I have this script:
scatter(X,Y)
p = polyfit(X,Y,1);
FX= polyval(p,X);
hold on
plot(X,FX)
which for the actual data XY gives me this chart:
In the chart you see the hidden line in blu that I traced manually on the picture. Normally I do this in excel adding an additional X point but obviously this does not work in Matlab. How can I obtain such extension in Matlab?
You can do the same thing: append a new value to X and regenerate FX using polyval
newX = [X; 140];
newFX = polyval(p, newX);
plot(newX, newFX);
this will work if X is a column vector. If it's a row vector then append horizontally using [X 140] instead.
Like in excell you need to add X points.
Here's an example:
scatter(X,Y);
p = polyfit(X,Y,1); %// estimating the line paramters
Now all you need is use different X values ( suppose maxX=140 ):
plotX = linspace( min(X), maxX, 100 );
FX= polyval(p,plotX);
plot( plotX, FX );
Related
I have a numerical set X, Y, Z and I would like to reproduce a heatmap with these values. The size of the bin is 20 x 20 and the range of the X and Y axes are from -150 to 150 with Z being the color. Within that bin it should contain the average of the Z values in that range.
In Origin contains this tool to make a heatmap with the average of the values, but I would like to do it in MATLAB. The graph I made in Origin and that I would like to do in MATLAB can be seen in figure 1.
I've tried something like
load xyz.dat
x = xyz(:,1);
y = xyz(:,2);
z = xyz(:,3);
tbl = table(x,y,z);
h = heatmap(tbl,'x','y','ColorVariable','z','ColorMethod','mean');
But it printed this warning
Warning: Error updating HeatmapChart. Values in the source table variable 'x' are not grouped into discrete categories. Use the discretize function to group your values.
heatmap expects discrete x and y values. You goal is to bin your x and y's into 20 discrete bins and average the z values for each bin, but x and y themselves are continuous.
To achieve your goal take the advice of the warning message and use discretize to bin your x and y values.
% I used the following stand ins for your data:
% x = rand(540, 1);
% y = rand(540, 1);
n_bins = 20; % Number of grid cells
% If you want the width of the grid cell to be 20, use
% n_bins = (max(x) - min(x)) / 20;
x_discrete = discretize(x, n_bins);
y_discrete = discretize(y, n_bins);
tbl = table(X_discrete,y_discrete,z, 'VariableNames', {'x', 'y', 'z'});
h = heatmap(tbl,'x','y','ColorVariable','z','ColorMethod','mean');
Note: Why was this not a problem with the sample data?
Using your sample data,
x = [49.8, 14.5, -60.7, -21.6, -10.6];
y = [45.3, 7.9, 23.9, -58.5, -55.4];
z = [0.2 , -0.06, -0.35, -0.15, -0.08];
tbl = table(x',y',z', 'VariableNames', {'x', 'y', 'z'});
h = heatmap(tbl,'x','y','ColorVariable','z','ColorMethod','mean');
Does not throw an error because it treats each x and y value as a separate category. heatmap uses a call to categorical to transform the continuous values into categorical values.
Aside from not really providing the output you want (each point would be its own box instead of averaging grid cells), categorical seems to have a limit in how many categorical values it will create. I wasn't able to find any documentation about exactly what that limit is, but by experimentation, it tops out in the mid 200's. Since your vectors are 540 elements long, you get the warning about using discretize instead.
MATLAB's surf command allows you to pass it optional X and Y data that specify non-cartesian x-y components. (they essentially change the basis vectors). I desire to pass similar arguments to a function that will draw a line.
How do I plot a line using a non-cartesian coordinate system?
My apologies if my terminology is a little off. This still might technically be a cartesian space but it wouldn't be square in the sense that one unit in the x-direction is orthogonal to one unit in the y-direction. If you can correct my terminology, I would really appreciate it!
EDIT:
Below better demonstrates what I mean:
The commands:
datA=1:10;
datB=1:10;
X=cosd(8*datA)'*datB;
Y=datA'*log10(datB*3);
Z=ones(size(datA'))*cosd(datB);
XX=X./(1+Z);
YY=Y./(1+Z);
surf(XX,YY,eye(10)); view([0 0 1])
produces the following graph:
Here, the X and Y dimensions are not orthogonal nor equi-spaced. One unit in x could correspond to 5 cm in the x direction but the next one unit in x could correspond to 2 cm in the x direction + 1 cm in the y direction. I desire to replicate this functionality but drawing a line instead of a surf For instance, I'm looking for a function where:
straightLine=[(1:10)' (1:10)'];
my_line(XX,YY,straightLine(:,1),straightLine(:,2))
would produce a line that traced the red squares on the surf graph.
