Would there be a function in matlab, or an easy way, to generate the quantile groups to which each data point belongs to?
Example:
x = [4 0.5 3 5 1.2];
q = quantile(x, 3);
ans =
1.0250 3.0000 4.2500
So I would like to see the following:
result = [2 1 2 3 1]; % The quantile groups
In other words, I am looking for the equivalent of this thread in matlab
Thanks!
You can go through all n quantiles in a loop and use logical indexing to find the quantile
n = 3;
q = quantile(x,n);
y = ones(size(x));
for k=2:n
y(x>=q(k)) = k;
end
Depending on how you define "quantile group", you could use:
If "quantile group" means how many values in q are less than x:
result = sum(bsxfun(#gt, x(:).', q(:)));
If "quantile group" means how many values in q are less than or equal to x:
result = sum(bsxfun(#ge, x(:).', q(:)));
If "quantile group" means index of the value in q which is closest to each value in x:
[~, result] = min(abs(bsxfun(#minus, x(:).', q(:))));
None of these returns the result given in your example, though: the first gives [2 0 1 3 1], the second [2 0 2 3 1], the third [3 1 2 3 1].
Related
I want to ask Matlab to tell me, for example, the greatest common divisor of polynomials of x^4+x^3+2x+2 and x^3+x^2+x+1 over fields like Z_3[x] (where an answer is x+1) and Z_5[x] (where an answer is x^2-x+2).
Any ideas how I would implement this?
Here's a simple implementation. The polynomials are encoded as arrays of coefficients, starting from the lowest degree: so, x^4+x^3+2x+2 is [2 2 0 1 1]. The function takes two polynomials p, q and the modulus k (which should be prime for the algorithm to work property).
Examples:
gcdpolyff([2 2 0 1 1], [1 1 1 1], 3) returns [1 1] meaning 1+x.
gcdpolyff([2 2 0 1 1], [1 1 1 1], 5) returns [1 3 2] meaning 1+3x+2x^2; this disagrees with your answer but I hand-checked and it seems that yours is wrong.
The function first pads arrays to be of the same length. As long as they are not equal, is identifies the higher-degree polynomial and subtracts from it the lower-degree polynomial multiplied by an appropriate power of x. That's all.
function g = gcdpolyff(p, q, k)
p = [p, zeros(1, numel(q)-numel(p))];
q = [q, zeros(1, numel(p)-numel(q))];
while nnz(mod(p-q,k))>0
dp = find(p,1,'last');
dq = find(q,1,'last');
if (dp>=dq)
p(dp-dq+1:dp) = mod(p(1+dp-dq:dp) - q(1:dq), k);
else
q(dq-dp+1:dq) = mod(q(dq-dp+1:dq) - p(1:dp), k);
end
end
g = p(1:find(p,1,'last'));
end
The names of the variables dp and dq are slightly misleading: they are not degrees of p and q, but rather degrees + 1.
I have the following two arrays:
A = [1 2;3 4] and B = [1 5 4]
I want to do the following operation:
for each element of A(call it A(i))
for each element of B~=b do
( (A(i) - 1)/(b-1) ) * ( (A(i) - 5)/(b-5) ) * ( (A(i)- 4)/(b-4) )
end
end
It means that, sometimes the numerator equals to zero, so the product should be zeros. And I want to do the operation for the elements of B which are not equal to the b in denominator to not make it Inf.
How can I do this for the whole matrix A instead of using for loop?
Code
A = [1 2;3 4];
B = [1 5 4];
m1 = bsxfun(#minus,A,permute([1 5 4],[3 1 2]));
m2 = bsxfun(#minus,B,permute([1 5 4],[3 1 2]));
for k1=1:size(A,1)
for k2=1:size(A,2)
t2 = squeeze(bsxfun(#rdivide,m1(k1,k2,:),m2));
t2(1:size(t2,1)+1:end)=1;
A1(k1,k2) = prod(t2(:)); %%// Output
end
end
Output
A1 =
0 -0.2500
-0.1111 0
You can remove the nested loops, but at least two issues there -
You would be going to 4th and 5th dimension with it, using bsxfun. So, debugging would be tough.
bsxfun with higher dimensions to my knowledge seems to get slower.
You could just do the operation, and correct later:
C = (A-1)./(B-1) .* (A-5)./(B-5) .* (A-4)./(B-4)
C(isinf(C)) = 0;
or
C(B==b) = 0;
Possibly you'd need bsxfun, I'm not clear on the size of the output you want...
