Tue Oct 19 17:00:16 2021

padua_test:
  Python version: 3.6.9
  Test padua()

padua_order_test
  Python version: 3.6.9
  padua_order converts the level L into the order N
  of any Padua rule.

     L         N

     0         1
     1         3
     2         6
     3        10
     4        15
     5        21
     6        28
     7        36
     8        45
     9        55
    10        66

padua_order_test:
  Normal end of execution.

padua_plot_test
  Python version: 3.6.9
  padua_plot plots the Padua points.

  Plot file stored as "padua_0.png"
  Plot file stored as "padua_1.png"
  Plot file stored as "padua_2.png"
  Plot file stored as "padua_3.png"
  Plot file stored as "padua_4.png"
  Plot file stored as "padua_5.png"
  Plot file stored as "padua_6.png"
  Plot file stored as "padua_7.png"
  Plot file stored as "padua_8.png"
  Plot file stored as "padua_9.png"
  Plot file stored as "padua_10.png"

padua_plot_test
  Normal end of execution

padua_points_test
  Python version: 3.6.9
  padua_points returns the points of a Padua rule.

  Level 0 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           0  
           0  


  Level 1 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
           0  

      1 :
          -1  
           1  

      2 :
          -1  
          -1  


  Level 2 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
         0.5  

      1 :
           1  
          -1  

      2 :
           0  
           1  

      3 :
           0  
        -0.5  

      4 :
          -1  
         0.5  

      5 :
          -1  
          -1  


  Level 3 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.707107  

      1 :
           1  
   -0.707107  

      2 :
         0.5  
           1  

      3 :
         0.5  
           0  

      4 :
         0.5  
          -1  

      5 :
        -0.5  
    0.707107  

      6 :
        -0.5  
   -0.707107  

      7 :
          -1  
           1  

      8 :
          -1  
           0  

      9 :
          -1  
          -1  


  Level 4 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.809017  

      1 :
           1  
   -0.309017  

      2 :
           1  
          -1  

      3 :
    0.707107  
           1  

      4 :
    0.707107  
    0.309017  

      5 :
    0.707107  
   -0.809017  

      6 :
           0  
    0.809017  

      7 :
           0  
   -0.309017  

      8 :
           0  
          -1  

      9 :
   -0.707107  
           1  

     10 :
   -0.707107  
    0.309017  

     11 :
   -0.707107  
   -0.809017  

     12 :
          -1  
    0.809017  

     13 :
          -1  
   -0.309017  

     14 :
          -1  
          -1  


  Level 5 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.866025  

      1 :
           1  
           0  

      2 :
           1  
   -0.866025  

      3 :
    0.809017  
           1  

      4 :
    0.809017  
         0.5  

      5 :
    0.809017  
        -0.5  

      6 :
    0.809017  
          -1  

      7 :
    0.309017  
    0.866025  

      8 :
    0.309017  
           0  

      9 :
    0.309017  
   -0.866025  

     10 :
   -0.309017  
           1  

     11 :
   -0.309017  
         0.5  

     12 :
   -0.309017  
        -0.5  

     13 :
   -0.309017  
          -1  

     14 :
   -0.809017  
    0.866025  

     15 :
   -0.809017  
           0  

     16 :
   -0.809017  
   -0.866025  

     17 :
          -1  
           1  

     18 :
          -1  
