I'm trying to find a way to generate these pretty correlation plots in MATLAB. These are generated in R using 'corrplot' function, but couldn't find any similar code in MATLAB. Any help would be appreciated.
As a quick description, this function will create a color scale of the correlation values, and create circles in each cell of the correlation matrix/plot with the associated color. The size of the circles is also an indicator of the magnitude of the correlation, with larger circles representing a stronger relationship (positive or negative). More details could be found here.
you can use plot-corrmat (or modify it, depending how articulate you are in matlab), to obtain similar visualizations of correlation matrices (top pic). Or use Correlation circles , that looks somewhat similar as well (bottom pic)...
https://github.com/elayden/plot-corrmat
I could write the below code to generate a similar graph, based on the code provided here
% Produce the input lower triangular matrix data
C = -1 + 2.*rand(12,12);
C = tril(C,-1);
C(logical(eye(size(C)))) = 1;
% Set [min,max] value of C to scale colors
clrLim = [-1,1];
% load('CorrColormap.mat') % Uncomment for custom CorrColormap
% Set the [min,max] of diameter where 1 consumes entire grid square
diamLim = [0.1, 1];
myLabel = {'ICA','Elev','Pr','Rmax','Rmin','Srad','Wspd','Tmin','Tmax','VPD','ET_o','AW'};
% Compute center of each circle
% This assumes the x and y values were not entered in imagesc()
x = 1 : 1 : size(C,2); % x edges
y = 1 : 1 : size(C,1); % y edges
[xAll, yAll] = meshgrid(x,y);
xAll(C==0)=nan; % eliminate cordinates for zero correlations
% Set color of each rectangle
% Set color scale
cmap = jet(256);
% cmap = CorrColormap; % Uncomment for CorrColormap
Cscaled = (C - clrLim(1))/range(clrLim); % always [0:1]
colIdx = discretize(Cscaled,linspace(0,1,size(cmap,1)));
% Set size of each circle
% Scale the size between [0 1]
Cscaled = (abs(C) - 0)/1;
diamSize = Cscaled * range(diamLim) + diamLim(1);
% Create figure
fh = figure();
ax = axes(fh);
hold(ax,'on')
colormap(ax,'jet');
% colormap(CorrColormap) %Uncomment for CorrColormap
tickvalues = 1:length(C);
x = zeros(size(tickvalues));
text(x, tickvalues, myLabel, 'HorizontalAlignment', 'right');
x(:) = length(C)+1;
text(tickvalues, x, myLabel, 'HorizontalAlignment', 'right','Rotation',90);
% Create circles
theta = linspace(0,2*pi,50); % the smaller, the less memory req'd.
h = arrayfun(#(i)fill(diamSize(i)/2 * cos(theta) + xAll(i), ...
diamSize(i)/2 * sin(theta) + yAll(i), cmap(colIdx(i),:),'LineStyle','none'),1:numel(xAll));
axis(ax,'equal')
axis(ax,'tight')
set(ax,'YDir','Reverse')
colorbar()
caxis(clrLim);
axis off
The exact graph is available here:
Fancy Correlation Plots in MATLAB
Related
I'm trying to fill an area between two curves with respect to a function which depends on the values of the curves.
Here is the code of what I've managed to do so far
i=50;
cc = #(xx,x,y) 1./(1+(exp(-xx)/(exp(-x)-exp(-y))));
n_vec = 2:0.1:10;
x_vec = linspace(2,10,length(n_vec));
y_vec = abs(sin(n_vec));
N=[n_vec,fliplr(n_vec)];
X=[x_vec,fliplr(y_vec)];
figure(1)
subplot(2,1,1)
hold on
plot(n_vec,x_vec,n_vec,y_vec)
hp = patch(N,X,'b')
plot([n_vec(i) n_vec(i)],[x_vec(i),y_vec(i)],'linewidth',5)
xlabel('n'); ylabel('x')
subplot(2,1,2)
xx = linspace(y_vec(i),x_vec(i),100);
plot(xx,cc(xx,y_vec(i),x_vec(i)))
xlabel('x'); ylabel('c(x)')
This code produces the following graph
The color code which I've added represent the color coding that each line (along the y axis at a point on the x axis) from the area between the two curves should be.
Overall, the entire area should be filled with a gradient color which depends on the values of the curves.
I've assisted the following previous questions but could not resolve a solution
MATLAB fill area between lines
Patch circle by a color gradient
Filling between two curves, according to a colormap given by a function MATLAB
NOTE: there is no importance to the functional form of the curves, I would prefer an answer which refers to two general arrays which consist the curves.
The surf plot method
The same as the scatter plot method, i.e. generate a point grid.