Let's take two vectors:
a = [1 ; 2; 3]
b = [0 ; 9 ; -5]
If I want minimum value of the vector and it's position I can simply:
[x, ix] = min(a)
I can also compare two vectors and get minimum values:
> min(a, b)
ans =
0
2
-5
But it is impossible to get positions of min values of two vectors:
> [x, ix] = min(a, b)
x =
0
2
-5
error: element number 2 undefined in return list
Why? How to get them? Is there a simple method?
here's how to do that:
[v id]=min([a,b]')
It's a matter of having the right insight:
[x,ix] = min([a b],[],2)
You must think about what the intended output of ix is.
This shows you in which vector the minimum is:
ix=a<b;
x=a.*ix+b.*not(ix);
I have a vector a=[1 2 3 1 4 2 5]'
I am trying to create a new vector that would give for each row, the occurence number of the element in a. For instance, with this matrix, the result would be [1 1 1 2 1 2 1]': The fourth element is 2 because this is the first time that 1 is repeated.
The only way I can see to achieve that is by creating a zero vector whose number of rows would be the number of unique elements (here: c = [0 0 0 0 0] because I have 5 elements).
I also create a zero vector d of the same length as a. Then, going through the vector a, adding one to the row of c whose element we read and the corresponding number of c to the current row of d.
Can anyone think about something better?
This is a nice way of doing it
C=sum(triu(bsxfun(#eq,a,a.')))
My first suggestion was this, a not very nice for loop
for i=1:length(a)
F(i)=sum(a(1:i)==a(i));
end
This does what you want, without loops:
m = max(a);
aux = cumsum([ ones(1,m); bsxfun(#eq, a(:), 1:m) ]);
aux = (aux-1).*diff([ ones(1,m); aux ]);
result = sum(aux(2:end,:).');
My first thought:
M = cumsum(bsxfun(#eq,a,1:numel(a)));
v = M(sub2ind(size(M),1:numel(a),a'))
on a completely different level, you can look into tabulate to get info about the frequency of the values. For example:
tabulate([1 2 4 4 3 4])
Value Count Percent
1 1 16.67%
2 1 16.67%
3 1 16.67%
4 3 50.00%
Please note that the solutions proposed by David, chappjc and Luis Mendo are beautiful but cannot be used if the vector is big. In this case a couple of naïve approaches are:
% Big vector
a = randi(1e4, [1e5, 1]);
a1 = a;
a2 = a;
% Super-naive solution
tic
x = sort(a);
x = x([find(diff(x)); end]);
for hh = 1:size(x, 1)
inds = (a == x(hh));
a1(inds) = 1:sum(inds);
end
toc
% Other naive solution
tic
x = sort(a);
y(:, 1) = x([find(diff(x)); end]);
y(:, 2) = histc(x, y(:, 1));
for hh = 1:size(y, 1)
a2(a == y(hh, 1)) = 1:y(hh, 2);
end
toc
% The two solutions are of course equivalent:
all(a1(:) == a2(:))
Actually, now the question is: can we avoid the last loop? Maybe using arrayfun?
I've a picture. I create the co-occurrence matrix (graycomatrix) to extract different properties (contrast, correlation) etc on it (graycoprops)
x = []
for a lot of pictures, do the same:
imgB = imread('currentLoopImage.jpg')
contrast = graycoprops(graycomatrix(rgb2gray(imgB)), 'Contrast')
correlation = graycoprops(graycomatrix(rgb2gray(imgB)), 'Correlation')
energy = graycoprops(graycomatrix(rgb2gray(imgB)), 'Energy')
homogeneity = graycoprops(graycomatrix(rgb2gray(imgB)), 'Homogeneity')
x = [x;contrast;correlation;energy;homogeneity]
The thing is that I need to save all the values on that matrix X, but I get the following error:
CAT arguments are not consistent in structure field names.
As this is the output I get from each type:
homogeneity =
Homogeneity: 0.8587
There are different types, so I can't save them on the X matrix.
The output matrix X, should save only the numbers, and ignore that "Homogenity"
Can someone tell me who can I do this?
From the graycoprops() example:
>> GLCM = [0 1 2 3;1 1 2 3;1 0 2 0;0 0 0 3];
>> stats = graycoprops(GLCM)
stats =
Contrast: 2.8947
Correlation: 0.0783
Energy: 0.1191
Homogeneity: 0.5658
Then just do:
>> x = struct2array(stats)
ans =
2.8947 0.0783 0.1191 0.5658
Also note that you can include all your images in an m x n x p matrix and process them all at once, instead of using the for loop. For example:
>> GLCM(:,:,2) = GLCM;
>> cell2mat(struct2cell(stats))
ans =
2.8947 2.8947
0.0783 0.0783
0.1191 0.1191
0.5658 0.5658