03 March 2022 10:03:05 AM

CLENSHAW_CURTIS_GRID_TEST
  C++ version
  Test the routines in the CLENSHAW_CURTIS_GRID library.

TEST005:
  CC_GRID returns a grid of Clenshaw-Curtis points.
  Here, we simply call for grids in the 1D case

  Spatial dimension of grid = 1

         1             0

         1            -1
         2             1

         1            -1
         2   6.12323e-17
         3             1

         1            -1
         2          -0.5
         3           0.5
         4             1

         1            -1
         2     -0.707107
         3   6.12323e-17
         4      0.707107
         5             1

         1            -1
         2     -0.809017
         3     -0.309017
         4      0.309017
         5      0.809017
         6             1

         1            -1
         2     -0.866025
         3          -0.5
         4   6.12323e-17
         5           0.5
         6      0.866025
         7             1

         1            -1
         2     -0.900969
         3      -0.62349
         4     -0.222521
         5      0.222521
         6       0.62349
         7      0.900969
         8             1

         1            -1
         2      -0.92388
         3     -0.707107
         4     -0.382683
         5   6.12323e-17
         6      0.382683
         7      0.707107
         8       0.92388
         9             1

         1            -1
         2     -0.939693
         3     -0.766044
         4          -0.5
         5     -0.173648
         6      0.173648
         7           0.5
         8      0.766044
         9      0.939693
        10             1

TEST01:
  CC_GRID returns a grid of Clenshaw-Curtis points.
  Here, we simply call for a specific grid.

  Spatial dimension of grid = 3

  Total number of points in the grid = 24


         I         Q          Grid orders:

         1         9         3         4         2

  Grid points:

         1            -1            -1            -1
         2            -1            -1             1
         3            -1          -0.5             1
         4            -1          -0.5            -1
         5            -1           0.5            -1
         6            -1           0.5             1
         7            -1             1             1
         8            -1             1            -1
         9   6.12323e-17             1            -1
        10   6.12323e-17             1             1
        11   6.12323e-17           0.5             1
        12   6.12323e-17           0.5            -1
        13   6.12323e-17          -0.5            -1
        14   6.12323e-17          -0.5             1
        15   6.12323e-17            -1             1
        16   6.12323e-17            -1            -1
        17             1            -1            -1
        18             1            -1             1
        19             1          -0.5             1
        20             1          -0.5            -1
        21             1           0.5            -1
        22             1           0.5             1
        23             1             1             1
        24             1             1            -1

TEST015:
  CC_GRID_INDEX returns an indexed grid of Clenshaw-Curtis points.

  Spatial dimension of grid = 3

  Total number of points in the grid = 24


         I         Q          Grid orders:

         1         9       3     4     2

  Grid indexed points:

         1                 0     0     0
         2                 0     0     1
         3                 0     1     1
         4                 0     1     0
         5                 0     2     0
         6                 0     2     1
         7                 0     3     1
         8                 0     3     0
         9                 1     3     0
        10                 1     3     1
        11                 1     2     1
        12                 1     2     0
        13                 1     1     0
        14                 1     1     1
        15                 1     0     1
        16                 1     0     0
        17                 2     0     0
        18                 2     0     1
        19                 2     1     1
        20                 2     1     0
        21                 2     2     0
        22                 2     2     1
        23                 2     3     1
        24                 2     3     0

TEST02:
  CC_GRIDS_MINMAX returns all Clenshaw Curtis grids
  whose Q value satisfies Q_MIN <= Q <= Q_MAX.
  Here, Q is the sum of the orders of the 1D rules, and
  Q_MIN = 3
  Q_MAX = 5

  Spatial dimension of grids = 2

  Number of grids = 9
  Number of points in the grids = 34

         I         Q          Grid orders:

         1         3         2         1
         2         3         1         2
         3         4         3         1
         4         4         2         2
         5         4         1         3
         6         5         4         1
         7         5         3         2
         8         5         2         3
         9         5         1         4

  Grid points:

         1            -1             0
         2             1             0
         3             0            -1
         4             0             1
         5            -1             0
         6   6.12323e-17             0
         7             1             0
         8            -1            -1
         9            -1             1
        10             1             1
        11             1            -1
        12             0            -1
        13             0   6.12323e-17
        14             0             1
        15            -1             0
        16          -0.5             0
        17           0.5             0
        18             1             0
        19            -1            -1
        20            -1             1
        21   6.12323e-17             1
        22   6.12323e-17            -1
        23             1            -1
        24             1             1
        25            -1            -1
        26            -1   6.12323e-17
        27            -1             1
        28             1             1
        29             1   6.12323e-17
        30             1            -1
        31             0            -1
        32             0          -0.5
        33             0           0.5
        34             0             1

TEST025:
  CC_LEVELS_MINMAX returns all Clenshaw Curtis grids
  whose LEVEL value satisfies
    LEVEL_MIN <= LEVEL <= LEVEL_MAX.
  Here, LEVEL is the sum of the levels of the 1D rules,
  and the order of the rule is 2**LEVEL - 1.

