Assume I have a 50x1 cell(say Q) with column matrices of varying dimensions (say 1568936x1 , 88x1,5040x1 ) etc
losing values isn't an issue. I need all the matrices inside the cell to be divisible by said number (say 500) so like 1568500x1 , 5000x1 skipping over 88x1 etc.
Currently I have:
z=cell(length(Q),1)
for p=1:length(z)
n=length(Q{p})
for w=1:length(z)
if n-mod(length(Q{w}),500)<500
w=w+1;
else
o=length(Q{w}-mod(length(Q{w}),500));
for k=1:length(z)
z=Q{w}((1:o));
end
end
end
end
but when I reach the 88x1 matrix it throws a dimensions exceeded error although I think I have covered that with the if condition where it should skip the matrix and move on to the next cell.
This should work fine:
Q = {
rand(58,1);
rand(168,1);
rand(33,1);
rand(199,1);
rand(100,1)
};
Q_len = numel(Q);
K = 50;
Z = cell(Q_len,1);
for i = 1:Q_len
Qi = Q{i};
Qi_len = numel(Qi);
k = floor(Qi_len / K) * K
Z{i} = Qi(1:k);
end
Given the starting vectors (shortened down in order to avoid excessive overloads), the final output Z is:
>> cellfun(#numel,Z)
ans =
50
150
0
150
100
If you want a shorter, one-liner version, here is one:
Q = {
rand(58,1);
rand(168,1);
rand(33,1);
rand(199,1);
rand(100,1)
};
K = 50;
Z = cellfun(#(x)x(1:(floor(numel(x)/K)*K)),Q,'UniformOutput',false);
Related
I am working on MatLab problems from my textbook and one of the problems (as an example of Neumann series iteration) asks me to follow the pseudocode below:
INPUT: A n x n matrix, b n x 1 vector, T a positive integer
OUTPUT: An approximation y of x after T iterations
STEP 1: Set y = zeros(n,1)
STEP 2: Set M = eye(n) - A
STEP 2: For i = 1,2,...,T do STEP 3
STEP 3: Set y = M*y + b
STEP 4: OUTPUT(y)
I am trying to find the smallest value of T such that the largest entry of the vector Ay - b in absolute value is less than the tolerance I set (the variable e as shown below). I then save T and E (the largest entry in absolute value of Ay - b).
function [T,E] = neumann(A,b,e)
n = size(A);
y = zeros(n(1,1),1);
M = eye(n(1,1)) - A;
t = 10000;
for ii = 1:t
y = M*y + b;
if max(abs(A*y - b)) < e
T = t;
E = max(abs(A*y - b));
break
end
end
end
A = [1.1,.2,-.2,.5;
.2,.9,.5,.3;
.1,0.,1.,.4;
.1,.1,.1,1.2];
b = [1;0;1;0];
[T_2, E_2] = neumann(A,b,1e-2);
[T_4, E_4] = neumann(A,b,1e-4);
[T_6, E_6] = neumann(A,b,1e-6);
output = [T_2, E_2; T_4, E_4; T_6, E_6];
Instead of getting the smallest possible T, the for loop goes through all of the iterations even though I used the break statement to end the loop's execution once the condition was met. I can't really figure out what's wrong with my loop. I followed the pseudocode as closely as possible. Any feedback or suggestions is appreciated, thank you in advance.
You always set T = t, you've perhaps forgotten what t is.
You define t = 10000 on line 5 of the neumann function, this doesn't change so your output T is always 10000.
Instead, I assume you wanted T = ii;, as ii is the current time step when the threshold is reached.
I have some MatLab function which calculates a Wavelet Bispectrum. In this a matrix is initialised and values (complex) are put in it after they are calculated in nested for loops. However when I time the the entire function I see a third of the time (~1000s) is spent adding these values to the matrix.
The Matrix size is (1025 x 1025) and so about 1million values are input. If I generate random numbers and put them in a matrix in a similar way it takes less than I second. So why is it taking up so much time in my code?
Anyone able to help me out?