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px = linspace(min(n_vec), max(n_vec), resolution(1));
py = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px, py);
Generate a logical array indicating whether the points are inside the polygon, but no need to extract the points:
in = inpolygon(px, py, N, X);
Generate Z. The value of Z indicates the color to use for the surface plot. Hence, it is generated using the your function cc.
pz = 1./(1+(exp(-py_)/(exp(-y_vec(i))-exp(-x_vec(i)))));
pz = repmat(pz',1,resolution(2));
Set Z values for points outside the area of interest to NaN so MATLAB won't plot them.
pz(~in) = nan;
Generate a bounded colourmap (delete if you want to use full colour range)
% generate colormap
c = jet(100);
[s,l] = bounds(pz,'all');
s = round(s*100);
l = round(l*100);
if s ~= 0
c(1:s,:) = [];
end
if l ~= 100
c(l:100,:) = [];
end
Finally, plot.
figure;
colormap(jet)
surf(px,py,pz,'edgecolor','none');
view(2) % x-y view
Feel free to turn the image arround to see how it looks like in the Z-dimention - beautiful :)
Full code to test:
i=50;
cc = #(xx,x,y) 1./(1+(exp(-xx)/(exp(-x)-exp(-y))));
n_vec = 2:0.1:10;
x_vec = linspace(2,10,length(n_vec));
y_vec = abs(sin(n_vec));
% generate grid
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px_ = linspace(min(n_vec), max(n_vec), resolution(1));
py_ = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px_, py_);
% extract points
in = inpolygon(px, py, N, X);
% generate z
pz = 1./(1+(exp(-py_)/(exp(-y_vec(i))-exp(-x_vec(i)))));
pz = repmat(pz',1,resolution(2));
pz(~in) = nan;
% generate colormap
c = jet(100);
[s,l] = bounds(pz,'all');
s = round(s*100);
l = round(l*100);
if s ~= 0
c(1:s,:) = [];
end
if l ~= 100
c(l:100,:) = [];
end
% plot
figure;
colormap(c)
surf(px,py,pz,'edgecolor','none');
view(2)
You can use imagesc and meshgrids. See comments in the code to understand what's going on.
Downsample your data
% your initial upper and lower boundaries
n_vec_long = linspace(2,10,1000000);
f_ub_vec_long = linspace(2, 10, length(n_vec_long));
f_lb_vec_long = abs(sin(n_vec_long));
% downsample
n_vec = linspace(n_vec_long(1), n_vec_long(end), 1000); % for example, only 1000 points
% get upper and lower boundary values for n_vec
f_ub_vec = interp1(n_vec_long, f_ub_vec_long, n_vec);
f_lb_vec = interp1(n_vec_long, f_lb_vec_long, n_vec);
% x_vec for the color function
x_vec = 0:0.01:10;
Plot the data
% create a 2D matrix with N and X position
[N, X] = meshgrid(n_vec, x_vec);
% evaluate the upper and lower boundary functions at n_vec
% can be any function at n you want (not tested for crossing boundaries though...)
f_ub_vec = linspace(2, 10, length(n_vec));
f_lb_vec = abs(sin(n_vec));
% make these row vectors into matrices, to create a boolean mask
F_UB = repmat(f_ub_vec, [size(N, 1) 1]);
F_LB = repmat(f_lb_vec, [size(N, 1) 1]);
% create a mask based on the upper and lower boundary functions
mask = true(size(N));
mask(X > F_UB | X < F_LB) = false;
% create data matrix
Z = NaN(size(N));
% create function that evaluates the color profile for each defined value
% in the vectors with the lower and upper bounds
zc = #(X, ub, lb) 1 ./ (1 + (exp(-X) ./ (exp(-ub) - exp(-lb))));
CData = zc(X, f_lb_vec, f_ub_vec); % create the c(x) at all X
% put the CData in Z, but only between the lower and upper bound.
Z(mask) = CData(mask);
% normalize Z along 1st dim
Z = normalize(Z, 1, 'range'); % get all values between 0 and 1 for colorbar
% draw a figure!
figure(1); clf;
ax = axes; % create some axes
sc = imagesc(ax, n_vec, x_vec, Z); % plot the data
ax.YDir = 'normal' % set the YDir to normal again, imagesc reverses it by default;
xlabel('n')
ylabel('x')
This already looks kinda like what you want, but let's get rid of the blue area outside the boundaries. This can be done by creating an 'alpha mask', i.e. set the alpha value for all pixels outside the previously defined mask to 0:
figure(2); clf;
ax = axes; % create some axes
hold on;
sc = imagesc(ax, n_vec, x_vec, Z); % plot the data
ax.YDir = 'normal' % set the YDir to normal again, imagesc reverses it by default;
% set a colormap
colormap(flip(hsv(100)))
% set alpha for points outside mask
Calpha = ones(size(N));
Calpha(~mask) = 0;
sc.AlphaData = Calpha;
% plot the other lines
plot(n_vec, f_ub_vec, 'k', n_vec, f_lb_vec, 'k' ,'linewidth', 1)
% set axis limits
xlim([min(n_vec), max(n_vec)])
ylim([min(x_vec), max(x_vec)])
there is no importance to the functional form of the curves, I would prefer an answer which refers to two general arrays which consist the curves.
