可视化两条线之间的异常附matlab代码

clcclear allclose allx = 1:.1:20;y = sin(x);ref = sin(x)/2;figureclimanomaly(x,y,ref);

function [hlin,href,htop,hbot] = climanomaly(x,y,ref,varargin)% CLIMANOMALY plots two lines (y vs. x and y vs. ref) and visualises% positive and negative anomalies by shading the area between both lines in% two different colors. This is useful for visualising anomalies of a time% series relative to a climatology. The function can further be used to% plot anomalies relative to a constant baseline or two threshold baselines% (positive anomaly above upper threshold, negative anomaly below lower% threshold).%%% Syntax%%  CLIMANOMALY(x,y,ref)%  CLIMANOMALY(...,'top',ColorSpec)%  CLIMANOMALY(...,'bottom',ColorSpec)%  CLIMANOMALY(...,'mainline','LineSpec')%  CLIMANOMALY(...,'refline','LineSpec')%  [hlin,href,htop,hbot] = CLIMANOMALY(...)%% %% Description%% CLIMANOMALY(x,y,ref) plots a y vs. x (main line) and y vs. ref (reference% line) and shades areas line values above zero; blue fills the area% between zero and any values below zero.% - To shade anomalies relative to a variable reference (e.g. a%   climatology) specify ref as a vector the length of y.% - To shade anomalies relative to a constant baseline, specify a single%   ref value.% - To shade anomalies relative to an upper and a lower threshold, specify%   two ref values (e.g., let ref be [-0.4 0.5] to shade all values less%   than 0.4 or greater than 0.5).%% CLIMANOMALY(...,'top',ColorSpec) specifies the top color shading, which% can be described by RGB values or any of the Matlab short-hand color% names (e.g., 'r' or 'red').%% CLIMANOMALY(...,'bottom',ColorSpec) specifies the bottom shading color.%% CLIMANOMALY(...,'mainline','LineSpec')% CLIMANOMALY(...,'refline','LineSpec')% Specifies line types, plot symbols and colors of the reference line.% LineSpec is a string of characters, e.g. 'b--*'. Refer to the 'plot'% documentation for more options. Use 'none' to plot the anomalies without% % By default, the main line will be plotted as a solid black line ('k-')% and the reference line as a dotted black line ('k:').% % [hlin,href,htop,hbot] = CLIMANOMALY(...) returns the graphics handles of% the main line, top, and bottom plots, respectively.%%%% Examples% % Example 1: Simple plot%% Example 2: Change line and patch appearance% x = 1:.1:20;% y = sin(x);% ref = sin(x)/2;% figure% [hlin,href,htop,hbot] = CLIMANOMALY(x,y,ref,'top','k','bottom',[.9 .9 .9],...%     'mainline','b-','refline','r--');% hlin.LineWidth = 2;% href.LineWidth = 2;% alpha(htop,0.7)% alpha(hbot,0.7)%% %% Author Info%% Jake Weis, University of Tasmania, Institute for Marine and Antarctic% Studies (IMAS), April 2021% % This function is based on the 'anomaly' function, written by Chad A.% Greene (<a href="matlab:web('https://github.com/chadagreene/CDT')">Climate Data Toolbox</a>).% Subfunction used: 'intersections' by Douglas M. Schwarz.%% See also: plot, boundedline, area, patch, and fill.%% Error checks:narginchk(3,inf)assert(numel(ref)<=2 | numel(ref)==numel(y),'Input error: The refold must either be one or two scalars or the length of y.')assert(numel(x)==numel(y),'Input error: The dimensions of x and y must agree.')assert(isvector(x),'Input error: x and y must be vectors of the same dimension.')assert(issorted(x),'Input error: x must be monotonically increasing.')%% Set defaults:% These are RGB values from cmocean's balance colormap (Thyng et al., 2016):topcolor = [0.7848    0.4453    0.3341];bottomcolor = [0.3267    0.5982    0.7311];% Reference line will be plotted by defaultmainspec = 'k-';refspec = 'k:';%% Input parsing:if nargin>3        % Top face color:    itop = find(strncmpi(varargin,'topcolor',3),1);    if ~isempty(itop)        topcolor = varargin{itop+1};        varargin(itop:itop+1) = [];    end        % Bottom face color:    ibot = find(strncmpi(varargin,'bottomcolor',3),1);    if ~isempty(ibot)        bottomcolor = varargin{ibot+1};        varargin(ibot:ibot+1) = [];    end        % Main and reference line properties:    imai = find(strncmpi(varargin,'mainline',3),1);    iref = find(strncmpi(varargin,'refline',3),1);    if ~isempty(imai)        mainspec = varargin{imai+1};        varargin(imai:imai+1) = [];    