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# nt2fr

## PURPOSE

Calculates the frequency matrix given the counting distribution matrix.

F=nt2fr(M,def)

## DESCRIPTION

``` NT2FR  Calculates the frequency matrix given the counting distribution matrix.

CALL: fr = nt2fr(NT);
fr = nt2fr(NT,def);

where

fr  = the frequency matrix,
NT  = the counting distribution matrix,
def = 0,1
k   = number of diagonals from main diagonal to be
set to zero (optional input argument).

If def=0 function computes the inverse to

N_T(u,v) = #{ (M_i,m_i); M_i>u, m_i<v }

and if def=1 the inverse to

N_T(u,v) = #{ (M_i,m_i); M_i>=u, m_i=<v }

where  (M_i,m_i)  are  cycles and v,u are in the discretization grid.```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:

## SOURCE CODE

```001 function F=nt2fr(M,def)
002 %NT2FR  Calculates the frequency matrix given the counting distribution matrix.
003 %
004 %  CALL: fr = nt2fr(NT);
005 %        fr = nt2fr(NT,def);
006 %
007 %  where
008 %
009 %        fr  = the frequency matrix,
010 %        NT  = the counting distribution matrix,
011 %        def = 0,1
012 %        k   = number of diagonals from main diagonal to be
013 %              set to zero (optional input argument).
014 %
015 %  If def=0 function computes the inverse to
016 %
017 %     N_T(u,v) = #{ (M_i,m_i); M_i>u, m_i<v }
018 %
019 %  and if def=1 the inverse to
020 %
021 %     N_T(u,v) = #{ (M_i,m_i); M_i>=u, m_i=<v }
022 %
023 %  where  (M_i,m_i)  are  cycles and v,u are in the discretization grid.
024 %
025
026
027 n=length(M); P=zeros(size(M));
028
029 if nargin<2
030 def=0;
031 end
032
033 if def==0
034 P(1:n-1,1:n-1)=M(1:n-1,1:n-1)+M(2:n,2:n)-M(1:n-1,2:n)-M(2:n,1:n-1);
035 else
036 P(2:n,2:n)=M(1:n-1,1:n-1)+M(2:n,2:n)-M(1:n-1,2:n)-M(2:n,1:n-1);
037 end
038
039 %if nargin==2
040 %  k_cut=k;
041 %else
042 %  k_cut=2;
043 %end
044
045 F=P;
046
047 %F=fliplr(triu(fliplr(P),k_cut));
048
049
050```

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

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