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| function varargout=wtc(x,y,varargin)
-validate and reformat timeseries.
[x,dt]=formatts(x);
[y,dty]=formatts(y);
if dt~=dty
error('timestep must be equal between time series')
end
t=(max(x(1,1),y(1,1)):dt:min(x(end,1),y(end,1)))'; %common time period
if length(t)<4
error('The two time series must overlap.')
end
n=length(t);
%----------default arguments for the wavelet transform-----------
Args=struct('Pad',1,... % pad the time series with zeroes (recommended)
'Dj',1/12, ... % this will do 12 sub-octaves per octave
'S0',2*dt,... % this says start at a scale of 2 years
'J1',[],...
'Mother','Morlet', ...
'MaxScale',[],... %a more simple way to specify J1
'MakeFigure',(nargout==0),...
'MonteCarloCount',10000,...
'BlackandWhite',1,...
'AR1',[0 0],...
'ArrowDensity',[30 30],...
'ArrowSize',0,...
'ArrowHeadSize',0);
Args=parseArgs(varargin,Args,{'BlackandWhite'});
if isempty(Args.J1)
if isempty(Args.MaxScale)
Args.MaxScale=(n*.17)*2*dt; %auto maxscale
end
Args.J1=round(log2(Args.MaxScale/Args.S0)/Args.Dj);
end
ad=mean(Args.ArrowDensity);
Args.ArrowSize=Args.ArrowSize*30*.03/ad;
Args.ArrowHeadSize=Args.ArrowHeadSize*Args.ArrowSize*220;
if ~strcmpi(Args.Mother,'morlet')
warning('Smoothing operator is designed for morlet wavelet.')
end
if strcmpi(Args.AR1,'auto')
Args.AR1=[ar1nv(x(:,2)) ar1nv(y(:,2))];
if any(isnan(Args.AR1))
error('Automatic AR1 estimation failed. Specify it manually (use arcov or arburg).')
end
end
nx=size(x,1);
sigmax=std(x(:,2));
ny=size(y,1);
sigmay=std(y(:,2));
%-----------:::::::::::::--------- ANALYZE ----------::::::::::::------------
[X,period,scale,coix] = wavelet(x(:,2),dt,Args.Pad,Args.Dj,Args.S0,Args.J1,Args.Mother);
[Y,period,scale,coiy] = wavelet(y(:,2),dt,Args.Pad,Args.Dj,Args.S0,Args.J1,Args.Mother);
%Smooth X and Y before truncating! (minimize coi)
sinv=1./(scale');
sX=smoothwavelet(sinv(:,ones(1,nx)).*(abs(X).^2),dt,period,Args.Dj,scale);
sY=smoothwavelet(sinv(:,ones(1,ny)).*(abs(Y).^2),dt,period,Args.Dj,scale);
% truncate X,Y to common time interval (this is first done here so that the coi is minimized)
dte=dt*.01; %to cricumvent round off errors with fractional timesteps
idx=find((x(:,1)>=(t(1)-dte))&(x(:,1)<=(t(end)+dte)));
X=X(:,idx);
sX=sX(:,idx);
coix=coix(idx);
idx=find((y(:,1)>=(t(1))-dte)&(y(:,1)<=(t(end)+dte)));
Y=Y(:,idx);
sY=sY(:,idx);
coiy=coiy(idx);
coi=min(coix,coiy);
% -------- Cross wavelet -------
Wxy=X.*conj(Y);
% ----------------------- Wavelet coherence ---------------------------------
sWxy=smoothwavelet(sinv(:,ones(1,n)).*Wxy,dt,period,Args.Dj,scale);
Rsq=abs(sWxy).^2./(sX.*sY);
if (nargout>0)||(Args.MakeFigure)
wtcsig=wtcsignif(Args.MonteCarloCount,Args.AR1,dt,length(t)*2,Args.Pad,Args.Dj,Args.S0,Args.J1,Args.Mother,.6);
wtcsig=(wtcsig(:,2))*(ones(1,n));
wtcsig=Rsq./wtcsig;
end
if Args.MakeFigure
Yticks = 2.^(fix(log2(min(period))):fix(log2(max(period))));
if Args.BlackandWhite
levels = [0 .5 .6 .7 .8 .9 1];
levels = [0 .7 .75 .8 .85 .9 .95 1];
% levels = [-1 -.7 -.5 .0 .5 .9 .95 1];
[cout,H]=safecontourf(t,log2(period),Rsq,levels);
colorbarf(cout,H)
cmap=[0 1;.5 .9;.6 .8;.7 .7;.8 .6;.9 .5;1 .4];
cmap=interp1(cmap(:,1),cmap(:,2),(0:.1:1)');
% cmap=[0 1;.7 .9;.75 .8;.8 .7;.85 .6;.9 .5;.95 .4;1 .3];
% cmap=interp1(cmap(:,1),cmap(:,2),(0:.05:1)');
cmap=cmap(:,[1 1 1]);
colormap(cmap)
set(gca,'YLim',log2([min(period),max(period)]), ...
