13 September 2023  10:26:51.892 AM
 
brent_test():
  FORTRAN77 version.
  Test brent().
 
TEST_ZERO_ALL
  Test the Brent ZERO routine, which seeks
  a root of a function F(X)
  in an interval [A,B].
 
  f_01(x) = sin ( x ) - x / 2
 
      A                 Z             B
    F(A)              F(Z)          F(B)
 
      1.00000000      1.89549427      2.00000000
    0.341471         0.00000       -0.907026E-01
 
  f_02(x) = 2 * x - exp ( - x )
 
      A                 Z             B
    F(A)              F(Z)          F(B)
 
      0.00000000      0.35173371      1.00000000
    -1.00000         0.00000         1.63212    
 
  f_03(x) = x * exp ( - x )
 
      A                 Z             B
    F(A)              F(Z)          F(B)
 
     -1.00000000      0.00000000      0.50000000
    -2.71828        0.267518E-23    0.303265    
 
  f_04(x) = exp ( x ) - 1 / ( 100 * x * x )
 
      A                 Z             B
    F(A)              F(Z)          F(B)
 
      0.00010000      0.09534462     20.00000000
    -999999.       -0.222045E-15    0.485165E+09
 
  f_05(x) = (x+3) * (x-1) * (x-1)
 
      A                 Z             B
    F(A)              F(Z)          F(B)
 
     -5.00000000     -3.00000000      2.00000000
    -72.0000         0.00000         5.00000    
 
TEST_LOCAL_MIN_ALL
  Test the LOCAL_MIN routine, which seeks
  a local minimizer of a function F(X)
  in an interval [A,B].
 
  g_01(x) = ( x - 2 ) * ( x - 2 ) + 1
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      0.00000000      2.00000000      3.14159265
     5.00000         1.00000         2.30323    
 
  g_02(x) = x * x + exp ( - x )
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      0.00000000      0.35173370      1.00000000
     1.00000        0.827184         1.36788    
 
  g_03(x) = x^4 + 2x^2 + x + 3
 
      A                 X             B
    F(A)              F(X)          F(B)
 
     -2.00000000     -0.23673290      2.00000000
     25.0000         2.87849         29.0000    
 
  g_04(x) = exp ( x ) + 1 / ( 100 x )
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      0.00010000      0.09534461      1.00000000
     101.000         1.20492         2.72828    
 
  g_05(x) = exp ( x ) - 2x + 1/(100x) - 1/(1000000x^2)
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      0.00020000      0.70320487      2.00000000
     25.9998        0.628026         3.39406    
 
  g_06(x) = -x*sin(10*pi*x)-1.0
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      1.80000000      1.85054759      1.90000000
    -1.00000        -2.85027        -1.00000    
 
  g_07(x) = max(-2(x-1),8(x-1)) + 25*(x-1)^2
 
      A                 X             B
    F(A)              F(X)          F(B)
 
     -1.20000000      0.99999289      2.70000000
     125.400        0.142220E-04     85.8500    

test_glomin_all():
  Test the Brent GLOMIN routine, which seeks
  a global minimizer of a function F(X)
  in an interval [A,B],
  given some upper bound M for F".

  Tolerances:
  e =   0.149012E-07
  t =   0.149012E-07
 
  h_01(x) = 2 - x
  M =    0.00000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      7.00000000      9.00000000      9.00000000
    -5.00000        -7.00000        -7.00000    
  Calls =        2
 
  h_01(x) = 2 - x
  M =    100.000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
      7.00000000      9.00000000      9.00000000
    -5.00000        -7.00000        -7.00000    
  Calls =       15
 
  h_02(x) = x * x
  M =    2.00000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
     -1.00000000      0.00000000      2.00000000
     1.00000         0.00000         4.00000    
  Calls =        4
 
  h_02(x) = x * x
  M =    2.10000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
     -1.00000000      0.00000000      2.00000000
     1.00000         0.00000         4.00000    
  Calls =        8
 
  h_03(x) = x^3 + x^2
  M =    14.0000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
     -0.50000000      0.00000057      2.00000000
    0.125000        0.326186E-12     12.0000    
  Calls =       37
 
  h_03(x) = x^3 + x^2
  M =    28.0000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
     -0.50000000      0.00000981      2.00000000
    0.125000        0.962435E-10     12.0000    
  Calls =       47
 
  h_04(x) = ( x + sin(x) ) * exp(-x*x)
  M =    72.0000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
    -10.00000000     -0.67957866     10.00000000
   -0.351770E-42   -0.824239        0.351770E-42
  Calls =      220
 
  h_05(x) = ( x - sin(x) ) * exp(-x*x)
  M =    72.0000    
 
      A                 X             B
    F(A)              F(X)          F(B)
 
    -10.00000000     -1.19513663     10.00000000
   -0.392246E-42   -0.634905E-01    0.392246E-42
  Calls =      456
 
brent_test():
  Normal end of execution.
 
13 September 2023  10:26:51.892 AM