Matrix element

For the description of the matrix element see section 9.13 on page .

The name of the XML element is matrix. It has the attribute dimensions, which indicates how many dimensions $d$ the matrix element has. Furthermore it has an optional attribute named domainNr, which specifies the number of the domain for the matrix element. If the attribute domainNr is missing, the domain number is $0$ .

The element contains first a XML element named defined_variables, wich contains for each variable, which the matrix element defines, in their order a variable element. These have the optional attribute number, which is the number (counting begins at $1$) of the element respectively variable defined in the matrix element. Furthermore the variable element contains a natural number / identifier for the variable, that is not used above the matrix element for another variable.

After the XML element for variable definitions defined_variables follows the XML element named areas, wich contains the vectors with the areas for the dimension ( $(Startvalue_k, \ldots, Endvalue_k)$ with $k=1 \ldots d$), to which the dimension variables ( $Variable_1, \ldots, Variable_d$) should be set to. They are listed in their order in the matrix element. The vectors all have the type area (type=ärea").

After the XML element for the areas areas follows the XML element named values, wich contains the vectors with the values ( $Value_{d+1}, \ldots, Value_{d+i}$), to which the variables should be set. They are listed in their order in the matrix element. The vectors all have the type matrix (type="matrix").

At the end, after the XML element for the values vectors values, the matrix element contains the XML element for the contained subobject.

An example for a matrix element:

<matrix dimensions="2">
   <defined_variables>
      <variable>7</variable>
      <variable>8</variable>
      <variable>9</variable>
      <variable>10</variable>
      <variable>11</variable>
   </defined_variables>
   <areas>
      <vector type=ärea">
         <value>3</value>
         <value>4</value>
      </vector>
      <vector type=ärea">
         <variable>2</variable>
         <value>7</value>
      </vector>
   </areas>
   <values>
      <vector type="matrix">
         <variable>1</variable>
         <value>3</value>
         <value>26.14</value>
      </vector>
      <vector type="matrix">
         <value>33.4</value>
         <value>-47</value>
         <variable>4</variable>
      </vector>
   </values>
   ...
   ...<!-- Fib subobject -->
</matrix>

An example for a matrix element with the optional attribute domainNr and number:

<matrix dimensions="2" domainNr="7">
   <defined_variables>
      <variable number="1">8</variable>
      <variable number="2">9</variable>
      <variable number="3">10</variable>
      <variable number="4">11</variable>
   </defined_variables>
   <areas>
      <vector type=ärea">
         <variable>3</variable>
         <variable>2</variable>
      </vector>
      <vector type=ärea">
         <value>-2</value>
         <value>0</value>
      </vector>
   </areas>
   <values>
      <vector type="matrix">
         <value>3</value>
         <variable>1</variable>
      </vector>
      <vector type="matrix">
         <value>0.44</value>
         <value>-7</value>
      </vector>
      <vector type="matrix">
         <value>6</value>
         <value>5</value>
      </vector>
      <vector type="matrix">
         <value>-1</value>
         <value>-1</value>
      </vector>
   </values>
   ...
   ...<!-- Fib subobject -->
</matrix>