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Commit 1fd0c8fd authored by marwan's avatar marwan
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adding Hirata's reconstruction method to recons.m

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crp_man.pdf
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mi.m
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......@@ -7,13 +7,13 @@ function varargout=mi(varargin)
% between all pairs of X1,X2,...,Xn using 10 bins. The result I
% is a N x N matrix.
%
% I=MI(X1,X2,...,Xn,N), where N is a scalar, determines the number
% of bins N.
%
% I=MI(X1,X2,...,Xn,L) or I=MI(X1,X2,...,Xn,N,L), where L is a
% scalar, computes mutual informations for shifting of the
% components of each pair of X1,X2,...,Xn until a maximal lag L.
%
% I=MI(X1,X2,...,Xn,N,L), where N is a scalar determining the number
% of bins N.
%
% [I S]=MI(...) computes the mutual information and the
% standard error (only for one- and two-dimensional data).
%
......@@ -60,6 +60,10 @@ function varargout=mi(varargin)
% $Revision$
%
% $Log$
% Revision 3.18 2016/03/03 14:57:40 marwan
% updated input/output check (because Mathworks is removing downwards compatibility)
% bug in crqad_big fixed (calculation of xcf).
%
% Revision 3.17 2016/02/05 17:16:37 marwan
% fix compatibility issues (R2014b)
%
......
recons.m
+ 214
− 95
View file @ 1fd0c8fd
......@@ -3,12 +3,20 @@ function varargout=recons(varargin)
% Y = RECONS(X) reconstructs a time series Y from the
% recurrence plot in the matrix X.
%
% Y = RECONS(X,NAME) reconstructs the time series using
% Y = RECONS(X,...,METHOD) specifies the reconstruction method
% where string METHOD can be either 'thiel' or 'hirata', using
% the method by Marco Thiel (defeault) or Yoshito Hirata.
%
% Y = RECONS(X,...,NAME) reconstructs the time series using
% the named cumulative distribution function, which can
% be 'norm' or 'Normal' (defeault), 'unif' or 'Uniform'.
% be 'norm' or 'Normal' (defeault), 'unif' or 'Uniform'. This
% is only necessary for the method by Thiel. The reconstruction
% from the Hirata will not be scaled.
%
% Y = RECONS(X,P) reconstructs the time series using
% the cumulative distribution function given by vector P.
% Y = RECONS(X,P,...) reconstructs the time series using the
% cumulative distribution function given by vector P (should be
% 2nd argument). This is only necessary for the method by Thiel.
% The reconstruction from the Hirata will not be scaled.
%
% See also CRP, CRP2, JRP, TWINSURR.
%
......@@ -16,6 +24,10 @@ function varargout=recons(varargin)
% Thiel, M., Romano, M. C., Kurths, J.:
% How much information is contained in a recurrence plot?,
% Phys. Lett. A, 330, 2004.
% Hirata, Y., Horai, S., Aihara, K.:
% Reproduction of distance matrices from recurrence plots
% and its applications,
% Eur. Phys. J. ST, 164, 2008.
% Copyright (c) 2008-
% Norbert Marwan, Potsdam Institute for Climate Impact Research, Germany
......@@ -29,6 +41,10 @@ function varargout=recons(varargin)
% $Revision$
%
% $Log$
% Revision 5.4 2016/03/03 14:57:40 marwan
% updated input/output check (because Mathworks is removing downwards compatibility)
% bug in crqad_big fixed (calculation of xcf).
%
% Revision 5.3 2009/03/24 08:34:10 marwan
% copyright address changed
%
......@@ -50,7 +66,7 @@ function varargout=recons(varargin)
errcode = 0; %xout = [];
narginchk(1,2)
narginchk(1,3)
nargoutchk(0,1)
if isnumeric(varargin{1})==1 % read RP
......@@ -65,119 +81,172 @@ N = size(X); maxN = prod(N)+1;
if N(1) ~= N(2)
error('Input must be square matrix.')
end
N = N(1);
try
% final distribution
errcode = 1;
i=(-5:10/(N(1)-1):5)';
fs=cumsum(10*(1/(sqrt(2*pi))).*exp(-(i).^2./2));
P=interp1(fs,i,[1:length(fs)],'nearest')';
i = (-5:10/(N-1):5)';
fs = cumsum(10*(1/(sqrt(2*pi))).*exp(-(i).^2./2));
P = interp1(fs,i,[1:length(fs)],'nearest')';
% check for input arguments of type char
method = 1; % default reconstruction method by Thiel
i_char = find(cellfun('isclass',varargin,'char'));
for i = i_char
if strcmpi(varargin{i}(1:3), 'thi')
method = 1;
disp('Use reconstruction by Thiel.')
