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.
Related
I have a large array, which looks like this:
1
4
5
3
6
2
7
4
3
I want to rearrange this array that it looks like this:
7 4 3
3 6 2
1 4 5
My original array has the size 13700x1, so I cannot do it manually and if I use the reshape function, the array gets shaped in the wrong way:
1 3 7
4 6 4
5 2 3
I hope my intention is clear. Thanks!
Try
tmpArray = [1
4
5
3
6
2
7
4
3]
flipud(reshape(tmpArray, 3, 3).')
x = [1,4,5,3,6,2,7,4,3]';
A = flipud(reshape(x,3,3)');
The other answers assume your vector contains a square number of elements, 4, 9, 16 .... This is true for the example vector, but not for the one you're actually working with (it's 13700x1 according to the question).
This means that the flipud(reshape()) approach will give an error:
Product of known dimensions, 3, not divisible into total number of
elements, 13924.
This is not a problem if you don't want a square matrix, as numbers that can be represented as a product of any of the numbers: 2, 5, 137.
If you want a square matrix, you need to pad the vector with zeros, NaNs or something else. This can be done the following way:
A = randi(100,13700,1); %% Random 13700x1 matrix
n = numel(A); %% Number of elements in A (13700 in this case)
elements = ceil(sqrt(n))^2; %% Number of elements needed in order to make a square matrix
B = [A; zeros(elements-n,1)]; %% Pad the vectors with zeros.
%% You can also d0 B = [A; nan(elements-n,1)];
final_matrix = flipud(reshape(B, sqrt(elements),[]).'); %% Final operation
Suppose A is a 3-D matrix as below (2 rows-2 columns-2 pages).
A(:,:,1)=[1,2;3,4];
A(:,:,2)=[5,6;7,8];
I want to have a vector, say "a", whose inputs are the average of diagonal elements of matrices on each page. So in this simple case, a=[(1+4)/2;(5+8)/2].
But I have difficulties in matlab to do so. I tried the codes below but failed.
mean(A(1,1,:),A(2,2,:))
You can use "partially linear indexing" in the two dimensions that define the diagonal, as follows:
Since partially linear indexing can only be applied on trailing dimensions, you first need to apply permute to rearrange dimensions, so that the first and second dimensions become second and third.
Now you leave the first dimension untouched, linearly-index the diagonals in the second and third dimensions (which effectly reduces those two dimensions to one), and apply mean along the (combined) second dimension.
Code:
B = permute(A, [3 1 2]); %// step 1: permute
result = mean(B(:,1:size(A,1)+1:size(A,1)*size(A,2)), 2); %// step 2: index and mean
In your example,
A(:,:,1)=[1,2;3,4];
A(:,:,2)=[5,6;7,8];
this gives
result =
2.5000
6.5000
You can use bsxfun for a generic solution -
[m,n,r] = size(A)
mean(A(bsxfun(#plus,[1:n+1:n^2]',[0:r-1]*m*n)),1)
Sample run -
>> A
A(:,:,1) =
8 4 1
7 6 3
1 5 8
A(:,:,2) =
1 7 6
8 5 2
1 2 7
A(:,:,3) =
6 2 8
1 1 6
1 4 5
A(:,:,4) =
8 1 6
1 5 1
9 2 7
>> [m,n,r] = size(A);
>> sum(A(bsxfun(#plus,[1:n+1:n^2]',[0:r-1]*m*n)),1)
ans =
22 13 12 20
>> mean(A(bsxfun(#plus,[1:n+1:n^2]',[0:r-1]*m*n)),1)
ans =
7.3333 4.3333 4 6.6667
This question pops up quite often in one form or another (see for example here or here). So I thought I'd present it in a general form, and provide an answer which might serve for future reference.
Given an arbitrary number n of vectors of possibly different sizes, generate an n-column matrix whose rows describe all combinations of elements taken from those vectors (Cartesian product) .