end        % Reference line:    iref = find(strncmpi(varargin,'refline',3),1);    if ~isempty(iref)        refspec = varargin{iref+1};        varargin(iref:iref+1) = [];    endend%% Data manipulation:% Convert ref into a top and a bottom column vector the length of yif numel(ref) == 1    reft = repmat(ref,numel(y),1);    refb = repmat(ref,numel(y),1);elseif numel(ref) == 2    reft = repmat(max(ref),numel(y),1);    refb = repmat(min(ref),numel(y),1);else    reft = ref(:);    refb = ref(:);end% Columnate inputs to ensure consistent behavior:x = x(:);y = double(y(:));% Archive the x and y values before tinkering with them (we'll plot the archived vals later).x_archive = x;y_archive = y;reft_archive = reft;refb_archive = refb;% If y contains nans, ignore them so filling will work:ind = (isfinite(y) & isfinite(reft) & isfinite(refb));x = x(ind);y = y(ind);reft = reft(ind);refb = refb(ind);% Find zero crossings so shading will meet the refline properly:% First for the bottom:[xct,yct] = intersections(x,y,x,reft); % intersections is a subfunction by Douglas Schwarz, included below.% Now for the top:[xcb,ycb] = intersections(x,y,x,refb); % intersections is a subfunction by Douglas Schwarz, included below.% Add zero crossings to the input dataset and sort them into the proper order:xb = [x;xcb];xt = [x;xct];yb = [y;ycb];yt = [y;yct];reft = [reft;yct];refb = [refb;ycb];[xb,ind] = sortrows(xb);yb = yb(ind);           % sorts yb with xbrefb = refb(ind);       % sorts refb with xb[xt,ind] = sortrows(xt);yt = yt(ind);           % sorts yt with xtreft = reft(ind);       % sorts reft with xt% Start thinking about this as two separate datasets which share refline values where they meet:yb(yb>refb) = refb(yb>refb);yt(yt<reft) = reft(yt<reft);%% Plot top and bottom y datasets using the area function:% Get initial hold state:hld = ishold;% Plot the top half:htop = fill([xt;flipud(xt)],[yt;flipud(reft)],topcolor,'LineStyle','none');hold on% Plot the bottom half:hbot = fill([xb;flipud(xb)],[yb;flipud(refb)],bottomcolor,'LineStyle','none');if ~strcmp(mainspec,'none')    % Plot the main line (the "archive" values are just the unmanipulated values the user entered)    hlin = plot(x_archive,y_archive,mainspec);else    hlin = cell(1,1);endif ~strcmp(refspec,'none')    % Plot the main line (the "archive" values are just the unmanipulated values the user entered)    href(1) = plot(x_archive,reft_archive,refspec);        if numel(ref) == 2        % Plot the main line (the "archive" values are just the unmanipulated values the user entered)        href(2) = plot(x_archive,refb_archive,refspec);    endelse    if numel(ref) ~= 2        href = cell(1,1);    else        href = cell(2,1);    endend% Return the hold state if necessary:if ~hld    hold offend%% Clean up:if nargout==0    clear hlin href htop hbotendend%% * * * * * * S U B F U N C T I O N S * * * * * * *function [x0,y0,iout,jout] = intersections(x1,y1,x2,y2,robust)%INTERSECTIONS Intersections of curves.%   Computes the (x,y) locations where two curves intersect.  The curves%   can be broken with NaNs or have vertical segments.%% Example:%   [X0,Y0] = intersections(X1,Y1,X2,Y2,ROBUST);%% where X1 and Y1 are equal-length vectors of at least two points and% represent curve 1.  Similarly, X2 and Y2 represent curve 2.% X0 and Y0 are column vectors containing the points at which the two% curves intersect.%% ROBUST (optional) set to 1 or true means to use a slight variation of the% algorithm that might return duplicates of some intersection points, and% then remove those duplicates.  The default is true, but since the% algorithm is slightly slower you can set it to false if you know that% your curves don't intersect at any segment boundaries.  Also, the robust% version properly handles parallel and overlapping segments.%% The algorithm can return two additional vectors that indicate which% segment pairs contain intersections and where they are:%%   [X0,Y0,I,J] = intersections(X1,Y1,X2,Y2,ROBUST);%% For each element of the vector I, I(k) = (segment number of (X1,Y1)) +% (how far along this segment the intersection is).  For example, if I(k) =% 45.25 then the intersection lies a quarter of the way between the line% segment connecting (X1(45),Y1(45)) and (X1(46),Y1(46)).  