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I have two contour maps in Matlab and each of the two maps has a single curve specifying a single Z-value. I want to super impose the two contour maps so that I can find the single solution where the two z-value curves intersect. How could I go about super imposing the two contour maps?
% the two contour maps are coded the exact same way, but with different z-values
x = 0.05:0.05:1;
y = 0.0:0.05:1;
[X, Y] = meshgrid(x, y);
% Z-value data is copied from excel and pasted into an array
Z = [data]
contourf(X, Y, Z);
pcolor(X, Y, Z); hold on
shading interp
title();
xlabel();
ylabel();
colorbar
val = %z-value to plot onto colormap
tol = %tolerance
idxZval = (Z <= val+tol) & (Z >= val-tol);
plot(X(idxZval), Y(idxZval))[enter image description here][1]
The end result you seek is possible using contourc or using contour specifying the same contours (isolines).
This answer extends this answer in Approach 1 using contourc and provides a simple solution with contour in Approach 2.
You might ask "Why Approach 1 when Approach 2 is so simple?"
Approach 1 provides a way to directly access the individual isolines in the event you require a numerical approach to searching for intersections.
Approach 1
Example Data:
% MATLAB R2018b
x = 0:0.01:1;
y = 0:0.01:1;
[X,Y] = meshgrid(x,y);
Z = sqrt(X.^3+Y); % Placeholder 1
W = sqrt(X.*Y + X.^2 + Y.^(2/3)); % Placeholder 2
Overlay Single Isoline from 2 Contour Plots
Mimicking this answer and using
v = [.5 0.75 .85 1]; % Values of Z to plot isolines
we can visualize these two functions, Z, and W, respectively.
We can overlay the isolines since they share the same (x,y) domain. For example, they both equal 0.8 as displayed below.
val = 0.8; % Isoline value to plot (for Z & W)
Ck = contourc(x,y,Z,[val val]);
Ck2 = contourc(x,y,W,[val val]);
figure, hold on, box on
plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2,'DisplayName',['Z = ' num2str(val)])
plot(Ck2(1,2:end),Ck2(2,2:end),'b-','LineWidth',2,'DisplayName',['W = ' num2str(val)])
legend('show')
Overlay Multiple Isolines from 2 Contour Plots
We can also do this for more isolines at a time.
v = [1 0.5]; % Isoline values to plot (for Z & W)
figure, hold on, box on
for k = 1:length(v)
Ck = contourc(x,y,Z,[v(k) v(k)]);
Ck2 = contourc(x,y,W,[v(k) v(k)]);
p(k) = plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2,'DisplayName',['Z = ' num2str(v(k))]);
p2(k) = plot(Ck2(1,2:end),Ck2(2,2:end),'b-','LineWidth',2,'DisplayName',['W = ' num2str(v(k))]);
end
p(2).LineStyle = '--';
p2(2).LineStyle = '--';
legend('show')
Approach 2
Without making it pretty...
% Single Isoline
val = 1.2;
contour(X,Y,Z,val), hold on
contour(X,Y,W,val)
% Multiple Isolines
v = [.5 0.75 .85 1];
contour(X,Y,Z,v), hold on
contour(X,Y,W,v)
It is straightforward to clean these up for presentation. If val is a scalar (single number), then c1 = contour(X,Y,Z,val); and c2 = contour(X,Y,W,val) gives access to the isoline for each contour plot.
I created two scatter plots and then used lsline to add regression lines for each plot. I used this code:
for i=1:2
x = ..;
y = ..;
scatter(x, y, 50, 'MarkerFaceColor',myColours(i, :));
end
h_lines = lsline;
However, the darker line extends far beyond the last data point in that scatter plot (which is at around x=0.3):
lsline doesn't seem to have properties that allow its horizontal range to be set. Is there a workaround to set this separately for the two lines, in Matlab 2016a?
For a single data set
This is a workaround rather than a solution. lsline internally calls refline, which plots a line filling the axis as given by their current limits (xlim and ylim). So you can change those limits to the extent you want for the line, call lsline, and then restore the limits.
Example:
x = randn(1,100);
y = 2*x + randn(1,100); % random, correlated data
plot(x, y, '.') % scatter plot
xlim([-1.5 1.5]) % desired limit for line
lsline % plot line
xlim auto % restore axis limit
For several data sets
In this case you can apply the same procedure for each data set sequentially, but you need to keep only one data set visible when you call lsline; otherwise when you call it to create the second line it will also create a new version of the first (with the wrong range).
