometry>
    </Grid>
    <Grid Name="Lug Nuts" GridType="Collection">
        <Grid Name="Lug Nut 0" GridType="Uniform">
            <Topology> ... </Topology>
            <Geometry> ... </Geometry>
        </Grid>
        <Grid Name="Lug Nut 1" GridType="Uniform">
            <Topology> ... </Topology>
            <Geometry> ... </Geometry>
        </Grid>
        <Grid Name="Lug Nut 2" GridType="Uniform">
            <Topology> ... </Topology>
            <Geometry> ... </Geometry>
        </Grid>
    </Grid>
    .
    .
    .

```

--------------------------------

### XML Comment Syntax Example

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Illustrates the syntax for adding comments within an XML document. Comments are ignored by parsers but are useful for documentation within the code.

```xml
<!--This is a Comment -->

```

--------------------------------

### Complete XDMF File for Two Quadrilaterals

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

An example of a complete XDMF XML file defining two quadrilaterals that share an edge. It includes Grid, Topology, and Geometry elements, suitable for visualization in VisIt or ParaView.

```xml
<?xml version="1.0" ?>
<!DOCTYPE Xdmf SYSTEM "Xdmf.dtd" []>
<Xdmf Version="2.0" xmlns:xi="[http://www.w3.org/2001/XInclude]">
    <Domain>
        <Grid Name="Two Quads">
            <Topology TopologyType="Quadrilateral" NumberOfElements="2">
                <DataItem Format="XML" DataType="Int" Dimensions="2 4">
                    0 1 2 3
                    1 6 7 2
                </DataItem>
            </Topology>
            <Geometry GeometryType="XYZ">
                <DataItem Format="XML" Dimensions="2 4 3">
                    0.0    0.0    0.0
                    1.0    0.0    0.0
                    1.0    1.0    0.0
                    0.0    1.0    0.0
                    0.0    0.0    2.0
                    1.0    0.0    2.0
                    1.0    1.0    2.0
                    0.0    1.0    2.0
                </DataItem>
            </Geometry>
        </Grid>
    </Domain>
</Xdmf>
```

--------------------------------

### XML Element Structure Example

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Demonstrates the basic structure of an XML element, including tags, attributes, and character data (CData). This is fundamental to understanding XDMF's XML representation.

```xml
<ElementTag 
    AttributeName="AttributeValue"
    AttributeName="AttributeValue"
    ... >
   CData
</ElementTag>

```

--------------------------------

### XDMF Time Element Examples

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Demonstrates different ways to specify temporal information within an XDMF file using the Time element. Supports Single, HyperSlab, List, and Range TimeTypes, each with specific data formats for the DataItem.

```xml
<Time Value="0.1" />
```

```xml
<Time TimeType="HyperSlab">
    <DataItem Format="XML" NumberType="Float" Dimensions="3">
        0.0 0.000001 100
    </DataItem>
</Time>
```

```xml
<Time TimeType="List">
    <DataItem Format="XML" NumberType="Float" Dimensions="7">
        0.0 0.1 0.5 1.0 1.1 10.0 100.5
    </DataItem>
</Time>
```

```xml
<Time TimeType="Range">
    <DataItem Format="XML" NumberType="Float" Dimensions="2">
        0.0 0.5
    </DataItem>
</Time>
```

--------------------------------

### XDMF Information Element Examples

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Illustrates the use of the Information element in XDMF for storing application-specific data that doesn't fit the standard data model. Values can be provided directly in the 'Value' attribute or within the CDATA section of the element.

```xml
<Information Name="XBounds" Value="0.0 10.0"/>
```

```xml
<Information Name="Bounds"> 0.0 10.0 100.0 110.0 200.0 210.0 </Information>
```

--------------------------------

### Uniform DataItem referencing Binary file data in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This example shows a 'Uniform' DataItem referencing data stored in a binary file. It specifies the file name ('PressureFile.bin') and the dimensions ('64 128 256') of the data within that file. The 'Format' is set to 'Binary'.

```xml
<DataItem ItemType="Uniform"
          Format="Binary"
          Dimensions="64 128 256">
  PressureFile.bin
</DataItem>
```

--------------------------------

### Define Subset Grid with All Section in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This example illustrates defining a Subset GridType in XDMF where the 'Section' attribute is 'All'. This configuration selects the entire target grid and allows for the addition of new attributes to it. The 'Reference' attribute specifies the path to the grid being targeted.

