Mon Mar 25 22:54:19 2024

cpr_test():
  Python version: 3.8.10
  Test cpr(), which uses the Chebyshev Proxy Rootfinder
  to determine all real zeros of a smooth function
  over an interval [a,b].

bessel_test():
  Seek real roots of the J0 Bessel function.

  Interstitial interpolation error norm =  6.5503158452884236e-15
  Number of roots =  12
  Roots computed by CPR:
[ 2.40482556  5.52007811  8.65372791 11.79153444 14.93091771 18.07106397
 21.21163663 24.35247153 27.49347913 30.63460647 33.77582021 36.91709835]
  Maximum residual at roots =  9.349203920171092e-15
  Exact roots:
[ 2.40482556  5.52007811  8.65372791 11.79153444 14.93091771 18.07106397
 21.21163663 24.35247153 27.49347913 30.63460647 33.77582021 36.91709835]
  Exact f(roots):
[-9.58688255e-17 -1.64951298e-17 -8.70443181e-17 -2.64819844e-16
 -7.02790803e-16 -6.47283946e-16  2.34410915e-16 -8.61488164e-16
  9.17693595e-16  4.66258274e-16 -1.70343369e-16 -4.57368418e-16]
  f ( froots ):
[ 3.54714655e-15  9.34920392e-15 -6.83744882e-15  7.99336731e-15
 -4.37112954e-15 -5.98232977e-15 -3.45936416e-15  7.18121836e-15
  6.86481796e-15 -9.26502330e-15  7.63407412e-15  5.14142241e-15]

newton_test():
  Seek real roots of the Newton example x^3-2x-5=0.

  Interstitial interpolation error norm =  5.684341886080802e-14
  Number of roots =  1
  Maximum residual at roots =  5.329070518200751e-15
  Exact real root   :  2.094551481542328
  Computed real root:  2.094551481542326
  Exact f(roots)    :  1.4210854715202004e-14
  Computed f(roots) :  -5.329070518200751e-15
  Error             :  1.7763568394002505e-15

jenkins_test():
  Seek real roots of the Jenkins function.
  p(x) = x^4 + 5.6562x^3 + 5.8854x^2
             + 7.3646x   + 6.1354

  Interstitial interpolation error norm =  4.547473508864641e-13
  Maximum residual at roots =  1.4477308241112041e-13
  Number of roots =  2
  Computed roots:
[-4.67405402 -1.        ]
  Exact roots:
[-4.67405402 -1.        ]
  f ( Computed roots ):
[1.44773082e-13 9.85878046e-14]
  f ( Exact roots):
[-1.86517468e-14 -8.88178420e-16]

cpr_test():
  Normal end of execution.
Mon Mar 25 22:54:19 2024