         0.5  

     19 :
          -1  
        -0.5  

     20 :
          -1  
          -1  


  Level 6 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.900969  

      1 :
           1  
    0.222521  

      2 :
           1  
    -0.62349  

      3 :
           1  
          -1  

      4 :
    0.866025  
           1  

      5 :
    0.866025  
     0.62349  

      6 :
    0.866025  
   -0.222521  

      7 :
    0.866025  
   -0.900969  

      8 :
         0.5  
    0.900969  

      9 :
         0.5  
    0.222521  

     10 :
         0.5  
    -0.62349  

     11 :
         0.5  
          -1  

     12 :
           0  
           1  

     13 :
           0  
     0.62349  

     14 :
           0  
   -0.222521  

     15 :
           0  
   -0.900969  

     16 :
        -0.5  
    0.900969  

     17 :
        -0.5  
    0.222521  

     18 :
        -0.5  
    -0.62349  

     19 :
        -0.5  
          -1  

     20 :
   -0.866025  
           1  

     21 :
   -0.866025  
     0.62349  

     22 :
   -0.866025  
   -0.222521  

     23 :
   -0.866025  
   -0.900969  

     24 :
          -1  
    0.900969  

     25 :
          -1  
    0.222521  

     26 :
          -1  
    -0.62349  

     27 :
          -1  
          -1  


  Level 7 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
     0.92388  

      1 :
           1  
    0.382683  

      2 :
           1  
   -0.382683  

      3 :
           1  
    -0.92388  

      4 :
    0.900969  
           1  

      5 :
    0.900969  
    0.707107  

      6 :
    0.900969  
           0  

      7 :
    0.900969  
   -0.707107  

      8 :
    0.900969  
          -1  

      9 :
     0.62349  
     0.92388  

     10 :
     0.62349  
    0.382683  

     11 :
     0.62349  
   -0.382683  

     12 :
     0.62349  
    -0.92388  

     13 :
    0.222521  
           1  

     14 :
    0.222521  
    0.707107  

     15 :
    0.222521  
           0  

     16 :
    0.222521  
   -0.707107  

     17 :
    0.222521  
          -1  

     18 :
   -0.222521  
     0.92388  

     19 :
   -0.222521  
    0.382683  

     20 :
   -0.222521  
   -0.382683  

     21 :
   -0.222521  
    -0.92388  

     22 :
    -0.62349  
           1  

     23 :
    -0.62349  
    0.707107  

     24 :
    -0.62349  
           0  

     25 :
    -0.62349  
   -0.707107  

     26 :
    -0.62349  
          -1  

     27 :
   -0.900969  
     0.92388  

     28 :
   -0.900969  
    0.382683  

     29 :
   -0.900969  
   -0.382683  

     30 :
   -0.900969  
    -0.92388  

     31 :
          -1  
           1  

     32 :
          -1  
    0.707107  

     33 :
          -1  
           0  

     34 :
          -1  
   -0.707107  

     35 :
          -1  
          -1  


  Level 8 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.939693  

      1 :
           1  
         0.5  

      2 :
           1  
   -0.173648  

      3 :
           1  
   -0.766044  

      4 :
           1  
          -1  

      5 :
     0.92388  
           1  

      6 :
     0.92388  
    0.766044  

      7 :
     0.92388  
    0.173648  

      8 :
     0.92388  
        -0.5  

      9 :
     0.92388  
   -0.939693  

     10 :
    0.707107  
    0.939693  

     11 :
    0.707107  
         0.5  

     12 :
    0.707107  
   -0.173648  

     13 :
    0.707107  
   -0.766044  

     14 :
    0.707107  
          -1  

     15 :
    0.382683  
           1  

     16 :