  LEVEL_MIN = 2
  LEVEL_MAX = 2

  Spatial dimension of grids = 2

  Number of grids = 3
  Number of points in the grids = 19

      Grid     Level           Grid Levels         Grid orders:
      ----     -----          ------------        ------------

         1         2         2         0         5         1
         2         2         1         1         3         3
         3         2         0         2         1         5

  Grid points:

         1            -1             0
         2     -0.707107             0
         3   6.12323e-17             0
         4      0.707107             0
         5             1             0
         6            -1            -1
         7            -1   6.12323e-17
         8            -1             1
         9   6.12323e-17             1
        10   6.12323e-17   6.12323e-17
        11   6.12323e-17            -1
        12             1            -1
        13             1   6.12323e-17
        14             1             1
        15             0            -1
        16             0     -0.707107
        17             0   6.12323e-17
        18             0      0.707107
        19             0             1

  LEVEL_MIN = 0
  LEVEL_MAX = 3

  Spatial dimension of grids = 2

  Number of grids = 10
  Number of points in the grids = 74

      Grid     Level           Grid Levels         Grid orders:
      ----     -----          ------------        ------------

         1         0         0         0         1         1
         2         1         1         0         3         1
         3         1         0         1         1         3
         4         2         2         0         5         1
         5         2         1         1         3         3
         6         2         0         2         1         5
         7         3         3         0         9         1
         8         3         2         1         5         3
         9         3         1         2         3         5
        10         3         0         3         1         9

  Grid points:

         1             0             0
         2            -1             0
         3   6.12323e-17             0
         4             1             0
         5             0            -1
         6             0   6.12323e-17
         7             0             1
         8            -1             0
         9     -0.707107             0
        10   6.12323e-17             0
        11      0.707107             0
        12             1             0
        13            -1            -1
        14            -1   6.12323e-17
        15            -1             1
        16   6.12323e-17             1
        17   6.12323e-17   6.12323e-17
        18   6.12323e-17            -1
        19             1            -1
        20             1   6.12323e-17
        21             1             1
        22             0            -1
        23             0     -0.707107
        24             0   6.12323e-17
        25             0      0.707107
        26             0             1
        27            -1             0
        28      -0.92388             0
        29     -0.707107             0
        30     -0.382683             0
        31   6.12323e-17             0
        32      0.382683             0
        33      0.707107             0
        34       0.92388             0
        35             1             0
        36            -1            -1
        37            -1   6.12323e-17
        38            -1             1
        39     -0.707107             1
        40     -0.707107   6.12323e-17
        41     -0.707107            -1
        42   6.12323e-17            -1
        43   6.12323e-17   6.12323e-17
        44   6.12323e-17             1
        45      0.707107             1
        46      0.707107   6.12323e-17
        47      0.707107            -1
        48             1            -1
        49             1   6.12323e-17
        50             1             1
        51            -1            -1
        52            -1     -0.707107
        53            -1   6.12323e-17
        54            -1      0.707107
        55            -1             1
        56   6.12323e-17             1
        57   6.12323e-17      0.707107
        58   6.12323e-17   6.12323e-17
        59   6.12323e-17     -0.707107
        60   6.12323e-17            -1
        61             1            -1
        62             1     -0.707107
        63             1   6.12323e-17
        64             1      0.707107
        65             1             1
        66             0            -1
        67             0      -0.92388
        68             0     -0.707107
        69             0     -0.382683
        70             0   6.12323e-17
        71             0      0.382683
        72             0      0.707107
        73             0       0.92388
        74             0             1

  LEVEL_MIN = 3
  LEVEL_MAX = 3

  Spatial dimension of grids = 2

  Number of grids = 4
  Number of points in the grids = 48

      Grid     Level           Grid Levels         Grid orders:
      ----     -----          ------------        ------------

         1         3         3         0         9         1
         2         3         2         1         5         3
         3         3         1         2         3         5
         4         3         0         3         1         9

  Grid points:

         1            -1             0
         2      -0.92388             0
         3     -0.707107             0
         4     -0.382683             0
         5   6.12323e-17             0
         6      0.382683             0
         7      0.707107             0
         8       0.92388             0
         9             1             0
        10            -1            -1
        11            -1   6.12323e-17
        12            -1             1
        13     -0.707107             1
        14     -0.707107   6.12323e-17
        15     -0.707107            -1
        16   6.12323e-17            -1
        17   6.12323e-17   6.12323e-17
        18   6.12323e-17             1
        19      0.707107             1
        20      0.707107   6.12323e-17
        21      0.707107            -1
        22             1            -1
        23             1   6.12323e-17
        24             1             1
        25            -1            -1
        26            -1     -0.707107
        27            -1   6.12323e-17
        28            -1      0.707107
        29            -1             1
        30   6.12323e-17             1
        31   6.12323e-17      0.707107
        32   6.12323e-17   6.12323e-17
        33   6.12323e-17     -0.707107
        34   6.12323e-17            -1
        35             1            -1
        36             1     -0.707107
        37             1   6.12323e-17
        38             1      0.707107
        39             1             1
        40             0            -1
        41             0      -0.92388
        42             0     -0.707107
        43             0     -0.382683
        44             0   6.12323e-17
        45             0      0.382683
        46             0      0.707107
        47             0       0.92388
        48             0             1

TEST03:
  CC_GRIDS_CONSTRAINED returns all Clenshaw Curtis grids
  satisfying a set of constraints.

  ORDER(I), the order of the 1D rule in dimension I,
  is constrained by 

    ORDER_MIN(I) <= ORDER(I) <= ORDER_MAX(I)

  We also define the total weighted order Q

    Q = ALPHA(1) * ORDER(1) + ... + ALPHA(N) * ORDER(N)

  and further constrain our grids to satisfy

    Q <= Q_MAX = 13

  Spatial dimension of grids = 2

 Dimension Order_min Order_max     Alpha

         1         1         5               2
         2         1         5               3

  Number of grids = 10
  Number of points in the grids = 36

         I               Q          Grid orders:

         1               5         1         1
         2               7         2         1
         3               9         3         1
         4              11         4         1
         5              13         5         1
         6               8         1         2
         7              10         2         2
         8              12         3         2
         9              11         1         3
        10              13         2         3

  Grid points:

         1             0             0
         2            -1             0
         3             1             0
         4            -1             0
         5   6.12323e-17             0
         6             1             0
         7            -1             0
         8          -0.5             0
         9           0.5             0
        10             1             0
        11            -1             0
        12     -0.707107             0
        13   6.12323e-17             0
        14      0.707107             0
        15             1             0
        16             0            -1
        17             0             1
        18            -1            -1
        19            -1             1
        20             1             1
        21             1            -1
        22            -1            -1
        23            -1             1
        24   6.12323e-17             1
        25   6.12323e-17            -1
        26             1            -1
        27             1             1
        28             0            -1
        29             0   6.12323e-17
        30             0             1
        31            -1            -1
        32            -1   6.12323e-17
        33            -1             1
        34             1             1
        35             1   6.12323e-17
        36             1            -1

TEST035:
  CC_LEVELS_CONSTRAINED returns all Clenshaw Curtis grids
  satisfying a set of constraints.

  The constraint on the levels of the 1D Clenshaw Curtis
  rule in spatial dimension I is:

    LEVEL_MIN(I) <= LEVEL(I) <= LEVEL_MAX(I) 

  The constraint on the levels making up a rule is:

    Sum ( 1 <= I <= DIM_NUM ) ALPHA(I) * LEVEL(I) <= Q_MAX.

    where Q_MAX = 13

  The relationship of level to order is roughly 

    ORDER = 2^LEVEL+1.

  Spatial dimension of grids = 2

 Dimension Level_min Level_max     Alpha

         1         1         5               2
         2         1         5               3

  Number of grids = 10
  Number of points in the grids = 358

         I               Q          Grid levels:

         1               5         1         1
         2               7         2         1
         3               9         3         1
         4              11         4         1
         5              13         5         1
         6               8         1         2
         7              10         2         2
         8              12         3         2
         9              11         1         3
        10              13         2         3

  Grid points:

