I am interested in sorting the columns of a matrix in terms of the values in 2 other vectors. As an example, suppose the matrix and vectors look like this:
M = [ 1 2 3 4 5 6 ;
7 8 9 10 11 12 ;
13 14 15 16 17 18 ]
v1 = [ 2 , 6 , 6 , 1 , 3 , 2 ]
v2 = [ 3 , 1 , 2 , 7 , 9 , 1 ]
I want to sort the columns of A in terms of their corresponding values in v1 and v2, with v1 taking precedence over v2. Additionally, I am interested in trying to sort the matrix in place as the matrices I am working with are very large. Currently, my crude solution looks like this:
MM = [ v1' ; v2' ; M ] ; ## concatenate the vectors with the matrix
MM[:,:] = sortcols(MM , by=x->(x[1],x[2]))
M[:,:] = MM[3:end,:]
which gives the desired result:
3x6 Array{Int64,2}:
4 6 1 5 2 3
10 12 7 11 8 9
16 18 13 17 14 15
Clearly my approach is not ideal is it requires computing and storing intermediate matrices. Is there a more efficient/elegant approach for sorting the columns of a matrix in terms of 2 other vectors? And can it be done in place to save memory?
Previously I have used sortperm for sorting an array in terms of the values stored in another vector. Is it possible to use sortperm with 2 vectors (and in-place)?
I would probably do it this way:
julia> cols = sort!([1:size(M,2);], by=i->(v1[i],v2[i]));
julia> M[:,cols]
3×6 Array{Int64,2}:
4 6 1 5 2 3
10 12 7 11 8 9
16 18 13 17 14 15
This should be pretty fast and uses only one temporary vector and one copy of the matrix. It's not fully in-place, but doing this operation completely in-place is not easy. You would need a sorting function that moves columns as it works, or alternatively a version of permute! that works on columns. You could start with the code for permute!! in combinatorics.jl and modify it to permute columns, reusing a single column-size temporary buffer.
I have the matrix:
a=[1 2
2 3
1 5
3 4
2 9];
I would like to simplify it by summing together the second column of rows whose first column element matches. Therefore the above matrix a should become:
a=[1 7
2 12
3 4];
I'm at a loss as to how to do this functionally, in other words without a for loop. Thank you!
Use accumarray and unique:
[u,~,subs] = unique(a(:,1))
out = [ u, accumarray(subs,a(:,2)) ]
out =
1 7
2 12
3 4
For the one-line solution, you'd need an external function:
function subs = unique3rdOutput( vec )
[~,~,subs] = unique(vec)
And then
out = [ unique(a(:,1)), accumarray(unique3rdOutput(a(:,1)),a(:,2)) ]
If you can ensure just positive integers in the first column, you can also use:
out = [ unique(a(:,1)) accumarray(a(:,1),a(:,2)) ]
or as suggested by Luis Mendo:
out = [ (1:max(a(:,1))).' accumarray(a(:,1),a(:,2)) ]
I have this 4 integer value output
example:
out = [ 8 7 6 5 ]
I would to save these 4 values in one place (in row i column j)
Such that when I try to access
array(i,j) I get the 4 values 8 7 6 5
I'm failing miserably. Any help is appreciated
If the number of values is the same for all i, and j, use a 3D array of size MxNx4:
array(1,1,:) = [8 7 6 5];
array(1,2,:) = [11 12 13 14];
You could imagine the four numbers are stacked on top of each other along a "depth" dimension in row i and column j.
array(i,j,:) gives the 1x1x4 array containing the four numbers corresponding to i, j. When accesing each group of four numbers, you may want to use squeeze to remove the singleton dimensions, i.e. to obtain the result as a column vector:
>> squeeze(array(1,1,:))
ans =
8
7
6
5
If the number of values may be different for each i and j, use a 2D cell array:
array{1,1} = [8 7 6 5];
array{1,2} = [11 12];
So array{i,j} gives the vector:
>> array{1,1}
ans =
8 7 6 5
I have a 12-D array and am using each dimension as an index value in an optimization problem.