I've included a sample of the code. It is putting the million or so values into the Bisp Matrix that takes over 1000s. WT is a matrix containing complex values and freq is a vector containing all the values that match the 1st dimension of the WT matrix.
`
nfreq = 1025;
Bisp = nan(nfreq, nfreq);
Norm = nan(nfreq, nfreq);
for j = 1 : nfreq
for k = 1 : nfreq
f3 = freq(j) + freq(k);
if f3 <= freq(end)
idx3 = find(freq <= f3);
idx3 = idx3(end);
x = (WT(j, :) .* WT(k, :)) .* conj(WT(indx3, :));
bb = nansum(x);
norm1 = nansum(abs(WT(j, :) .* WT(k, :)).^2);
norm2 = nansum(abs(WT(idx3, :).^2));
a = sqrt(norm1 * norm2);
Norm(j, k) = a;
Bisp(j, k) = bb; **This takes about 1000seconds**
end
end
end
`
I have a .csv file with data on each line in the format (x,y,z,t,f), where f is the value of some function at location (x,y,z) at time t. So each new line in the .csv gives a new set of coordinates (x,y,z,t), with accompanying value f. The .csv is not sorted.
I want to use imagesc to create a video of this data in the xy-plane, as time progresses. The way I've done this is by reformatting M into something more easily usable by imagesc. I'm doing three nested loops, roughly like this
M = csvread('file.csv');
uniqueX = unique(M(:,1));
uniqueY = unique(M(:,2));
uniqueT = unique(M(:,4));
M_reformatted = zeros(length(uniqueX), length(uniqueY), length(uniqueT));
for i = 1:length(uniqueX)
for j = 1:length(uniqueY)
for k = 1:length(uniqueT)
M_reformatted(i,j,k) = M( ...
M(:,1)==uniqueX(i) & ...
M(:,2)==uniqueY(j) & ...
M(:,4)==uniqueT(k), ...
5 ...
);
end
end
end
once I have M_reformatted, I can loop through timesteps k and use imagesc on M_reformatted(:,:,k). But doing the above nested loops is very slow. Is it possible to vectorize the above? If so, an outline of the approach would be very helpful.
edit: as noted in answers/comments below, I made a mistake in that there are several possible z-values, which I haven't taken into account. If only a single z-value, the above would be ok.
This vectorized solution allows for negative values of x and y and is many times faster than the non-vectorized solution (close to 20x times for the test case at the bottom).
The idea is to sort the x, y, and t values in lexicographical order using sortrows and then using reshape to build the time slices of M_reformatted.
The code:
idx = find(M(:,3)==0); %// find rows where z==0
M2 = M(idx,:); %// M2 has only the rows where z==0
M2(:,3) = []; %// delete z coordinate in M2
M2(:,[1 2 3]) = M2(:,[3 1 2]); %// change from (x,y,t,f) to (t,x,y,f)
M2 = sortrows(M2); %// sort rows by t, then x, then y
numT = numel(unique(M2(:,1))); %// number of unique t values
numX = numel(unique(M2(:,2))); %// number of unique x values
numY = numel(unique(M2(:,3))); %// number of unique y values
%// fill the time slice matrix with data
M_reformatted = reshape(M2(:,4), numY, numX, numT);
Note: I am assuming y refers to the columns of the image and x refers to the rows. If you want these flipped, use M_reformatted = permute(M_reformatted,[2 1 3]) at the end of the code.
The test case I used for M (to compare the result to other solutions) has a NxNxN space with T times slices:
N = 10;
T = 10;
[x,y,z] = meshgrid(-N:N,-N:N,-N:N);
numPoints = numel(x);
x=x(:); y=y(:); z=z(:);
s = repmat([x,y,z],T,1);
t = repmat(1:T,numPoints,1);
M = [s, t(:), rand(numPoints*T,1)];
M = M( randperm(size(M,1)), : );
I don't think you need to vectorize. I think you change your algorithm.
