S3L_grade_detailed_down and S3L_grade_detailed_up

The S3L_grade_detailed_down and S3L_grade_detailed_up functions differ from S3L_grade_down and S3L_grade_up in two respects:

• Both grade along a single axis of A, as specified by the axis argument.

• Both store a set of indices, but these indices do not indicate element positions directly. Instead, each stored index indicates the index of the corresponding element of A that has either

  • The j-th smallest value along the specified axis - S3L_grade_detailed_down

  • The j-th largest value along the specified axis - S3L_grade_detailed_up

This means G is an integer array whose rank and extents are the same as those of A.

Repeating the 3 x 3 sample array shown above,

Example 8-106

   _         _
  | 6   2   4 |
  |           |
  | 1   3   8 |
  |           |
  | 9   7   5 |
   -         -

if S3_grade_detailed_down is called from a C program with the axis argument = 0, upon completion, G will contain the following values:

Example 8-107

   _         _
  | 1   2   2 |
  |           |
  | 2   1   0 |
  |           |
  | 0   0   1 |
   -         -

If, instead, axis = 1, G will contain

Example 8-108

   _         _
  | 0   2   1 |
  |           |
  | 2   1   0 |
  |           |
  | 0   1   2 |
   -         -

If S3L_grade_detailed_up is called from a C program with axis = 0, G will contain

Example 8-109

   _         _
  | 1   0   0 |
  |           |
  | 0   1   2 |
  |           |
  | 2   2   1 |
   -         -

If S3L_grade_detailed_up is called from a C program with axis = 1, G will contain

Example 8-110

   _         _
  | 2   0   1 |
  |           |
  | 0   1   2 |
  |           |
  | 2   1   0 |
   -         -

For F77 or F90 calls, each index value in these examples, including the axis argument, would be increased by 1.