How to make normalized frequency distribution plot for 2D matrices? - matlab

I have two 80*80 matrices. I would like to plot normalized frequency plot. I tried to normalize the 80* 80 grid with the following code:
A = per_monsoon_postmon; % (A is my 80*80 matrix)
A = rand (80,80);
minA = repmat(min(A), [size(A, 1), 1]);
normA = max(A) - min(A);
normA = repmat(normA, [length(normA) 1]);
normalizedA = (A - minA)./normA;
But this code didn't give me the desired result, as grids with nan values also has a number in it. For eg. earlier grid 1*1 is nan now it has a value of 0.8340. Could you please help me how to normalize the 2D matrix and then plot frequency distribution plot in MATLAB? Is there a way to directly plot normalized frequency distribution plot?

If you have nan values in your verctor you might have problems. I would first replace the nans (for example with zeros).
Normalisation between 0 and one works like this:
a=rand(80,80); %generates random 80x80 array
a=a-min(min(a)); %shifts the values from 0 to n, min(min() ) because it is 2x2
a=a./max(max(a));% shifts to 0 to 1
If you want tot plot these values in 3d I would use a surf plot therefore you first generate the sample values and then feed them the z values
[x,y]=meshgrid(1:80);
surf(x,y,z)

Related

matlab scatter plot using colorbar for 2 vectors

I have a two columns of data. X = Model values of NOx concentrations and Y = Observations of NOx concentrations. Now, I want to scatter plot X, Y (markers varying with colors) as well as the colourbar which would show me the counts (i.e. number of data points in that range). X and Y are daily data for a year, i.e. 365 rows.
Please help me. Any help is greatly appreciated.
I have attached a sample image.
If I understand you correctly, the real problem is creating the color information, which is, creating a bivariate histogram. Luckily, MATLAB has a function, hist3, for that in the Statistics & Machine Learning Toolbox. The syntax is
[N,C] = hist3(X,nbins)
where X is a m-by-2 matrix containing the data, and nbins is a 1-by-2 vector containing the number of bins in each dimension. The return value N is a matrix of size nbins(1)-by-nbins(2), and contains the histogram data. C is a 1-by-2 cell array, containing the bin centers in both dimensions.
% Generate sample data
X = randn(10000, 1);
Y = X + rand(10000, 1);
% Generate histogram
[N,C] = hist3([X,Y], [100,100]);
% Plot
imagesc(C{1},C{2},N);
set(gca,'YDir','normal');
colormap(flipud(pink));
colorbar;
Result:

Using interp2 in Matlab with NaN inputs

I have some observational data that is relatively complete, but contains some NaN values, in an matrix in matlab and I want to interpolate them to a more evenly spaced grid using interp2
So, to keep things simple lets say I have one complete (no NaN values) matrix, and one that looks something like:
A = [ 1 2 3 4;
2 3 2 NaN;
0 2 3 4;
0 NaN 4 5 ]
with B and C being complete matrices, interp2 won't accept an input matrix with NaN values. So if I do something like this:
[AI,BI] = meshgrid(a,b) %# matrices to interpolate data to, arbitrary
CI = interp2(A,B,C,AI,BI) %# interpolation, A has NaN values
I get an error:
Error using griddedInterpolant
The coordinates of the input points must be finite values; Inf and NaN are not permitted.
Can anyone suggest either a solution, or reasonable work around that doesn't obstruct my data?
Sorry the quick fix I gave in comment does not work directly for 2D data (it does work that simply with interp1 though, if you ever need it).
For gridded data, if you have NaNs in your grid then you do not have a uniform grid and you cannot use interp2 directly. In this case you have to use griddata first, to re-interpolate your data over a uniform grid (patch the holes basically).
(1) Let's show an example inspired from the Matlab doc:
%% // define a surface
[A,B] = meshgrid(-3:0.25:3);
C = peaks(A,B);
%// poke some holes in it (in every coordinate set)
A(15,3:8) = NaN ;
B(14:18,13) = NaN ;
C(8,16:21) = NaN ;
(2) Now let's fix your data on a clean grid:
%// identify indices valid for the 3 matrix
idxgood=~(isnan(A) | isnan(B) | isnan(C));
%// define a "uniform" grid without holes (same boundaries and sampling than original grid)
[AI,BI] = meshgrid(-3:0.25:3) ;
%// re-interpolate scattered data (only valid indices) over the "uniform" grid
CI = griddata( A(idxgood),B(idxgood),C(idxgood), AI, BI ) ;
(3) Once your grid is uniform, you can then use interp2 if you want to mesh on a finer grid for example:
[XI,YI] = meshgrid(-3:0.1:3) ; %// create finer grid
ZI = interp2( AI,BI,CI,XI,YI ) ; %// re-interpolate
However, note that if this is all what you wanted to do, you could also use griddata only, and do everything in one step:
%// identify indices valid for the 3 matrix
idxgood=~(isnan(A) | isnan(B) | isnan(C));
%// define a "uniform" grid without holes (finer grid than original grid)
[XI,YI] = meshgrid(-3:0.1:3) ;
%// re-interpolate scattered data (only valid indices) over the "uniform" grid
ZI = griddata( A(idxgood),B(idxgood),C(idxgood), XI, YI ) ;
This produces the exact same grid and data than we obtained on step (3) above.
Last note: In case your NaNs are on the border of your domain, by default these functions cannot "interpolate" values for these border. To force them to do so, look at the extrapolation options of these functions, or simply interpolate on a slightly smaller grid which doesn't have NaN on the border.

Is there anyway to find the density of histogram values in MATLAB?

I have 7 vectors ranged between 0 and 0.99. The number of entries in each vector is different, so it would be "unfair" to compare their histograms because there should be a direct correlation between a bin count and the number of entries, assuming the variables are spaced. I'm interested in plotting a smooth curve of the density of the values. So, for a vector a with say n values from 0 and 0.99, I would like an x-axis of 0 to 0.99, with the y-axis being the probabilities associated with those values.
Any ideas or insight?
Not sure what kind of smoothing you want, but some idea how to start:
%some example vectors of different length
p=[10,100,1000,10000];
D=arrayfun(#(x)(rand(x,1)),p,'uni',false);
%defining the range
support=[0:.1:1];
%make sure we don't miss a value
esupport=support;
esupport(end+1)=inf;
%define a function which uses histc to calculate the emperical probability for each bin
epdf_bin=#(x)histc(x,esupport)/numel(x);
%evaluate emperical probability
E=cellfun(epdf_bin,D,'uni',false);
M=cat(2,E{:});
%plot
bar(M);
%print legend
legend(arrayfun(#num2str,p,'uni',false));
%fix x axis labels
set(gca,'XTick',.5:numel(support))
set(gca,'XTickLabel',support)
[h,b] = hist( my_data, Nbins );
plot( b, h / sum(h) );

Easy way to filter Infs in a scatter3 plot

Given the following code, how would one make the Inf values invisible in the scatter plot without color manipulation?
J = rand(20, 40, 5);
J(J>.6 & J<.4) = Inf;
% Plot a scatter matrix
shape = size(J);
[x,y,z] = meshgrid(1:shape(1), 1:shape(2), 1:shape(3));
scatter3(x(:), y(:), z(:), 4, J(:), 'fill');
Data that have NaN values are made invisible when plotting with MATLAB, which you can exploit in your case. Since you want to make the Infinte values as invisible, you can convert all those to NaNs and then plot them. Here you can take help of logical indexing to index into Inf element positions. Thus, the code would be -
J(isinf(J))=NaN
%// ... Plot J
One method could be to change the values higher than a certain threshold to NaN (or any other number). I believe NaN values will not show up in your scatter plot. You can do this with the same code you are already using.
J(J>10^6) = NaN;

Matlab - multiple variables normalized histogram?

I'm working on MATLAB, where I have a vector which I need to split into two classes and then get a histogram of both resulting vectors (which have different sizes). The values represent height records so the interval is about 140-185.
How can I get a normalized histogram of both resulting vectors in different colors. I was able to get both normalized vectors in the same colour (which is indistiguible) and and also a histogram with different colours but not not normalized...
I hope you understand my question and will be able to help me.
Thanks in advance :)
Maybe this is what you need:
matrix = [155+10*randn(2000,1) 165+10*randn(2000,1)];
matrix(1:1100,1) = NaN;
matrix(1101:2000,2) = NaN; %// example data
[y x] = hist(matrix, 15); %// 15 is desired number of bins
y = bsxfun(#rdivide, y, sum(y)) / (x(2)-x(1)); %// normalize to area 1
bar(x,y) %// plots each column of y vs x. Automatically uses different colors