For example,
vectors = { [1 2], [3 6 9], [10 20] }
should give
combs = [ 1 3 10
1 3 20
1 6 10
1 6 20
1 9 10
1 9 20
2 3 10
2 3 20
2 6 10
2 6 20
2 9 10
2 9 20 ]
The ndgrid function almost gives the answer, but has one caveat: n output variables must be explicitly defined to call it. Since n is arbitrary, the best way is to use a comma-separated list (generated from a cell array with ncells) to serve as output. The resulting n matrices are then concatenated into the desired n-column matrix:
vectors = { [1 2], [3 6 9], [10 20] }; %// input data: cell array of vectors
n = numel(vectors); %// number of vectors
combs = cell(1,n); %// pre-define to generate comma-separated list
[combs{end:-1:1}] = ndgrid(vectors{end:-1:1}); %// the reverse order in these two
%// comma-separated lists is needed to produce the rows of the result matrix in
%// lexicographical order
combs = cat(n+1, combs{:}); %// concat the n n-dim arrays along dimension n+1
combs = reshape(combs,[],n); %// reshape to obtain desired matrix
A little bit simpler ... if you have the Neural Network toolbox you can simply use combvec:
vectors = {[1 2], [3 6 9], [10 20]};
combs = combvec(vectors{:}).' % Use cells as arguments
which returns a matrix in a slightly different order:
combs =
1 3 10
2 3 10
1 6 10
2 6 10
1 9 10
2 9 10
1 3 20
2 3 20
1 6 20
2 6 20
1 9 20
2 9 20
If you want the matrix that is in the question, you can use sortrows:
combs = sortrows(combvec(vectors{:}).')
% Or equivalently as per #LuisMendo in the comments:
% combs = fliplr(combvec(vectors{end:-1:1}).')
which gives
combs =
1 3 10
1 3 20
1 6 10
1 6 20
1 9 10
1 9 20
2 3 10
2 3 20
2 6 10
2 6 20
2 9 10
2 9 20
If you look at the internals of combvec (type edit combvec in the command window), you'll see that it uses different code than #LuisMendo's answer. I can't say which is more efficient overall.
If you happen to have a matrix whose rows are akin to the earlier cell array you can use:
vectors = [1 2;3 6;10 20];
vectors = num2cell(vectors,2);
combs = sortrows(combvec(vectors{:}).')
I've done some benchmarking on the two proposed solutions. The benchmarking code is based on the timeit function, and is included at the end of this post.
I consider two cases: three vectors of size n, and three vectors of sizes n/10, n and n*10 respectively (both cases give the same number of combinations). n is varied up to a maximum of 240 (I choose this value to avoid the use of virtual memory in my laptop computer).
The results are given in the following figure. The ndgrid-based solution is seen to consistently take less time than combvec. It's also interesting to note that the time taken by combvec varies a little less regularly in the different-size case.
Benchmarking code
Function for ndgrid-based solution:
function combs = f1(vectors)
n = numel(vectors); %// number of vectors
combs = cell(1,n); %// pre-define to generate comma-separated list
[combs{end:-1:1}] = ndgrid(vectors{end:-1:1}); %// the reverse order in these two
%// comma-separated lists is needed to produce the rows of the result matrix in
%// lexicographical order
combs = cat(n+1, combs{:}); %// concat the n n-dim arrays along dimension n+1
combs = reshape(combs,[],n);
Function for combvec solution:
function combs = f2(vectors)
combs = combvec(vectors{:}).';
Script to measure time by calling timeit on these functions:
nn = 20:20:240;
t1 = [];
t2 = [];
for n = nn;
%//vectors = {1:n, 1:n, 1:n};
vectors = {1:n/10, 1:n, 1:n*10};
t = timeit(#() f1(vectors));
t1 = [t1; t];
t = timeit(#() f2(vectors));
t2 = [t2; t];
end
Here's a do-it-yourself method that made me giggle with delight, using nchoosek, although it's not better than #Luis Mendo's accepted solution.
For the example given, after 1,000 runs this solution took my machine on average 0.00065935 s, versus the accepted solution 0.00012877 s. For larger vectors, following #Luis Mendo's benchmarking post, this solution is consistently slower than the accepted answer. Nevertheless, I decided to post it in hopes that maybe you'll find something useful about it:
Code:
tic;
v = {[1 2], [3 6 9], [10 20]};
L = [0 cumsum(cellfun(#length,v))];
V = cell2mat(v);
J = nchoosek(1:L(end),length(v));
J(any(J>repmat(L(2:end),[size(J,1) 1]),2) | ...
any(J<=repmat(L(1:end-1),[size(J,1) 1]),2),:) = [];
V(J)
toc
gives
ans =
1 3 10
1 3 20
1 6 10
1 6 20
1 9 10
1 9 20
2 3 10
2 3 20
2 6 10
2 6 20
2 9 10
2 9 20
Elapsed time is 0.018434 seconds.
