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Text File  |  1993-10-07  |  2KB  |  105 lines
  1. {
  2.     Gaussian Integration
  3.  
  4.         10/20/87
  5.  
  6.     order            - order of integral (# of sample points)
  7.     xmin            - interval begin
  8.     xmax            - interval end
  9.     f(x)            - integrand
  10.     integ            - integral value
  11. }
  12.             { Defaults }
  13. order = 24 ;
  14. xmin = -1 ;
  15. xmax = 1 ;
  16.  
  17. integ = q1(ceil(order/2-.25)) * (xmax-xmin)/2 ;
  18.  
  19. q1(i) = if( i-1.5, wght(i)*(f1(absc(i))+f1(-absc(i))) + q1(i-1),
  20.         wght(1)*(f1(absc(1))+if(even,f1(-absc(1)),0)) ) ;
  21.  
  22. even = floor(order/2+.25) - order/2 + .25 ;
  23.  
  24. f1(u) = f((xmax*(1+u)+xmin*(1-u))/2) ;
  25.  
  26.             { Abscissas }
  27. absc(i) =    select( order,
  28.             0,
  29.             .577350269189626,        { n = 2 }
  30.             select( i,            { n = 3 }
  31.                 0,
  32.                 .774596669241483
  33.             ),
  34.             0, 0,
  35.             select( i,            { n = 6 }
  36.                 .238619186083197,
  37.                 .661209386466265,
  38.                 .932469514203152
  39.             ),
  40.             0, 0, 0, 0, 0,
  41.             select( i,            { n = 12 }
  42.                 .125233408511469,
  43.                 .367831498998180,
  44.                 .587317954286617,
  45.                 .769902674194305,
  46.                 .904117256370475,
  47.                 .981560634246719
  48.             ),
  49.             0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  50.             select( i,            { n = 24 }
  51.                 .064056892862606,
  52.                 .191118867473616,
  53.                 .315042679696163,
  54.                 .433793507626045,
  55.                 .545421471388840,
  56.                 .648093651936976,
  57.                 .740124191578554,
  58.                 .820001985973903,
  59.                 .886415527004401,
  60.                 .938274552002733,
  61.                 .974728555971309,
  62.                 .995187219997021
  63.             )
  64.         ) ;
  65.  
  66.             { Weights }
  67. wght(i) =    select( order,
  68.             0,
  69.             1,                { n = 2 }
  70.             select( i,            { n = 3 }
  71.                 .888888888888888,
  72.                 .555555555555555
  73.             ),
  74.             0, 0,
  75.             select( i,            { n = 6 }
  76.                 .467913934572691,
  77.                 .360761573048139,
  78.                 .171324492379170
  79.             ),
  80.             0, 0, 0, 0, 0,
  81.             select( i,            { n = 12 }
  82.                 .249147045813403,
  83.                 .233492536538355,
  84.                 .203167426723066,
  85.                 .160078328543346,
  86.                 .106939325995318,
  87.                 .047175336386512
  88.             ),
  89.             0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  90.             select( i,            { n = 24 }
  91.                 .127938195346752,
  92.                 .125837456346828,
  93.                 .121670472927803,
  94.                 .115505668053726,
  95.                 .107444270115966,
  96.                 .097618652104114,
  97.                 .086190161531953,
  98.                 .073346481411080,
  99.                 .059298584915437,
  100.                 .044277438817420,
  101.                 .028531388628934,
  102.                 .012341229799987
  103.             )
  104.         ) ;
  105.