Yorick Standard Library

Package series (in series.i) -

Index of documented functions or symbols:

S

series_n

DOCUMENT series_n(r, s)
  returns the minimum number n of terms required for the geometric
  series
     1 + r + r^2 + r^3 + ... + r^n = s
  to reach at least the given value s.  An alternate viewpoint is
  that n is the minimum number of terms required to achieve the
  sum s, with a ratio no larger than r.
  Returns 0 if r<1 and s>1/(1-r), or if s<1.
  The routine makes the most sense for r>1 and s substantially
  greater than 1.  The intended use is to determine the minimum
  number of zones required to span a given thickness t with a given
  minimum zone size z, and maximum taper ratio r (assumed >1 here):
     n= series_n(r, t/z);
  With this n, you have the option of adjusting r or z downwards
  (using series_r or series_s, respectively) to achieve the final
  desired zoning.
  R or S or both may be arrays, as long as they are conformable.

series_r

DOCUMENT series_r(s, n)
  returns the ratio r of the finite geometric series, given the sum s:
     1 + r + r^2 + r^3 + ... + r^n = s
  Using n<0 will return the the reciprocal of n>0 result, that is,
     series_r(s, -n) == 1.0/series_r(s, n)
  If n==0, returns s-1 (the n==1 result).
  S or N or both may be arrays, as long as they are conformable.

series_s

DOCUMENT series_s(r, n)
  returns the sum s of the finite geometric series
     1 + r + r^2 + r^3 + ... + r^n
  Using n<0 is equivalent to using the reciprocal of r, that is,
     series_s(r, -n) == series_s(1./r, n)
  R or N or both may be arrays, as long as they are conformable.