'YDir','reverse', 'layer','top', ...
'YTick',log2(Yticks(:)), ...
'YTickLabel',num2str(Yticks'), ...
'layer','top')
ylabel('Frequency (in years)')
xlabel('Time')
hold on
%phase plot
aWxy=angle(Wxy);
lowRidx=find(Rsq<.5); %remove phase indication where Rsq is low
aaa=aWxy;
aaa(lowRidx)=NaN;
%[xx,yy]=meshgrid(t(1:5:end),log2(period));
phs_dt=round(length(t)/30); tidx=max(floor(phs_dt/2),1):phs_dt:length(t);
phs_dp=round(length(period)/30); pidx=max(floor(phs_dp/2),1):phs_dp:length(period);
% phaseplot(t(tidx),log2(period(pidx)),aaa(pidx,tidx),Args.ArrowSize,Args.ArrowHeadSize);
if ~all(isnan(wtcsig))
[c,h] = contour(t,log2(period),wtcsig,[1 1],'k');
set(h,'linewidth',3) %
end
%suptitle([sTitle ' coherence']);
% plot(t,log2(coi),'k','linewidth',2,'LineStyle','--') %
hold off
else
H=imagesc(t,log2(period),Rsq);
%[c,H]=safecontourf(t,log2(period),Rsq,[0:.05:1]);
%set(H,'linestyle','none')
set(gca,'clim',[0 1])
HCB=safecolorbar;
set(gca,'YLim',log2([min(period),max(period)]), ...
'YDir','reverse', 'layer','top', ...
'YTick',log2(Yticks(:)), ...
'YTickLabel',num2str(Yticks'), ...
'layer','top')
ylabel('')
hold on
%phase plot
aWxy=angle(Wxy);
lowRidx=find(Rsq<.5); %remove phase indication where Rsq is low
aaa=aWxy;
aaa(lowRidx)=NaN;
%[xx,yy]=meshgrid(t(1:5:end),log2(period));
phs_dt=round(length(t)/30); tidx=max(floor(phs_dt/2),1):phs_dt:length(t);
phs_dp=round(length(period)/30); pidx=max(floor(phs_dp/2),1):phs_dp:length(period);
phaseplot(t(tidx),log2(period(pidx)),aaa(pidx,tidx),Args.ArrowSize,Args.ArrowHeadSize);
if ~all(isnan(wtcsig))
[c,h] = contour(t,log2(period),wtcsig,[1 1],'k');
set(h,'linewidth',2)
end
%suptitle([sTitle ' coherence']);
tt=[t([1 1])-dt*.5;t;t([end end])+dt*.5];
hcoi=fill(tt,log2([period([end 1]) coi period([1 end])]),'w');
set(hcoi,'alphadatamapping','direct','facealpha',.5)
hold off
end
end
varargout={Rsq,period,scale,coi,wtcsig};
varargout=varargout(1:nargout);
12345678910111213141516 | function [cout,H]=safecontourf(varargin)
vv=sscanf(version,'%i.');
if (version('-release')<14)|(vv(1)<7)
[cout,H]=contourf(varargin{:});
else
[cout,H]=contourf('v6',varargin{:});
end
function hcb=safecolorbar(varargin)
vv=sscanf(version,'%i.');
if (version('-release')<14)|(vv(1)<7)
hcb=colorbar(varargin{:});
else
hcb=colorbar('v6',varargin{:});
end |
Je vous communique également le code responsable du colorbar:
function hcb=colorbarf(cout,H,loc)
changeNextPlot = 1;
% colorbar must have output parameters from the contourf function
if (nargin < 2)
error('colorbarf requires a minimum of two input parameters');
end
% default location for colorbar
if nargin<3, loc = 'vert'; end
% if an axes handle is passed for the location
ax = [];
if nargin==3,
if ishandle(loc)
ax = loc;
if ~strcmp(get(ax,'type'),'axes'),
error('Requires axes handle.');
end
units = get(ax,'units'); set(ax,'units','pixels');
rect = get(ax,'position'); set(ax,'units',units)
if rect(3) > rect(4), loc = 'horiz'; else loc = 'vert'; end
changeNextPlot = 0;
end
end
h = gca;
if (nargin == 2)
% Search for existing colorbar so that we can plot over it if we find it
ch = get(findobj(gcf,'type','axes','tag','Colorbar')); ax = [];
for i=1:length(ch),
ud = ch(i).UserData; % ch.UserData changed to ch(i).UserData - suggested by P. Brickley
d = ud.PlotHandle;
if prod(size(d))==1 && isequal(d,h),
ax = findobj(gcf,'type','axes','tag','Colorbar');
pos = ch.Position;
if pos(3)<pos(4), loc = 'vert'; else loc = 'horiz'; end
changeNextPlot = 0;
break;
end
end
elseif ((nargin == 3) && (~ishandle(loc)))
% Search for existing colorbar so that we can plot over it if we find it
ch = get(findobj(gcf,'type','axes','tag','Colorbar')); ax = [];