         1            -1            -1
         2            -1   6.12323e-17
         3            -1             1
         4   6.12323e-17             1
         5   6.12323e-17   6.12323e-17
         6   6.12323e-17            -1
         7             1            -1
         8             1   6.12323e-17
         9             1             1
        10            -1            -1
        11            -1   6.12323e-17
        12            -1             1
        13     -0.707107             1
        14     -0.707107   6.12323e-17
        15     -0.707107            -1
        16   6.12323e-17            -1
        17   6.12323e-17   6.12323e-17
        18   6.12323e-17             1
        19      0.707107             1
        20      0.707107   6.12323e-17
        21      0.707107            -1
        22             1            -1
        23             1   6.12323e-17
        24             1             1
        25            -1            -1
        26            -1   6.12323e-17
        27            -1             1
        28      -0.92388             1
        29      -0.92388   6.12323e-17
        30      -0.92388            -1
        31     -0.707107            -1
        32     -0.707107   6.12323e-17
        33     -0.707107             1
        34     -0.382683             1
        35     -0.382683   6.12323e-17
        36     -0.382683            -1
        37   6.12323e-17            -1
        38   6.12323e-17   6.12323e-17
        39   6.12323e-17             1
        40      0.382683             1
        41      0.382683   6.12323e-17
        42      0.382683            -1
        43      0.707107            -1
        44      0.707107   6.12323e-17
        45      0.707107             1
        46       0.92388             1
        47       0.92388   6.12323e-17
        48       0.92388            -1
        49             1            -1
        50             1   6.12323e-17
        51             1             1
        52            -1            -1
        53            -1   6.12323e-17
        54            -1             1
        55     -0.980785             1
        56     -0.980785   6.12323e-17
        57     -0.980785            -1
        58      -0.92388            -1
        59      -0.92388   6.12323e-17
        60      -0.92388             1
        61      -0.83147             1
        62      -0.83147   6.12323e-17
        63      -0.83147            -1
        64     -0.707107            -1
        65     -0.707107   6.12323e-17
        66     -0.707107             1
        67      -0.55557             1
        68      -0.55557   6.12323e-17
        69      -0.55557            -1
        70     -0.382683            -1
        71     -0.382683   6.12323e-17
        72     -0.382683             1
        73      -0.19509             1
        74      -0.19509   6.12323e-17
        75      -0.19509            -1
        76   6.12323e-17            -1
        77   6.12323e-17   6.12323e-17
        78   6.12323e-17             1
        79       0.19509             1
        80       0.19509   6.12323e-17
        81       0.19509            -1
        82      0.382683            -1
        83      0.382683   6.12323e-17
        84      0.382683             1
        85       0.55557             1
        86       0.55557   6.12323e-17
        87       0.55557            -1
        88      0.707107            -1
        89      0.707107   6.12323e-17
        90      0.707107             1
        91       0.83147             1
        92       0.83147   6.12323e-17
        93       0.83147            -1
        94       0.92388            -1
        95       0.92388   6.12323e-17
        96       0.92388             1
        97      0.980785             1
        98      0.980785   6.12323e-17
        99      0.980785            -1
       100             1            -1
       101             1   6.12323e-17
       102             1             1
       103            -1            -1
       104            -1   6.12323e-17
       105            -1             1
       106     -0.995185             1
       107     -0.995185   6.12323e-17
       108     -0.995185            -1
       109     -0.980785            -1
       110     -0.980785   6.12323e-17
       111     -0.980785             1
       112      -0.95694             1
       113      -0.95694   6.12323e-17
       114      -0.95694            -1
       115      -0.92388            -1
       116      -0.92388   6.12323e-17
       117      -0.92388             1
       118     -0.881921             1
       119     -0.881921   6.12323e-17
       120     -0.881921            -1
       121      -0.83147            -1
       122      -0.83147   6.12323e-17
       123      -0.83147             1
       124      -0.77301             1
       125      -0.77301   6.12323e-17
       126      -0.77301            -1
       127     -0.707107            -1
       128     -0.707107   6.12323e-17
       129     -0.707107             1
       130     -0.634393             1
       131     -0.634393   6.12323e-17
       132     -0.634393            -1
       133      -0.55557            -1
       134      -0.55557   6.12323e-17
       135      -0.55557             1
       136     -0.471397             1
       137     -0.471397   6.12323e-17
       138     -0.471397            -1
       139     -0.382683            -1
       140     -0.382683   6.12323e-17
       141     -0.382683             1
       142     -0.290285             1
       143     -0.290285   6.12323e-17
       144     -0.290285            -1
       145      -0.19509            -1
       146      -0.19509   6.12323e-17
       147      -0.19509             1
       148    -0.0980171             1
       149    -0.0980171   6.12323e-17
       150    -0.0980171            -1
       151   6.12323e-17            -1
       152   6.12323e-17   6.12323e-17
       153   6.12323e-17             1
       154     0.0980171             1
       155     0.0980171   6.12323e-17
       156     0.0980171            -1
       157       0.19509            -1
       158       0.19509   6.12323e-17
       159       0.19509             1
       160      0.290285             1
       161      0.290285   6.12323e-17
       162      0.290285            -1
       163      0.382683            -1
       164      0.382683   6.12323e-17
       165      0.382683             1
       166      0.471397             1
       167      0.471397   6.12323e-17
       168      0.471397            -1
       169       0.55557            -1
       170       0.55557   6.12323e-17
       171       0.55557             1
       172      0.634393             1
       173      0.634393   6.12323e-17
       174      0.634393            -1
       175      0.707107            -1
       176      0.707107   6.12323e-17
       177      0.707107             1
       178       0.77301             1
       179       0.77301   6.12323e-17
