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Compressed Sparse Column (CSC) Format
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This standard data format consists of the following data:

.. code-block:: Fortran

   integer                   :: m      ! number of rows (unsymmetric only)
   integer                   :: n      ! number of columns
   integer, size(n+1)        :: ptr    ! column pointers (may have type long)
   integer, size(ptr(n+1)-1) :: row    ! row indices
   real,    size(ptr(n+1)-1) :: val    ! numerical values

Non-zero matrix entries are ordered by increasing column index and stored in
the arrays row(:) and val(:) such that row(k) holds
the row number and val(k) holds the value of the k-th entry.
The ptr(:) array stores column pointers such that ptr(i) is
the position in row(:) and val(:) of
the first entry in the i-th column, and ptr(n+1) is one more
than the total number of entries. ptr(:) may be either 32-bit (Fortran default integer) or 64-bit (Fortran integer(long)).
There must be no duplicate or out of range entries.
Entries that are zero, including those on the diagonal, need not be specified.

For **symmetric matrices**, only the lower triangular entries of :math:`A`
should be supplied. For **unsymmetric matrices**, all entries in the matrix
should be supplied.

Note that most SPRAL routines offer **no checking** of user data, and the
behaviour of these routines with misformatted data is undefined. You may use
routines from the :f:mod:`spral_matrix_util` package to convert data to and
check data stored in this format.

To illustrate the CSC format, the matrix

.. math::

   \left( \begin{array}{ccccc}
      1.1 & 2.2 &     & 3.3 &     \\
      2.2 &     & 4.4 &     &     \\
          & 4.4 & 5.5 &     & 6.6 \\
      3.3 &     &     & 7.7 & 8.8 \\
          &     & 6.6 & 8.8 & 9.9
   \end{array} \right)

is described by the following data:

.. code-block:: fortran

   n = 5
   ptr(1:6) = (/ 1,             4,   5,        7,        9,    10 /)
   row(1:9) = (/ 1,   2,   4,   3,   3,   5,   4,   5,   5 /)
   val(1:9) = (/ 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9 /)