04-Mar-2026 09:21:43

test_nls_test()
  MATLAB/Octave version 11.1.0
  Test test_nls().

p00_title_test():
  p00_title() returns the title for each test.

  Test Title

       1:  "Linear function, full rank."
       2:  "Linear function, rank 1."
       3:  "Linear function, rank 1, zero columns and rows."
       4:  "Rosenbrock function."
       5:  "Helical valley function."
       6:  "Powell singular function."
       7:  "Freudenstein-Roth function."
       8:  "Bard function."
       9:  "Kowalik and Osborne function."
       10:  "Meyer function."
       11:  "Watson function."
       12:  "Box 3-dimensional function."
       13:  "Jennrich-Sampson function."
       14:  "Brown and Dennis function."
       15:  "Chebyquad function."
       16:  "Brown almost-linear function."
       17:  "Osborne function 1."
       18:  "Osborne function 2."
       19:  "Hanson function 1."
       20:  "Hanson function 2."
       21:  "McKeown problem 1."
       22:  "McKeown problem 2."
       23:  "McKeown problem 3."
       24:  "Devilliers-Glasser function 1."
       25:  "Devilliers-Glasser function 2."
       26:  "The Madsen function."

p00_title_test():
  Normal end of execution.

p00_mn_test():
  p00_mn() returns information about the value or range of
  m: the number of equations or functions;
  n: the number of variables.

  Test Title
  m, n information

  1 "Linear function, full rank."
      m arbitrary and n arbitrary and m => n.
  2 "Linear function, rank 1."
      m arbitrary and n arbitrary and m => n.
  3 "Linear function, rank 1, zero columns and rows."
      m arbitrary and n arbitrary and m => n.
  4 "Rosenbrock function."
      m = 2, n = 2
  5 "Helical valley function."
      m = 3, n = 3
  6 "Powell singular function."
      m = 4, n = 4
  7 "Freudenstein-Roth function."
      m = 2, n = 2
  8 "Bard function."
      m = 15, n = 3
  9 "Kowalik and Osborne function."
      m = 11, n = 4
  10 "Meyer function."
      m = 16, n = 3
  11 "Watson function."
      m = 31, 2 <= n <= 31
  12 "Box 3-dimensional function."
      m arbitrary and m => n and n = 3.
  13 "Jennrich-Sampson function."
      m arbitrary and m => n and n = 2.
  14 "Brown and Dennis function."
      m arbitrary and m => n and n = 4.
  15 "Chebyquad function."
      m arbitrary and n arbitrary and m => n.
  16 "Brown almost-linear function."
      m arbitrary and n arbitrary and m == n.
  17 "Osborne function 1."
      m = 33, n = 5
  18 "Osborne function 2."
      m = 65, n = 11
  19 "Hanson function 1."
      m = 16, n = 2
  20 "Hanson function 2."
      m = 16, n = 3
  21 "McKeown problem 1."
      m = 3, n = 2
  22 "McKeown problem 2."
      m = 4, n = 3
  23 "McKeown problem 3."
      m = 10, n = 5
  24 "Devilliers-Glasser function 1."
      m = 24, n = 4
  25 "Devilliers-Glasser function 2."
      m = 16, n = 5
  26 "The Madsen function."
      m = 3, n = 2

p00_f_test():
  p00_f() evaluates m objective functions at the n-point x.
  Use x=p00_start(), fx=p00_f(x);
  Print norms of x and fx.

  1 "Linear function, full rank."
  m = 5, n = 3
  ||x|| = 1.73205
  ||fx|| = 3.74166

  2 "Linear function, rank 1."
  m = 5, n = 3
  ||x|| = 1.73205
  ||fx|| = 42.4853

  3 "Linear function, rank 1, zero columns and rows."
  m = 5, n = 3
  ||x|| = 1.73205
  ||fx|| = 6.08276

  4 "Rosenbrock function."
  m = 2, n = 2
  ||x|| = 1.56205
  ||fx|| = 4.91935

  5 "Helical valley function."
  m = 3, n = 3
  ||x|| = 1
  ||fx|| = 50

  6 "Powell singular function."
  m = 4, n = 4
  ||x|| = 3.31662
  ||fx|| = 14.6629

  7 "Freudenstein-Roth function."
  m = 2, n = 2
  ||x|| = 2.06155
  ||fx|| = 20.0125

  8 "Bard function."
  m = 15, n = 3
  ||x|| = 1.73205
  ||fx|| = 6.45614

  9 "Kowalik and Osborne function."
  m = 11, n = 4
  ||x|| = 0.734115
  ||fx|| = 0.0728915

  10 "Meyer function."
  m = 16, n = 3
  ||x|| = 4007.8
  ||fx|| = 41153.5

  11 "Watson function."
  m = 31, n = 5
  ||x|| = 0
  ||fx|| = 5.47723

  12 "Box 3-dimensional function."
  m = 5, n = 3
  ||x|| = 22.3607
  ||fx|| = 26.4232

