Now first off, I am not even sure this is called a matrix, and I am new to MATLAB. But let's say I have a "matrix" that looks like this:
for n=1:10
...
someImage = mat(:,:,n) %The "matrix"
...
end
where n could be the frames in a video, for example, and the first 2 ':' are the row and column data for the 2D image (the frame).
If I only wanted the first ':' of data (the row? column? element?), how would I access only that?
Intuitively, I think something like:
row1 = mat(:,0,0)
row2 = mat(0,:,0)
row3 = mat(0,0,:)
but that doesn't seem to be working.
P.S. I know that these aren't really rows, the terminology for all this would also be greatly appreciated
Also, it may not have anything to do with this, but I am using a MATLAB GUI as well, and the "matrix" is stored like this:
handles.mat(:,:,n)
I don't think it has anything to do with my actual question, but it might so I will put it here
-Thanks!
One point I would like to make before starting: MATLAB starts indexing at 1, and not 0. This is a common mistake that most people who have a C/Java/Python programming background make going into MATLAB.
Also, by doing:
row1 = mat(:,1,1);
This accesses all of the rows for the first column and the first frame of your video. Be aware that this will produce a M x 1 vector, where M denotes the number of rows for a frame in your video.
Also:
row2 = mat(1,:,1);
This accesses all of the columns in the first row of the first frame. Be aware that this will produce a 1 x N vector, where N denotes the number of columns for a frame in your video.
Also:
row3 = mat(1,1,:);
This accesses all of the pixels in the entire video sequence at row 1 and column 1. You can think of this as a temporal slice at the top left corner of your video sequence. Be aware that this will produce a 1 x 1 x T vector, where T is the number of frames in your video. If you access just a single pixel location in your video, the first two dimensions are superfluous, and so you can use the squeeze command to shrink all of the singleton dimensions so that it simplifies to a T x 1 vector. In other words, do this:
row3 = squeeze(mat(1,1,:));
FWIW, you do have the right terminology. Rows and columns are used in image / video processing all the time. As for the "matrix", you can call this a temporal sequence or a frame sequence in terms of video processing. It certainly is a 3D matrix, but people in this domain denote it as either one of the two as it is really a sequence of images / frames stacked on top of each other.
Related
I have two 3D arrays:
shape is a 240 x 121 x 10958 array
area is a 240 x 1 x 10958 array
The values of the arrays are of the type double. Both have NaN as fill values where there is no relevant data.
For each [240 x 121] page of the shape array, there are several elements filled by the same number. For example, there will be a block of 1s, a block of 2s, etc. For each corresponding page of the area array there is a single column of numeric values 240 rows long. What I need to do is progressively go through each page of the shape array (moving along the 3rd, 10958-long axis) and replace each numbered element in that page with the number that fills the row of the matching number in the area array.
For example, if I'm looking at shape(:,:,500), I want to replace all the 8s on that page with area(8,1,500). I need to do this for numbers 1 through 20, and I need to do it for all 10958 pages of the array.
If I extract a single page and only replace one number I can get it to work:
shapetest = shape(:,:,500);
shapetest(shapetest==8)=area(8,1,500);
This does exactly what I need for one page and for one number. Going through numbers 1-20 with a for loop doesn't seem like an issue, but I can't find a vectorized way to do this for all the pages of the original 3D array. In fact, I couldn't even get it work for a single page without extracting that page as its own matrix like I did above. I tried things like this to no avail:
shape(shape(:,:,500)==8)=area(8,1,500);
If I can't do it for one page, I'm even more lost as to how to do it for all at once. But I'm inexperienced in MATLAB, and I think I am just ignorant of the proper syntax.
Instead, I ended up using a cell array and the following very inefficient nested for loops:
MyCell=num2cell(shape,[2 1]);
shapetest3=reshape(MyCell,1,10958);
for w=1:numel(shapetest3)
test_result{1,w}=zeros(121,240)*NaN;
end
for k=1:10958
for i=1:29040 % 121 x 240
for n=1:20
if shapetest3{1,k}(i)==n
test_result{1,k}(i)=area(n,1,k);
end
end
end
end
This gets the job done, and I can easily turn it back to an array, but it is very slow, and I am confident there is a much better vectorized way. I'd appreciate any help or tips. Thanks in advance.
To vectorize the mapping operation, we can use shape as an index into area. But because the mapping is different for each plane, we need to loop over the planes to accomplish this. In short, it'll look like this:
test_result = zeros(size(shape)); % pre-allocate output
for k=1:size(area,3) % loop over planes
lut = area(:,1,k);
test_result(:,:,k) = lut(shape(:,:,k));
end
The above only works if shape only contains integer values in the range [1,N], where N = size(area,1). That is, for other values in shape we'll be doing wrong indexing. We will need to fix shape to avoid this. The question here is, what do we want to do with those out-of-range values?