```xml
<Grid Name="Portion" GridType="Subset" Section="All">
    <!-- Select the entire grid and add an  attribute -->
    <Grid Name="Target" Reference="XML">
        /Xdmf/Domain/Grid[@Name="Main Grid"]
    </Grid>
    <Attribute Name="New Values" Center="Cell">
        <DataItem Format="XML" Dimensions="3">
            100 150 200
        </DataItem>
    </Attribute>
</Grid>
```

--------------------------------

### DataItem Function Examples in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Demonstrates various operations using the DataItem element with the 'Function' attribute in XDMF. This includes arithmetic operations, mathematical functions (SIN, COS, etc.), JOIN for array concatenation/interlacing, and WHERE for conditional extraction. References to other DataItems are supported using XPath.

```xml
<DataItem ItemType="Function" 
          Function="$0 + $1"
          Dimensions="3">
    <DataItem Dimensions="3">
        1.0 2.0 3.0
    </DataItem>
    <DataItem Dimensions="3">
        4.1 5.2 6.3
    </DataItem>
</DataItem>
```

```xml
<DataItem Name="MyFunction" 
          ItemType="Function"
          Function="10 + $0">
    <DataItem Reference="/Xdmf/DataItem[1]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="ABS($0 * $1)">
    <DataItem Reference="/Xdmf/DataItem[1]" />
    <DataItem Reference="/Xdmf/DataItem[2]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="$0[5:15]">
    <DataItem Reference="/Xdmf/DataItem[1]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="JOIN($0 ; $1)">
    <DataItem Reference="/Xdmf/DataItem[1]" />
    <DataItem Reference="/Xdmf/DataItem[2]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="JOIN($0 , $1, $2)">
    <DataItem Reference="/Xdmf/DataItem[1]" />
    <DataItem Reference="/Xdmf/DataItem[2]" /> 
    <DataItem Reference="/Xdmf/DataItem[3]" />
</DataItem>
```

--------------------------------

### Fully Qualified Uniform DataItem in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This example shows a fully qualified 'Uniform' DataItem in XDMF, explicitly defining 'ItemType', 'Format', 'NumberType', 'Precision', 'Rank', and 'Dimensions'. This specifies a 1-dimensional array of 32-bit floating-point numbers with a precision of 4, containing the values 1.0, 2.0, and 3.0.

```xml
<DataItem ItemType="Uniform"
          Format="XML"
          NumberType="Float" 
          Precision="4"
          Rank="1" 
          Dimensions="3">
  1.0 2.0 3.0
</DataItem>
```

--------------------------------

### XDMF HyperSlab Data Subset Specification

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Specifies a subset of a DataItem using start, stride, and count for each dimension. This allows for efficient selection of data regions without loading the entire dataset. The format includes dimensions for the slab and the target DataItem.

```xml
<DataItem ItemType="HyperSlab"
          Dimensions="25 50 75 3"
          Type="HyperSlab">
    <DataItem Dimensions="3 4" 
              Format="XML">
        0 0 0 0 
        2 2 2 1 
        25 50 75 3
    </DataItem>
    <DataItem
        Name="Points"
        Dimensions="100 200 300 3"
        Format="HDF">
        MyData.h5:/XYZ
    </DataItem>
</DataItem>
```

--------------------------------

### Define Cell-Centered Attribute in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This example demonstrates defining an attribute named 'Cell Values' centered on cell centers. It uses an XML formatted DataItem with a single dimension.

```xml
<Attribute Name="Cell Values" Center="Cell">
    <DataItem Format="XML" Dimensions="3">
        3000 2000 1000
    </DataItem>
</Attribute>
```

--------------------------------

### XDMF Geometry Element Definition

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Defines the XYZ coordinates of mesh points. Supports various organizations like XYZ, XY, X_Y_Z, VXVYVZ, ORIGIN_DXDYDZ, and ORIGIN_DXDY. The example shows an XYZ organization for 8 points.

```xml
<Geometry GeometryType="XYZ">
    <DataItem Format="XML" Dimensions="2 4 3">
        0.0    0.0    0.0
        1.0    0.0    0.0
        1.0    1.0    0.0
        0.0    1.0    0.0 
        0.0    0.0    2.0
        1.0    0.0    2.0
        1.0    1.0    2.0
        0.0    1.0    2.0
    </DataItem>
</Geometry>
```

--------------------------------

### Define Vector Finite Element Function in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This example shows the definition of a vector finite element function of family 'CG' and degree '1' on a 2D simplicial mesh. It contains two DataItems for degrees of freedom indices and their corresponding vector component values.

```xml
<Attribute ItemType="FiniteElementFunction" ElementFamily="CG" ElementDegree="1" ElementCell="triangle" Name="u" Center="Other" AttributeType="Vector">
  <DataItem Dimensions="8 6" NumberType="UInt" Format="XML">
    6 12 8 7 13 9
    6 2 8 7 3 9
    12 16 14 13 17 15
    12 8 14 13 9 15
    2 8 4 3 9 5 
    2 0 4 3 1 5
    8 14 10 9 15 11
    8 4 10 9 5 11
  </DataItem>
  <DataItem Dimensions="18 1" NumberType="Float" Format="XML">
    0
    1
    0
    0.5
    0.5
    1
    0
    0
    0.5
    0.5
    1
    1
    0.5
    0
    1
    0.5
    1
    0
  </DataItem>
</Attribute>
```

--------------------------------

### Minimal XDMF XML File Structure

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Presents the essential structure of an empty XDMF XML file, including the XML declaration, DOCTYPE, and the root XDmf element. This serves as a basic template.