I'm still not certain of what your input data are about, and what you want to plot. However, from how you want to plot it, I can help.
When you call
surf(XX,YY,eye(10)); view([0 0 1]);
and want to get only the "red parts", i.e. the maxima of the function, you are essentially selecting a subset of the XX, YY matrices using the diagonal matrix as indicator. So you could select those points manually, and use plot to plot them as a line:
Xplot = diag(XX);
Yplot = diag(YY);
plot(Xplot,Yplot,'r.-');
The call to diag(XX) will take the diagonal elements of the matrix XX, which is exactly where you'll get the red patches when you use surf with the z data according to eye().
Result:
Also, if you're just trying to do what your example states, then there's no need to use matrices just to take out the diagonal eventually. Here's the same result, using elementwise operations on your input vectors:
datA = 1:10;
datB = 1:10;
X2 = cosd(8*datA).*datB;
Y2 = datA.*log10(datB*3);
Z2 = cosd(datB);
XX2 = X2./(1+Z2);
YY2 = Y2./(1+Z2);
plot(Xplot,Yplot,'rs-',XX2,YY2,'bo--','linewidth',2,'markersize',10);
legend('original','vector')
Result:
Matlab has many built-in function to assist you.
In 2D the easiest way to do this is polar that allows you to make a graph using theta and rho vectors:
theta = linspace(0,2*pi,100);
r = sin(2*theta);
figure(1)
polar(theta, r), grid on
So, you would get this.
There also is pol2cart function that would convert your data into x and y format:
[x,y] = pol2cart(theta,r);
figure(2)
plot(x, y), grid on
This would look slightly different
Then, if we extend this to 3D, you are only left with plot3. So, If you have data like:
theta = linspace(0,10*pi,500);
r = ones(size(theta));
z = linspace(-10,10,500);
you need to use pol2cart with 3 arguments to produce this:
[x,y,z] = pol2cart(theta,r,z);
figure(3)
plot3(x,y,z),grid on
Finally, if you have spherical data, you have sph2cart:
theta = linspace(0,2*pi,100);
phi = linspace(-pi/2,pi/2,100);
rho = sin(2*theta - phi);
[x,y,z] = sph2cart(theta, phi, rho);
figure(4)
plot3(x,y,z),grid on
view([-150 70])
That would look this way
Generate a plot showing the graphs of
y=(2*a+1)*exp(-x)-(a+1)*exp(2*x)
in the range x ∈ <-2, 4> for all integer values of a between -3 and 3
I know how to make typical plot for 2 values and set a range on the axes, but how to draw the graph dependent on the parameter a?
To elaborate on Ben Voigt's comment: A more advanced technique would be to replace the for-loop with a call to bsxfun to generate a matrix of evaluations of M(i,j) = f(x(i),a(j)) and call plot with this matrix. Matlab will then use the columns of the matrix and plot each column with individual colors.
%%// Create a function handle of your function
f = #(x,a) (2*a+1)*exp(-x)-(a+1)*exp(2*x);
%%// Plot the data
x = linspace(-2, 4);
as = -3:3;
plot(x, bsxfun(f,x(:),as));
%%// Add a legend
legendTexts = arrayfun(#(a) sprintf('a == %d', a), as, 'uni', 0);
legend(legendTexts, 'Location', 'best');
You could also create the evaluation matrix using ndgrid, which explicitly returns all combinations of the values of x and as. Here you have to pay closer attention on properly vectorizing the code. (We were lucky that the bsxfun approach worked without having to change the original f.)
f = #(x,a) (2*a+1).*exp(-x)-(a+1).*exp(2*x); %// Note the added dots.
[X,As] = ndgrid(x,as);
plot(x, f(X,As))
However for starters, you should get familiar with loops.
You can do it using a simple for loop as follows. You basically loop through each value of a and plot the corresponding y function.
clear
clc
close all
x = -2:4;
%// Define a
a = -3:3;
%// Counter for legend
p = 1;
LegendText = cell(1,numel(a));
figure;
hold on %// Important to keep all the lines on the same plot.
for k = a
CurrColor = rand(1,3);
y= (2*k+1).*exp(-x)-(k+1).*exp(2.*x);
plot(x,y,'Color',CurrColor);
%// Text for legend
LegendText{p} = sprintf('a equals %d',k);
p = p+1;
end
legend(LegendText,'Location','best')
Which gives something like this:
You can customize the graph as you like. Hope that helps get you started!
