wt.m

交互小波分析及其一致性分析

function varargout=wt(d,varargin)
%% Continous Wavelet Transform
% Creates a figure of wavelet power in units of
% normalized variance.
%
% USAGE: [wave,period,scale,coi,sig95]=wt(d[,settings])
% 
% d: a time series
% wave: the wavelet transform of d
% period: a vector of "Fourier" periods associated with wave
% scale: a vector of wavelet scales associated with wave
% coi: the cone of influence
%
% Settings: Pad: pad the time series with zeros? 
% .         Dj: Scales per octave (default: '1/12')
% .         S0: Minimum scale
% .         J1: Total number of scales
% .         Mother: Mother wavelet (default 'morlet')
% .         MaxScale: An easier way of specifying J1
% .         MakeFigure: Make a figure or simply return the output.
% .         BlackandWhite: Create black and white figures
% .         AR1: the ar1 coefficient of the series 
% .              (default='auto' using the Allen&Smith method. See ar1.m)
%
% Settings can also be specified using abbreviations. e.g. ms=MaxScale.
% For detailed help on some parameters type help wavelet.
%
%
% Example:
%      wt([0:200;sin(0:200)],'dj',1/20,'bw','maxscale',32)
%
% (C) Aslak Grinsted 2002-2004
%
% http://www.pol.ac.uk/home/research/waveletcoherence/

% -------------------------------------------------------------------------
%   Copyright (C) 2002-2004, Aslak Grinsted
%   This software may be used, copied, or redistributed as long as it is not
%   sold and this copyright notice is reproduced on each copy made.  This
%   routine is provided as is without any express or implied warranties
%   whatsoever.


% ------validate and reformat timeseries.
[d,dt]=formatts(d);

n=size(d,1);
sigma2=var(d(:,2));

%----------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),...
            'BlackandWhite',0,...
            'AR1','auto');
Args=parseArgs(varargin,Args,{'BlackandWhite'});
if isempty(Args.J1)
    if isempty(Args.MaxScale)
        Args.MaxScale=(n*.17)*2*dt; %automaxscale
    end
    Args.J1=round(log2(Args.MaxScale/Args.S0)/Args.Dj);
end

if strcmpi(Args.AR1,'auto')
    Args.AR1=ar1(d(:,2));
    if any(isnan(Args.AR1))
        error('Automatic AR1 estimation failed. Specify it manually (use arcov or arburg).')
    end
end



%----------------::::::::---------- Analyze: ---------:::::::::::::-----------------


[wave,period,scale,coi] = wavelet(d(:,2),dt,Args.Pad,Args.Dj,Args.S0,Args.J1,Args.Mother);

t=d(:,1);
power = (abs(wave)).^2 ;        % compute wavelet power spectrum
[signif,fft_theor] = wave_signif(1.0,dt,scale,0,Args.AR1,-1,-1,Args.Mother);
sig95 = (signif')*(ones(1,n));  % expand signif --> (J+1)x(N) array
sig95 = power ./ (sigma2*sig95);
Yticks = 2.^(fix(log2(min(period))):fix(log2(max(period))));

if Args.MakeFigure

    if Args.BlackandWhite
        levels = [0.25,0.5,1,2,4,8,16] ;
        
        [cout,H]=safecontourf(t,log2(period),log2(abs(power/sigma2)),log2(levels));%,log2(levels));  %*** or use 'contourfill'
        cout(1,:)=2.^cout(1,:);

        HCB=colorbarf(cout,H);
        barylbls=rats([0 levels 0]');
        barylbls([1 end],:)=' ';
        barylbls(:,find(all(barylbls==' ',1)))=[];
        set(HCB,'yticklabel',barylbls);
        cmap=(1:-.01:.5)'*.9;
        cmap(:,2:3)=cmap(:,[1 1]);
        %cmap(:,1:2)=cmap(:,1:2)*.8;
        colormap(cmap);
        set(gca,'YLim',log2([min(period),max(period)]), ...
            'YDir','reverse', ...
            'YTick',log2(Yticks(:)), ...
            'YTickLabel',num2str(Yticks'), ...
            'layer','top')
        %xlabel('Time')
        ylabel('Period')
        hold on

        [c,h] = contour(t,log2(period),sig95,[1 1],'k');
        set(h,'linewidth',3)
        plot(t,log2(coi),'k','linewidth',3)
        %hcoi=fill([t([1 1:end end])],log2([period(end) coi period(end)]),'r')
        %set(hcoi,'alphadatamapping','direct','facealpha',.3)

        hold off
    else
        H=imagesc(t,log2(period),log2(abs(power/sigma2)));%,log2(levels));  %*** or use 'contourfill'
        %logpow=log2(abs(power/sigma2));
        %[c,H]=safecontourf(t,log2(period),logpow,[min(logpow(:)):.25:max(logpow(:))]);
        %set(H,'linestyle','none')
        
        clim=get(gca,'clim'); %center color limits around log2(1)=0
        clim=[-1 1]*max(clim(2),3);
        set(gca,'clim',clim)
        
        HCB=safecolorbar;
        set(HCB,'ytick',-7:7);
        barylbls=rats(2.^(get(HCB,'ytick')'));
        barylbls([1 end],:)=' ';
        barylbls(:,find(all(barylbls==' ',1)))=[];
        set(HCB,'yticklabel',barylbls);
        
        
        set(gca,'YLim',log2([min(period),max(period)]), ...
            'YDir','reverse', ...
            'YTick',log2(Yticks(:)), ...
            'YTickLabel',num2str(Yticks'), ...
            'layer','top')
        %xlabel('Time')
        ylabel('Period')
        hold on

        
        
        [c,h] = contour(t,log2(period),sig95,[1 1],'k');
        set(h,'linewidth',2)
        %plot(t,log2(coi),'k','linewidth',3)
        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
    set(gca,'box','on','layer','top');
end
varargout={wave,period,scale,coi,sig95};
varargout=varargout(1:nargout);



function [cout,H]=safecontourf(varargin) %R14 HACK --- fix.
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