```xml
<?xml version="1.0" ?>
<!DOCTYPE Xdmf SYSTEM "Xdmf.dtd" []>
<Xdmf Version="2.0">
</Xdmf>

```

--------------------------------

### XDMF with Shared Geometry DataItem

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Demonstrates an XDMF structure where the Geometry DataItem is a direct child of the Domain, allowing multiple Grids to share the same geometry data. This is useful when geometries are identical but topologies differ.

```xml
<?xml version="1.0" ?>
<!DOCTYPE Xdmf SYSTEM "Xdmf.dtd" []>
<Xdmf Version="2.0" xmlns:xi="[http://www.w3.org/2001/XInclude]">
    <Domain>
        <DataItem Name="Point Data" Format="XML" Dimensions="2 4 3">
            0.0    0.0    0.0
            1.0    0.0    0.0
            1.0    1.0    0.0
            0.0    1.0    0.0
            0.0    0.0    2.0
            1.0    0.0    2.0
            1.0    1.0    2.0
            0.0    1.0    2.0
        </DataItem>
        <Grid Name="Two Quads">
            <Topology Type="Quadrilateral" NumberOfElements="2" >
                <DataItem Format="XML" 
                          DataType="Int"
                          Dimensions="2 4">
                    0 1 2 3
                    1 6 7 2
                </DataItem>
            </Topology>
            <Geometry GeometryType="XYZ">
                <DataItem Reference="XML">
                    /Xdmf/Domain/DataItem[@Name="Point Data"]
                </DataItem>
            </Geometry>
        </Grid>
    </Domain>
</Xdmf>
```

--------------------------------

### Define Quadrilateral Topology using XML

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This XML snippet defines a topology for two quadrilateral elements. It specifies the TopologyType as 'Quadrilateral' and the NumberOfElements as '2'. The DataItem contains the connectivity information, defining the indices into the geometry that form each cell. The dimensions attribute '2 4' indicates the structure of the connectivity data.

```xml
<Topology TopologyType="Quadrilateral" NumberOfElements="2">
    <DataItem Format="XML" DataType="Int" Dimensions="2 4">
        0 1 2 3
        1 6 7 2
    </DataItem>
</Topology>
```

--------------------------------

### XInclude Syntax for File Inclusion in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

Shows how to use XInclude within an XDMF XML file to include external content. This allows for modularity and inclusion of non-XML files.

```xml
<Xdmf Version="2.0" xmlns:xi="http://www.w3.org/2001/XInclude">
  <xi:include href="Example3.xmf"/>
</Xdmf>

```

--------------------------------

### Uniform DataItem referencing HDF5 data in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This snippet demonstrates how a 'Uniform' DataItem can reference data stored in an HDF5 file. It specifies the file ('OutputData.h5'), the dataset path ('/Results/Iteration 100/Part 2/Pressure'), the data type ('Float'), precision ('8' for 64-bit), and dimensions ('64 128 256').

```xml
<DataItem ItemType="Uniform"
          Format="HDF"
          NumberType="Float" 
          Precision="8"
          Dimensions="64 128 256">
  OutputData.h5:/Results/Iteration 100/Part 2/Pressure
</DataItem>
```

--------------------------------

### DataItem Function: Array Manipulation with JOIN

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/index

Demonstrates the use of the JOIN function within a DataItem to manipulate arrays. JOIN can be used to concatenate arrays sequentially or interlace elements from multiple arrays.

```xml
<DataItem ItemType="Function"
          Function="JOIN($0 ; $1)">
    <DataItem Reference="/Xdmf/DataItem[1]" />
    <DataItem Reference="/Xdmf/DataItem[2]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="JOIN($0 , $1, $2)">
    <DataItem Reference="/Xdmf/DataItem[1]" />
    <DataItem Reference="/Xdmf/DataItem[2]" /> 
    <DataItem Reference="/Xdmf/DataItem[3]" />
</DataItem>
```

--------------------------------

### Define Subset Grid with DataItem Section in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This snippet demonstrates how to define a Subset GridType in XDMF, specifically when the 'Section' attribute is 'DataItem'. It shows how to select a portion of another grid using a DataItem and how to assign new attributes to the selected subset. The 'Reference' attribute in the 'Grid' element points to the target grid.