  13 "Jennrich-Sampson function."
  m = 4, n = 2
  ||x|| = 0.5
  ||fx|| = 3.61455

  14 "Brown and Dennis function."
  m = 6, n = 4
  ||x|| = 26
  ||fx|| = 1808.17

  15 "Chebyquad function."
  m = 5, n = 3
  ||x|| = 0.935414
  ||fx|| = 0.339935

  16 "Brown almost-linear function."
  m = 5, n = 5
  ||x|| = 1.11803
  ||fx|| = 6.0777

  17 "Osborne function 1."
  m = 33, n = 5
  ||x|| = 1.87096
  ||fx|| = 0.937564

  18 "Osborne function 2."
  m = 65, n = 11
  ||x|| = 11.8695
  ||fx|| = 1.44687

  19 "Hanson function 1."
  m = 16, n = 2
  ||x|| = 10.0011
  ||fx|| = 18.6281

  20 "Hanson function 2."
  m = 16, n = 3
  ||x|| = 25.0004
  ||fx|| = 10.4093

  21 "McKeown problem 1."
  m = 3, n = 2
  ||x|| = 0.141421
  ||fx|| = 0.59498

  22 "McKeown problem 2."
  m = 4, n = 3
  ||x|| = 0.173205
  ||fx|| = 0.969451

  23 "McKeown problem 3."
  m = 10, n = 5
  ||x|| = 0.223607
  ||fx|| = 1.15475

  24 "Devilliers-Glasser function 1."
  m = 24, n = 4
  ||x|| = 10.0233
  ||fx|| = 352.527

  25 "Devilliers-Glasser function 2."
  m = 16, n = 5
  ||x|| = 45.1476
  ||fx|| = 182.162

  26 "The Madsen function."
  m = 3, n = 2
  ||x|| = 3.16228
  ||fx|| = 13.012

p00_sol_test():
  p00_sol() returns an n vector x which is an approximate
  minimizer of the objective function p00_f(x).

  1 "Linear function, full rank."
  m = 5, n = 3
  ||x|| = 1.73205
  ||fx|| = 1.41421

  2 "Linear function, rank 1."
  m = 5, n = 3
  ||x|| = 0.0787296
  ||fx|| = 0.953463

  3 "Linear function, rank 1, zero columns and rows."
  m = 5, n = 3
  ||x|| = 0.371154
  ||fx|| = 1.55839

  4 "Rosenbrock function."
  m = 2, n = 2
  ||x|| = 1.41421
  ||fx|| = 0

  5 "Helical valley function."
  m = 3, n = 3
  ||x|| = 1
  ||fx|| = 0

  6 "Powell singular function."
  m = 4, n = 4
  ||x|| = 0
  ||fx|| = 0

  7 "Freudenstein-Roth function."
  m = 2, n = 2
  ||x|| = 6.40312
  ||fx|| = 0

  8 "Bard function."
  m = 15, n = 3
  ||x|| = 2.6045
  ||fx|| = 0.090636

  9 "Kowalik and Osborne function."
  m = 11, n = 4
  ||x|| = 0.331289
  ||fx|| = 0.0175369

  10 "Meyer function."
  m = 16, n = 3
  ||x|| = 0.00619093
  ||fx|| = 62376

  11 "Watson function."
  m = 31, n = 5
  ||x|| = 1.34751
  ||fx|| = 0.130975

  12 "Box 3-dimensional function."
  m = 5, n = 3
  ||x|| = 10.0995
  ||fx|| = 0

  13 "Jennrich-Sampson function."
  m = 4, n = 2
  An approximate solution is not given!

  14 "Brown and Dennis function."
  m = 6, n = 4
  An approximate solution is not given!

  15 "Chebyquad function."
  m = 5, n = 3
  An approximate solution is not given!

  16 "Brown almost-linear function."
  m = 5, n = 5
  ||x|| = 2.23607
  ||fx|| = 0

  17 "Osborne function 1."
  m = 33, n = 5
  ||x|| = 2.45647
  ||fx|| = 0.0111605

  18 "Osborne function 2."
  m = 65, n = 11
  ||x|| = 9.38185
  ||fx|| = 0.200344

  19 "Hanson function 1."
  m = 16, n = 2
  ||x|| = 8.84506
  ||fx|| = 14.4465

  20 "Hanson function 2."
  m = 16, n = 3
  ||x|| = 23.4935
  ||fx|| = 6.05085

  21 "McKeown problem 1."
  m = 3, n = 2
  ||x|| = 0.00020111
  ||fx|| = 0.428487

  22 "McKeown problem 2."
  m = 4, n = 3
  ||x|| = 0.000605887
  ||fx|| = 0.8925

  23 "McKeown problem 3."
  m = 10, n = 5
  ||x|| = 0.000204817
  ||fx|| = 1

  24 "Devilliers-Glasser function 1."
  m = 24, n = 4
  ||x|| = 0.204817
  ||fx|| = 324.567

  25 "Devilliers-Glasser function 2."
  m = 16, n = 5
  ||x|| = 53.9536
  ||fx|| = 0

  26 "The Madsen function."
  m = 3, n = 2
  ||x|| = 0.711752
  ||fx|| = 0.879317

test_nls_test():
  Normal end of execution.

04-Mar-2026 09:21:43