       180       0.77301            -1
       181       0.83147            -1
       182       0.83147   6.12323e-17
       183       0.83147             1
       184      0.881921             1
       185      0.881921   6.12323e-17
       186      0.881921            -1
       187       0.92388            -1
       188       0.92388   6.12323e-17
       189       0.92388             1
       190       0.95694             1
       191       0.95694   6.12323e-17
       192       0.95694            -1
       193      0.980785            -1
       194      0.980785   6.12323e-17
       195      0.980785             1
       196      0.995185             1
       197      0.995185   6.12323e-17
       198      0.995185            -1
       199             1            -1
       200             1   6.12323e-17
       201             1             1
       202            -1            -1
       203            -1     -0.707107
       204            -1   6.12323e-17
       205            -1      0.707107
       206            -1             1
       207   6.12323e-17             1
       208   6.12323e-17      0.707107
       209   6.12323e-17   6.12323e-17
       210   6.12323e-17     -0.707107
       211   6.12323e-17            -1
       212             1            -1
       213             1     -0.707107
       214             1   6.12323e-17
       215             1      0.707107
       216             1             1
       217            -1            -1
       218            -1     -0.707107
       219            -1   6.12323e-17
       220            -1      0.707107
       221            -1             1
       222     -0.707107             1
       223     -0.707107      0.707107
       224     -0.707107   6.12323e-17
       225     -0.707107     -0.707107
       226     -0.707107            -1
       227   6.12323e-17            -1
       228   6.12323e-17     -0.707107
       229   6.12323e-17   6.12323e-17
       230   6.12323e-17      0.707107
       231   6.12323e-17             1
       232      0.707107             1
       233      0.707107      0.707107
       234      0.707107   6.12323e-17
       235      0.707107     -0.707107
       236      0.707107            -1
       237             1            -1
       238             1     -0.707107
       239             1   6.12323e-17
       240             1      0.707107
       241             1             1
       242            -1            -1
       243            -1     -0.707107
       244            -1   6.12323e-17
       245            -1      0.707107
       246            -1             1
       247      -0.92388             1
       248      -0.92388      0.707107
       249      -0.92388   6.12323e-17
       250      -0.92388     -0.707107
       251      -0.92388            -1
       252     -0.707107            -1
       253     -0.707107     -0.707107
       254     -0.707107   6.12323e-17
       255     -0.707107      0.707107
       256     -0.707107             1
       257     -0.382683             1
       258     -0.382683      0.707107
       259     -0.382683   6.12323e-17
       260     -0.382683     -0.707107
       261     -0.382683            -1
       262   6.12323e-17            -1
       263   6.12323e-17     -0.707107
       264   6.12323e-17   6.12323e-17
       265   6.12323e-17      0.707107
       266   6.12323e-17             1
       267      0.382683             1
       268      0.382683      0.707107
       269      0.382683   6.12323e-17
       270      0.382683     -0.707107
       271      0.382683            -1
       272      0.707107            -1
       273      0.707107     -0.707107
       274      0.707107   6.12323e-17
       275      0.707107      0.707107
       276      0.707107             1
       277       0.92388             1
       278       0.92388      0.707107
       279       0.92388   6.12323e-17
       280       0.92388     -0.707107
       281       0.92388            -1
       282             1            -1
       283             1     -0.707107
       284             1   6.12323e-17
       285             1      0.707107
       286             1             1
       287            -1            -1
       288            -1      -0.92388
       289            -1     -0.707107
       290            -1     -0.382683
       291            -1   6.12323e-17
       292            -1      0.382683
       293            -1      0.707107
       294            -1       0.92388
       295            -1             1
       296   6.12323e-17             1
       297   6.12323e-17       0.92388
       298   6.12323e-17      0.707107
       299   6.12323e-17      0.382683
       300   6.12323e-17   6.12323e-17
       301   6.12323e-17     -0.382683
       302   6.12323e-17     -0.707107
       303   6.12323e-17      -0.92388
       304   6.12323e-17            -1
       305             1            -1
       306             1      -0.92388
       307             1     -0.707107
       308             1     -0.382683
       309             1   6.12323e-17
       310             1      0.382683
       311             1      0.707107
       312             1       0.92388
       313             1             1
       314            -1            -1
       315            -1      -0.92388
       316            -1     -0.707107
       317            -1     -0.382683
       318            -1   6.12323e-17
       319            -1      0.382683
       320            -1      0.707107
       321            -1       0.92388
       322            -1             1
       323     -0.707107             1
       324     -0.707107       0.92388
       325     -0.707107      0.707107
       326     -0.707107      0.382683
       327     -0.707107   6.12323e-17
       328     -0.707107     -0.382683
       329     -0.707107     -0.707107
       330     -0.707107      -0.92388
       331     -0.707107            -1
       332   6.12323e-17            -1
       333   6.12323e-17      -0.92388
       334   6.12323e-17     -0.707107
       335   6.12323e-17     -0.382683
       336   6.12323e-17   6.12323e-17
       337   6.12323e-17      0.382683
       338   6.12323e-17      0.707107
       339   6.12323e-17       0.92388
       340   6.12323e-17             1
       341      0.707107             1
       342      0.707107       0.92388
       343      0.707107      0.707107
       344      0.707107      0.382683
       345      0.707107   6.12323e-17
       346      0.707107     -0.382683
       347      0.707107     -0.707107
       348      0.707107      -0.92388
       349      0.707107            -1
       350             1            -1
       351             1      -0.92388
       352             1     -0.707107
       353             1     -0.382683
       354             1   6.12323e-17
       355             1      0.382683
       356             1      0.707107
       357             1       0.92388
       358             1             1

