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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

## CROSS-REFERENCE INFORMATION

This function calls:
 crossdef level v crossing definitions and nomenclature
This function is called by:
 crossdef level v crossing definitions and nomenclature

## 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 %
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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