A(:,:,i1,i2,i3,i4,i5,i6,i7,i8,i9,i10)
each index value i is a value from 1 to 5.
I want to sort A from greatest to least and keep track of the indices so I know which indices correspond to to what value of A.
So my ideal output would be a 2 column cell/array with one column being the value and the other other column being the index values.
For a simple 3D example: say I have a 3D array: A(:,:,i1).
Where:
A(:,:,1) = 2
A(:,:,2) = 6
A(:,:,3) = 13
A(:,:,4) = 11
A(:,:,5) = 5
I would like my output to be:
13 3
11 4
6 2
5 5
2 1
EDIT:
assume I have 1x1x3x3 sized input such that
A(1,1,1,1) = 3
A(1,1,2,1) = 1
A(1,1,3,1) = 23
A(1,1,1,2) = 12
A(1,1,2,2) = 9
A(1,1,3,2) = 8
A(1,1,1,3) = 33
A(1,1,2,3) = 14
A(1,1,3,3) = 6
the expected output would be:
33 [1,1,1,3]
23 [1,1,3,1]
14 [1,1,2,3]
12 [1,1,1,2]
9 [1,1,2,2]
8 [1,1,3,2]
6 [1,1,3,3]
3 [1,1,1,1]
1 [1,1,2,1]
This should be a generic code for any multi-dimensional input array -
%// Sort A and get the indices
[sorted_vals,sorted_idx] = sort(A(:),'descend');
%// Set storage for indices as a cell array and then store sorted indices into it
c = cell([1 numel(size(A))]);
[c{:}] = ind2sub(size(A),sorted_idx);
%// Convert c to the requested format and concatenate with cell arary version of
%// sorted values for the desired output
out = [num2cell(sorted_vals) mat2cell([c{:}],ones(1,numel(A)),numel(size(A)))];
The generic code owes its gratitude to this fine solution.
I guess this is what you want:
b=A(:);
[sorted_b,ind]=sort(b,'descend');
[dim1,dim2,dim3,dim4]=ind2sub(size(A),ind);
%arranging in the form you want
yourCell=cell(size(b,1),2);
yourCell(:,1)=mat2cell(sorted_b,ones(size(b,1),1),1);
%arranging indices -> maybe vectorized way is there for putting values in "yourCell"
for i=1:size(b,1)
yourCell{i,2}=[dim1(i) dim2(i) dim3(i) dim4(i)];
end
For the array A, given by you, my output looks like:
33 [1,1,1,3]
23 [1,1,3,1]
14 [1,1,2,3]
12 [1,1,1,2]
9 [1,1,2,2]
8 [1,1,3,2]
6 [1,1,3,3]
3 [1,1,1,1]
1 [1,1,2,1]
which matches with your output.
I have around 100 1D arrays I'd like to merge to a matrix.
The arrays have 140 to 180 columns.
Is it possible to merge these 1 x (140-180) arrays to a matrix with a dimension of 100 (amount of arrays) x 180 ?
All the arrays contain numbers. I want to expand the 1x140 array to a 1x180 array by means of interpolation.
In a simplified form, it should be something like this:
A = [1 5 7 8 3]
B = [1 3 5]
result=
[1 5 7 8 3
1 2 3 4 5]
The array B (1x3) is expanded to an 1x5 matrix. And the values in between are interpolated.
Basically, I thought of using "vertcat" after all arrays are expanded by a same amount of columns.
Thanks in advance,
Koen
How about this?
array = {[1 5 7 8 3],[1 3 5]}; % example data
N = 5; % desired length (180 in your case)
aux = cellfun(#(v) interp1(linspace(0,1,length(v)),v,linspace(0,1,N)), array, 'uni', false);
result = cat(1,aux{:});
It uses linear interpolation. For your example, this gives
>> result
result =
1 5 7 8 3
1 2 3 4 5
Note that linear interpolation modifies all values of the vector except first and last, in general. For example, with N=5 the vector [1 3 4 5] would get interpolated to [1 2.5 3.5 4.25 5]. You could use other forms of interpolation by passing an extra argument to interp1, see help interp1.