    0.382683  
    0.766044  

     17 :
    0.382683  
    0.173648  

     18 :
    0.382683  
        -0.5  

     19 :
    0.382683  
   -0.939693  

     20 :
           0  
    0.939693  

     21 :
           0  
         0.5  

     22 :
           0  
   -0.173648  

     23 :
           0  
   -0.766044  

     24 :
           0  
          -1  

     25 :
   -0.382683  
           1  

     26 :
   -0.382683  
    0.766044  

     27 :
   -0.382683  
    0.173648  

     28 :
   -0.382683  
        -0.5  

     29 :
   -0.382683  
   -0.939693  

     30 :
   -0.707107  
    0.939693  

     31 :
   -0.707107  
         0.5  

     32 :
   -0.707107  
   -0.173648  

     33 :
   -0.707107  
   -0.766044  

     34 :
   -0.707107  
          -1  

     35 :
    -0.92388  
           1  

     36 :
    -0.92388  
    0.766044  

     37 :
    -0.92388  
    0.173648  

     38 :
    -0.92388  
        -0.5  

     39 :
    -0.92388  
   -0.939693  

     40 :
          -1  
    0.939693  

     41 :
          -1  
         0.5  

     42 :
          -1  
   -0.173648  

     43 :
          -1  
   -0.766044  

     44 :
          -1  
          -1  


  Level 9 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.951057  

      1 :
           1  
    0.587785  

      2 :
           1  
           0  

      3 :
           1  
   -0.587785  

      4 :
           1  
   -0.951057  

      5 :
    0.939693  
           1  

      6 :
    0.939693  
    0.809017  

      7 :
    0.939693  
    0.309017  

      8 :
    0.939693  
   -0.309017  

      9 :
    0.939693  
   -0.809017  

     10 :
    0.939693  
          -1  

     11 :
    0.766044  
    0.951057  

     12 :
    0.766044  
    0.587785  

     13 :
    0.766044  
           0  

     14 :
    0.766044  
   -0.587785  

     15 :
    0.766044  
   -0.951057  

     16 :
         0.5  
           1  

     17 :
         0.5  
    0.809017  

     18 :
         0.5  
    0.309017  

     19 :
         0.5  
   -0.309017  

     20 :
         0.5  
   -0.809017  

     21 :
         0.5  
          -1  

     22 :
    0.173648  
    0.951057  

     23 :
    0.173648  
    0.587785  

     24 :
    0.173648  
           0  

     25 :
    0.173648  
   -0.587785  

     26 :
    0.173648  
   -0.951057  

     27 :
   -0.173648  
           1  

     28 :
   -0.173648  
    0.809017  

     29 :
   -0.173648  
    0.309017  

     30 :
   -0.173648  
   -0.309017  

     31 :
   -0.173648  
   -0.809017  

     32 :
   -0.173648  
          -1  

     33 :
        -0.5  
    0.951057  

     34 :
        -0.5  
    0.587785  

     35 :
        -0.5  
           0  

     36 :
        -0.5  
   -0.587785  

     37 :
        -0.5  
   -0.951057  

     38 :
   -0.766044  
           1  

     39 :
   -0.766044  
    0.809017  

     40 :
   -0.766044  
    0.309017  

     41 :
   -0.766044  
   -0.309017  

     42 :
   -0.766044  
   -0.809017  

     43 :
   -0.766044  
          -1  

     44 :
   -0.939693  
    0.951057  

     45 :
   -0.939693  
    0.587785  

     46 :
   -0.939693  
           0  

     47 :
   -0.939693  
   -0.587785  

     48 :
   -0.939693  
   -0.951057  

     49 :
          -1  
           1  

     50 :
          -1  
    0.809017  

     51 :
          -1  
    0.309017  

     52 :
          -1  
   -0.309017  

     53 :
          -1  
   -0.809017  

     54 :
          -1  
          -1  


  Level 10 Padua points:

  Row: 
      0       
      1       

  Col
      0 :
           1  
    0.959493  

      1 :
           1  
    0.654861  

      2 :
           1  
    0.142315  

      3 :
           1  
   -0.415415  

      4 :
           1  
   -0.841254  

      5 :
           1  
          -1  

      6 :
    0.951057  
           1  

      7 :
    0.951057  
    0.841254  

      8 :
    0.951057  
    0.415415  

      9 :
    0.951057  
   -0.142315  

     10 :
    0.951057  
   -0.654861  

     11 :
    0.951057  
   -0.959493  

     12 :
    0.809017  
    0.959493  

     13 :
    0.809017  
    0.654861  

     14 :
    0.809017  
    0.142315  

     15 :
    0.809017  
   -0.415415  

     16 :
    0.809017  
   -0.841254  

     17 :
    0.809017  
          -1  

     18 :
    0.587785  
           1  

     19 :
    0.587785  
    0.841254  

     20 :
    0.587785  
    0.415415  

     21 :
    0.587785  
   -0.142315  

     22 :
    0.587785  
   -0.654861  

     23 :
    0.587785  
   -0.959493  

     24 :
    0.309017  
    0.959493  

     25 :
    0.309017  
    0.654861  

     26 :
    0.309017  
    0.142315  

     27 :
    0.309017  
   -0.415415  

     28 :
    0.309017  
   -0.841254  

     29 :
    0.309017  
          -1  

     30 :
           0  
           1  

     31 :
           0  
    0.841254  

     32 :
           0  
    0.415415  

     33 :
           0  
   -0.142315  

     34 :
           0  
   -0.654861  

     35 :
           0  
   -0.959493  

     36 :
   -0.309017  
    0.959493  

     37 :
   -0.309017  
    0.654861  

     38 :
   -0.309017  
    0.142315  

     39 :
   -0.309017  
   -0.415415  

     40 :
   -0.309017  
   -0.841254  

     41 :
   -0.309017  
          -1  

     42 :
   -0.587785  
           1  

     43 :
   -0.587785  
    0.841254  

     44 :
   -0.587785  
    0.415415  

     45 :
   -0.587785  
   -0.142315  

     46 :
   -0.587785  
   -0.654861  

     47 :
   -0.587785  
   -0.959493  

     48 :
   -0.809017  
    0.959493  

     49 :
   -0.809017  
    0.654861  

     50 :
   -0.809017  
    0.142315  

     51 :
   -0.809017  
   -0.415415  

     52 :
   -0.809017  
   -0.841254  

     53 :
   -0.809017  
          -1  

     54 :
   -0.951057  
           1  

     55 :
   -0.951057  
    0.841254  

     56 :
   -0.951057  
    0.415415  

     57 :
   -0.951057  
   -0.142315  

     58 :
   -0.951057  
   -0.654861  

     59 :
   -0.951057  
   -0.959493  

     60 :
          -1  
    0.959493  

     61 :
          -1  
    0.654861  

     62 :
          -1  
    0.142315  

     63 :
          -1  
   -0.415415  

     64 :
          -1  
   -0.841254  

     65 :
          -1  
          -1  


padua_points_test:
  Normal end of execution.

padua_points_set_test
  Python version: 3.6.9
  padua_points_set looks the Padua points up in a table.

  Level 3  Padua points

     0               1        0.707107
                     1        0.707107
     1               1       -0.707107
                     1       -0.707107
     2             0.5               1
                   0.5               1
     3             0.5               0
                   0.5               0
     4             0.5              -1
                   0.5              -1
     5            -0.5        0.707107
                  -0.5        0.707107
     6            -0.5       -0.707107
                  -0.5       -0.707107
     7              -1               1
                    -1               1
     8              -1               0
                    -1               0
     9              -1              -1
                    -1              -1

  Level 4  Padua points

     0               1        0.809017
                     1        0.809017
     1               1       -0.309017
                     1       -0.309017
     2               1              -1
                     1              -1
     3        0.707107               1
              0.707107               1
     4        0.707107        0.309017
              0.707107        0.309017
     5        0.707107       -0.809017
              0.707107       -0.809017
     6               0        0.809017
                     0        0.809017
     7               0       -0.309017
                     0       -0.309017
     8               0              -1
                     0              -1
     9       -0.707107               1
             -0.707107               1
    10       -0.707107        0.309017
             -0.707107        0.309017
    11       -0.707107       -0.809017
             -0.707107       -0.809017
    12              -1        0.809017
                    -1        0.809017
    13              -1       -0.309017
                    -1       -0.309017
    14              -1              -1
                    -1              -1

padua_points_set_test:
  Normal end of execution.

padua_weights_test
  Python version: 3.6.9
  padua_weights returns the weights of a Padua rule.