TEST04
  CLENSHAW_CURTIS_COMPUTE computes
  a Clenshaw-Curtis quadrature rule over [-1,1]
  of given order.

    Order  W             X


         1
                         2               0

         2
                         1              -1
                         1               1

         3
                  0.333333              -1
                   1.33333     6.12323e-17
                  0.333333               1

         4
                  0.111111              -1
                  0.888889            -0.5
                  0.888889             0.5
                  0.111111               1

         5
                 0.0666667              -1
                  0.533333       -0.707107
                       0.8     6.12323e-17
                  0.533333        0.707107
                 0.0666667               1

         6
                      0.04              -1
                  0.360743       -0.809017
                  0.599257       -0.309017
                  0.599257        0.309017
                  0.360743        0.809017
                      0.04               1

         7
                 0.0285714              -1
                  0.253968       -0.866025
                  0.457143            -0.5
                  0.520635     6.12323e-17
                  0.457143             0.5
                  0.253968        0.866025
                 0.0285714               1

         8
                 0.0204082              -1
                  0.190141       -0.900969
                  0.352242        -0.62349
                  0.437208       -0.222521
                  0.437208        0.222521
                  0.352242         0.62349
                  0.190141        0.900969
                 0.0204082               1

         9
                  0.015873              -1
                  0.146219        -0.92388
                  0.279365       -0.707107
                  0.361718       -0.382683
                  0.393651     6.12323e-17
                  0.361718        0.382683
                  0.279365        0.707107
                  0.146219         0.92388
                  0.015873               1

        10
                 0.0123457              -1
                  0.116567       -0.939693
                  0.225284       -0.766044
                   0.30194            -0.5
                  0.343863       -0.173648
                  0.343863        0.173648
                   0.30194             0.5
                  0.225284        0.766044
                  0.116567        0.939693
                 0.0123457               1

TEST045
  To compute a single Clenshaw Curtis weight or abscissa,
  CC_ABSCISSA computes one abscissa,
  CC_WEIGHT computes one weight.

  We use these routines wastefully,
  to compute the order 10 rule one value at a time.

     Order       W               X

        10
                 0.0123457              -1
                  0.116567       -0.939693
                  0.225284       -0.766044
                   0.30194            -0.5
                  0.343863       -0.173648
                  0.343863        0.173648
                   0.30194             0.5
                  0.225284        0.766044
                  0.116567        0.939693
                 0.0123457               1

TEST05
  CLENSHAW_CURTIS_COMPUTE computes a Clenshaw-Curtis rule;

  The integration interval is [-1,1].
  Quadrature order will vary.
  Integrand will vary.