It is difficult to achieve this using patch.
However, you may use scatter plots to "fill" the area with coloured dots. Alternatively, and probably better, use surf plot and generate z coordinates using your cc function (See my seperate solution).
The scatter plot method
First, make a grid of points (resolution 500*500) inside the rectangular space bounding the two curves.
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px = linspace(min(n_vec), max(n_vec), resolution(1));
py = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px, py);
figure;
scatter(px(:), py(:), 1, 'r');
The not-interesting figure of the point grid:
Next, extract the points inside the polygon defined by the two curves.
in = inpolygon(px, py, N, X);
px = px(in);
py = py(in);
hold on;
scatter(px, py, 1, 'k');
Black points are inside the area:
Finally, create color and plot the nice looking gradient colour figure.
% create color for the points
cid = 1./(1+(exp(-py)/(exp(-y_vec(i))-exp(-x_vec(i)))));
c = jet(101);
c = c(round(cid*100)+1,:); % +1 to avoid zero indexing
% plot
figure;
scatter(px,py,16,c,'filled','s'); % use size 16, filled square markers.
Note that you may need a fairly dense grid of points to make sure the white background won't show up. You may also change the point size to a bigger value (won't impact performance).
Of cause, you may use patch to replace scatter but you will need to work out the vertices and face ids, then you may patch each faces separately with patch('Faces',F,'Vertices',V). Using patch this way may impact performance.
Complete code to test:
i=50;
cc = #(xx,x,y) 1./(1+(exp(-xx)/(exp(-x)-exp(-y))));
n_vec = 2:0.1:10;
x_vec = linspace(2,10,length(n_vec));
y_vec = abs(sin(n_vec));
% generate point grid
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px_ = linspace(min(n_vec), max(n_vec), resolution(1));
py_ = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px_, py_);
% extract points
in = inpolygon(px, py, N, X);
px = px(in);
py = py(in);
% generate color
cid = 1./(1+(exp(-py)/(exp(-y_vec(i))-exp(-x_vec(i)))));
c = jet(101);
c = c(round(cid*100)+1,:); % +1 to avoid zero indexing
% plot
figure;
scatter(px,py,16,c,'filled','s');
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 about four series of data on a Matlab plot, two of them are quite close and can only be differentiated with a zoom. How do I depict the zoomed part within the existing plot for the viewer. I have checked similar posts but the answers seem very unclear.
I look for something like this:
Here is a suggestion how to do this with MATLAB. It may need some fine tuning, but it will give you the result:
function pan = zoomin(ax,areaToMagnify,panPosition)
% AX is a handle to the axes to magnify
% AREATOMAGNIFY is the area to magnify, given by a 4-element vector that defines the
% lower-left and upper-right corners of a rectangle [x1 y1 x2 y2]
% PANPOSTION is the position of the magnifying pan in the figure, defined by
% the normalized units of the figure [x y w h]
%
fig = ax.Parent;
pan = copyobj(ax,fig);
pan.Position = panPosition;
pan.XLim = areaToMagnify([1 3]);
pan.YLim = areaToMagnify([2 4]);
pan.XTick = [];
pan.YTick = [];
rectangle(ax,'Position',...
[areaToMagnify(1:2) areaToMagnify(3:4)-areaToMagnify(1:2)])
xy = ax2annot(ax,areaToMagnify([1 4;3 2]));
annotation(fig,'line',[xy(1,1) panPosition(1)],...
[xy(1,2) panPosition(2)+panPosition(4)],'Color','k')
annotation(fig,'line',[xy(2,1) panPosition(1)+panPosition(3)],...
[xy(2,2) panPosition(2)],'Color','k')
end
function anxy = ax2annot(ax,xy)
% This function converts the axis unites to the figure normalized unites
% AX is a handle to the figure
% XY is a n-by-2 matrix, where the first column is the x values and the
% second is the y values
% ANXY is a matrix in the same size of XY, but with all the values
% converted to normalized units
pos = ax.Position;
% white area * ((value - axis min) / axis length) + gray area
normx = pos(3)*((xy(:,1)-ax.XLim(1))./range(ax.XLim))+ pos(1);
normy = pos(4)*((xy(:,2)-ax.YLim(1))./range(ax.YLim))+ pos(2);
anxy = [normx normy];
end
Note that the units of areaToMagnify are like the axis units, while the units of panPosition are between 0 to 1, like the position property in MATLAB.