Explanation:
L gets the lengths of each vector using cellfun. Although cellfun is basically a loop, it's efficient here considering your number of vectors will have to be relatively low for this problem to even be practical.
V concatenates all the vectors for easy access later (this assumes you entered all your vectors as rows. v' would work for column vectors.)
nchoosek gets all the ways to pick n=length(v) elements from the total number of elements L(end). There will be more combinations here than what we need.
J =
1 2 3
1 2 4
1 2 5
1 2 6
1 2 7
1 3 4
1 3 5
1 3 6
1 3 7
1 4 5
1 4 6
1 4 7
1 5 6
1 5 7
1 6 7
2 3 4
2 3 5
2 3 6
2 3 7
2 4 5
2 4 6
2 4 7
2 5 6
2 5 7
2 6 7
3 4 5
3 4 6
3 4 7
3 5 6
3 5 7
3 6 7
4 5 6
4 5 7
4 6 7
5 6 7
Since there are only two elements in v(1), we need to throw out any rows where J(:,1)>2. Similarly, where J(:,2)<3, J(:,2)>5, etc... Using L and repmat we can determine whether each element of J is in its appropriate range, and then use any to discard rows that have any bad element.
Finally, these aren't the actual values from v, just indices. V(J) will return the desired matrix.
how to Compare Values in Array on Specific Indexes in Matlab?
Suppose:
A= [2 2 3 3 3 4 4 4 5 5 6 6 7 8 8]
so i want to Find that
on index 2,3,4,5,6 values or same or not ?
Note: Index can be Dynamically Entered.
Number(length) of Values in Array also can be changed..
To check if they are all equal: use diff to subtract pairs of values, and then check if all those differences are 0.
A = [2 2 3 3 3 4 4 4 5 5 6 6 7 8 8];
ind = [2 3 4 5 6];
result = ~any(diff(A(ind)));
This is faster than using unique. With A and ind as in your example,
>> tic
for cont = 1:1e5
result = ~any(diff(A(ind)));
end
toc
tic
for cont = 1:1e5
result=numel(unique(A(ind)))==1;
end
toc
Elapsed time is 0.371142 seconds.
Elapsed time is 4.754007 seconds.
Hey this should do the trick:
A= [2 2 3 3 3 4 4 4 5 5 6 6 7 8 8];
B= [1,3,5];
C=A(B);
result=numel(unique(C))==1;
Here A is your data.
B is the index vector.
C contains the elements corresponding to the index vector.
result is 1 if all values were the same and 0 otherwise.
You can even "shorten" the code further by joining the two line:
result=numel(unique(A(B)))==1;
There are some ways, it depends on your taste.
For example, if the variable indexing contain the corresponding indexes:
unique(A(indexing));
will give you a vector with the unique elements in the sub-vector A(indexing). Then you just need to check the length:
length(unique(A(indexing))) == 1
I would avoid the use of numel when the function length is available (it is much more clearer what you are trying to achieve).
Other option is to compare the first element to the rest of the element in the sub-vector:
sub_vector = A(indexing);
all(sub_vector == sub_vector(1));
The second option assumes that the sub-vector will never be empty!
suppose there are arrays A and B, both of which can have any arbitrary numbers and size. for example
A=[1 2 3]
B=[4 8 52 7 10]
i was wondering if there was any way to check if any of the elements in A are contained in B without using a loop? Once again, the numbers and size of the array will be arbitrary so i can't hard code it. Any help and input would be appreciated. Thanks!
You mean like this:
A=[1 2 3]; B=[4 8 52 7 10]
ismember(A,B)
ans =
0 0 0
Add to #NasserM.Abbasi: ismember will work regardless shapes and sizes, it is always element-wise. So if you have A=[1 2; 3 4] and B=[1 3; 4 2; 1 2],
then ismember will return :
ismember(A,B); % -> [1 1; 1 1] due to element-wise membership check
ismember(A,B, 'rows'); % -> [1 0] since it checks row-wise.
use ismember carefully according to the possible shapes in A and B.