  Level 0 Padua weightss:

     0:             4

  Level 1 Padua weightss:

     0:             2
     1:             1
     2:             1

  Level 2 Padua weightss:

     0:      0.666667
     1:   3.70074e-17
     2:      0.444444
     3:       2.22222
     4:      0.666667
     5:   3.70074e-17

  Level 3 Padua weightss:

     0:      0.111111
     1:      0.111111
     2:      0.222222
     3:       1.33333
     4:      0.222222
     5:      0.888889
     6:      0.888889
     7:    -0.0555556
     8:      0.333333
     9:    -0.0555556

  Level 4 Padua weightss:

     0:      0.061173
     1:     0.0810492
     2:   -0.00888889
     3:     0.0533333
     4:      0.625924
     5:       0.38741
     6:      0.545807
     7:      0.983082
     8:     0.0711111
     9:     0.0533333
    10:      0.625924
    11:       0.38741
    12:      0.061173
    13:     0.0810492
    14:   -0.00888889

  Level 5 Padua weightss:

     0:     0.0207407
     1:     0.0385185
     2:     0.0207407
     3:     0.0318931
     4:       0.32885
     5:       0.32885
     6:     0.0318931
     7:      0.280452
     8:       0.63761
     9:      0.280452
    10:     0.0451439
    11:      0.554113
    12:      0.554113
    13:     0.0451439
    14:      0.187696
    15:      0.346093
    16:      0.187696
    17:    -0.0103704
    18:     0.0503704
    19:     0.0503704
    20:    -0.0103704

  Level 6 Padua weightss:

     0:     0.0142543
     1:     0.0263393
     2:     0.0195727
     3:   -0.00302343
     4:     0.0120937
     5:      0.174314
     6:       0.22089
     7:      0.100638
     8:      0.167723
     9:      0.402706
    10:      0.324506
    11:       0.01935
    12:     0.0247921
    13:      0.372182
    14:      0.448963
    15:      0.195332
    16:      0.167723
    17:      0.402706
    18:      0.324506
    19:       0.01935
    20:     0.0120937
    21:      0.174314
    22:       0.22089
    23:      0.100638
    24:     0.0142543
    25:     0.0263393
    26:     0.0195727
    27:   -0.00302343

  Level 7 Padua weightss:

     0:    0.00635588
     1:     0.0140523
     2:     0.0140523
     3:    0.00635588
     4:    0.00864992
     5:      0.106201
     6:      0.150581
     7:      0.106201
     8:    0.00864992
     9:     0.0964699
    10:      0.255773
    11:      0.255773
    12:     0.0964699
    13:     0.0177137
    14:      0.249093
    15:      0.340804
    16:      0.249093
    17:     0.0177137
    18:      0.122182
    19:      0.315027
    20:      0.315027
    21:      0.122182
    22:     0.0126387
    23:      0.197994
    24:      0.283218
    25:      0.197994
    26:     0.0126387
    27:     0.0594932
    28:      0.130648
    29:      0.130648
    30:     0.0594932
    31:   -0.00328798
    32:     0.0133787
    33:     0.0206349
    34:     0.0133787
    35:   -0.00328798

  Level 8 Padua weightss:

     0:    0.00493068
     1:     0.0102646
     2:     0.0111146
     3:    0.00670609
     4:   -0.00126984
     5:    0.00406163
     6:     0.0640019
     7:     0.0996591
     8:     0.0883832
     9:     0.0363315
    10:      0.063426
    11:      0.169947
    12:       0.19275
    13:      0.125834
    14:    0.00677249
    15:     0.0100477
    16:       0.16481
    17:      0.247731
    18:      0.217084
    19:     0.0837633
    20:     0.0893669
    21:      0.236402
    22:      0.272941
    23:      0.178433
    24:     0.0101587
    25:     0.0100477
    26:       0.16481
    27:      0.247731
    28:      0.217084
    29:     0.0837633
    30:      0.063426
    31:      0.169947
    32:       0.19275
    33:      0.125834
    34:    0.00677249
    35:    0.00406163
    36:     0.0640019
    37:     0.0996591
    38:     0.0883832
    39:     0.0363315
    40:    0.00493068
    41:     0.0102646
    42:     0.0111146
    43:    0.00670609
    44:   -0.00126984

  Level 9 Padua weightss:

     0:    0.00255069
     1:    0.00608423
     2:    0.00742152
     3:    0.00608423
     4:    0.00255069
     5:    0.00323908
     6:     0.0431759
     7:     0.0701525
     8:     0.0701525
     9:     0.0431759
    10:    0.00323908
    11:      0.040319
    12:      0.114298
    13:      0.141335
    14:      0.114298
    15:      0.040319
    16:    0.00750617
    17:      0.114216
    18:      0.180218
    19:      0.180218
    20:      0.114216
    21:    0.00750617
    22:     0.0623497
    23:      0.173042
    24:      0.216942
    25:      0.173042
    26:     0.0623497
    27:    0.00818618
    28:      0.129536
    29:      0.206141
    30:      0.206141
    31:      0.129536
    32:    0.00818618
    33:     0.0556455
    34:      0.152439
    35:      0.187711
    36:      0.152439
    37:     0.0556455
    38:     0.0046594
    39:     0.0835452
    40:       0.13708
    41:       0.13708
    42:     0.0835452
    43:     0.0046594
    44:     0.0242529
    45:     0.0572733
    46:     0.0700826
    47:     0.0572733
    48:     0.0242529
    49:   -0.00136861
    50:    0.00483798
    51:    0.00887631
    52:    0.00887631
    53:    0.00483798
    54:   -0.00136861

  Level 10 Padua weightss:

     0:    0.00213535
     1:    0.00470574
     2:    0.00589175
     3:    0.00525003
     4:    0.00284323
     5:  -0.000624076
     6:    0.00171962
     7:     0.0284347
     8:     0.0486334
     9:      0.053265
    10:      0.040996
    11:     0.0161094
    12:     0.0285577
    13:     0.0806621
    14:      0.105321
    15:     0.0965987
    16:     0.0572471
    17:    0.00288377
    18:     0.0046107
    19:     0.0793285
    20:      0.131369
    21:      0.143017
    22:      0.109039
    23:     0.0398129
    24:     0.0460306
    25:      0.128358
    26:      0.169606
    27:      0.156232
    28:     0.0931136
    29:     0.0050865
    30:    0.00570484
    31:     0.0982275
    32:      0.163504
    33:      0.176419
    34:      0.134728
    35:     0.0489489
    36:     0.0460306
    37:      0.128358
    38:      0.169606
    39:      0.156232
    40:     0.0931136
    41:     0.0050865
    42:     0.0046107
    43:     0.0793285
    44:      0.131369
    45:      0.143017
    46:      0.109039
    47:     0.0398129
    48:     0.0285577
    49:     0.0806621
    50:      0.105321
    51:     0.0965987
    52:     0.0572471
    53:    0.00288377
    54:    0.00171962
    55:     0.0284347
    56:     0.0486334
    57:      0.053265
    58:      0.040996
    59:     0.0161094
    60:    0.00213535
    61:    0.00470574
    62:    0.00589175
    63:    0.00525003
    64:    0.00284323
    65:  -0.000624076

padua_weights_test
  Normal end of execution

padua_weights_set_test
  Python version: 3.6.9
  padua_weights_set looks up Padua weights in a table.

  Level 3  Padua weights

     0        0.111111        0.111111
     1        0.111111        0.111111
     2        0.222222        0.222222
     3         1.33333         1.33333
     4        0.222222        0.222222
     5        0.888889        0.888889
     6        0.888889        0.888889
     7      -0.0555556      -0.0555556
     8        0.333333        0.333333
     9      -0.0555556      -0.0555556

  Maximum difference = 7.77156e-16

  Level 4  Padua weights

     0        0.061173        0.061173
     1       0.0810492       0.0810492
     2     -0.00888889     -0.00888889
     3       0.0533333       0.0533333
     4        0.625924        0.625924
     5         0.38741         0.38741
     6        0.545807        0.545807
     7        0.983082        0.983082
     8       0.0711111       0.0711111
     9       0.0533333       0.0533333
    10        0.625924        0.625924
    11         0.38741         0.38741
    12        0.061173        0.061173
    13       0.0810492       0.0810492
    14     -0.00888889     -0.00888889

  Maximum difference = 1.22125e-15

padua_weights_set_test
  Normal end of execution.

padua_test:
  Normal end of execution.
Tue Oct 19 17:00:17 2021