end
if strcmpi(varargin{i}(1:3), 'hir')
method = 2;
disp('Use reconstruction by Hirata')
end
if strcmpi(varargin{i}(1:3), 'uni')
P = (0:1/(N-1):1)';
disp('Use uniform distribution.')
end
end
if nargin > 1 & isnumeric(varargin{2})==1
P = varargin{2};
elseif nargin > 1 & ischar(varargin{2})==1
if strcmpi(varargin{2}(1:3), 'uni')
P = (0:1/(N(1)-1):1)';
disp('uni')
end
end
P(isnan(P)) = []; % remove NaN from distribution
h_waitbar = waitbar(0,'Reconstruct trajectory'); drawnow
h_waitbar = waitbar(0,'Remove double columns'); drawnow
% number of non-neighbours
% remove double rows
errcode = 2;
[X2 uniI J]=unique(X,'rows');
uniI = sort(uniI);
if method == 2;
%%%%% Method by Hirata
% calculate weights
waitbar(0, h_waitbar, 'Calculate weights'); drawnow
W = 10000*ones(N,N);
errcode = 3;
for i = 1:N, waitbar(i/N)
neighb = find(X(i,:)); % neighbours of i
% number of intersections
Ninter = sum(X(neighb,:).*repmat(X(i,:),length(neighb),1),2);
% number of union
Nunion = sum((X(neighb,:)+repmat(X(i,:),length(neighb),1))>0,2);
W(i, neighb) = (1 - Ninter./Nunion)';
end
% this are the removed rows
rem = setdiff(1:length(X2),uniI);
%X3(rem,:) = X(rem,:);
% shortest path
dists = zeros(N,N);
waitbar(0, h_waitbar, 'Calculate shortest paths'); drawnow
for i = 1:N, waitbar(i/N)
sds = dijkstra(W,i);
dists(i,:) = sds;
end
% this are the corresponding columns
for i = 1:length(rem), waitbar(i/length(rem))
% [dummy, dblI(i), a2] = intersect(X, X(rem(i),:), 'rows');
X2 = X;
X2(rem,:) = -1;
dblI(i) = find(all((X2 == repmat(X(rem(i),:), size(X2,2), 1))'));
end
% number of non-neighbours
errcode = 3;
waitbar(0, h_waitbar, 'Search neighbours'); drawnow
NN = maxN*ones(N);
%N = zeros(size(X1));
for i = 1:size(X,1), waitbar(i/size(X,1))
if ~ismember(i,rem)
% indices of RPs at i
I = find(X(i,:));
I(ismember(I,rem)) = [];
% number of non-neighbours
n = sum((X(I,:) - repmat(X(i,:),length(I),1)) == 1,2);
NN(i,I) = n';
r = cmdscale(dists);
xneu = r(:,1);
else
%%%%% Method by Thiel
% remove double rows
errcode = 2;
[X2 uniI J]=unique(X,'rows');
uniI = sort(uniI);
% this are the removed rows
rem = setdiff(1:length(X2),uniI);
%X3(rem,:) = X(rem,:);
% this are the corresponding columns
for i = 1:length(rem), waitbar(i/length(rem))
% [dummy, dblI(i), a2] = intersect(X, X(rem(i),:), 'rows');
X2 = X;
X2(rem,:) = -1;
dblI(i) = find(all((X2 == repmat(X(rem(i),:), size(X2,2), 1))'));
end
end
errcode = 4;
% remove entries on the main diagonal in N
i(1:size(NN,1)) = 1; NN(find(diag(i))) = maxN;
% determine the both indices where N == 0 for all i
iNaN = NN == maxN; i = find(iNaN); NN2 = NN; NN2(i) = zeros(size(i)); % remove NaNs
n = sum(NN2,1);
borderI=find(n==0);
borderI(ismember(borderI,rem)) = [];
k = borderI(1);
r = k; % start point in the rank order vector
errcode = 5;
waitbar(0, h_waitbar, 'Reconstructing time series'); drawnow
while min(NN(:)) < maxN
% look for the minimal N(k,:)
waitbar(length(r)/N(1))
[dummy kneu] = min(NN(k,:));
if ~isempty(dummy) kneu = find(NN(k,:) == dummy); else break, end
if length(kneu) > 1 % if a set of minimal N exist
[dummy kneu_index] = min(NN(kneu,k));
kneu=kneu(kneu_index);
% number of non-neighbours
errcode = 3;
waitbar(0, h_waitbar, 'Search neighbours'); drawnow
NN = maxN*ones(N);
%N = zeros(size(X1));
for i = 1:size(X,1), waitbar(i/size(X,1))
if ~ismember(i,rem)
% indices of RPs at i
I = find(X(i,:));
I(ismember(I,rem)) = [];
% number of non-neighbours
n = sum((X(I,:) - repmat(X(i,:),length(I),1)) == 1,2);
NN(i,I) = n';
end
end
NN(:,k) = maxN;
kold = k;
k=kneu;
r = [r; k]; % add the new found index to the rank order vector
if length(r) > N(1) + 1
delete(h_waitbar)
disp(['Critical abort. Could not find enough corresponding neigbours.',10,'Perhaps the recurrence threshold is too small.'])
