4.11 _JT_ storage_ COO_ - coordinate format

• Status: IMPLEMENTED
• Current value: 10
• Also requires:

  Variable	Meaning	Value
  ia(_JT_ nunk_)	number of unknowns	2
  ia(_JT_ nelem_)	number of active elements	3

• Description:

  In this format, a is a vector of length ia(_JT_ nelem_) containing all the active elements of A. The first ia(_JT_ nunk_) elements of a must contain the main diagonal elements of A, but the remaining elements can be in any order. The map array ja is a vector of length 2 * ia(_JT_ nelem_) . Then the first ia(_JT_ nelem_) elements of ja contain the row indices of A, and the next ia(_JT_ nelem_) elements contain the column indices of A.

  Advantages:

  • stores no extra zero elements (unless you want to)
  • elements can be in any order (except for main diagonal)
  • matrix-vector multiply implemented as single loop, so longer vector length

  Disadvantage:

  • two indirect references in matrix-vector multiply

  Example:

  A = $$\left(\vphantom{ \begin{array}{ccccc} 11 & 0 & 0 & 14 & 15 \\ ... ...& 0 \\ 41 & 0 & 0 & 44 & 45 \\ 51 & 0 & 0 & 54 & 55 \end{array} }\right.$$$$\begin{array}{ccccc} 11 & 0 & 0 & 14 & 15 \\ 0 & 22 & 0 & 0 &... ...& 33 & 0 & 0 \\ 41 & 0 & 0 & 44 & 45 \\ 51 & 0 & 0 & 54 & 55 \end{array}$$ $$\left.\vphantom{ \begin{array}{ccccc} 11 & 0 & 0 & 14 & 15 \\ ... ...& 0 \\ 41 & 0 & 0 & 44 & 45 \\ 51 & 0 & 0 & 54 & 55 \end{array} }\right)$$

  could be represented in COO format by the arrays a and ja as:
  
  a = ( 11, 22, 33, 44, 55, 41, 51, 14, 54, 15, 45 )
  
  ja = ( 1, 2, 3, 4, 5, 4, 5, 1, 5, 1, 5, 1, 2, 3, 4, 5, 1, 1, 4, 4, 5, 5 )
  
  or as:
  
  a = ( 11, 22, 33, 44, 55, 14, 15, 41, 45, 51, 54 )
  
  ja = ( 1, 2, 3, 4, 5, 1, 1, 4, 4, 5, 5, 1, 2, 3, 4, 5, 4, 5, 1, 5, 1, 5 )