As an example, preparing shape to deal with NaN values:
code = size(area,1) + 1; % this is an unused code word
shape(isnan(shape)) = code;
area(code,1,:) = NaN;
This replaces all NaN values in shape with the value code, which is one larger than any code value we were mapping. Then, we extend area to have one more value, a value for the input code. The value we fill in here is the value that the output test_result will have where shape is NaN. In this case, we write NaN, such that NaN in the input maps to NaN in the output.
Something similar can be done with values below 0 and above 240 (shape(shape<1 | shape>240) = code), or with non-integer values (shape(mod(shape,1)~=0) = code).
I'm dealing with a predictive block-matching motion estimation algorithm. This means, the values of motion vectors are found using the previously found values and I am stuck with a really trivial thing.
I'm dealing with images divided into blocks, so I should have a motion vector for each block. I created a 2xN matrix motion_vectors, where N is the number of all blocks (blocks_in_the_first_row*blocks_in_the_first_column). The first row is the x coordinate and second row the y coordinate of the motion vector.
I have 2 predictors to help to estimate the motion vector of the current block.
If my current block is at position (i,j) then the positions of the predictors are (i, j-1) (the block "on top)" and (i-1, j) (the block on the left).
My problem is, that I can't figure out a way how to adress the predictor blocks (in for loops) in motion_vectors since the dimensions are different (one is a 2xN matrix, the other blocks_in_row x blocks_in_column). I also wouldn't like to change the dimensions of motion_vectors, since then I would need a two-"layer" array. One for the x coordinates and one for y, but that doesn't fit to the further design.
I hope I made myself understandable, if not, please let me know.
Thanks for any clues!
If you're accessing an element of motion_vectors, you're getting data about a corresponding block. That means that there's a system of translating between an index 1 through N, where N is blocks_in_row*blocks_in_column, and a specific block. If index 1 is the top-left block, index 2 is the block to its right, and you increment as reading a book (left-to-right and wrap to the next row), then you would translate as follows:
row_of_block = floor((index_in_motion_vector-1)/number_of_columns) + 1
col_of_block = mod((index_in_motion_vector-1), number_of_columns) + 1
(This is called row-major ordering.)
If instead index 1 is the top-left block and index 2 is the block below it, and you wrap to the top of the next column when done with one, then the conversion would be
row_of_block = mod((index_in_motion_vector-1), number_of_rows) + 1
col_of_block = floor((index_in_motion_vector-1)/number_of_rows) + 1
(This is called column-major ordering, and is what MATLAB uses by default.)
So, if you're iterating 1 to N, you can just use those conversions. If you'd like to iterate 1 through number_of_rows, and 1 through number_of_columns you would do the opposite.
If you're using the book-like indexing of blocks (row-major ordering), the conversion to index of the motion vector would be
col_in_motion_vector = (row_of_block-1)*number_of_columns + column_of_block
If you're using the second, top-to-bottom-and-wrap method of indexing blocks (column-major ordering), the conversion would instead be
col_in_motion_vector = (column_of_block-1)*number_of_rows + row_of_block
I have a small MATLAB script (included below) for handling data read from a CSV file with two columns and hundreds of thousands of rows. Each entry is a natural number, with zeros only occurring in the second column. This code is taking a truly incredible amount of time (hours) to run what should be achievable in at most some seconds. The profiler identifies that approximately 100% of the run time is spent writing a matrix of zeros, whose size varies depending on input, but in all usage is smaller than 1000x1000.
The code is as follows
function [data] = DataHandler(D)
n = size(D,1);
s = max(D,1);
data = zeros(s,s);
for i = 1:n
data(D(i,1),D(i,2)+1) = data(D(i,1),D(i,2)+1) + 1;
end
It's the data = zeros(s,s); line that takes around 100% of the runtime. I can make the code run quickly by just changing out the s's in this line for 1000, which is a sufficient upper bound to ensure it won't run into errors for any of the data I'm looking at.
Obviously there're better ways to do this, but being that I just bashed the code together to quickly format some data I wasn't too concerned. As I said, I fixed it by just replacing s with 1000 for my purposes, but I'm perplexed as to why writing that matrix would bog MATLAB down for several hours. New code runs instantaneously.
I'd be very interested if anyone has seen this kind of behaviour before, or knows why this would be happening. Its a little disconcerting, and it would be good to be able to be confident that I can initialize matrices freely without killing MATLAB.
Your call to zeros is incorrect. Looking at your code, D looks like a D x 2 array. However, your call of s = max(D,1) would actually generate another D x 2 array. By consulting the documentation for max, this is what happens when you call max in the way you used:
C = max(A,B) returns an array the same size as A and B with the largest elements taken from A or B. Either the dimensions of A and B are the same, or one can be a scalar.
Therefore, because you used max(D,1), you are essentially comparing every value in D with the value of 1, so what you're actually getting is just a copy of D in the end. Using this as input into zeros has rather undefined behaviour. What will actually happen is that for each row of s, it will allocate a temporary zeros matrix of that size and toss the temporary result. Only the dimensions of the last row of s is what is recorded. Because you have a very large matrix D, this is probably why the profiler hangs here at 100% utilization. Therefore, each parameter to zeros must be scalar, yet your call to produce s would produce a matrix.