if nargout
varargout{1} = NaN;
errcode = 4;
% remove entries on the main diagonal in N
i(1:size(NN,1)) = 1; NN(find(diag(i))) = maxN;
% determine the both indices where N == 0 for all i
iNaN = NN == maxN; i = find(iNaN); NN2 = NN; NN2(i) = zeros(size(i)); % remove NaNs
n = sum(NN2,1);
borderI=find(n==0);
borderI(ismember(borderI,rem)) = [];
k = borderI(1);
r = k; % start point in the rank order vector
errcode = 5;
waitbar(0, h_waitbar, 'Reconstructing time series'); drawnow
while min(NN(:)) < maxN
% look for the minimal N(k,:)
waitbar(length(r)/N(1))
[dummy kneu] = min(NN(k,:));
if ~isempty(dummy) kneu = find(NN(k,:) == dummy); else break, end
if length(kneu) > 1 % if a set of minimal N exist
[dummy kneu_index] = min(NN(kneu,k));
kneu=kneu(kneu_index);
end
NN(:,k) = maxN;
kold = k;
k=kneu;
r = [r; k]; % add the new found index to the rank order vector
if length(r) > N(1) + 1
delete(h_waitbar)
disp(['Critical abort. Could not find enough corresponding neigbours.',10,'Perhaps the recurrence threshold is too small.'])
if nargout
varargout{1} = NaN;
end
return
end
return
end
end
errcode = 6;
% adjust length of the distribution
P = interp1((1:length(P))/length(P), P, (1:length(r))/length(r),'cubic');
% assign the distribution to the rank order series
waitbar(0, h_waitbar, 'Assigning distribution'); drawnow
clear xneu
for i = 1:length(r);
xneu(r(i)) = P(i);
waitbar(i/length(r))
end
errcode = 7;
% add the removed (doubled) elements
for i =1:length(rem)
xneu(rem(i)) = xneu(dblI(i));
errcode = 6;
% adjust length of the distribution
P = interp1((1:length(P))/length(P), P, (1:length(r))/length(r),'cubic');
% assign the distribution to the rank order series
waitbar(0, h_waitbar, 'Assigning distribution'); drawnow
clear xneu
for i = 1:length(r);
xneu(r(i)) = P(i);
waitbar(i/length(r))
end
errcode = 7;
% add the removed (doubled) elements
for i =1:length(rem)
xneu(rem(i)) = xneu(dblI(i));
end
end
delete(h_waitbar)
......@@ -248,3 +317,53 @@ catch
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sds = dijkstra(dm, s)
% DIJSKSTRA Shortest path for weighted graph.
% SDS = DIJKSTRA(DM, S) calculates the shortest paths
% from vertex S to all other vertices of the graph DM.
%DMAX = length(dm) + 1;
DMAX = 100001;
n = size(dm,1);
visited = zeros(1,n);
% allocate 1 at the starting node and DMAX for the rest.
visited = zeros(n,1);
sds = DMAX * ones(n,1);
sds(s) = 0;
c = n-1;
while(c > 0)
% find the shortest path among not-visited nodes.
j = 1;
while (visited(j) == 1)
j = j+1;
end
dmin = sds(j);
k = j;
for i=j:n
if(visited(i) == 0)
if(dmin > sds(i))
dmin = sds(i);
k = i;
end
end
end
visited(k) = 1;
c = c - 1;
% [c k]
% find nodes connected to k and increment
for i=1:n
if((visited(i) == 0)&(dm(k,i) >= 0))
if (sds(i) > sds(k) + dm(k,i))
sds(i) = sds(k) + dm(k,i);
end
end
end
end
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