      Order     F1              F2              F3

       1           -0.16         2.22222         1.41421
       2         1.75866        0.689655         1.93185
       3        0.479555         1.71137         1.58676
       4        0.479555         1.54284         1.10354
       5        0.479377         1.58133         1.52315
       6        0.479422         1.58446         1.49143
       7        0.479428         1.58181         1.33096
       8        0.479428          1.5823         1.48396
       9        0.479428         1.58222         1.47649
      10        0.479428         1.58223         1.39131
      11        0.479428         1.58223         1.47392
      12        0.479428         1.58223         1.47059
      13        0.479428         1.58223         1.41541
      14        0.479428         1.58223         1.46934
      15        0.479428         1.58223         1.46761
      16        0.479428         1.58223         1.42832

  Exact         0.479428         1.58223         1.46045

TEST06
  CLENSHAW_CURTIS_SET sets up a Clenshaw-Curtis rule;

  The integration interval is [-1,1].
  Quadrature order will vary.
  Integrand will vary.

  Order     F1              F2              F3

       1           -0.16         2.22222         1.41421
       2         1.75866        0.689655         1.93185
       3        0.479555         1.71137         1.58676
       4        0.479555         1.54284         1.10354
       5        0.479377         1.58133         1.52315
       6        0.479422         1.58446         1.49143
       7        0.479428         1.58181         1.33096
       8        0.479428          1.5823         1.48396
       9        0.479428         1.58222         1.47649
      10        0.479428         1.58223         1.39131
      11        0.479428         1.58223         1.47392
      12        0.479428         1.58223         1.47059
      13        0.479428         1.58223         1.41541
      14        0.479428         1.58223         1.46934
      15        0.479428         1.58223         1.46761
      16        0.479428         1.58223         1.42832

  Exact         0.479428         1.58223         1.46045

TEST07
  DTABLE_WRITE0 writes a Clenshaw-Curtis
  quadrature rule to a file.

  Spatial dimension = 1
  Computing the rule of order = 9

  Write abscissas to file "cc_x_d1_o9.txt".
  Write weights to file "cc_w_d1_o9.txt".
  Write region to file "cc_r_d1_o9.txt".

TEST08
  CLENSHAW_CURTIS_COMPUTE_ND computes
  a multidimensional Clenshaw-Curtis quadrature rule
  over the hypercube [-1,1]^ND of given
  (possibly different) orders in each dimension.

  In this example, we use the SAME ORDER
  in all dimensions.

  Spatial dimension DIM_NUM = 2
  1D orders =   5  5
  Number of points = 25

      Weight           X(1)           X(2)
  --------------  --------------  --------------

      0.00444444              -1              -1
       0.0355556              -1       -0.707107
       0.0533333              -1     6.12323e-17
       0.0355556              -1        0.707107
      0.00444444              -1               1
       0.0355556       -0.707107              -1
        0.284444       -0.707107       -0.707107
        0.426667       -0.707107     6.12323e-17
        0.284444       -0.707107        0.707107
       0.0355556       -0.707107               1
       0.0533333     6.12323e-17              -1
        0.426667     6.12323e-17       -0.707107
            0.64     6.12323e-17     6.12323e-17
        0.426667     6.12323e-17        0.707107
       0.0533333     6.12323e-17               1
       0.0355556        0.707107              -1
        0.284444        0.707107       -0.707107
        0.426667        0.707107     6.12323e-17
        0.284444        0.707107        0.707107
       0.0355556        0.707107               1
      0.00444444               1              -1
       0.0355556               1       -0.707107
       0.0533333               1     6.12323e-17
       0.0355556               1        0.707107
      0.00444444               1               1

               4

TEST09
  CLENSHAW_CURTIS_COMPUTE_ND computes
  a multidimensional Clenshaw-Curtis quadrature rule
  over the hypercube [-1,1]^ND of given
  (possibly different) orders in each dimension.

  In this example, we use DIFFERENT ORDERS
  in each dimension.