```xml
<Grid Name="Portion" GridType="Subset" Section="DataItem">
    <!-- Select 2 cells from another grid. 
         Which 2 are defined by the DataItem -->
    <DataItem 
        DataType="Int"
        Dimensions="2"
        Format="XML">
        0 2
    </DataItem>
    <Grid Name="Target" Reference="XML">
        /Xdmf/Domain/Grid[@Name="Main Grid"]
    </Grid>
    <Attribute Name="New Values" Center="Cell">
        <DataItem Format="XML" Dimensions="2">
            100 150
        </DataItem>
    </Attribute>
</Grid>
```

--------------------------------

### Define Mixed Topology using XML

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This XML snippet defines a mixed topology consisting of three elements: a Tet, a Polygon, and a Hex. It sets TopologyType to 'Mixed' and NumberOfElements to '3'. The DataItem includes connectivity data for each cell, with specific requirements for cell types like Polygon that need to define the number of nodes before their connectivity.

```xml
<Topology TopologyType="Mixed" NumberOfElements="3" >
    <DataItem Format="XML" DataType="Int" Dimensions="20">
        6 0 1 2 7
        3 4 4 5 6 7
        9 8 9 10 11 12 13 14 15
    </DataItem>
</Topology>
```

--------------------------------

### Basic Uniform DataItem in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This is the simplest form of a DataItem element in XDMF, specifying a single array of values. Since 'ItemType' is not specified, 'Uniform' is assumed. The default 'Format' is XML and 'NumberType' is a 32-bit floating-point value.

```xml
<DataItem Dimensions="3">
    1.0 2.0 3.0
</DataItem>
```

--------------------------------

### Define Face Set with Attributes in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This snippet demonstrates how to define a 'Set' of type 'Face' to specify attributes on a subset of faces. It includes DataItems for cell indices, face indices within cells, and the attribute values themselves.

```xml
<Set Name="Ids" SetType="Face">
    <DataItem Format="XML" Dimensions="4" >
        1 2 3 4
    </DataItem>
    <DataItem Format="XML" Dimensions="4" >
        0 0 0 0
    </DataItem> 
    <Attribute Name="Example" Center="Face">
        <DataItem Format="XML" Dimensions="4" >
            100.0 110.0 100.0 200.0
        </DataItem>
    </Attribute>
</Set>
```

--------------------------------

### DataItem Function: Arithmetic and Mathematical Operations

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/index

Defines a DataItem element that performs arithmetic or mathematical operations on child DataItem elements. It supports basic arithmetic, trigonometric functions, and other mathematical operations. Elements are referenced by their zero-based index ($X).

```xml
<DataItem ItemType="Function" 
          Function="$0 + $1"
          Dimensions="3">
    <DataItem Dimensions="3">
        1.0 2.0 3.0
    </DataItem>
    <DataItem Dimensions="3">
        4.1 5.2 6.3
    </DataItem>
</DataItem>
```

```xml
<DataItem Name="MyFunction" 
          ItemType="Function"
          Function="10 + $0">
    <DataItem Reference="/Xdmf/DataItem[1]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="ABS($0 * $1)">
    <DataItem Reference="/Xdmf/DataItem[1]" />
    <DataItem Reference="/Xdmf/DataItem[2]" />
</DataItem>
```

```xml
<DataItem ItemType="Function"
          Function="$0[5:15]">
    <DataItem Reference="/Xdmf/DataItem[1]" />
</DataItem>
```

--------------------------------

### Define Mixed Topology for an Octahedron in XDMF

Source: https://www.xdmf.org/index.php/XDMF_Model_and_Format/.html

This code snippet shows how to define a mixed topology for an octahedron within an XDMF structure. It specifies the 'Mixed' TopologyType and uses a DataItem to describe the polyhedron, including its cell type, number of faces, and the node indices for each face. The associated GeometryType is 'XYZ'.

```xml
<Domain>
  <Grid Name="Octahedron" GridType="Uniform">
    <Topology TopologyType="Mixed">
      <DataItem Dimensions="26" NumberType="Int" Precision="4" Format="XML">
        <!-- polyhedron cell type = 16, 8 faces, each face = 3 points, 3 point indices -->
        16
         8
         3 0 1 4
         3 0 1 5
         3 1 2 4
         3 1 2 5
         3 2 3 4
         3 2 3 5
         3 3 0 4
         3 3 0 5
      </DataItem>
    </Topology>
    <Geometry GeometryType="XYZ">
      <DataItem Rank="2" Dimensions="6 3" NumberType="Float" Precision="8" Format="XML">
        -1. -1.  0.
        -1.  1.  0.
         1.  1.  0.
         1. -1.  0.
         0.  0.  1.
         0.  0. -1.
      </DataItem>
    </Geometry>
  </Grid>
</Domain>
```
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