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🔥 内容介绍
climanomaly plots two lines (y vs. x and y vs. ref) and visualisespositive and negative anomalies by shading the area between both lines intwo different colors. This is useful for visualising anomalies of a timeseries relative to a climatology. The function can further be used toplot anomalies relative to a constant baseline or two threshold baselines(positive anomaly above upper threshold, negative anomaly below lowerthreshold).
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 (referenceline) and shades areas line values above zero; blue fills the areabetween zero and any values below zero.
-
To shade anomalies relative to a variable reference (e.g. aclimatology) specify ref as a vector the length of y.
-
To shade anomalies relative to a constant baseline, specify a singleref value.
-
To shade anomalies relative to an upper and a lower threshold, specifytwo ref values (e.g., let ref be [-0.4 0.5] to shade all values lessthan 0.4 or greater than 0.5).
climanomaly(…,’top’,ColorSpec) specifies the top color shading, whichcan be described by RGB values or any of the Matlab short-hand colornames (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. By default, the main line will be plottedas a solid black line (‘k-‘) and the reference line as a dotted blackline (‘k:’).
[hlin,href,htop,hbot] = climanomaly(…) returns the graphics handles ofthe main line, top, and bottom plots, respectively.
📣 部分代码
clc
clear all
close all
x = 1:.1:20;
y = sin(x);
ref = sin(x)/2;
figure
climanomaly(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
in positive and negative anomalies by shading the area between both lines
for visualising anomalies of a time two different colors. This is useful
function can further be used to series relative to a climatology. The
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)
'top',ColorSpec) CLIMANOMALY(...,
'bottom',ColorSpec) CLIMANOMALY(...,
'mainline','LineSpec') CLIMANOMALY(...,
'refline','LineSpec') CLIMANOMALY(...,
[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
let ref be [-0.4 0.5] to shade all values less two ref values (e.g.,
than 0.4 or greater than 0.5).
'top',ColorSpec) specifies the top color shading, which CLIMANOMALY(...,
can be described by RGB values or any of the Matlab short-hand color
'r' or 'red'). names (e.g.,
'bottom',ColorSpec) specifies the bottom shading color. CLIMANOMALY(...,
'mainline','LineSpec') CLIMANOMALY(...,
'refline','LineSpec') CLIMANOMALY(...,
Specifies line types, plot symbols and colors of the reference line.
'b--*'. Refer to the 'plot' LineSpec is a string of characters, e.g.
for more options. Use 'none' to plot the anomalies without documentation
'k-') By default, the main line will be plotted as a solid black line (
'k:'). and the reference line as a dotted black line (
[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
'top','k','bottom',[.9 .9 .9],... [hlin,href,htop,hbot] = CLIMANOMALY(x,y,ref,
'mainline','b-','refline','r--');
hlin.LineWidth = 2;
href.LineWidth = 2;
alpha(htop,0.7)
alpha(hbot,0.7)
% Author Info
for Marine and Antarctic Jake Weis, University of Tasmania, Institute
Studies (IMAS), April 2021
function is based on the 'anomaly' function, written by Chad A. This
"matlab:web('https://github.com/chadagreene/CDT')">Climate Data Toolbox</a>). Greene (<a href=
'intersections' by Douglas M. Schwarz. Subfunction used:
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 default
mainspec = '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) = [];
end
end
%% Data manipulation:
% Convert ref into a top and a bottom column vector the length of y
if 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:
for the bottom: First
[xct,yct] = intersections(x,y,x,reft); % intersections is a subfunction by Douglas Schwarz, included below.
for the top: Now
[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 xb
refb = refb(ind); % sorts refb with xb
[xt,ind] = sortrows(xt);
yt = yt(ind); % sorts yt with xt
reft = reft(ind); % sorts reft with xt
% Start thinking about this as two separate datasets which share refline values where they meet:
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);
end
if ~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);
end
else
if numel(ref) ~= 2
href = cell(1,1);
else
href = cell(2,1);
end
end
% Return the hold state if necessary:
if ~hld
hold off
end
%% Clean up:
if nargout==0
clear hlin href htop hbot
end
end
%% * * * * * * 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.
where two curves intersect. The curves Computes the (x,y) locations
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.
which the two X0 and Y0 are column vectors containing the points at
curves intersect.
set to 1 or true means to use a slight variation of the ROBUST (optional)
return duplicates of some intersection points, and algorithm that might
then remove those duplicates. The default is true, but since the
set it to false if you know that algorithm is slightly slower you can
't intersect at any segment boundaries. Also, the robust your curves don
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 = AB.
Once we have our solution we just have to look at t1 and t2 to determine
then the two whether L1 and L2 intersect. If 0 <= t1 < 1 and 0 <= t2 < 1
in the output. line segments cross and we can include (x0,y0)
In principle, we have to perform this computation on every pair of line
in the input data. This can be quite a large number of pairs so segments
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
for each smallest enclosing rectangles (with sides parallel to the axes)
if they overlap. If they do then we have to line segment pair and see
if the line segments compute t1 and t2 (via the AB computation) to see
if they don't then the line segments cannot cross. In a cross, but
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
'th line segment of curve 1 overlaps with the rectangle enclosing the i
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
in advantage of the fact that NaNs propagate through calculations,
in the calculation of dxy1 and dxy2, which we particular subtraction (
need anyway) and addition.
in the At the same time we can remove redundant combinations of i and j
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));
end
i(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
if that plane of AA is near singular. Process any such lastwarn to see
if they are colinear (overlap) or merely segment pairs to determine
test consists of checking to see if one of the endpoints parallel. That
done by of the curve 2 segment lies on the curve 1 segment. This is
checking the cross product
(x1(2),y1(2)) - (x1(1),y1(1)) x (x2(2),y2(2)) - (x1(1),y1(1)).
then the segments overlap. If this is close to zero
% If the robust option is false then we assume no two segment pairs are
do the computation. If A is ever singular parallel and just go ahead and
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).';
end
else % non-robust option
for k = 1:n
[L,U] = lu(AA(:,:,k));
T(:,k) = U(LB(:,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).';
end
end
end
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