Example:
x = randn(1,100); y = 2*x + randn(1,100); % random, correlated data
h = plot(x, y, 'b.'); % scatter plot
axis([min(x) max(x) min(y) max(y)]) % desired limit for line
lsline % plot line
xlim auto % restore axis limit
hold on
x = 2*randn(1,100) - 5; y = 1.2*x + randn(1,100) + 6; % random, correlated data
plot(x, y, 'r.') % scatter plot
axis([min(x) max(x) min(y) max(y)]) % desired limit for line
set(h, 'HandleVisibility', 'off'); % hide previous plot
lsline % plot line
set(h, 'HandleVisibility', 'on'); % restore visibility
xlim auto % restore axis limit
Yet another solution: implement your own hsline. It's easy!
In MATLAB, doing a least squares fit of a straight line is trivial. Given column vectors x and y with N elements, b = [ones(N,1),x] \ y; are the parameters to the best fit line. [1,x1;1,x2]*b are the y locations of two points along the line with x-coordinates x1 and x2. Thus you can write (following Luis' example, and getting the exact same output):
N = 100;
x = randn(N,1); y = 2*x + randn(N,1); % random, correlated data
h = plot(x, y, 'b.'); % scatter plot
hold on
b = [ones(N,1),x] \ y;
x = [min(x);max(x)];
plot(x,[ones(2,1),x] * b, 'b-')
x = 2*randn(N,1) - 5; y = 1.2*x + randn(N,1) + 6; % random, correlated data
plot(x, y, 'r.') % scatter plot
b = [ones(N,1),x] \ y;
x = [min(x);max(x)];
plot(x,[ones(2,1),x] * b, 'r-')
You can get the points that define the line using
h_lines =lsline;
h_lines(ii).XData and h_lines(ii).YData will contain 2 points that define the lines for each ii=1,2 line. Use those to create en equation of a line, and plot the line in the range you want.
I have some vectors with defined position and orientation. I could show them in space by using the below code:
theta = [pi/2,-pi/2,pi/2,pi/2,pi/2,pi/2,pi/2];
r = 0.25; % magnitude (length) of arrow to plot
x = [4,3.5,3.75,4.5,8,10,12]; y = [8.5,8.2,8.3,8,9,10,8];
u = r * cos(theta); % convert polar (theta,r) to cartesian
v = r * sin(theta);
h = quiver(x,y,u,v,'linewidth',2);
set(gca, 'XLim', [2 15], 'YLim', [4 15]);
As is clear from the image, in some regions the number of arrows is more than in other places. I want to show the arrows by color, where each color represents the density of the arrows.
Could anyone help me to do that? It would also be a good solution if there is a continuous background color which shows local densities.
Edit: Below are some options for colouring the background of the plot depending on the density of your points. I'm editing this into the top of my answer because it actually answers your question - individually colouring quiver arrows based on density!
x = rand(200,1)*10; y = rand(200,1)*10; % Set up random points
r = 1; u = r * cos(x); v = r * sin(y); % Quiver directions
colormap winter; c = colormap; % Set colourmap and assign to matrix
% Get density of points broken into a 10x10 grid
[n,~,~,binX,binY] = histcounts2(x,y,[10,10]);
% Get colour based on histogram density and chosen colormap colours
col = c(ceil(n(sub2ind(size(n), binX, binY))/max(n(:))*size(c,1)),:);
figure; hold on;
% Each quiver point must be plotted individually (slow!) because colours can
% only be applied to individual quivers. This could be sped up by plotting
% all of the same colour at once.
for ii = 1:size(x,1);
quiver(x(ii),y(ii),u(ii),v(ii),0,'color',col(ii,:));
end
Output:
Note: unlike the below example, you cannot use hist3 because you need it to return the bin index too. You could try this File Exchange function to achieve the same result (untested).
Here is an option using hist3 to get the density (in this example I use a 10x10 grid, as specified when calling hist3). Then using pcolor to display the density, and shading interp to smooth the colours.
Note: hist3 requires the Stats & ML toolbox, if you have Matlab 2015b or newer you can instead use the standard function histcounts2(x,y).
% Generate points and quiver directions
x = rand(200,1)*10; y = rand(200,1)*10;
u = r * cos(x); v = r * sin(y);
% Get density of points, format for input to pcolor
n = hist3([x,y],[10,10]); % Get density of points broken into a 10x10 grid
colx = linspace(min(x),max(x),size(n,1)+1);
coly = linspace(min(y),max(y),size(n,1)+1);
n = n'; n(size(n,2)+1,size(n,1)+1) = 0;
% Plot
figure
pcolor(colx,coly,n) % Density plot
hold on; colorbar; % Hold on for next plot and show colour bar key
quiver(x,y,u,v,'r') % Quiver plot
shading interp % Smooth plot colours
Output:
Edit: making the colours more muted
You can control the colours using colormap. This could be one of the defaults, or you can create a custom map of RGB triplets and have whatever colours you want! Here is an example, simply calling colormap bone; at the end of the above code:
In a custom colour map, you could make the colours even more muted / less contrasting.
