I wish to append a row-vector (and later, also a column vector) to an existing x by y by z matrix. So basically "Add a new row (at the "bottom") for each z in the original 3d matrix. Consider the following short Matlab program
appendVector = [1 2 3 4 5]; % Small matrix for brevity. Actual matrices used are much larger.
origMatrix = ones(5,5,3);
appendMatrix = [origMatrix( ... ); appendVector];
My question is: How do I adress (using Matlab-style matrix adressing, not a "manual" C-like loop) origMatrix( ... ) in order to append the vector above? Feel free to also include a suggestion on how to do the same operation for a column-vector (I am thinking that the correct way to do the latter is to simply use the '-operator in Matlab).
A "row" in a 3D matrix is actually a multi-dimensional array.
size(origMatrix(1,:,:))
% 5 3
So to append a row, you would need to append a 5 x 3 array.
toAppend = rand(5, 3);
appendMatrix = cat(1, origMatrix, toAppend);
You could append just a 5 element vector and specify an index for the third dimension. In this case, the value for the "row" for all other indices in the third dimension would be filled with zeros.
appendVector = [1 2 3 4 5];
origMatrix = ones(5,5,3);
appendMatrix = origMatrix;
appendMatrix(end+1, :, 1) = appendVector;
If instead, you want to append the same vector along the third dimension, you could use repmat to turn your vector into a 1 x 5 x 3 array and then append that.
appendVector = repmat([1 2 3 4 5], 1, 1, size(origMatrix, 3));
appendMatrix = cat(1, origMatrix, appendVector);
Related
I have a situation analogous to the following
z = magic(3) % Data matrix
y = [1 2 2]' % Column indices
So,
z =
8 1 6
3 5 7
4 9 2
y represents the column index I want for each row. It's saying I should take row 1 column 1, row 2 column 2, and row 3 column 2. The correct output is therefore 8 5 9.
I worked out I can get the correct output with the following
x = 1:3;
for i = 1:3
result(i) = z(x(i),y(i));
end
However, is it possible to do this without looping?
Two other possible ways I can suggest is to use sub2ind to find the linear indices that you can use to sample the matrix directly:
z = magic(3);
y = [1 2 2];
ind = sub2ind(size(z), 1:size(z,1), y);
result = z(ind);
We get:
>> result
result =
8 5 9
Another way is to use sparse to create a sparse matrix which you can turn into a logical matrix and then sample from the matrix with this logical matrix.
s = sparse(1:size(z,1), y, 1, size(z,1), size(z,2)) == 1; % Turn into logical
result = z(s);
We also get:
>> result
result =
8
5
9
Be advised that this only works provided that each row index linearly increases from 1 up to the end of the rows. This conveniently allows you to read the elements in the right order taking advantage of the column-major readout that MATLAB is based on. Also note that the output is also a column vector as opposed to a row vector.
The link posted by Adriaan is a great read for the next steps in accessing elements in a vectorized way: Linear indexing, logical indexing, and all that.
there are many ways to do this, one interesting way is to directly work out the indexes you want:
v = 0:size(y,2)-1; %generates a number from 0 to the size of your y vector -1
ind = y+v*size(z,2); %generates the indices you are looking for in each row
zinv = z';
zinv(ind)
>> ans =
8 5 9
For matrices with dimensions equal or less then 2 the command is:
For instance:
>> mat2str(ones(2,2))
ans =
[1 1;1 1]
However, as the help states, this does not work for higher dimensions:
>> mat2str(rand(2,2,2))
Error using mat2str (line 49)
Input matrix must be 2-D.
How to output matrices with higher dimensions than 2 with that is code compatible, without resorting to custom made for loops?
This isn't directly possible because there is no built-in character to represent concatenation in the third dimension (an analog to the comma and semicolon in 2D). One potential workaround for this would be to perform mat2str on all "slices" in the third dimension and wrap them in a call to cat which, when executed, would concatenate all of the 2D matrices in the third dimension to recreate your input matrix.
M = reshape(1:8, [2 2 2]);
arrays = arrayfun(#(k)mat2str(M(:,:,k)), 1:size(M, 3), 'uni', 0);
result = ['cat(3', sprintf(', %s', arrays{:}), ')'];
result =
'cat(3, [1 3;2 4], [5 7;6 8])'
isequal(eval(result), M)
1
UPDATE
After thinking about this some more, a more elegant solution is to flatten the input matrix, run mat2str on that, and then in the string used to recreate the data, we utilize reshape combined with the original dimensions to provide a command which will recreate the data. This will work for any dimension of data.
result = sprintf('reshape(%s, %s);', mat2str(M(:)), mat2str(size(M)));
So for the following 4D input
M = randi([0 9], 1, 2, 3, 4);
result = sprintf('reshape(%s, %s);', mat2str(M(:)), mat2str(size(M)));
'reshape([6;9;4;6;5;2;6;1;7;2;1;7;2;1;6;2;2;8;3;1;1;3;8;5], [1 2 3 4]);'
Now if we reconstruct the data using this generated string, we can ensure that we get the correct data back.
Mnew = eval(result);
size(Mnew)
1 2 3 4
isequal(Mnew, M)
1
By specifying both the class and precision inputs to mat2str, we can even better approximate the input data including floating point numbers.
M = rand(1,2,3,4,5);
result = sprintf('reshape(%s, %s);', mat2str(M(:),64,'class'), mat2str(size(M)));
isequal(eval(result), M)
1
If I have a Cell array 2*2 where A{i,j} is a matrix, and I have two vectors v=1:2,c=1:2.
I want A(v,c) to return only A{1,1} and A{2,2} but matlab returns every combination of the two(aka also returns A{1,2} and A{2,1}).
Is there a way without using loops or cellfun ?
What I suspect you are doing is something like this:
B = A(v, c);
When you specify vectors to index into A, it finds the intersection of coordinates and gives you those elements. As such, with your indexing you are basically returning all of the elements in A.
If you want just the top left and lower right elements, use sub2ind instead. You can grab the column-major indices of those locations in your cell array, then slice into your cell array with these indices:
ind = sub2ind(size(A), v, c);
B = A(ind);
Example
Let's create a sample 2 x 2 cell array:
A = cell(2,2);
A{1,1} = ones(2);
A{1,2} = 2*ones(2);
A{2,1} = 3*ones(2);
A{2,2} = 4*ones(2);
Row 1, column 1 is a 2 x 2 matrix of all 1s. Row 1, column 2 is a 2 x 2 matrix of 2s, row 2 column 1 is a 2 x 2 matrix of all 3s and the last entry is a 2 x 2 matrix of all 4s.
With v = 1:2; c=1:2;, running the above code gives us:
>> celldisp(B)
B{1} =
1 1
1 1
B{2} =
4 4
4 4
As you can see, we picked out the top left and bottom right entries exactly.
Minor Note
If it's seriously just a cell array of 2 x 2, and you only want to pick out the top left and lower right elements, you can just do:
B = A([1 4]);
sub2ind would equivalently return 1 and 4 as the column major indices for the top left and lower right elements. This avoids the sub2ind call and still achieves what you want.
I have a 3 dimensional (or higher) array that I want to aggregate by another vector. The specific application is to take daily observations of spatial data and average them to get monthly values. So, I have an array with dimensions <Lat, Lon, Day> and I want to create an array with dimensions <Lat, Lon, Month>.
Here is a mock example of what I want. Currently, I can get the correct output using a loop, but in practice, my data is very large, so I was hoping for a more efficient solution than the second loop:
% Make the mock data
A = [1 2 3; 4 5 6];
X = zeros(2, 3, 9);
for j = 1:9
X(:, :, j) = A;
A = A + 1;
end
% Aggregate the X values in groups of 3 -- This is the part I would like help on
T = [1 1 1 2 2 2 3 3 3];
X_agg = zeros(2, 3, 3);
for i = 1:3
X_agg(:,:,i) = mean(X(:,:,T==i),3);
end
In 2 dimensions, I would use accumarray, but that does not accept higher dimension inputs.
Before getting to your answer let's first rewrite your code in a more general way:
ag = 3; % or agg_size
X_agg = zeros(size(X)./[1 1 ag]);
for i = 1:ag
X_agg(:,:,i) = mean(X(:,:,(i-1)*ag+1:i*ag), 3);
end
To avoid using the for loop one idea is to reshape your X matrix to something that you can use the mean function directly on.
splited_X = reshape(X(:), [size(X_agg), ag]);
So now splited_X(:,:,:,i) is the i-th part
that contains all the matrices that should be aggregated which is X(:,:,(i-1)*ag+1:i*ag)) (like above)
Now you just need to find the mean in the 3rd dimension of splited_X:
temp = mean(splited_X, 3);
However this results in a 4D matrix (where its 3rd dimension size is 1). You can again turn it into 3D matrix using reshape function:
X_agg = reshape(temp, size(X_agg))
I have not tried it to see how much more efficient it is, but it should do better for large matrices since it doesn't use for loops.
I have written a for loop code and I want to write in more succinct way without using a for loop, but instead use matrix conditional.
I am teaching myself matlab and I would appreciate any feedback.
I want to create a new matrix, the first column is y, and the second column is filled with zero except for the y's whose indices are contained in the indices matrix. And in the latter case, add 1 instead of 0.
Thanks.
y=[1;2;3;4;5;6;7];
indices=[1;3;5];
[m,n]=size(y);
tem=zeros(m,1);
data=[y,tem];
[r,c]=size(indices);
for i=1:r
a=indices(i);
data(a,2 )=1;
end
Output:
data =
1 1
2 0
3 1
4 0
5 1
6 0
7 0
A shorter alternative:
data = [y(:), full(sparse(indices, 1, 1, numel(y), 1))];
The resulting matrix data is composed of two column vectors: y(:) and a sparse array, with "1"s at the positions corresponding to indices.
Using proper initialization and sparse matrices can be really useful in MATLAB.
How about
data = zeros( m, 2 );
data(:,1) = y;
data( indices, 2 ) = 1;