What I believe you intended should have been:
s = max(D(:));
This finds the overall maximum of the matrix D by unrolling D into a single vector and finding the overall maximum. If you do this, your code should run faster.
As a side note, this post may interest you:
Faster way to initialize arrays via empty matrix multiplication? (Matlab)
It was shown in this post that doing zeros(n,n) is in fact slow and there are several neat tricks to initializing an array of zeros. One way is to accomplish this by empty matrix multiplication:
data = zeros(n,0)*zeros(0,n);
One of my personal favourites is that if you assume that data was not declared / initialized, you can do:
data(n,n) = 0;
If I can also comment, that for loop is quite inefficient. What you are doing is calculating a 2D histogram / accumulation of data. You can replace that for loop with a more efficient accumarray call. This also avoids allocating an array of zeros and accumarray will do that under the hood for you.
As such, your code would basically become this:
function [data] = DataHandler(D)
data = accumarray([D(:,1) D(:,2)+1], 1);
accumarray in this case will take all pairs of row and column coordinates, stored in D(i,1) and D(i,2) + 1 for i = 1, 2, ..., size(D,1) and place all that match the same row and column coordinates into a separate 2D bin, we then add up all of the occurrences and the output at this 2D bin gives you the total tally of how many values at this 2D bin which corresponds to the row and column coordinate of interest mapped to this location.
I'm working with matrices in Matlab which have five columns and several million rows. I'm interested in picking particular groups of this data. Currently I'm doing this using plot3() and the brush/select data tool.
I plot the first three columns of the matrix as X,Y, Z and highlight the matrix region I'm interested in. I then use the brush/select tool's "Create variable" tool to export that region as a new matrix.
The problem is that when I do that, the remaining two columns of the original, bigger matrix are dropped. I understand why- they weren't plotted and hence the figure tool doesn't know about them. I need all five columns of that subregion though in order to continue the processing pipeline.
I'm adding the appropriate 4th and 5th column values to the exported matrix using a horrible nested if loop approach- if columns 1, 2 and 3 match in both the original and exported matrix, attach columns 4/5 of the original matrix to the exported one. It's bad design and agonizingly slow. I know there has to be a Matlab function/trick for this- can anyone help?
Thanks!
This might help:
1. I start with matrix 1 with columns X,Y,Z,A,B
2. Using the brush/select tool, I create a new (subregion) matrix 2 with columns X,Y,Z
3. I then loop through all members of matrix 2 against all members of matrix 1. If X,Y,Z match for a pair of rows, I append A and B
from that row in matrix 1 to the appropriate row in matrix 2.
4. I become very sad as this takes forever and shows my ignorance of Matlab.
If I understand your situation correctly here is a simple way to do it:
Assuming you have a matrix like so: M = [A B C D E] where each letter is a Nx1 vector.
You select a range, this part is not really clear to me, but suppose you can create the following:
idxA,idxB and idxC, that are 1 if they are in the region and 0 otherwise.
Then you can simply use:
M(idxA&idxB&idxC,:)
and you will get the additional two columns as well.
I would like to use a for loop within a for loop (I think) to produce a number of vectors which I can use separately to use polyfit with.
I have a 768x768 matrix and I have split this into 768 separate cell vectors. However I want to split each 1x768 matrix into sections of 16 points - i.e. 48 new vectors which are 16 values in length. I want then to do some curve fitting with this information.
I want to name each of the 48 vectors something different however I want to do this for each of the 768 columns. I can easily do this for either separately but I was hoping that there was a way to combine them. I tried to do this as a for statement within a for statement however it doesn't work, I wondered if anyone could give me some hints on how to produce what I want. I have attached the code.
Qne is my 768*768 matrix with all the points.
N1=768;
x=cell(N,1);
for ii=1:N1;
x{ii}=Qnew(1:N1,ii);
end
for iii = 1:768;
x2{iii}=x{iii};
for iv = 1:39
N2=20;
x3{iii}=x2{iii}(1,(1+N2*iv:N2+N2*iv));
%Gx{iv}=(x3{iv});
end
end
Use a normal 2D matrix for your inner split. Why? It's easy to reshape, and many of the fitting operations you'll likely use will operate on columns of a matrix already.
for ii=1:N1
x{ii} = reshape(Qnew(:, ii), 16, 48);
end
Now x{ii} is a 2D matrix, size 16x48. If you want to address the jj'th split window separately, you can say x{ii}(:, jj). But often you won't have to. If, for example, you want the mean of each window, you can just say mean(x{ii}), which will take the mean of each column, and give you a 48-element row vector back out.
Extra reference for the unasked question: If you ever want overlapping windows of a vector instead of abutting, see buffer in the signal processing toolbox.
Editing my answer:
Going one step further, a 3D matrix is probably the best representation for equal-sized vectors. Remembering that reshape() reads out columnwise, and fills the new matrix columnwise, this can be done with a single reshape:
x = reshape(Qnew, 16, 48, N1);
x is now a 16x48x768 3D array, and the jj'th window of the ii'th vector is now x(:, jj, ii).