07-Jan-2022 22:44:34

line_fekete_rule_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test line_fekete_rule().

line_fekete_rule_bos_levenberg_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 5
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:

     1:           -1
     2:    -0.663664
     3:  -0.00700701
     4:     0.641642
     5:            1

  Saved plot in file "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 5
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 5

  Estimated Fekete points XF:

     1:           -1
     2:    -0.663664
     3:  -0.00700701
     4:     0.641642
     5:            1

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 5
  with the Legendre basis and uniform weight.

ind =

           1
         989
        2516
        4055
        5001


  NF = 5

  Estimated Fekete points XF:

     1:           -1
     2:      -0.6048
     3:        0.006
     4:       0.6216
     5:            1

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_monomial_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 5
  using the monomial basis and uniform weight.

  NF = 5

  Estimated Fekete points XF:

     1:           -1
     2:       -0.656
     3:            0
     4:       0.6248
     5:            1

  Graphics saved as "line_fekete_monomial.png"

  Sum(WF) = 2

line_fekete_rule_bos_levenberg_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 11
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:

     1:           -1
     2:    -0.937938
     3:    -0.791792
     4:    -0.573574
     5:    -0.299299
     6:    -0.003003
     7:     0.299299
     8:      0.56957
     9:      0.78979
    10:     0.937938
    11:            1

  Saved plot in file "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 11
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 11

  Estimated Fekete points XF:

     1:           -1
     2:    -0.937938
     3:    -0.791792
     4:    -0.573574
     5:    -0.299299
     6:    -0.003003
     7:     0.299299
     8:      0.56957
     9:      0.78979
    10:     0.937938
    11:            1

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 11
  with the Legendre basis and uniform weight.

ind =

           1
         195
         654
        1135
        1764
        2487
        3200
        3854
        4346
        4805
        5001


  NF = 11

  Estimated Fekete points XF:

     1:           -1
     2:      -0.9224
     3:      -0.7388
     4:      -0.5464
     5:      -0.2948
     6:      -0.0056
     7:       0.2796
     8:       0.5412
     9:        0.738
    10:       0.9216
    11:            1

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_monomial_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 11
  using the monomial basis and uniform weight.

  NF = 11

  Estimated Fekete points XF:

     1:           -1
     2:      -0.8996
     3:      -0.7056
     4:      -0.5676
     5:      -0.4124
     6:       -0.046
     7:       0.3084
     8:       0.4948
     9:       0.6512
    10:       0.8868
    11:            1

  Graphics saved as "line_fekete_monomial.png"

  Sum(WF) = 2

line_fekete_rule_bos_levenberg_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 21
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:

     1:           -1
     2:    -0.983984
     3:    -0.943944
     4:    -0.881882
     5:      -0.7998
     6:      -0.6997
     7:    -0.581582
     8:    -0.449449
     9:    -0.307307
    10:    -0.157157
    11:    -0.001001
    12:     0.153153
    13:     0.305305
    14:     0.449449
    15:     0.581582
    16:       0.6997
    17:     0.801802
    18:     0.883884
    19:     0.943944
    20:     0.983984
    21:            1

  Saved plot in file "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 21
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 21

  Estimated Fekete points XF:

     1:           -1
     2:    -0.983984
     3:    -0.943944
     4:    -0.881882
     5:      -0.7998
     6:      -0.6997
     7:    -0.581582
     8:    -0.449449
     9:    -0.307307
    10:    -0.157157
    11:    -0.001001
    12:     0.153153
    13:     0.305305
    14:     0.449449
    15:     0.581582
    16:       0.6997
    17:     0.801802
    18:     0.883884
    19:     0.943944
    20:     0.983984
    21:            1

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 21
  with the Legendre basis and uniform weight.

ind =

           1
          55
         186
         323
         514
         747
         969
        1486
        1785
        2131
        2498
        2866
        3228
        3553
        3857
        4079
        4487
        4678
        4816
        4947
        5001


  NF = 21

  Estimated Fekete points XF:

     1:           -1
     2:      -0.9784
     3:       -0.926
     4:      -0.8712
     5:      -0.7948
     6:      -0.7016
     7:      -0.6128
     8:       -0.406
     9:      -0.2864
    10:       -0.148
    11:      -0.0012
    12:        0.146
    13:       0.2908
    14:       0.4208
    15:       0.5424
    16:       0.6312
    17:       0.7944
    18:       0.8708
    19:        0.926
    20:       0.9784
    21:            1

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_monomial_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 21
  using the monomial basis and uniform weight.

  NF = 21

  Estimated Fekete points XF:

     1:           -1
     2:      -0.9816
     3:        -0.95
     4:      -0.8932
     5:      -0.8324
     6:      -0.7228
     7:      -0.5588
     8:      -0.4528
     9:      -0.3268
    10:      -0.1552
    11:       0.0132
    12:       0.1692
    13:       0.3184
    14:       0.4524
    15:       0.5972
    16:       0.7368
    17:        0.838
    18:       0.8968
    19:       0.9516
    20:       0.9824
    21:            1

  Graphics saved as "line_fekete_monomial.png"

  Sum(WF) = 2

line_fekete_rule_bos_levenberg_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomial space of dimension M = 41
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  Estimated Fekete points XF:

     1:           -1
     2:    -0.995996
     3:    -0.985986
     4:     -0.96997
     5:    -0.947948
     6:     -0.91992
     7:    -0.887888
     8:     -0.84985
     9:    -0.805806
    10:    -0.757758
    11:    -0.703704
    12:    -0.647648
    13:    -0.585586
    14:    -0.521522
    15:    -0.453453
    16:    -0.383383
    17:    -0.309309
    18:    -0.235235
    19:    -0.157157
    20:   -0.0810811
    21:    -0.001001
    22:    0.0770771
    23:     0.157157
    24:     0.233233
    25:     0.309309
    26:     0.381381
    27:     0.453453
    28:     0.521522
    29:     0.585586
    30:     0.647648
    31:     0.703704
    32:     0.757758
    33:     0.805806
    34:      0.84985
    35:     0.887888
    36:      0.91992
    37:     0.947948
    38:      0.96997
    39:     0.985986
    40:     0.995996
    41:            1

  Saved plot in file "line_fekete_bos_levenberg.png"

line_fekete_chebyshev_test:
  Seek Fekete points in [-1,1]
  using 1000 equally spaced sample points
  for polynomials of degree M = 41
  with the Chebyshev basis
  and weight 1/sqrt(1-x^2).

  NF = 41

  Estimated Fekete points XF:

     1:           -1
     2:    -0.995996
     3:    -0.985986
     4:     -0.96997
     5:    -0.947948
     6:     -0.91992
     7:    -0.887888
     8:     -0.84985
     9:    -0.805806
    10:    -0.757758
    11:    -0.703704
    12:    -0.647648
    13:    -0.585586
    14:    -0.521522
    15:    -0.453453
    16:    -0.383383
    17:    -0.309309
    18:    -0.235235
    19:    -0.157157
    20:   -0.0810811
    21:    -0.001001
    22:    0.0770771
    23:     0.157157
    24:     0.233233
    25:     0.309309
    26:     0.381381
    27:     0.453453
    28:     0.521522
    29:     0.585586
    30:     0.647648
    31:     0.703704
    32:     0.757758
    33:     0.805806
    34:      0.84985
    35:     0.887888
    36:      0.91992
    37:     0.947948
    38:      0.96997
    39:     0.985986
    40:     0.995996
    41:            1

  Graphics saved as "line_fekete_chebyshev.png"

  Sum(WF) = 3.14159

line_fekete_legendre_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 41
  with the Legendre basis and uniform weight.

ind =

           1
          15
          50
          86
         136
         244
         311
         406
         506
         622
         750
         885
        1042
        1206
        1362
        1512
        1699
        1845
        2171
        2331
        2524
        2697
        2880
        3060
        3232
        3410
        3559
        3845
        3967
        4108
        4250
        4382
        4497
        4596
        4690
        4758
        4866
        4916
        4952
        4987
        5001


  NF = 41

  Estimated Fekete points XF:

     1:           -1
     2:      -0.9944
     3:      -0.9804
     4:       -0.966
     5:       -0.946
     6:      -0.9028
     7:       -0.876
     8:       -0.838
     9:       -0.798
    10:      -0.7516
    11:      -0.7004
    12:      -0.6464
    13:      -0.5836
    14:       -0.518
    15:      -0.4556
    16:      -0.3956
    17:      -0.3208
    18:      -0.2624
    19:       -0.132
    20:       -0.068
    21:       0.0092
    22:       0.0784
    23:       0.1516
    24:       0.2236
    25:       0.2924
    26:       0.3636
    27:       0.4232
    28:       0.5376
    29:       0.5864
    30:       0.6428
    31:       0.6996
    32:       0.7524
    33:       0.7984
    34:        0.838
    35:       0.8756
    36:       0.9028
    37:        0.946
    38:        0.966
    39:       0.9804
    40:       0.9944
    41:            1

  Graphics saved as "line_fekete_legendre.png"

  Sum(WF) = 2

line_fekete_monomial_test:
  Seek Fekete points in [-1,1]
  using 5001 equally spaced sample points
  for polynomials of degree M = 41
  using the monomial basis and uniform weight.
[Warning: Rank deficient, rank = 36, tol =  7.110318e-12.] 
[> In line_fekete_monomial (line 81)
  In line_fekete_monomial_test (line 46)
  In line_fekete_rule_test (line 31)
  In run (line 91)
] 

  NF = 36

  Estimated Fekete points XF:

     1:           -1
     2:      -0.9912
     3:      -0.9756
     4:       -0.948
     5:      -0.9184
     6:       -0.892
     7:      -0.8596
     8:      -0.8164
     9:      -0.7712
    10:      -0.6964
    11:      -0.5908
    12:      -0.5328
    13:      -0.4716
    14:      -0.4004
    15:      -0.3292
    16:       -0.256
    17:      -0.1764
    18:      -0.0284
    19:       0.0372
    20:       0.1052
    21:        0.238
    22:       0.3648
    23:       0.4256
    24:       0.4888
    25:       0.5712
    26:       0.6532
    27:       0.7344
    28:        0.776
    29:        0.812
    30:        0.874
    31:       0.9176
    32:       0.9488
    33:        0.974
    34:       0.9908
    35:       0.9968
    36:            1

  Graphics saved as "line_fekete_monomial.png"

  Sum(WF) = 2

line_fekete_rule_test():
  Normal end of execution.

07-Jan-2022 22:44:42