for i=1:length(ch),
ud = ch(i).UserData; % ch.UserData changed to ch(i).UserData - suggested by P. Brickley
d = ud.PlotHandle;
if prod(size(d))==1 && isequal(d,h),
ax = findobj(gcf,'type','axes','tag','Colorbar');
pos = ch.Position;
if pos(3)<pos(4), loc = 'vert'; else loc = 'horiz'; end
changeNextPlot = 0;
break;
end
end
end
origNextPlot = get(gcf,'NextPlot');
if strcmp(origNextPlot,'replacechildren') || strcmp(origNextPlot,'replace'),
set(gcf,'NextPlot','add')
end
%%%%%%%%%%%%%% Filled Colorbar %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Blair Greenan Dec 16, 1998
% strip out the information about the contours from the output of the contourf
% function
i = 1;
while ~isempty(cout)
C1(i) = cout(1,1); % contour level C1(i) = cout(1,1)
N1 = cout(2,1); % number of points in contour N1 = cout(2,1)
% Version 1.4 removed for loop to speed things up
cout(:,1:N1+1) = []; % shrink the matrix
if (N1 > 1) % has to be more than 1 point in contour to be valid ***VERSION 1.5 to accomodate MATLAB6****
i = i + 1;
end
end
C2 = unique(C1); % find the unique contour levels and sort
numLevels = length(C2);
if strcmp(get(H,'type'),'hggroup') %added by Aslak Grinsted to ensure v7 compatibility
H=get(H,'children');
end
for j = 1:length(H)
colors(j) = get(H(j),'CData'); % get the color used to fill the patches
%set(H(j),'CData')
end
colors = unique(colors); % create a list of unique colors used in fills
minc = min(colors);
maxc = max(colors);
colors(isnan(colors))=[];
if ((length(colors)-numLevels)>1)
% chop off extra colors that don't have a corresponding contour level
colors(1:((length(colors)-numLevels)-1))=[];
end
% special case where no mimima is enclosed by a contour
if (length(colors) == numLevels)
colors(length(colors)+1)=NaN;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if loc(1)=='v', % Append vertical scale to right of current plot
if isempty(ax),
units = get(h,'units'); set(h,'units','normalized')
pos = get(h,'Position');
[az,el] = view;
stripe = 0.075; edge = 0.02;
if all([az,el]==[0 90]), space = 0.05; else space = .1; end
set(h,'Position',[pos(1) pos(2) pos(3)*(1-stripe-edge-space) pos(4)])
rect = [pos(1)+(1-stripe-edge)*pos(3) pos(2) stripe*pos(3) pos(4)];
ud.origPos = pos;
% Create axes for stripe and
% create DeleteProxy object (an invisible text object in
% the target axes) so that the colorbar will be deleted
% properly.
ud.DeleteProxy = text('parent',h,'visible','off',...
'tag','ColorbarDeleteProxy',...
'handlevisibility','off',...
'deletefcn','eval(''delete(get(gcbo,''''userdata''''))'','''')');
ax = axes('Position', rect,'Tag','TMW_COLORBAR');
set(ud.DeleteProxy,'userdata',ax)
set(h,'units',units)
else % if colobar axes already exist
axes(ax);
ud = get(ax,'userdata');
end
% Create color stripe by drawing the appropriate number of filled rectangles
if any(isnan(colors)) % if the bottom level is not filled
for j = 1:length(C2)+1
k = j - 1; % don't fill bottom rectangle on colorbar
x(1) = 0;
x(2) = 1;
x(3) = 1;
x(4) = 0;
y(1) = (j-1)*(1/(length(C2)+1));
y(2) = (j-1)*(1/(length(C2)+1));
y(3) = j*(1/(length(C2)+1));
y(4) = j*(1/(length(C2)+1));
if (k == 0)
hfill = fill(x,y,colors(length(colors))); % fill with NaN
else
hfill = fill(x,y,colors(k));
end
hold on
end
else %we have filled the bottom contour level
for j = 1:length(C2)+1
x(1) = 0;
x(2) = 1;
x(3) = 1;
x(4) = 0;
y(1) = (j-1)*(1/(length(C2)+1));
y(2) = (j-1)*(1/(length(C2)+1));
y(3) = j*(1/(length(C2)+1));
y(4) = j*(1/(length(C2)+1));
hfill = fill(x,y,colors(j));
hold on
end
end
set(ax,'YAxisLocation','right')
set(ax,'xtick',[])
ylimits = get(gca,'ylim');
myYticks = ylimits(1):(ylimits(2)-ylimits(1))/(length(C2)+1):ylimits(2)...