Similarly for% the vector J and the segments in (X2,Y2).%% You can also get intersections of a curve with itself.  Simply pass in% only one curve, i.e.,%%   [X0,Y0] = intersections(X1,Y1,ROBUST);%% where, as before, ROBUST is optional.% Version: 1.12, 27 January 2010% Author:  Douglas M. Schwarz% Email:   dmschwarz=ieee*org, dmschwarz=urgrad*rochester*edu% Real_email = regexprep(Email,{'=','*'},{'@','.'})% Theory of operation:%% Given two line segments, L1 and L2,%%   L1 endpoints:  (x1(1),y1(1)) and (x1(2),y1(2))%   L2 endpoints:  (x2(1),y2(1)) and (x2(2),y2(2))%% we can write four equations with four unknowns and then solve them.  The% four unknowns are t1, t2, x0 and y0, where (x0,y0) is the intersection of% L1 and L2, t1 is the distance from the starting point of L1 to the% intersection relative to the length of L1 and t2 is the distance from the% starting point of L2 to the intersection relative to the length of L2.%% So, the four equations are%%    (x1(2) - x1(1))*t1 = x0 - x1(1)%    (x2(2) - x2(1))*t2 = x0 - x2(1)%    (y1(2) - y1(1))*t1 = y0 - y1(1)%    (y2(2) - y2(1))*t2 = y0 - y2(1)%% Rearranging and writing in matrix form,%%  [x1(2)-x1(1)       0       -1   0;      [t1;      [-x1(1);%        0       x2(2)-x2(1)  -1   0;   *   t2;   =   -x2(1);%   y1(2)-y1(1)       0        0  -1;       x0;       -y1(1);%        0       y2(2)-y2(1)   0  -1]       y0]       -y2(1)]%% Let's call that A*T = B.  We can solve for T with T = A\B.%% Once we have our solution we just have to look at t1 and t2 to determine% whether L1 and L2 intersect.  If 0 <= t1 < 1 and 0 <= t2 < 1 then the two% line segments cross and we can include (x0,y0) in the output.%% In principle, we have to perform this computation on every pair of line% segments in the input data.  This can be quite a large number of pairs so% we will reduce it by doing a simple preliminary check to eliminate line% segment pairs that could not possibly cross.  The check is to look at the% smallest enclosing rectangles (with sides parallel to the axes) for each% line segment pair and see if they overlap.  If they do then we have to% compute t1 and t2 (via the A\B computation) to see if the line segments% cross, but if they don't then the line segments cannot cross.  In a% typical application, this technique will eliminate most of the potential% line segment pairs.% Input checks.narginchk(2,5)% Adjustments when fewer than five arguments are supplied.switch nargin    case 2        robust = true;        x2 = x1;        y2 = y1;        self_intersect = true;    case 3        robust = x2;        x2 = x1;        y2 = y1;        self_intersect = true;    case 4        robust = true;        self_intersect = false;    case 5        self_intersect = false;end% x1 and y1 must be vectors with same number of points (at least 2).if sum(size(x1) > 1) ~= 1 || sum(size(y1) > 1) ~= 1 || ...        length(x1) ~= length(y1)    error('X1 and Y1 must be equal-length vectors of at least 2 points.')end% x2 and y2 must be vectors with same number of points (at least 2).if sum(size(x2) > 1) ~= 1 || sum(size(y2) > 1) ~= 1 || ...        length(x2) ~= length(y2)    error('X2 and Y2 must be equal-length vectors of at least 2 points.')end% Force all inputs to be column vectors.x1 = x1(:);y1 = y1(:);x2 = x2(:);y2 = y2(:);% Compute number of line segments in each curve and some differences we'll% need later.n1 = length(x1) - 1;n2 = length(x2) - 1;xy1 = [x1 y1];xy2 = [x2 y2];dxy1 = diff(xy1);dxy2 = diff(xy2);% Determine the combinations of i and j where the rectangle enclosing the% i'th line segment of curve 1 overlaps with the rectangle enclosing the% j'th line segment of curve 2.[i,j] = find(repmat(min(x1(1:end-1),x1(2:end)),1,n2) <= ...    repmat(max(x2(1:end-1),x2(2:end)).',n1,1) & ...    repmat(max(x1(1:end-1),x1(2:end)),1,n2) >= ...    repmat(min(x2(1:end-1),x2(2:end)).',n1,1) & ...    repmat(min(y1(1:end-1),y1(2:end)),1,n2) <= ...    repmat(max(y2(1:end-1),y2(2:end)).',n1,1) & ...    repmat(max(y1(1:end-1),y1(2:end)),1,n2) >= ...    