I know the locations of spheres (center and radius) in a box. I want to extract cross sections. I am able to plot the spheres placed in a cube using the following Matlab code:
[X,Y,Z] = sphere;
for SpNum = 1:NumSpheres
surf( X*Radius(SpNum)+Center(SpNum,1), Y*Radius(SpNum)+Center(SpNum,2), Z*Radius(SpNum)+Center(SpNum,3), ...
'FaceColor','r' );
%shading interp;
hold on;
end
axis tight; daspect([1 1 1]);
In the above code, each sphere could have different radius and they do not overlap (so the centers are also different).
The above code does not however generate cross sections. I want to extract cross sections similar to what we get from say X-ray CT data: a series of images in the Z-direction. I think 'interp2/interp3' and 'slice' functions are the relevant functions, but I am not sure how to use them to generate the cross sections. I would appreciate if anyone could give pointers or provide some sample code for my problem?
-- Thanks in advance.
Update:
I tried using meshgrid to generate the grid points followed by the function F(X,Y,Z) as follows:
[X,Y,Z] = meshgrid(1:100,1:100,1:100);
F = zeros(size(X),'uint8');
for SpNum = 1:NumSpheres
F( sqrt((X - Center(SpNum,1)).^2 + (Y - Center(SpNum,2)).^2 + (Z - Center(SpNum,3)).^2) <= Radius(SpNum) ) = 1;
end
surf(F);
followed by:
z = 1;
I = interp3(X, Y, Z, X*Radius(SpNum)+Center(SpNum,1), Y*Radius(SpNum)+Center(SpNum,2), Z*Radius(SpNum)+Center(SpNum,3), z, 'spline');
figure, imshow(I);
I know that interp3 is the function to use since it interpolates the values of the function F(X,Y,Z) which represent the spheres at different location within a bounded box (say 1:100, 1:100, 1:100). The interpolated values at particular 'z' (= 1, 2, 3... 100) should give me 100 cross sections (in the form of 2-D images).
The flaw is in the function F itself, since 'surf' throws an error saying that F should be an array - "CData must be an M-by-N matrix or M-by-N-by-3 array".
Can anyone please help.
I finally figured it. For the benefit of others, here is the code.
% A 3-D matrix 'F' which has its value at particular coordinate set to 255 if it belongs to any one of the spheres and 0 otherwise.
[X,Y,Z] = meshgrid(1:100,1:100,1:100);
F = zeros(size(X));
for SpNum = 1:NumSpheres
F( sqrt((X - Center(SpNum,1)).^2 + (Y - Center(SpNum,2)).^2 + (Z - Center(SpNum,3)).^2) <= Radius(SpNum) ) = 255;
end
% Extract cross sections from F using interp3 function along the z-axis.
I = zeros(size(X));
for z = 1:100
I(:,:,z) = interp3(X, Y, Z, F, 1:100, (1:100)', z, 'spline');
end
implay(I,4);
You could test and visualize the output by setting Center (a 3-D vector) and Radius of each sphere (some arbitrary NumSpheres) to some random values. The above code will display a window with cross-sections.
Previously, I was trying to use 'surf' to render the spheres which is not right. To render, you have to use the first code snippet. Another mistake I made was using a row vector for the 6th argument instead of column vector.
Hope this helps.
--
Cheers,
Ram.
Matlab newb here. I have searched and haven't found how to do the following:
x=0.1:1/100:10;
y=exp(a(a>=-1&a<=1)*sqrt(x));
plot(x,y)
I realize that the dimensions of x and a don't match, but I just want to express: "what does y look like when a constant, a, is constrained between -1 and 1", for example.
Any hints are appreciated. Thanks in advance.
Assuming a and x are independent, you can go along these lines, using bsxfun to compute y for all combinations of a and x:
x = 0.1:1/100:10; %// define x values
a = linspace(-1,1,10); %// define a values
y = exp( bsxfun(#times, a, sqrt(x).') ); %'// compute y for all combinations
plot(x,y); %// this plots each column of y. Each colum represents a value of a
Or plot as a 3D graph (y as a function of a and x):
mesh(a,x,y)
xlabel('a')
ylabel('x')
zlabel('y')
You can do as follows:
x=0.1:1/100:10; % 991 clips
a=-1:1/495:1; % use 1/495 here to make it also 991 clips
y=exp(a.*sqrt(x));
plot(x,y)
This will give you the following figure: