MATLAB: 90% Percentile of Matrix

90th percentile

Hi! I am trying to find a way to calculate the 90% percentile of a matrix (1,n) . I provide an example below, and the value I would need to find is 0.292. (Note the matrix will changes in length). How could this be done?

[0.289, 0.254, 0.287, 0.292, 0.289, 0.267, 0.289, 0.304, 0.284, 0.282]

Best Answer

Here are two possibilities, the second of which gives you the exact value in your Question:

v = [0.289, 0.254, 0.287, 0.292, 0.289,	0.267, 0.289, 0.304, 0.284, 0.282];
Out1 = prctile(v, 90)
Out2 = interp1(linspace(1/numel(v),1,numel(v)), sort(v), 0.9)

producing:

Out1 =
    0.2980
Out2 =
    0.2920

Related Solutions

MATLAB: Contourplot with nonuniform data leads to strange interpolation

There is no need for any interpolation, griddata, meshgrid, ndgrid, or changing the number of points. As long as the data is stored in order (i.e. not randomly) then you can just use reshape (and possibly a transpose, depending on the order of the data) and it will work just fine. All you need is just one line:

contourf(reshape(omega,4,4),reshape(M,4,4),reshape(eta,4,4))

Together with your example values:

omega = [107.841,153.211,228.0715,316.7175,117.0895,166.2985,247.9645,343.765,122.9353,174.6745,260.5285,364.1815,125.989,177.6410,267.334,373.6045];
M     = [0.0911,0.1231,0.1785,0.2435,0.0628,0.0828,0.1159,0.1550,0.0412,0.0518, 0.0696,0.0902, 0.0319,0.0378,0.0480,0.0600];
eta   = [0.4094,0.4466,0.4846,0.5076,0.4140,0.4554,0.4942,0.5218,0.3813,0.4167, 0.4601,0.4935,0.3460,0.3816,0.4174,0.4600];
contourf(reshape(omega,4,4),reshape(M,4,4),reshape(eta,4,4))
hold on
scatter(omega,M,'ro');

which give this plot

MATLAB: How to replace values above a given percentile by nans

Here is an alternative function that ignores NaN values. It's not a nice one-liner like Star Striders but it does produce the same output as the prctile function in the stats toolbox.

function pctl = percentile(v,p)
% v is a vector of data; example v = [8 9 nan 13 15 11 nan 3 5 7];
% p is a percentile; example p = 75;
% pctl is the exact p_th percentile of v.
vsort = reshape(sort(v(~isnan(v))),1,[]); %row vector
pd = p/100 * numel(vsort);
idx = floor(pd + 0.5) + [0,1];
md = pd - idx(1);
idx(idx<1) = 1; 
idx(idx>numel(vsort)) = numel(vsort); 
pctl = sum(vsort(idx) .* (0.5+[-md,md]));
end  % <-- only needed if this function is within a script

Comparison

v = [8 9 nan 13 15 11 nan 3 5 7];
p = 82; 
percentile(v,p)      %  = 13.120000   this function
prctile(v,p)         %  = 13.120000   stat's toolbox
pct(v(~isnan(v)),p)  %  = 13.115995   the one-liner approximation

To apply it to your data,

t = array2table(vertcat(horzcat((1:1000)', (1001:2000)'), NaN(10, 2)));
t.Var1(t.Var1 > percentile(t.Var1, 99)) = nan;
t.Var2(t.Var2 > percentile(t.Var2, 99)) = nan;

Best Answer

Related Solutions

MATLAB: Contourplot with nonuniform data leads to strange interpolation

MATLAB: How to replace values above a given percentile by nans

Related Question