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crossdef

PURPOSE ^

level v crossing definitions and nomenclature

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

  CROSSDEF level v crossing definitions and nomenclature 
 
  Definition of level v crossing:   
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the 
  figure below denote local minimum, maximum, first value, last 
  value, down- and up-crossing, respectively. The remaining 
  sampled values are indicated with a '.'. Values that are identical 
  with v, but do not cross the level is indicated with the letter 'o'.
 
  We have a level up-crossing at index, k, if 
 
            x(k) <  v and v < x(k+1) 
  or if 
            x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 
 
  where di is  the index to the previous downcrossing.
  Similarly there is a level down-crossing at index, k, if 
  
            x(k) >  v and v > x(k+1)
   or if 
            x(k) == v and v > x(k+1) and x(r) > v  for some ui < r <= k-1 
 
  where ui is  the index to the previous upcrossing.
 
  The first (F) value is a up crossing if  x(1) = v and x(2) > v. 
  Similarly, it is a down crossing if      x(1) = v and x(2) < v. 
 
       M
     .   .                  M                   M
   .      . .             .                   .   . 
 F            d               .             .       L
  ----------------------u-------d-------o--------------------- level v
                .     .           .   .   u
                  .                 m
            m
 
  See also  perioddef, wavedef, tpdef, findcross, dat2tp

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 % CROSSDEF level v crossing definitions and nomenclature 
002 %
003 % Definition of level v crossing:   
004 %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
005 % Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the 
006 % figure below denote local minimum, maximum, first value, last 
007 % value, down- and up-crossing, respectively. The remaining 
008 % sampled values are indicated with a '.'. Values that are identical 
009 % with v, but do not cross the level is indicated with the letter 'o'.
010 %
011 % We have a level up-crossing at index, k, if 
012 %
013 %           x(k) <  v and v < x(k+1) 
014 % or if 
015 %           x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1 
016 %
017 % where di is  the index to the previous downcrossing.
018 % Similarly there is a level down-crossing at index, k, if 
019 % 
020 %           x(k) >  v and v > x(k+1)
021 %  or if 
022 %           x(k) == v and v > x(k+1) and x(r) > v  for some ui < r <= k-1 
023 %
024 % where ui is  the index to the previous upcrossing.
025 %
026 % The first (F) value is a up crossing if  x(1) = v and x(2) > v. 
027 % Similarly, it is a down crossing if      x(1) = v and x(2) < v. 
028 %
029 %      M
030 %    .   .                  M                   M
031 %  .      . .             .                   .   . 
032 %F            d               .             .       L
033 % ----------------------u-------d-------o--------------------- level v
034 %               .     .           .   .   u
035 %                 .                 m
036 %           m
037 %
038 % See also  perioddef, wavedef, tpdef, findcross, dat2tp
039 
040 % history:
041 % by Per A. Brodtkorb 19.09.1999
042 
043 more on
044 help crossdef
045 more off
046

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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