You only need one loop to step through the lines of the CSV file. For every line, you have (x,y,z,t,f) so just store it in M_reformatted where it belongs. Something like this:
M_reformatted = zeros(max(M(:,1)), max(M(:,2)), max(M(:,4)));
for line = 1:size(M,2)
z = M(line, 3);
if z ~= 0, continue; end;
x = M(line, 1);
y = M(line, 2);
t = M(line, 4);
f = M(line, 5);
M_reformatted(x, y, t) = f;
end
Also note that pre-allocating M_reformatted is a very good idea, but your code may have been getting the size wrong (depending on the data). I think using max like I did will always do the right thing.
I want to take weighted sum of two matrices in GPUarray to be fast. for example my code on cpu is given below:
mat1 = rand(19,19);
mat2= rand(19,19);
Receptive_fieldsize = [4,3];
overlap = 1;
Output = GetweightedSum(mat1,mat2, Receptive_fieldsize,overlap); %this will output in an 6x6 matrix
where as my function body is:
function Output = GetweightedSum(mat1,mat2, RF,overlap)
gap = RF(1) - overlap;
size_mat = size(mat1);
output_size=[6,6];
for u=1: output_size(1)
for v=1: output_size(2)
min_u = (u - 1) * gap + 1;
max_u = (u - 1) * gap + RF(1);
min_v = (v - 1) * gap + 1;
max_v = (v - 1) * gap + RF(2);
input1 = mat1(min_u:max_u,min_v:max_v);
input2 = mat2(min_u:max_u,min_v:max_v);
Output(u,v) = sum(sum(input1 .*input2));
end
end
How can i convert it to GPUfunciton. Can i do it directly, OR can i use for loop in GPU code. I am totally new to GPU so don't know anything about it.
Will be thankful if some one guid me, or change the above code as reference to GPU function so that i may learn from it.
Regards
See if the codes and the comments alongside them make sense to you -
function Output = GetweightedSumGPU(mat1,mat2, RF,overlap)
%// Create parameters
gap = RF(1) - overlap;
output_size=[6,6];
sz1 = output_size(1);
sz2 = output_size(2);
nrows = size(mat1,1); %// get number of rows in mat1
%// Copy data to GPU
gmat1 = gpuArray(mat1);
gmat2 = gpuArray(mat2);
start_row_ind = gpuArray([1:RF(1)]'); %//' starting row indices for each block
col_offset = gpuArray([0:RF(2)-1]*nrows); %// column offset for each block
%// Linear indices for each block
ind = bsxfun(#plus,start_row_ind,col_offset);
%// Linear indices along rows and columns respectively
ind_rows = bsxfun(#plus,ind(:),[0:sz1-1]*gap);
ind_rows_cols = bsxfun(#plus,ind_rows,permute([0:sz2-1]*gap*nrows,[1 3 2]));
%// Elementwise multiplication, summing and gathering back result to CPU
Output = gather(reshape(sum(gmat1(ind_rows_cols).*gmat2(ind_rows_cols),1),sz1,sz2));
return;
I need to filter an image using a bank of filters in Matlab. My first attempt was to use a simple for loop to repeatedly call the "imfilter" function for each filter in the bank.
I will need to repeat this process many times for my application, so I need to this step to be as efficient as possible. Therefore, I was wondering if there was any way this operation could be vectorized to speed up the process. In an effort to simplify things, all of my filter kernels are the same size (9x9).
As an example of what I am going for, my filters are set up in a 9x9x32 element block, which needs to be applied to my image. I thought about replicating the image into a block (e.g. 100x100x32), but I'm not sure if there's a way to apply an operation like convolution without resorting to loops. Does anyone have suggestions for a good way of tackling this problem?
