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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
I have a heat map
and want to convert this 2D matrix to a 3D volume/shape/surface data points for further processing. Not simply display it in 3D using surf.
What would be a good way to do this?
With a lot of help from this community I could come closer:
I shrunk the size to 45x45 px for simplicity.
I = (imread("TESTGREYPLASTIC.bmp"))./2+125;
Iinv = 255-(imread("TESTGREYPLASTIC.bmp"))./2-80;%
for i = 1:45
for j = 1:45
A(i, j, I(i,j) ) = 1;
A(i, j, Iinv(i,j) ) = 1;
end
end
volshow(A)
Its not ideal but the matrix is what I wanted now. Maybe the loop can be improved to run faster when dealing with 1200x1200 points.
How do I create a real closed surface now?
Following your conversation with #BoilermakerRV, I guess you are looking for one of the following two results:
A list of 3d points, where x and y are index of pixels in the image, and z is value of corresponding pixels. The result will be an m*n by 3 matrix.
An m by n by 256 volume of zeros and ones, that for (i,j)-th pixel in the image, all voxels of the (i, j)-the pile of the volume are 0, except the one at I(i, j).
Take a look at the following example that generates both results:
close all; clc; clear variables;
I = rgb2gray(imread('data2.png'));
imshow(I), title('Data as image')
% generating mesh grid
[m, n] = size(I);
[X, Y] = meshgrid(1:n, 1:m);
% converting image to list of 3-d points
P = [Y(:), X(:), I(:)];
figure
scatter3(P(:, 1), P(:, 2), P(:, 3), 3, P(:, 3), '.')
colormap jet
title('Same data as a list of points in R^3')
% converting image to 256 layers of voxels
ind = sub2ind([m n 256], Y(:), X(:), I(:));
V = zeros(m, n, 256);
V(ind) = 1.0;
figure
h = slice(V, [250], [250], [71]) ;
[h.EdgeColor] = deal('none');
colormap winter
camlight
title('And finally, as a matrix of 0/1 voxels')
The contour plot that is shown can't be generated with "2D" data. It requires three inputs as follows:
[XGrid,YGrid] = meshgrid(-4:.1:4,-4:.1:4);
C = peaks(XGrid,YGrid);
contourf(XGrid,YGrid,C,'LevelStep',0.1,'LineStyle','none')
colormap('gray')
axis equal
Where XGrid, YGrid and C are all NxN matrices defining the X values, Y values and Z values for every point, respectively.
If you want this to be "3D", simply use surf:
surf(XGrid,YGrid,C)
I am using histograms in Matlab to look at the distribution of some data from my experiments. I want to find the mean distribution (mean height of the bars) from a group of tests then produce an average histogram.
By using this code:
data = zeros(26,31);
for i = 1:length(files6)
x = csvread(files6(i).name);
x = x(1:end,:);
time = x(:,1);
variable = x(:,3);
thing(:,1) = x(:,1);
thing(:,2) = x(:,3);
figure()
binCenter = {0:tbinstep:tbinend 0:varbinstep:varbinend};
hist3(thing, 'Ctrs', binCenter, 'CDataMode','auto','FaceColor','interp');
colorbar
[N,C] = hist3(thing, 'Ctrs', binCenter);
data = data + N;
clearvars x time variable
end
avedata = data / i;
I can find the mean of N, which will be the Z value for the plot (histogram) I want, and I have X,Y (which are the same for all tests) from:
x = 0:tbinstep:tbinend;
y = 0:varbinstep:varbinend;
But how do I bring these together to make the graphical out that shows the average height of the bars? I can't use hist3 again as that will just calculate the distribution of avedata.
AT THE RISK OF STARTING AN XY PROBLEM using bar3 has been suggested, but that asks the question "how do I go from 2 vectors and a matrix to 1 matrix bar3 can handle? I.e. how do I plot x(1), y(1), avedata(1,1) and so on for all the data points in avedata?"
TIA
By looking at hist3 source code in matlab r2014b, it has his own plotting implemented inside that prepares data and plot it using surf method. Here is a function that reproduce the same output highly inspired from the hist3 function with your options ('CDataMode','auto','FaceColor','interp'). You can put this in a new file called hist3plot.m:
function [ h ] = hist3plot( N, C )
%HIST3PLOT Summary of this function goes here
% Detailed explanation goes here
xBins = C{1};
yBins = C{2};
% Computing edges and width
nbins = [length(xBins), length(yBins)];
xEdges = [0.5*(3*xBins(1)-xBins(2)), 0.5*(xBins(2:end)+xBins(1:end-1)), 0.5*(3*xBins(end)-xBins(end-1))];
yEdges = [0.5*(3*yBins(1)-yBins(2)), 0.5*(yBins(2:end)+yBins(1:end-1)), 0.5*(3*yBins(end)-yBins(end-1))];
xWidth = xEdges(2:end)-xEdges(1:end-1);
yWidth = yEdges(2:end)-yEdges(1:end-1);
del = .001; % space between bars, relative to bar size
% Build x-coords for the eight corners of each bar.
xx = xEdges;
xx = [xx(1:nbins(1))+del*xWidth; xx(2:nbins(1)+1)-del*xWidth];
xx = [reshape(repmat(xx(:)',2,1),4,nbins(1)); NaN(1,nbins(1))];
xx = [repmat(xx(:),1,4) NaN(5*nbins(1),1)];
xx = repmat(xx,1,nbins(2));
% Build y-coords for the eight corners of each bar.
yy = yEdges;
yy = [yy(1:nbins(2))+del*yWidth; yy(2:nbins(2)+1)-del*yWidth];
yy = [reshape(repmat(yy(:)',2,1),4,nbins(2)); NaN(1,nbins(2))];
yy = [repmat(yy(:),1,4) NaN(5*nbins(2),1)];
yy = repmat(yy',nbins(1),1);
% Build z-coords for the eight corners of each bar.
zz = zeros(5*nbins(1), 5*nbins(2));
zz(5*(1:nbins(1))-3, 5*(1:nbins(2))-3) = N;
zz(5*(1:nbins(1))-3, 5*(1:nbins(2))-2) = N;
zz(5*(1:nbins(1))-2, 5*(1:nbins(2))-3) = N;
zz(5*(1:nbins(1))-2, 5*(1:nbins(2))-2) = N;
% Plot the bars in a light steel blue.
cc = repmat(cat(3,.75,.85,.95), [size(zz) 1]);
% Plot the surface
h = surf(xx, yy, zz, cc, 'CDataMode','auto','FaceColor','interp');
% Setting x-axis and y-axis limits
xlim([yBins(1)-yWidth(1) yBins(end)+yWidth(end)]) % x-axis limit
ylim([xBins(1)-xWidth(1) xBins(end)+xWidth(end)]) % y-axis limit
end
You can then call this function when you want to plot outputs from Matlab's hist3 function. Note that this can handle non uniform positionning of bins:
close all; clear all;
data = rand(10000,2);
xBins = [0,0.1,0.3,0.5,0.6,0.8,1];
yBins = [0,0.1,0.3,0.5,0.6,0.8,1];
figure()
hist3(data, {xBins yBins}, 'CDataMode','auto','FaceColor','interp')
title('Using hist3')
figure()
[N,C] = hist3(data, {xBins yBins});
hist3plot(N, C); % The function is called here
title('Using hist3plot')
Here is a comparison of the two outputs:
So if I understand your question and code correctly, you are plotting the distribution of multiple experiments' data as histograms, then you want to calculate the average shape of all the previous histograms.
I usually avoid giving approaches the asker isn't explicitly asking for, but for this one I must comment that it is a very strange thing to do. I've never heard of calculating the average shape of multiple histograms before. So just in case, you could simply append all your experiment's data into a single variable, and plot a normalized histogram of that using histogram2. This code outputs a relative frequency histogram. (Other normalization methods)
% Append all data in a single matrix
x = []
for i = 1:length(files6)
x = [x; csvread(files6(i).name)];
end
% Plot normalized bivariate histogram, normalized
xEdges = 0:tbinstep:tbinend;
yEdges = 0:varbinstep:varbinend;
histogram2(x(:,1), x(:,3), xEdges, yEdges, 'Normalize', 'Probability')
Now, if you really are looking to draw the average shape of multiple histograms, then yes, use bar3. Since bar3 doesn't accept an (x,y) value argument, you can follow the other answer, or modify the XTickLabel and YTickLabel property to match whatever your bin range is, afterwards.
... % data = yourAverageData;
% Save axis handle to `h`
h = bar3(data);
% Set property of axis
h.XTickLabels = 0:tbinstep:tbinend;
h.YTickLabels = 0:varbinstep:varbinend;
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 am trying to fit a 3D surface polynomial of n-degrees to some data points in 3D space. My system requires the surface to be monotonically increasing in the area of interest, that is the partial derivatives must be non-negative. This can be achieved using Matlab's built in lsqlin function.
So here's what I've done to try and achieve this:
I have a function that takes in four parameters;
x1 and x2 are my explanatory variables and y is my dependent variable. Finally, I can specify order of polynomial fit. First I build the design matrix A using data from x1 and x2 and the degree of fit I want. Next I build the matrix D that is my container for the partial derivatives of my datapoints. NOTE: the matrix D is double the length of matrix A since all datapoints must be differentiated with respect to both x1 and x2. I specify that Dx >= 0 by setting b to be zeroes.
Finally, I call lsqlin. I use "-D" since Matlab defines the function as Dx <= b.
function w_mono = monotone_surface_fit(x1, x2, y, order_fit)
% Initialize design matrix
A = zeros(length(x1), 2*order_fit+2);
% Adjusting for bias term
A(:,1) = ones(length(x1),1);
% Building design matrix
for i = 2:order_fit+1
A(:,(i-1)*2:(i-1)*2+1) = [x1.^(i-1), x2.^(i-1)];
end
% Initialize matrix containing derivative constraint.
% NOTE: Partial derivatives must be non-negative
D = zeros(2*length(y), 2*order_fit+1);
% Filling matrix that holds constraints for partial derivatives
% NOTE: Matrix D will be double length of A since all data points will have a partial derivative constraint in both x1 and x2 directions.
for i = 2:order_fit+1
D(:,(i-1)*2:(i-1)*2+1) = [(i-1)*x1.^(i-2), zeros(length(x2),1); ...
zeros(length(x1),1), (i-1)*x2.^(i-2)];
end
% Limit of derivatives
b = zeros(2*length(y), 1);
% Constrained LSQ fit
options = optimoptions('lsqlin','Algorithm','interior-point');
% Final weights of polynomial
w_mono = lsqlin(A,y,-D,b,[],[],[],[],[], options);
end
So now I get some weights out, but unfortunately they do not at all capture the structure of the data. I've attached an image so you can just how bad it looks. .
I'll give you my plotting script with some dummy data, so you can try it.
%% Plot different order polynomials to data with constraints
x1 = [-5;12;4;9;18;-1;-8;13;0;7;-5;-8;-6;14;-1;1;9;14;12;1;-5;9;-10;-2;9;7;-1;19;-7;12;-6;3;14;0;-8;6;-2;-7;10;4;-5;-7;-4;-6;-1;18;5;-3;3;10];
x2 = [81.25;61;73;61.75;54.5;72.25;80;56.75;78;64.25;85.25;86;80.5;61.5;79.25;76.75;60.75;54.5;62;75.75;80.25;67.75;86.5;81.5;62.75;66.25;78.25;49.25;82.75;56;84.5;71.25;58.5;77;82;70.5;81.5;80.75;64.5;68;78.25;79.75;81;82.5;79.25;49.5;64.75;77.75;70.25;64.5];
y = [-6.52857142857143;-1.04736842105263;-5.18750000000000;-3.33157894736842;-0.117894736842105;-3.58571428571429;-5.61428571428572;0;-4.47142857142857;-1.75438596491228;-7.30555555555556;-8.82222222222222;-5.50000000000000;-2.95438596491228;-5.78571428571429;-5.15714285714286;-1.22631578947368;-0.340350877192983;-0.142105263157895;-2.98571428571429;-4.35714285714286;-0.963157894736842;-9.06666666666667;-4.27142857142857;-3.43684210526316;-3.97894736842105;-6.61428571428572;0;-4.98571428571429;-0.573684210526316;-8.22500000000000;-3.01428571428571;-0.691228070175439;-6.30000000000000;-6.95714285714286;-2.57232142857143;-5.27142857142857;-7.64285714285714;-2.54035087719298;-3.45438596491228;-5.01428571428571;-7.47142857142857;-5.38571428571429;-4.84285714285714;-6.78571428571429;0;-0.973684210526316;-4.72857142857143;-2.84285714285714;-2.54035087719298];
% Used to plot the surface in all points in the grid
X1 = meshgrid(-10:1:20);
X2 = flipud(meshgrid(30:2:90).');
figure;
for i = 1:4
w_mono = monotone_surface_fit(x1, x2, y, i);
y_nr = w_mono(1)*ones(size(X1)) + w_mono(2)*ones(size(X2));
for j = 1:i
y_nr = w_mono(j*2)*X1.^j + w_mono(j*2+1)*X2.^j;
end
subplot(2,2,i);
scatter3(x1, x2, y); hold on;
axis tight;
mesh(X1, X2, y_nr);
set(gca, 'ZDir','reverse');
xlabel('x1'); ylabel('x2');
zlabel('y');
% zlim([-10 0])
end
I think it may have something to do with the fact that I haven't specified anything about the region of interest, but really I don't know. Thanks in advance for any help.
Alright I figured it out.
The main problem was simply an error in the plotting script. The value of y_nr should be updated and not overwritten in the loop.
Also I figured out that the second derivative should be monotonically decreasing. Here's the updated code if anybody is interested.
%% Plot different order polynomials to data with constraints
x1 = [-5;12;4;9;18;-1;-8;13;0;7;-5;-8;-6;14;-1;1;9;14;12;1;-5;9;-10;-2;9;7;-1;19;-7;12;-6;3;14;0;-8;6;-2;-7;10;4;-5;-7;-4;-6;-1;18;5;-3;3;10];
x2 = [81.25;61;73;61.75;54.5;72.25;80;56.75;78;64.25;85.25;86;80.5;61.5;79.25;76.75;60.75;54.5;62;75.75;80.25;67.75;86.5;81.5;62.75;66.25;78.25;49.25;82.75;56;84.5;71.25;58.5;77;82;70.5;81.5;80.75;64.5;68;78.25;79.75;81;82.5;79.25;49.5;64.75;77.75;70.25;64.5];
y = [-6.52857142857143;-1.04736842105263;-5.18750000000000;-3.33157894736842;-0.117894736842105;-3.58571428571429;-5.61428571428572;0;-4.47142857142857;-1.75438596491228;-7.30555555555556;-8.82222222222222;-5.50000000000000;-2.95438596491228;-5.78571428571429;-5.15714285714286;-1.22631578947368;-0.340350877192983;-0.142105263157895;-2.98571428571429;-4.35714285714286;-0.963157894736842;-9.06666666666667;-4.27142857142857;-3.43684210526316;-3.97894736842105;-6.61428571428572;0;-4.98571428571429;-0.573684210526316;-8.22500000000000;-3.01428571428571;-0.691228070175439;-6.30000000000000;-6.95714285714286;-2.57232142857143;-5.27142857142857;-7.64285714285714;-2.54035087719298;-3.45438596491228;-5.01428571428571;-7.47142857142857;-5.38571428571429;-4.84285714285714;-6.78571428571429;0;-0.973684210526316;-4.72857142857143;-2.84285714285714;-2.54035087719298];
% Used to plot the surface in all points in the grid
X1 = meshgrid(-10:1:20);
X2 = flipud(meshgrid(30:2:90).');
figure;
for i = 1:4
w_mono = monotone_surface_fit(x1, x2, y, i);
% NOTE: Should only have 1 bias term
y_nr = w_mono(1)*ones(size(X1));
for j = 1:i
y_nr = y_nr + w_mono(j*2)*X1.^j + w_mono(j*2+1)*X2.^j;
end
subplot(2,2,i);
scatter3(x1, x2, y); hold on;
axis tight;
mesh(X1, X2, y_nr);
set(gca, 'ZDir','reverse');
xlabel('x1'); ylabel('x2');
zlabel('y');
% zlim([-10 0])
end
And here's the updated function
function [w_mono, w] = monotone_surface_fit(x1, x2, y, order_fit)
% Initialize design matrix
A = zeros(length(x1), 2*order_fit+1);
% Adjusting for bias term
A(:,1) = ones(length(x1),1);
% Building design matrix
for i = 2:order_fit+1
A(:,(i-1)*2:(i-1)*2+1) = [x1.^(i-1), x2.^(i-1)];
end
% Initialize matrix containing derivative constraint.
% NOTE: Partial derivatives must be non-negative
D = zeros(2*length(y), 2*order_fit+1);
for i = 2:order_fit+1
D(:,(i-1)*2:(i-1)*2+1) = [(i-1)*x1.^(i-2), zeros(length(x2),1); ...
zeros(length(x1),1), -(i-1)*x2.^(i-2)];
end
% Limit of derivatives
b = zeros(2*length(y), 1);
% Constrained LSQ fit
options = optimoptions('lsqlin','Algorithm','active-set');
w_mono = lsqlin(A,y,-D,b,[],[],[],[],[], options);
w = lsqlin(A,y);
end
Finally a plot of the fitting (Have used a new simulation, but fit also works on given dummy data).