home *** CD-ROM | disk | FTP | other *** search
/ Chip 2002 June / Chip_2002-06_cd1.bin / zkuste / derive / download / Setup.exe / %MAINDIR% / Math / Misc.mth < prev    next >
Encoding:
Text File  |  2002-05-15  |  2.2 KB  |  64 lines
  1. "File MISC.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
  2.  
  3. SQUARE_WAVE(x):=(-1)^FLOOR(x)
  4.  
  5. RATIO_TEST(t,n):=LIM(ABS(LIM(t,n,n+1)/t),n,inf)
  6.  
  7. LIM2(u,x,y,x0,y0):=LIM(u,[y,x],[y0+@1*(x-x0),x0])
  8.  
  9. LEFT_RIEMANN(u,x,a,b,n):=(b-a)/n*SUM(LIM(u,x,a+(b-a)*k_/n),k_,0,n-1)
  10.  
  11. INT_PARTS(u,v,x):=u*INT(v,x)-INT(INT(v,x)*DIF(u,x),x)
  12.  
  13. "DEF_INT_PARTS contributed A. van der Meer:"
  14.  
  15. DEF_INT_PARTS(u,v,x,a,b):=(LIM(u*INT(v,x),x,b,-1)-LIM(u*INT(v,x),x,a,1))-INT(I~
  16. NT(v,x)*DIF(u,x),x,a,b)
  17.  
  18. INVERSE(u,x):=ITERATE(u,x,x,-1)
  19.  
  20. INT_SUBST(y,x,u):=LIM(INT(LIM(y,x,INVERSE(u,x))*DIF(INVERSE(u,x),x),x),x,u)
  21.  
  22. DEF_INT_SUBST(y,x,u,a,b):=INT(LIM(y,x,INVERSE(u,x))*DIF(INVERSE(u,x),x),x,LIM(~
  23. u,x,a),LIM(u,x,b))
  24.  
  25. PROVE_SUM(t,k,a,n,s):=[LIM(t,k,a)-LIM(s,n,a),s+LIM(t,k,n+1)-LIM(s,n,n+1)]
  26.  
  27. POLY_COEFF(u,x,n):=SUBST(QUOTIENT(u,x^n),x,0)
  28.  
  29. POLY_DEGREE(u,x):=PROG(IF(u=0,RETURN(-1)),IF(IDENTICAL?(u,x),RETURN(1)),IF(SUM~
  30. ?(u),RETURN(MAX(VECTOR(POLY_DEGREE(v,x),v,TERMS(u))))),IF(POWER?(u) OR PRODUCT~
  31. ?(u),SUM(POLY_DEGREE(v SUB 1,x)*v SUB 2,v,FACTORS(u)),0))
  32.  
  33. random_sign:=2*RANDOM(2)-1
  34.  
  35. RANDOM_POLY(x,d,s):=SUM(random_sign*RANDOM(s)*x^j,j,0,d-1)+(1+RANDOM(s))*x^d
  36.  
  37. RANDOM_VECTOR(n,s):=VECTOR(random_sign*RANDOM(s),j,1,n)
  38.  
  39. RANDOM_MATRIX(m,n,s):=VECTOR(RANDOM_VECTOR(n,s),k,1,m)
  40.  
  41. "RANDOM_NORMAL contributed by Jim FitzSimons, email cherry@neta.com"
  42.  
  43. RANDOM_NORMAL(s,m):=s*SQRT(-2*LOG(RANDOM(1)))*COS(2*pi*RANDOM(1))+m
  44.  
  45. GOODNESS_OF_FIT(u,x,a):=SQRT(SUM((LIM(u,x,a SUB k SUB 1)-a SUB k SUB 2)^2,k,1,~
  46. DIMENSION(a))/DIMENSION(a))
  47.  
  48. "Linear correlation coefficient of a two-column x-y matrix:"
  49.  
  50. LCC_AUX(x,y,n):=(n*x*y-SUM(x)*SUM(y))/SQRT((n*SUM(x SUB k_^2,k_,1,n)-SUM(x)^2)~
  51. *(n*SUM(y SUB k_^2,k_,1,n)-SUM(y)^2))
  52.  
  53. LINEAR_CORRELATION_COEFFICIENT(a):=LCC_AUX(a` SUB 1,a` SUB 2,DIMENSION(a))
  54.  
  55. POLY_INTERPOLATE_AUX(a,x,k,n):=PRODUCT((x-a SUB j_ SUB 1)/(a SUB k SUB 1-a SUB~
  56.  j_ SUB 1),j_,1,k-1)*PRODUCT((x-a SUB j_ SUB 1)/(a SUB k SUB 1-a SUB j_ SUB 1)~
  57. ,j_,k+1,n)
  58.  
  59. POLY_INTERPOLATE(a,x):=SUM(a SUB k_ SUB 2*POLY_INTERPOLATE_AUX(a,x,k_,DIMENSIO~
  60. N(a)),k_,1,DIMENSION(a))
  61.  
  62. POLY_INTERPOLATE_EXPRESSION(u,x,a):=POLY_INTERPOLATE(VECTOR([a SUB k_,LIM(u,x,~
  63. a SUB k_)],k_,1,DIMENSION(a)),x)
  64.