Additionally, you can use caxis to scale the colour axis of a plot! Simply call
caxis([0,2*max(n(:))]);
at the end of the above code to double the maximum colour map value. You can tweak the 2 to get desired results:
this looks way less fancy but specifies the arrow color as function of the number of arrows in a certain number of bins of the x-axis
close all;
cm=colormap;
theta = [pi/2,-pi/2,pi/2,pi/2,pi/2,pi/2,pi/2];
r = 0.25; % magnitude (length) of arrow to plot
x = [4,3.5,3.75,4.5,8,10,12]; y = [8.5,8.2,8.3,8,9,10,8];
[n,c]=hist(x,5); %count arroes in bins
u = r * cos(theta); % convert polar (theta,r) to cartesian
v = r * sin(theta);
figure;hold on
for ii=1:numel(n) %quiver bin by bin
if n(ii)>0
if ii==1
wx=find(x<(c(ii)+(c(ii+1) - c(ii))/2)); %Which X to plot
elseif ii==numel(n)
wx=find(x>c(numel(n)-1));
else
wx=find((x>(c(ii)-(c(ii)-c(ii-1))/2)).*(x<(c(ii+1)-(c(ii+1)-c(ii))/2)));
end
indCol=ceil( (size(cm,1)*n(ii)-0) / max(n));%color propto density of arrows %in this bin
col = cm(indCol,:);%color for this bin
h = quiver(x(wx),y(wx),u(wx),v(wx),0,'linewidth',2,'color',col);
end
end
colorbar
caxis([0 max(n)])
I have 3 vectors of data, X (position), Y (position) both of which are not regularly spaced, and Z(value of interest at each location). I tried contourf, which doesn't work because it needs a matrix for Z input.
You can also use griddata.
%Generate random data
x = rand(30,1);
y = rand(30,1);
z = rand(30,1);
%Create regular grid across data space
[X,Y] = meshgrid(linspace(min(x),max(x),n), linspace(min(y),max(y),n))
%create contour plot
contour(X,Y,griddata(x,y,z,X,Y))
%mark original data points
hold on;scatter(x,y,'o');hold off
For a contour plot you actually need either a matrix of z values, or a set (vector) of z-values evaluated on a grid. You cannot define contours using isolated Z values at (X,Y) points on the grid (i.e. what you claim you have).
You need to have the generating process (or function) provide values for a grid of (x,y) points.
If not, then you can create a surface from nonuniform data as #nate correctly pointed out, and then draw the contours on that surface.
Consider the following (random) example:
N = 64; % point set
x = -2 + 4*rand(N,1); % random x vector in[-2,2]
y = -2 + 4*rand(N,1); % random y vector in[-2,2]
% analytic function, or z-vector
z = x.*exp(-x.^2-y.^2);
% construct the interpolant function
F = TriScatteredInterp(x,y,z);
t = -2:.25:2; % sample uniformly the surface for matrices (qx, qy, qz)
[qx, qy] = meshgrid(t, t);
qz = F(qx, qy);
contour(qx, qy, qz); hold on;
plot(x,y,'bo'); hold off
The circles correspond to the original vector points with values (x,y,z) per point, the contours on the contours of the interpolant surface.
Hi I have the 3D matrix daily_renewables_excess which I am trying to plot a 3D bar graph for the x y and z dimensions in axis.
The size(daily_renewables_excess) is 11,7,10. So I am trying to get a 3D bar chart with 11 x intervals of x, 7 of y and 10 of z.
However when i try
figure;
bar3(daily_renewables_excess(:,:,:))
I get an error saying "Error using bar3 (line 39)
Inputs must be 2-D."
From my understanding of the documentation, the bar3 function will plot a 3D bar as above.
Do I need to rearrange the matrices somehow?
thank you
Since you have a 3D matrix (volume) you cannot simultaneously show 3 intervals (3 axis) + a scale value for the bars (4th variable). This would amount to plotting a 4D diagram (e.g. using color to color-code the 4-th dimension, bar size to size-code it, or even vertical stacking).
For example, the following volume D is of size [11x10x7] and you can get 7 bar3 plots by indexing in the 3rd (z) dimension
% random 3D input
D = randi(10, [11, 10, 7]);
[m,n,l] = size(D);
% plot bar for first z-
figure; bar3(D(:,:,1));
What you can do instead is reshape in either x- or y- dimesions, sort (in order to keep the notion of ordered intervals (in x- or y- respectively) and plot with bar3 the resulting matrices.
% reshape to x
Dx = reshape(D, m*l, n);
Dx = sort(Dx, 1, 'descend');
figure; bar3(Dx)
% reshape to y
Dy = reshape(D, m, n*l);
Dy = sort(Dy, 2, 'descend');
figure; bar3(Dy)