Here is an example:
x = -5:0.1:5;
subplot(3,3,[4 5 7 8])
plot(x,cos(x-2),x,sin(x),x,-x-0.5,x,0.1.*x+0.1)
ax = gca;
area = [-0.4 -0.4 0.25 0.25];
inlarge = subplot(3,3,3);
panpos = inlarge.Position;
delete(inlarge);
inlarge = zoomin(ax,area,panpos);
title(inlarge,'Zoom in')
I would like to convert a image processing program(part of the program below) from Matlab to Simulink and possibly convert the simulink diagram into C code later on. I have 0 experience in Simulink and was wondering if there's any limitations on the types of matlab program/functions that can be converted and how I would go about doing this. Thanks.
clear all
clc
% Read in an image 1
C1 = imread('cloud1.jpg');
Cloud1 = C1(:,:,1); % use only one color
%Cloud1 = Cloud1'; % transpose to get (x,y) instead of (y,x)
Cloud1_xsize = size(Cloud1,2); % get x size of image
Cloud1_ysize = size(Cloud1,1); % get y size of image
%figure(3), imshow(Cloud1) % to plot you need to transpose back to their coordinate system
%hold on
% Read in an image 2
C2 = imread('cloud2.jpg');
Cloud2 = C2(:,:,1); % use only one color
%Cloud2 = Cloud2'; % transpose to get (x,y) instead of (y,x)
Cloud2_xsize = size(Cloud2,2); % get x size of image
Cloud2_ysize = size(Cloud2,1); % get y size of image
%figure(2), imshow(Cloud2)
%hold on
% show the shift in the initial images several times
num = 0;
for k = 1:4
num=num+1;
pause(.5)
figure(1), h1=imshow(C1)
xlabel('FIGURE 1')
F(num) = getframe(gcf);
%image(F.cdata)
%colormap(F.colormap)
pause(0.25)
figure(1), h2=imshow(C2)
xlabel('FIGURE 2')
num=num+1;
F(num) = getframe(gcf);
%image(F.cdata)
%colormap(F.colormap)
end
% Play the movie twenty times
%movie(F,20)
%%%% Set the template size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% First calc the number of pixels in the shortest direction of the image (usually y direction)
MinSize = min(Cloud1_xsize, Cloud1_ysize); % number of pixels in shortest direction
%%% N is the minimum number of boxes in the shorter direction (usually y direction).
%%% In the shorter axis (usually y)there will be N-2 boxes analyzed.
%%% This is because the top and bottom boxes are considered too close to the edge to use.
%%% In the larger direction (usually x) there may be more boxes.
N = 6;
EdgeBoxSize = 1; % the number of edge boxes along each edge
TempWidth = floor(MinSize / N); % the pixel width of each template box
TempHeight = TempWidth; % make the template height and width the same size so corr part works good
%%% Now calculate the exact number of boxes in x and y directions
%%% This depends on the number of x versus y pixels.
Nx = floor(Cloud1_xsize/TempWidth);
Ny = floor(Cloud1_ysize/TempWidth);
I am trying to produce this graph using Matlab. The built-in ellipsoid function is confusing. For this problem I have two variables ( width and length ) and a constant height.
to make it very simple I want to show that the width is changing while we approach the tip but height is constant. w,x,h are the variables shown in the graph.
I would really appreciate it if someone can help.
The following code gets you a long way, I think. See example output:
I added enought comments that you should be able to take it from here...
% plot ellipsoid in 3D
% height and width of ellipsoid:
e_h = 10;
e_w = 3;
% position where the "quivers" (arrows) go:
q_offset = 2; % distance from axis
q_scale = 0.5; % multiplier to give parabola some size
q_spacing = 0.5; % distance between arrows
q_height = 2.5; % height above XY plane where arrows are drawn
N = 1000; % number of points for drawing
theta = linspace(0, 2*pi, N); % parameter to help drawing ellipse
zerov = zeros(1, N); % array of zeros that I will need
% coordinates of main ellipse:
x = e_w * sin(theta);
y = zeros(size(x));
z = e_h * cos(theta);
% plot main ellipse:
figure;
plot3(x, y, z)
% secondary plot
y2 = q_scale*(e_w.^2 - x.^2) + 2; % offset parabola - what your plot looked like...
hold on
plot3(x, y2, zerov+q_height); % plotting the parabola in the XY plane at height
axis equal % make the plot dimensions isotropic
% add quivers
q_base = -e_w:q_spacing:e_w; % x coordinate; y and z are fixed
q_length = (e_w.^2 - q_base.^2)*q_scale; % length of quiver - just an equation I chose
q0 = zeros(size(q_base)); % another vector I will need multiple times
q1 = ones(size(q_base)); % ditto
% plot the arrows: the "-1" argument means "don't scale"
quiver3(q_base, q0+q_offset, q_height*q1, q0, q_length, q0, -1)