Plotting Problems on Matlab How could I draw? - matlab

I am trying to plot level curve of f(x,y) = y^4 - 2xy^2 + x^3 - x over [-5,4] x [-3,3], but I am stuck. This my code and how should I continue to it?
My Code:
x = linspace(-5, 4, 25);
y = linspace(-3, 3, 25);
[X,Y] = meshgrid(x,y);
z = #(x,y) y.^4-2*x*y.^2+x^3-x;
Z = z(X,Y);
surf(X,Y,Z)


You could do something like:
clear
x = linspace(-5, 4, 25);
y = linspace(-3, 3, 25);
[X,Y] = meshgrid(x,y);
z = #(x,y) y.^4-2.*x.*y.^2+x.^3-x;
Z = z(X,Y);
% Probing some line parallel to the x axis:
y_probe = 0;
% Probing a point to calculate the gradient in:
x_probe = -3;
% Getting all points for which x = x_probe:
z_probe = z(x, y_probe);
% Compute the gradient:
dx = gradient(x);
dz = gradient(z_probe);
dzdx = dz./dx;
clf
subplot(121)
surf(X,Y,Z)
hold on
plot3(x, ones(1,length(y)) .* y_probe, z_probe ,'r','linewidth',2)
subplot(122)
plot(x, z_probe,'r','linewidth',1)
hold on
xi = find(x > x_probe, 1);
plot(x, dzdx(xi) .* (x - x(xi)) + z_probe(xi),'k--','linewidth',1);
h = quiver(x(xi), z_probe(xi), -dx(xi), dz(xi),'k','LineWidth',2);
xlim([min(x) max(x)])
ylim([min(z_probe) max(z_probe)])
To get:

Related

Random Points in an n-Dimensional Hypersphere

This Matlab code,
creates a set of random points defined by Cartesian coordinates and
uniformly distributed over the interior of an n-dimensional
hypersphere of radius r with center at the origin.
the source is here.
clear all
clc
m = 20000;
n = 2;
r = 2;
%// generate circle boundary
C = [3 4]; %// center [x y]
t = linspace(0, 2*pi, 100);
x = r*cos(t) + C(1);
y = r*sin(t) + C(2);
C_rep = repmat( C,m,1);
X = randn(m,n);
s2 = sum(X.^2,2);
X = X.*repmat(r*(rand(m,1).^(1/n))./sqrt(s2),1,n)+ C_rep;
%% Plot
figure(1), clf
plot(x,y,'b')
hold on
plot(C(1),C(2),'r.', 'MarkerSize', 50) % center point
hold on
plot(X(:,1),X(:,2),'g.','markersize',2);
axis equal;zoom off; zoom on;drawnow;shg;
ax = axis;
This is the output:
which is not what I want.
How to make the points distributed around a center point C?
When n = 2, 3, 4, k dimentions
What does s2 mean?

How can I plot a surface generated by a function f(x,y) where the values x and y are subject to constraints?

I'm new to Matlab and I have a function
and
How can I plot:

Define your X and Y in a linear array
X = linspace(-2, 2, 1000);
Y = linspace(-2, 2, 1000);
Mesh them so you have a grid of x and y
[x,y] = meshgrid(X,Y);
Get the value for your function
f = sqrt(x.^2 + y.^2);
Define your domain
D = (1 <= x.^2 + y.^2);
Set everything outside your domain to nan's so it won't plot
f(~D) = nan;
Plot the surface
surf(x,y,f, 'linestyle', 'none')

Matlab scatter and histogram plot

I have 20 numerical data points with x and y coordinates. I would like to plot them in a 2D plot. They will be concentrated around an x and y coordinate. To better visualise this behaviour, I would like to add histogram bars on top of the 2D scatter plot for the x axis, and histogram bars on the right of the 2D plot for the y axis this way, they do not interfere with the axis labels. Now, my 20 numerical points are in fact two sets of 10 and I would like to have both sets plotted in different colours. Something like this:
python plot
How can I do this?
Update:
FWHM11Avg = [3.88,3.43,3.16,3.22,3.73,2.43,2.88,3.01,3.59,2.17];
FWHM11Med = [4.4,3.1,3,3.15,3.9,2,3.00,2.85,3.85,2.2];
FWHM12Avg = [3.50,2.30,2.97,2.97,2.98,2.28,2.94,2.36,3.51,1.7];
FWHM12Med = [3.3,2.1,2.9,2.8,2.9,2.1,2.8,2.30,3.5,1.7];
minx = min([FWHM11Avg; FWHM11Med]);
maxx = max([FWHM11Avg; FWHM11Med]);
miny = min([FWHM12Avg; FWHM12Med]);
maxy = max([FWHM12Avg; FWHM12Med]);
% make figure
figure(1)
clf
% first subplot -- y-data histc
ah1 = subplot(2, 2, 1);
y_bins = 1.5:.25:4.5;
n = hist(FWHM12Avg, y_bins);
bar(y_bins, n, 'vertical', 'on')
hold on
hist(FWHM12Med, y_bins)
bar(y_bins, n, 'vertical', 'on')
% x-data histc
ah2 = subplot(2, 2, 4);
x_bins = 1.5:.25:4.5;
n = hist(FWHM11Avg, x_bins);
bar(x_bins, n, 'horizontal', 'on')
hold on
n = hist(FWHM11Med, x_bins);
bar(x_bins, n, 'horizontal', 'on')
% scatterplot
ah3 = subplot(2, 2, 2);
hold on
scatter(FWHM11Avg, FWHM11Med)
scatter(FWHM12Avg, FWHM12Med)
% link axes, adjust histc orientation
linkaxes([ah1, ah3], 'y')
linkaxes([ah3, ah2], 'x')
set(ah3,'XLim',[minx, maxx]);
set(ah3,'YLim',[miny, maxy]);
ah1.Box = 'off';
ah1.View = [180, -90];
ah1.Visible = 'off';
ah2.Visible = 'off';
ah2.Box = 'off';
ah2.View = [0, -90];
Also there seems not to be an option available for adding numerical axes to the histograms to see how many points there are in a bar - at least in the documentation I did not see any option. Is that so?
Second Update with applied suggestions to the above syntax:
FWHM11Avg = [3.88,3.43,3.16,3.22,3.73,2.43,2.88,3.01,3.59,2.17];
FWHM11Med = [4.4,3.1,3,3.15,3.9,2,3.00,2.85,3.85,2.2];
FWHM12Avg = [3.50,2.30,2.97,2.97,2.98,2.28,2.94,2.36,3.51,1.7];
FWHM12Med = [3.3,2.1,2.9,2.8,2.9,2.1,2.8,2.30,3.5,1.7];
minx = min([FWHM11Avg; FWHM11Med]);
maxx = max([FWHM11Avg; FWHM11Med]);
miny = min([FWHM12Avg; FWHM12Med]);
maxy = max([FWHM12Avg; FWHM12Med]);
% make figure
figure(1)
clf
% first subplot -- y-data histc
ah1 = subplot(2, 2, 1);
y_bins = 1.5:.25:4.5;
n = hist(FWHM12Avg, y_bins);
bar(y_bins, n, 'vertical', 'on')
hold on
hist(FWHM12Med, y_bins)
bar(y_bins, n, 'vertical', 'on')
% x-data histc
ah2 = subplot(2, 2, 4);
x_bins = 1.5:.25:4.5;
n = hist(FWHM11Avg, x_bins);
bar(x_bins, n, 'horizontal', 'on')
hold on
n = hist(FWHM11Med, x_bins);
bar(x_bins, n, 'horizontal', 'on')
% scatterplot
ah3 = subplot(2, 2, 2);
hold on
scatter(FWHM11Avg, FWHM11Med)
scatter(FWHM12Avg, FWHM12Med)
% link axes, adjust histc orientation
linkaxes([ah1, ah3], 'y')
linkaxes([ah3, ah2], 'x')
set(ah3,'XLim',[minx, maxx]);
set(ah3,'YLim',[miny, maxy]);
set(ah1,'Box','off');
set(ah1,'View',[180, -90]);
set(ah1,'Visible','off');
set(ah2,'Visible','off');
set(ah2,'Box','off');
set(ah2,'View',[0, -90]);

Please research before asking. There is a function in Matlab scatterhist which does this
x0 = 6.1;
y0 = 3.2;
n = 50;
r = rand(n ,1 );
theta = 2*pi*rand(n, 1);
x = x0 + r.*cos(theta);
y = y0 + r.*sin(theta);
scatterhist(x,y, 'Direction','out', 'Location', 'NorthEast')
Edit: Using the data you provided. Is this what you want?
FWHM11Avg = [3.88,3.43,3.16,3.22,3.73,2.43,2.88,3.01,3.59,2.17];
FWHM11Med = [4.4,3.1,3,3.15,3.9,2,3.00,2.85,3.85,2.2];
FWHM12Avg = [3.50,2.30,2.97,2.97,2.98,2.28,2.94,2.36,3.51,1.7];
FWHM12Med = [3.3,2.1,2.9,2.8,2.9,2.1,2.8,2.30,3.5,1.7];
% make figure
figure(1)
clf
FWHM11Avg = FWHM11Avg(:);
FWHM11Med = FWHM11Med(:);
FWHM12Avg = FWHM12Avg(:);
FWHM12Med = FWHM12Med(:);
minX = min([FWHM11Avg; FWHM12Avg]);
maxX = max([FWHM11Avg; FWHM12Avg]);
minY = min([FWHM11Med; FWHM12Med]);
maxY = max([FWHM11Med; FWHM12Med]);
resX = 0.25;
resY = 0.25;
nBinsX = ceil((maxX - minX) / resX);
nBinsY = ceil((maxY - minY) / resY);
label = vertcat( ...
num2cell(repmat('FWHM11', size(FWHM11Avg)),2), ...
num2cell(repmat('FWHM12', size(FWHM11Avg)),2));
Avg = vertcat(FWHM11Avg, FWHM12Avg);
Med = vertcat(FWHM11Med, FWHM12Med);
% scatterplot
scatterhist(Avg, Med, 'Group', label, 'Direction','out', ...
'Location', 'NorthEast', 'NBins', [nBinsX, nBinsY])

This is something I've been using lately:
% generate some random data
mu = [1 2];
sigma = [1 0.5; 0.5 2];
R = chol(sigma);
my_data1 = repmat(mu,100,1) + randn(100,2)*R;
mu = [2 1];
sigma = [3 -0.5; -0.5 2];
R = chol(sigma);
my_data2 = repmat(mu,100,1) + randn(100,2)*R;
% find limits
minx = min([my_data1(:, 1); my_data2(:, 1)]);
maxx = max([my_data1(:, 1); my_data2(:, 1)]);
miny = min([my_data1(:, 2); my_data2(:, 2)]);
maxy = max([my_data1(:, 2); my_data2(:, 2)]);
% make figure
figure(1)
clf
% first subplot -- y-data histogram
ah1 = subplot(2, 2, 1);
histogram(my_data1(:, 2), 'Orientation','horizontal', 'Normalization', 'probability', 'BinWidth', 0.5)
hold on
histogram(my_data2(:, 2), 'Orientation','horizontal', 'Normalization', 'probability', 'BinWidth', 0.5)
% x-data histogram
ah2 = subplot(2, 2, 4);
histogram(my_data1(:, 1), 'Normalization', 'probability', 'BinWidth', 0.5)
hold on
histogram(my_data2(:, 1), 'Normalization', 'probability', 'BinWidth', 0.5)
% scatterplot
ah3 = subplot(2, 2, 2);
hold on
scatter(my_data1(:, 1), my_data1(:, 2))
scatter(my_data2(:, 1), my_data2(:, 2))
% link axes, adjust histogram orientation
linkaxes([ah1, ah3], 'y')
linkaxes([ah3, ah2], 'x')
ah3.XLim = [minx, maxx];
ah3.YLim = [miny, maxy];
ah1.Box = 'off';
ah1.View = [180, -90];
ah1.Visible = 'off';
ah2.Visible = 'off';
ah2.Box = 'off';
ah2.View = [0, -90];
producing this plot
This code assumes a recent version of MATLAB (I use 2014b), but can be easily adapted using the old histogram functions (hist, histc) and the set(..) syntax for graphical objects.

Contour plot for 3D vector

I am trying to produce a contour plot for the 3D vectors returned by a custom function in the xy plane where z = 0.
I tried this but I just get an empty graph:
% Stand in for the real function I want to plot.
f = #(x, y, z) [x ^ 2, y ^ 2, x * y + z];
x = linspace(-5, 5, 50);
y = linspace(-5, 5, 50);
z = zeros(length(x), length(y), 3);
% I know this can be vectorized but the function I really want to graph can't
% be.
for i = 1:length(x)
for j = 1:length(y)
z(i, j, :) = f(x(i), y(j), 0);
end
end
figure;
axis equal;
contour(x, y, z);

You should mention what your axis will be. You have x,y and 3 outputs from f.
If you consider 3 outputs of your f as the ones to be plotted then you should use,
contour(z(:,:,1),z(:,:,2),z(:,:,3));
Which will give you this,
I think what you are looking for, is a function with one output, like,
f = #(x, y,z) [x ^ 2 + y ^ 2 + x * y + z ];
x = linspace(-5, 5, 50);
y = linspace(-5, 5, 50);
z = zeros(length(x), length(y));
for i = 1:length(x)
for j = 1:length(y)
z(i, j) = f(x(i), y(j),0);
end
end
contour(x,y,z,20);

How to plot a hyper plane in 3D for the SVM results?

I just wondering how to plot a hyperplane of the SVM results.
For example, here we are using two features, we can plot the decision boundary in 2D. But if how can we plot a hyperplane in 3D if we use 3 features?
load fisheriris;
features = meas(1:100,:);
featureSelcted = features(1:100,1:2); % For example, featureSelcted = features(1:100,1:3) can not be plotted
groundTruthGroup = species(1:100);
svmStruct = svmtrain(featureSelcted, groundTruthGroup, ...
'Kernel_Function', 'rbf', 'boxconstraint', Inf, 'showplot', true, 'Method', 'QP');
svmClassified = svmclassify(svmStruct,featureSelcted,'showplot',true);
A similar solution in R can be found at svm-fit-hyperplane, but a Matlab implementation would be handy.

Here is a function to plot 3D SVM results in MATLAB.
function [] = svm_3d_matlab_vis(svmStruct,Xdata,group)
sv = svmStruct.SupportVectors;
alphaHat = svmStruct.Alpha;
bias = svmStruct.Bias;
kfun = svmStruct.KernelFunction;
kfunargs = svmStruct.KernelFunctionArgs;
sh = svmStruct.ScaleData.shift; % shift vector
scalef = svmStruct.ScaleData.scaleFactor; % scale vector
group = group(~any(isnan(Xdata),2));
Xdata =Xdata(~any(isnan(Xdata),2),:); % remove rows with NaN
% scale and shift data
Xdata1 = repmat(scalef,size(Xdata,1),1).*(Xdata+repmat(sh,size(Xdata,1),1));
k = 50;
cubeXMin = min(Xdata1(:,1));
cubeYMin = min(Xdata1(:,2));
cubeZMin = min(Xdata1(:,3));
cubeXMax = max(Xdata1(:,1));
cubeYMax = max(Xdata1(:,2));
cubeZMax = max(Xdata1(:,3));
stepx = (cubeXMax-cubeXMin)/(k-1);
stepy = (cubeYMax-cubeYMin)/(k-1);
stepz = (cubeZMax-cubeZMin)/(k-1);
[x, y, z] = meshgrid(cubeXMin:stepx:cubeXMax,cubeYMin:stepy:cubeYMax,cubeZMin:stepz:cubeZMax);
mm = size(x);
x = x(:);
y = y(:);
z = z(:);
f = (feval(kfun,sv,[x y z],kfunargs{:})'*alphaHat(:)) + bias;
t = strcmp(group, group{1});
% unscale and unshift data
Xdata1 =(Xdata1./repmat(scalef,size(Xdata,1),1)) - repmat(sh,size(Xdata,1),1);
x =(x./repmat(scalef(1),size(x,1),1)) - repmat(sh(1),size(x,1),1);
y =(y./repmat(scalef(2),size(y,1),1)) - repmat(sh(2),size(y,1),1);
z =(z./repmat(scalef(3),size(z,1),1)) - repmat(sh(3),size(z,1),1);
figure
plot3(Xdata1(t, 1), Xdata1(t, 2), Xdata1(t, 3), 'b.');
hold on
plot3(Xdata1(~t, 1), Xdata1(~t, 2), Xdata1(~t, 3), 'r.');
hold on
% load unscaled support vectors for plotting
sv = svmStruct.SupportVectorIndices;
sv = [Xdata1(sv, :)];
plot3(sv(:, 1), sv(:, 2), sv(:, 3), 'go');
legend(group{1},group{end},'support vectors')
x0 = reshape(x, mm);
y0 = reshape(y, mm);
z0 = reshape(z, mm);
v0 = reshape(f, mm);
[faces,verts,colors] = isosurface(x0, y0, z0, v0, 0, x0);
patch('Vertices', verts, 'Faces', faces, 'FaceColor','k','edgecolor', 'none', 'FaceAlpha', 0.5);
grid on
box on
view(3)
hold off
end
Example plot:
% load data
load fisheriris;
% train svm using three features for two species
svmStruct = svmtrain(meas(1:100,1:3),species(1:100),'showplot','false','kernel_function','rbf',...
'boxconstraint',1,'kktviolationlevel',0.05,'tolkkt',5e-3);
% run function described above
svm_3d_matlab_vis(svmStruct,meas(1:100,1:3),species(1:100))