由The GNU Scientific Library (GSL) (http://www.gnu.org/software/gsl/)在SMath项目的作用域中创建。由уни发布。
这是一个开源项目。MIT许可证下共享的源代码SVN存储库

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Features of GNU Scientific Library (GSL)

版本2.7.8829.21568

Functions

Additional components that add new mathematical functions to the SMath Studio program, necessary for solving problems from various fields.

  1. gsl_deriv_backward("1:expression", "2:number", "3:number")
    (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive backward difference algorithm with a step-size of h.
  2. gsl_deriv_central("1:expression", "2:number", "3:number")
    (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive central difference algorithm with a step-size of h.
  3. gsl_deriv_forward("1:expression", "2:number", "3:number")
    (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive forward difference algorithm with a step-size of h.
  4. gsl_interp("expression")
    (cmd) returns short description for commands: ?|help|types
  5. gsl_interp("1:string", "2:vector", "3:vector", "4:number")
    (type,vx,vy,x) returns the interpolated value of y for a given point x, using the interpolation type and data arrays vx and vy.
  6. gsl_sf_airy("expression")
    (cmd) returns short description for commands: ?|help|flags
  7. gsl_sf_airy("1:expression", "2:number")
    (flags,x) compute the Airy function.
  8. gsl_sf_bessel("expression")
    (cmd) returns short description for commands: ?|help|flags|I?|J?|Y?|K?|i?|j?|y?|k?
  9. gsl_sf_bessel("1:string", "2:number")
    (flags,x) compute the Bessel function.
  10. gsl_sf_bessel("1:string", "2:expression", "3:number")
    (flags,n|nu|l,x) compute the Bessel function.
  11. gsl_sf_clausen("number")
    (x) calculate the Clausen integral.
  12. gsl_sf_dawson("number")
    (x) calculate the Dawson integral.
  13. gsl_sf_debye("1:number", "2:number")
    (n,x) calculate the Debye function.
  14. gsl_sf_dilog("complexNumber")
    (x) calculate the Dilogarithm.
  15. gsl_sf_ellint_D("1:number", "2:number")
    (ϕ,k) compute the incomplete elliptic integral D(ϕ,k).
  16. gsl_sf_ellint_Dcomp("number")
    (k) compute the complete elliptic integral D(k).
  17. gsl_sf_ellint_E("1:number", "2:number")
    (ϕ,k) compute the incomplete elliptic integral E(ϕ,k).
  18. gsl_sf_ellint_Ecomp("number")
    (k) compute the complete elliptic integral E(k).
  19. gsl_sf_ellint_F("1:number", "2:number")
    (ϕ,k) compute the incomplete elliptic integral F(ϕ,k).
  20. gsl_sf_ellint_Kcomp("number")
    (k) compute the complete elliptic integral K(k).
  21. gsl_sf_ellint_P("1:number", "2:number", "3:number")
    (ϕ,k,n) compute the incomplete elliptic integral P(ϕ,k,n).
  22. gsl_sf_ellint_Pcomp("1:number", "2:number")
    (k,n) compute the complete elliptic integral Π(k,n).
  23. gsl_sf_ellint_RC("1:number", "2:number")
    (x,y) compute the incomplete elliptic integral RC(x,y).
  24. gsl_sf_ellint_RD("1:number", "2:number", "3:number")
    (x,y,z) compute the incomplete elliptic integral RD(x,y,z).
  25. gsl_sf_ellint_RF("1:number", "2:number", "3:number")
    (x,y,z) compute the incomplete elliptic integral RF(x,y,z).
  26. gsl_sf_ellint_RJ("1:number", "2:number", "3:number", "4:number")
    (x,y,z,p) compute the incomplete elliptic integral RJ(x,y,z,p).
  27. gsl_sf_erf("number")
    (x) compute the error function erf(x), where erf(x) = 2/Sqrt[Pi] Int[Exp[-t^2], {t,0,x}].
  28. gsl_sf_erf_Q("number")
    (x) compute the upper tail of the Gaussian probability function Q(x) = (1/sqrt{2 Pi}) int(x,infty, dt exp(-t^2/2)).
  29. gsl_sf_erf_Z("number")
    (x) compute the Gaussian probability density function Z(x) = (1/sqrt{2 Pi}) exp(-x^2/2).
  30. gsl_sf_erfc("number")
    (x) compute the complementary error function erfc(x) = 2/Sqrt[Pi] Int[Exp[-t^2], {t,x,Infinity}].
  31. gsl_sf_eta("number")
    (s) calculate the eta function η(s) for arbitrary s.
  32. gsl_sf_eta_int("number")
    (n) calculate the eta function η(n) for integer n.
  33. gsl_sf_hazard("number")
    (x) compute the Hazard function, also known as the inverse Mill's ratio.
  34. gsl_sf_hzeta("1:number", "2:number")
    (s,q) calculate the Hurwitz zeta function ζ(s,q) for s > 1, q > 0.
  35. gsl_sf_log_erfc("number")
    (x) compute the logarithm of the complementary error function log(erfc(x)).
  36. gsl_sf_zeta("number")
    (s) calculate the Riemann zeta function ζ(s) for arbitrary s ≠ 1.
  37. gsl_sf_zeta_int("number")
    (n) calculate the Riemann zeta function ζ(n) for integer n ≠ 1.
  38. gsl_sf_zetam1("number")
    (s) calculate the Riemann zeta function ζ(s) minus one for arbitrary s ≠ 1.
  39. gsl_sf_zetam1_int("number")
    (n) calculate the Riemann zeta function ζ(n) minus one for integer n ≠ 1.
  40. gslbsimp("expression")
    (cmd) returns short description for commands: ?|help
  41. gslbsimp("1:function", "2:function", "3:number")
    (ode,y(x),xmax) implicit Bulirsch-Stoer method of Bader and Deuflhard.
  42. gslbsimp("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) implicit Bulirsch-Stoer method of Bader and Deuflhard.
  43. gslbsimp("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) implicit Bulirsch-Stoer method of Bader and Deuflhard.
  44. gslbsimp("1:vector", "2:number", "3:number", "4:number", "5:function", "6:function")
    (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Bulirsch-Stoer method of Bader and Deuflhard.
  45. gslmsadams("expression")
    (cmd) returns short description for commands: ?|help
  46. gslmsadams("1:function", "2:function", "3:number")
    (ode,y(x),xmax) variable-coefficient linear multistep Adams method in Nordsieck form.
  47. gslmsadams("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) variable-coefficient linear multistep Adams method in Nordsieck form.
  48. gslmsadams("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) variable-coefficient linear multistep Adams method in Nordsieck form.
  49. gslmsadams("1:vector", "2:number", "3:number", "4:number", "5:function", "6:function")
    (ics,xmin,xmax,steps,D(x,y),J(x,y)) no description
  50. gslmsdbf("expression")
    (cmd) returns short description for commands: ?|help
  51. gslmsdbf("1:function", "2:function", "3:number")
    (ode,y(x),xmax) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
  52. gslmsdbf("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
  53. gslmsdbf("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
  54. gslmsdbf("1:vector", "2:number", "3:number", "4:number", "5:function", "6:function")
    (ics,xmin,xmax,steps,D(x,y),J(x,y)) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
  55. gslrk1imp("expression")
    (cmd) returns short description for commands: ?|help
  56. gslrk1imp("1:function", "2:function", "3:number")
    (ode,y(x),xmax) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
  57. gslrk1imp("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
  58. gslrk1imp("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
  59. gslrk1imp("1:vector", "2:number", "3:number", "4:number", "5:function", "6:function")
    (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
  60. gslrk2("expression")
    (cmd) returns short description for commands: ?|help
  61. gslrk2("1:function", "2:function", "3:number")
    (ode,y(x),xmax) explicit embedded Runge-Kutta (2,3) method.
  62. gslrk2("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) explicit embedded Runge-Kutta (2,3) method.
  63. gslrk2("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta (2,3) method.
  64. gslrk2imp("expression")
    (cmd) returns short description for commands: ?|help
  65. gslrk2imp("1:function", "2:function", "3:number")
    (ode,y(x),xmax) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
  66. gslrk2imp("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
  67. gslrk2imp("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
  68. gslrk2imp("1:vector", "2:number", "3:number", "4:number", "5:function", "6:function")
    (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
  69. gslrk4("expression")
    (cmd) returns short description for commands: ?|help
  70. gslrk4("1:function", "2:function", "3:number")
    (ode,y(x),xmax) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
  71. gslrk4("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
  72. gslrk4("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
  73. gslrk4imp("expression")
    (cmd) returns short description for commands: ?|help
  74. gslrk4imp("1:function", "2:function", "3:number")
    (ode,y(x),xmax) implicit Gaussian 4th order Runge-Kutta method.
  75. gslrk4imp("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) implicit Gaussian 4th order Runge-Kutta method.
  76. gslrk4imp("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian 4th order Runge-Kutta method.
  77. gslrk4imp("1:vector", "2:number", "3:number", "4:number", "5:function", "6:function")
    (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian 4th order Runge-Kutta method.
  78. gslrk8pd("expression")
    (cmd) returns short description for commands: ?|help
  79. gslrk8pd("1:function", "2:function", "3:number")
    (ode,y(x),xmax) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
  80. gslrk8pd("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
  81. gslrk8pd("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
  82. gslrkck("expression")
    (cmd) returns short description for commands: ?|help
  83. gslrkck("1:function", "2:function", "3:number")
    (ode,y(x),xmax) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
  84. gslrkck("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
  85. gslrkck("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
  86. gslrkf45("expression")
    (cmd) returns short description for commands: ?|help
  87. gslrkf45("1:function", "2:function", "3:number")
    (ode,y(x),xmax) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
  88. gslrkf45("1:function", "2:function", "3:number", "4:number")
    (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
  89. gslrkf45("1:vector", "2:number", "3:number", "4:number", "5:function")
    (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Cash-Karp (4,5) method.