  Spatial dimension DIM_NUM = 3
  1D orders =   2  4  3
  Number of points = 24

      Weight           X(1)           X(2)           X(3)
  --------------  --------------  --------------  --------------

        0.037037              -1              -1              -1
        0.148148              -1              -1     6.12323e-17
        0.037037              -1              -1               1
        0.296296              -1            -0.5              -1
         1.18519              -1            -0.5     6.12323e-17
        0.296296              -1            -0.5               1
        0.296296              -1             0.5              -1
         1.18519              -1             0.5     6.12323e-17
        0.296296              -1             0.5               1
        0.037037              -1               1              -1
        0.148148              -1               1     6.12323e-17
        0.037037              -1               1               1
        0.037037               1              -1              -1
        0.148148               1              -1     6.12323e-17
        0.037037               1              -1               1
        0.296296               1            -0.5              -1
         1.18519               1            -0.5     6.12323e-17
        0.296296               1            -0.5               1
        0.296296               1             0.5              -1
         1.18519               1             0.5     6.12323e-17
        0.296296               1             0.5               1
        0.037037               1               1              -1
        0.148148               1               1     6.12323e-17
        0.037037               1               1               1

               8

TEST10
  Use DTABLE_WRITE0 to write out a multidimensional rule.
  CLENSHAW_CURTIS_COMPUTE_ND computes
  a multidimensional Clenshaw-Curtis quadrature rule
  over the hypercube [-1,1]^ND of given
  (possibly different) orders in each dimension.

  In this example, we use the SAME ORDER
  in all dimensions.

  Spatial dimension DIM_NUM = 4
  1D orders =   3  3  3  3
  Number of points = 81

  Write abscissas to file "cc_x_d4_o81.txt".
  Write weights to file "cc_w_d4_o81.txt".
  Write region to file "cc_r_d4_o81.txt".

TEST11
  CC_ABSCISSA_LEVEL_1D reports the level on which
  a Clenshaw Curtis abscissa of given index will first
  be generated, assuming a series of grids that grow
  in order as 2^LEVEL+1.

  Base B = 5
  ORDER 2^B+1 = 33

         I  Level(I)

         0         1
         1         5
         2         4
         3         5
         4         3
         5         5
         6         4
         7         5
         8         2
         9         5
        10         4
        11         5
        12         3
        13         5
        14         4
        15         5
        16         0
        17         5
        18         4
        19         5
        20         3
        21         5
        22         4
        23         5
        24         2
        25         5
        26         4
        27         5
        28         3
        29         5
        30         4
        31         5
        32         1

TEST12
  CC_ABSCISSA_LEVEL_1D can also be called for values
  outside the standard range of 0 through 2^LEVEL_MAX.
  In that case, a MOD operation is applied first,
  to make a sensible result.

  Base B = 5
  ORDER = 2^B+1 = 33

         I  Mod(I,O)  Level(I)

         6         6         4
        95        29         5
        80        14         4
        47        14         4
        30        30         4
       -12        21         5
        11        11         5
        -7        26         4
       -15        18         4
        56        23         5
       -13        20         3
        34         1         5
        28        28         3
        71         5         5
        76        10         4
       -20        13         5
        88        22         4
        22        22         4
        -9        24         2
       -19        14         4

TEST13
  CC_ABSCISSA_LEVEL_ND reports the level on which
  a Clenshaw Curtis abscissa of given index will first
  be generated, assuming a series of grids that grow
  in order as 2^LEVEL+1.

  This routine is applied for multidimensional cases.

  Base B = 3
  ORDER 2^B+1 = 9
  DIM_NUM = 2

         I         J  Level(I,J)

         0         0         2
         0         1         4
         0         2         3
         0         3         4
         0         4         1
         0         5         4
         0         6         3
         0         7         4
         0         8         2
         1         0         4
         1         1         6
         1         2         5
         1         3         6
         1         4         3
         1         5         6
         1         6         5
         1         7         6
         1         8         4
         2         0         3
         2         1         5
         2         2         4
         2         3         5
         2         4         2
         2         5         5
         2         6         4
         2         7         5
         2         8         3
         3         0         4
         3         1         6
         3         2         5
         3         3         6
         3         4         3
         3         5         6
         3         6         5
         3         7         6
         3         8         4
         4         0         1
         4         1         3
         4         2         2
         4         3         3
         4         4         0
         4         5         3
         4         6         2
         4         7         3
         4         8         1
         5         0         4
         5         1         6
         5         2         5
         5         3         6
         5         4         3
         5         5         6
         5         6         5
         5         7         6
         5         8         4
         6         0         3
         6         1         5
         6         2         4
         6         3         5
         6         4         2
         6         5         5
         6         6         4
         6         7         5
         6         8         3
         7         0         4
         7         1         6
         7         2         5
         7         3         6
         7         4         3
         7         5         6
         7         6         5
         7         7         6
         7         8         4
         8         0         2
         8         1         4
         8         2         3
         8         3         4
         8         4         1
         8         5         4
         8         6         3
         8         7         4
         8         8         2

CLENSHAW_CURTIS_GRID_TEST
  Normal end of execution.

03 March 2022 10:03:05 AM