-((ylimits(2)-ylimits(1))/(length(C2)+1));
set(gca,'ytick',myYticks);
myStr{1} = ' ';
for kk = 1:length(C2)
myStr{kk+1} = num2str(C2(kk));
end
myStr{(length(C2)+2)} = ' ';
set(gca,'YTickLabel',myStr)
set(gca,'CLim',[minc maxc])
% set up axes deletefcn
set(ax,'tag','Colorbar','deletefcn','colorbar(''delete'')')
elseif loc(1)=='h', % Append horizontal scale to top of current plot
if isempty(ax),
units = get(h,'units'); set(h,'units','normalized')
pos = get(h,'Position');
stripe = 0.075; space = 0.1;
set(h,'Position',...
[pos(1) pos(2)+(stripe+space)*pos(4) pos(3) (1-stripe-space)*pos(4)])
rect = [pos(1) pos(2) pos(3) stripe*pos(4)];
ud.origPos = pos;
% Create axes for stripe and
% create DeleteProxy object (an invisible text object in
% the target axes) so that the colorbar will be deleted
% properly.
ud.DeleteProxy = text('parent',h,'visible','off',...
'tag','ColorbarDeleteProxy',...
'handlevisibility','off',...
'deletefcn','eval(''delete(get(gcbo,''''userdata''''))'','''')');
ax = axes('Position', rect,'Tag','TMW_COLORBAR');
set(ud.DeleteProxy,'userdata',ax)
set(h,'units',units)
else % if colobar axes already exist
axes(ax);
ud = get(ax,'userdata');
end
% Create color stripe by drawing the appropriate number of filled rectangles
if any(isnan(colors)) % if the bottom level is not filled
for j = 1:length(C2)+1
k = j - 1; % don't fill bottom rectangle on colorbar
y(1) = 0;
y(2) = 1;
y(3) = 1;
y(4) = 0;
x(1) = (j-1)*(1/(length(C2)+1));
x(2) = (j-1)*(1/(length(C2)+1));
x(3) = j*(1/(length(C2)+1));
x(4) = j*(1/(length(C2)+1));
if (k == 0)
hfill = fill(x,y,colors(length(colors))); % fill with NaN
else
hfill = fill(x,y,colors(k));
end
hold on
end
else %we have filled the bottom contour level
for j = 1:length(C2)+1
y(1) = 0;
y(2) = 1;
y(3) = 1;
y(4) = 0;
x(1) = (j-1)*(1/(length(C2)+1));
x(2) = (j-1)*(1/(length(C2)+1));
x(3) = j*(1/(length(C2)+1));
x(4) = j*(1/(length(C2)+1));
hfill = fill(x,y,colors(j));
hold on
end
end
set(ax,'ytick',[])
xlimits = get(gca,'xlim');
myXticks = xlimits(1):(xlimits(2)-xlimits(1))/(length(C2)+1):xlimits(2)...
-((xlimits(2)-xlimits(1))/(length(C2)+1));
set(gca,'xtick',myXticks);
myStr{1} = ' ';
for kk = 1:length(C2)
myStr{kk+1} = num2str(C2(kk));
end
myStr{(length(C2)+2)} = ' ';
set(gca,'XTickLabel',myStr)
set(gca,'CLim',[minc maxc])
% set up axes deletefcn
set(ax,'tag','Colorbar','deletefcn','colorbar(''delete'')')
else
error('COLORBAR expects a handle, ''vert'', or ''horiz'' as input.')
end
if ~isfield(ud,'DeleteProxy'), ud.DeleteProxy = []; end
if ~isfield(ud,'origPos'), ud.origPos = []; end
ud.PlotHandle = h;
set(ax,'userdata',ud)
set(gcf,'CurrentAxes',h)
set(gcf,'NextPlot',origNextPlot)
if nargout>0, hcb = ax; end |
Wavelet coherence et colorbar
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