4.9 _JT_ storage_ ELL_ - ELLPACK-ITPACK, or row-packed format

• Status: IMPLEMENTED
• Current value: 8
• Also requires:

  Variable	Meaning	Value
  ia(_JT_ idim_)	leading dimension	3
  ia(_JT_ nrows_)	number of rows	2
  ia(_JT_ maxnz_)	maximum number of non-zero elements in any column	4

• Description:

  In this format, all zeros are removed from each row, so that the matrix is essentially left-justified, and the main diagonal elements are stored in the first column. Thus the coefficient is stored in an ia(_JT_ nrows_) x ia(_JT_ maxnz_) array. A companion ia(_JT_ nrows_) x ia(_JT_ maxnz_) array maps the column in the reduced matrix to the column in the original matrix for each element. NSPCG calls this primary format, but does not require the main diagonal elements to be in the first column. Example:

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

  would be represented in ELL format by the arrays a and ja as follows:

  a = $$\left(\vphantom{ \begin{array}{ccc} 11 & 14 & 15 \\ 22 & 0 & 0 \\ 33 & 0 & 0 \\ 44 & 41 & 45 \\ 55 & 51 & 54 \end{array} }\right.$$$$\begin{array}{ccc} 11 & 14 & 15 \\ 22 & 0 & 0 \\ 33 & 0 & 0 \\ 44 & 41 & 45 \\ 55 & 51 & 54 \end{array}$$ $$\left.\vphantom{ \begin{array}{ccc} 11 & 14 & 15 \\ 22 & 0 & 0 \\ 33 & 0 & 0 \\ 44 & 41 & 45 \\ 55 & 51 & 54 \end{array} }\right)$$    and    ja = $$\left(\vphantom{ \begin{array}{ccc} 1 & 4 & 5 \\ 2 & 0 & 0 \\ 3 & 0 & 0 \\ 4 & 1 & 5 \\ 5 & 1 & 4 \end{array} }\right.$$$$\begin{array}{ccc} 1 & 4 & 5 \\ 2 & 0 & 0 \\ 3 & 0 & 0 \\ 4 & 1 & 5 \\ 5 & 1 & 4 \end{array}$$ $$\left.\vphantom{ \begin{array}{ccc} 1 & 4 & 5 \\ 2 & 0 & 0 \\ 3 & 0 & 0 \\ 4 & 1 & 5 \\ 5 & 1 & 4 \end{array} }\right)$$

  Note that the main diagonal elements must be in the first column of array a.