repmat(min(y2(1:end-1),y2(2:end)).',n1,1));% Force i and j to be column vectors, even when their length is zero, i.e.,% we want them to be 0-by-1 instead of 0-by-0.i = reshape(i,[],1);j = reshape(j,[],1);% Find segments pairs which have at least one vertex = NaN and remove them.% This line is a fast way of finding such segment pairs.  We take% advantage of the fact that NaNs propagate through calculations, in% particular subtraction (in the calculation of dxy1 and dxy2, which we% need anyway) and addition.% At the same time we can remove redundant combinations of i and j in the% case of finding intersections of a line with itself.if self_intersect    remove = isnan(sum(dxy1(i,:) + dxy2(j,:),2)) | j <= i + 1;else    remove = isnan(sum(dxy1(i,:) + dxy2(j,:),2));endi(remove) = [];j(remove) = [];% Initialize matrices.  We'll put the T's and B's in matrices and use them% one column at a time.  AA is a 3-D extension of A where we'll use one% plane at a time.n = length(i);T = zeros(4,n);AA = zeros(4,4,n);AA([1 2],3,:) = -1;AA([3 4],4,:) = -1;AA([1 3],1,:) = dxy1(i,:).';AA([2 4],2,:) = dxy2(j,:).';B = -[x1(i) x2(j) y1(i) y2(j)].';% Loop through possibilities.  Trap singularity warning and then use% lastwarn to see if that plane of AA is near singular.  Process any such% segment pairs to determine if they are colinear (overlap) or merely% parallel.  That test consists of checking to see if one of the endpoints% of the curve 2 segment lies on the curve 1 segment.  This is done by% checking the cross product%%   (x1(2),y1(2)) - (x1(1),y1(1)) x (x2(2),y2(2)) - (x1(1),y1(1)).%% If this is close to zero then the segments overlap.% If the robust option is false then we assume no two segment pairs are% parallel and just go ahead and do the computation.  If A is ever singular% a warning will appear.  This is faster and obviously you should use it% only when you know you will never have overlapping or parallel segment% pairs.if robust    overlap = false(n,1);    warning_state = warning('off','MATLAB:singularMatrix');    % Use try-catch to guarantee original warning state is restored.    try        lastwarn('')        for k = 1:n            T(:,k) = AA(:,:,k)\B(:,k);            [~,last_warn] = lastwarn;            lastwarn('')            if strcmp(last_warn,'MATLAB:singularMatrix')                % Force in_range(k) to be false.                T(1,k) = NaN;                % Determine if these segments overlap or are just parallel.                overlap(k) = rcond([dxy1(i(k),:);xy2(j(k),:) - xy1(i(k),:)]) < eps;            end        end        warning(warning_state)    catch err        warning(warning_state)        rethrow(err)    end    % Find where t1 and t2 are between 0 and 1 and return the corresponding    % x0 and y0 values.    in_range = (T(1,:) >= 0 & T(2,:) >= 0 & T(1,:) <= 1 & T(2,:) <= 1).';    % For overlapping segment pairs the algorithm will return an    % intersection point that is at the center of the overlapping region.    if any(overlap)        ia = i(overlap);        ja = j(overlap);        % set x0 and y0 to middle of overlapping region.        T(3,overlap) = (max(min(x1(ia),x1(ia+1)),min(x2(ja),x2(ja+1))) + ...            min(max(x1(ia),x1(ia+1)),max(x2(ja),x2(ja+1)))).'/2;        T(4,overlap) = (max(min(y1(ia),y1(ia+1)),min(y2(ja),y2(ja+1))) + ...            min(max(y1(ia),y1(ia+1)),max(y2(ja),y2(ja+1)))).'/2;        selected = in_range | overlap;    else        selected = in_range;    end    xy0 = T(3:4,selected).';        % Remove duplicate intersection points.    [xy0,index] = unique(xy0,'rows');    x0 = xy0(:,1);    y0 = xy0(:,2);        % Compute how far along each line segment the intersections are.    if nargout > 2        sel_index = find(selected);        sel = sel_index(index);        iout = i(sel) + T(1,sel).';        jout = j(sel) + T(2,sel).';    endelse % non-robust option    for k = 1:n        [L,U] = lu(AA(:,:,k));        T(:,k) = U\(L\B(:,k));    end        % Find where t1 and t2 are between 0 and 1 and return the corresponding    % x0 and y0 values.    in_range = (T(1,:) >= 0 & T(2,:) >= 0 & T(1,:) < 1 & T(2,:) < 1).';    x0 = T(3,in_range).';    y0 = T(4,in_range).';        % Compute how far along each line segment the intersections are.    if nargout > 2        iout = i(in_range) + T(1,in_range).';        jout = j(in_range) + T(2,in_range).';    endendend