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# ecross

## PURPOSE

Extracts exact level v crossings

## SYNOPSIS

t0 = ecross(t,f,ind,v)

## DESCRIPTION

``` ECROSS Extracts exact level v crossings

CALL t0 = ecross(t,f,ind,v);

t0  = vector of  exact level v crossings.
t,f = vectors of arguments and functions values, respectively.
ind = indices to level v crossings as found by findcross.
v   = scalar or vector (of size(ind)) defining the level(s) to cross.

ECROSS interpolates t and f linearly to find the exact level v
crossings, i.e., the points where f(t0) = v

Example
t = linspace(0,7*pi,250); x = sin(t);
ind = findcross(x,0.75)
t0 = ecross(t,x,ind,0.75);
plot(t,x,'.',t(ind),x(ind),'r.',...
t, ones(size(t))*.75, t0,ones(size(t0))*0.75,'g.')

## CROSS-REFERENCE INFORMATION

This function calls:
 error Display message and abort function.
This function is called by:
 Chapter3 % CHAPTER3 Demonstrates distributions of wave characteristics dat2steep Extracts waveheights and steepnesses from data. dat2wa Extracts sequence of wavelengths from data.

## SOURCE CODE

```001 function t0 = ecross(t,f,ind,v)
002 %ECROSS Extracts exact level v crossings
003 %
004 %  CALL t0 = ecross(t,f,ind,v);
005 %
006 %  t0  = vector of  exact level v crossings.
007 %  t,f = vectors of arguments and functions values, respectively.
008 %  ind = indices to level v crossings as found by findcross.
009 %  v   = scalar or vector (of size(ind)) defining the level(s) to cross.
010 %
011 % ECROSS interpolates t and f linearly to find the exact level v
012 % crossings, i.e., the points where f(t0) = v
013 %
014 % Example
015 %  t = linspace(0,7*pi,250); x = sin(t);
016 %  ind = findcross(x,0.75)
017 %  t0 = ecross(t,x,ind,0.75);
018 %  plot(t,x,'.',t(ind),x(ind),'r.',...
019 %  t, ones(size(t))*.75, t0,ones(size(t0))*0.75,'g.')
020 %
022
023 % Tested on: Matlab 6.0
024 % revised pab Feb2004
025 % By pab 18.06.2001
026
027 error(nargchk(4,4,nargin))
028
029 t0 = t(ind)+(v-f(ind)).*(t(ind+1)-t(ind))./(f(ind+1)-f(ind));
030 return
031
032```

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

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