Other than pre allocating the space, there is not a faster way to arrive at an exact solution. If approximations are ok, then you might be able to decompose the 32 filters into a set of linear combinations of a smaller number of filters, say eight. See for instance Steerable filters.
http://people.csail.mit.edu/billf/papers/steerpaper91FreemanAdelson.pdf
edit: here is a tool to help apply filters to images.
function FiltIm = ApplyFilterBank(im,filters)
%#function FiltIm = ApplyFilterBank(im,filters)
%#
%#assume im is a single layer image, and filters is a cell array
nFilt = length(filters);
maxsz = 0;
for i = 1:nFilt
maxsz = max(maxsz,max(size(filters{i})));
end
FiltIm = zeros(size(im,1), size(im,2), nFilt);
im = padimage(im,maxsz,'symmetric');
for i = 1:nFilt
FiltIm(:,:,i) = unpadimage(imfilter(im,filters{i}),maxsz);
end
function o = padimage(i,amnt,method)
%#function o = padimage(i,amnt,method)
%#
%#padarray which operates on only the first 2 dimensions of a 3 dimensional
%#image. (of arbitrary number of layers);
%#
%#String values for METHOD
%# 'circular' Pads with circular repetion of elements.
%# 'replicate' Repeats border elements of A.
%# 'symmetric' Pads array with mirror reflections of itself.
%#
%#if(amnt) is length 1, then pad all sides same amount
%#
%#if(amnt) is length 2, then pad y direction amnt(1), and x direction amnt(2)
%#
%#if(amnt) is length 4, then pad sides unequally with order LTRB, left top right bottom
if(nargin < 3)
method = 'replicate';
end
if(length(amnt) == 1)
o = zeros(size(i,1) + 2 * amnt, size(i,2) + 2* amnt, size(i,3));
for n = 1:size(i,3)
o(:,:,n) = padarray(i(:,:,n),[amnt,amnt],method,'both');
end
end
if(length(amnt) == 2)
o = zeros(size(i,1) + 2 * amnt(1), size(i,2) + 2* amnt(2), size(i,3));
for n = 1:size(i,3)
o(:,:,n) = padarray(i(:,:,n),amnt,method,'both');
end
end
if(length(amnt) == 4)
o = zeros(size(i,1) + amnt(2) + amnt(4), size(i,2) + amnt(1) + amnt(3), size(i,3));
for n = 1:size(i,3)
o(:,:,n) = padarray(padarray(i(:,:,n),[amnt(2), amnt(1)],method,'pre'),[amnt(4), amnt(3)],method,'post');
end
end
function o = unpadimage(i,amnt)
%#un does padimage
%#if length(amnt == 1), unpad equal on each side
%#if length(amnt == 2), first amnt is left right, second up down
%#if length(amnt == 4), then [left top right bottom];
switch(length(amnt))
case 1
sx = size(i,2) - 2 * amnt;
sy = size(i,1) - 2 * amnt;
l = amnt + 1;
r = size(i,2) - amnt;
t = amnt + 1;
b = size(i,1) - amnt;
case 2
sx = size(i,2) - 2 * amnt(1);
sy = size(i,1) - 2 * amnt(2);
l = amnt(1) + 1;
r = size(i,2) - amnt(1);
t = amnt(2) + 1;
b = size(i,1) - amnt(2);
case 4
sx = size(i,2) - (amnt(1) + amnt(3));
sy = size(i,1) - (amnt(2) + amnt(4));
l = amnt(1) + 1;
r = size(i,2) - amnt(3);
t = amnt(2) + 1;
b = size(i,1) - amnt(4);
otherwise
error('illegal unpad amount\n');
end
if(any([sx,sy] < 1))
fprintf('unpadimage newsize < 0, returning []\n');
o = [];
return;
end
o = zeros(sy, sx, size(i,3));
for n = 1:size(i,3)
o(:,:,n) = i(t:b,l:r,n);
end
New Answer: Use colfilt() or block filtering style. Matlab can transform your image into large matrix where each distinct 9x9 pixel area is a single column (81 elements). Make it using im2col() method. If your image is N by M the result matrix would be 81 X (N-8)*(M-8).
Then you can concatenate all your filters to single matrix (each filter is a row) and multiply those huge matrices. This will give you the result of all filters. Now you have to reconstruct back 32 result images from the result matrix. use col2im() method.
For more information type 'doc colfilt'
This method works almost as fast as mex file and doesnt require any 'for' loop
Old answer:
Do you want to get different 32 results or single result for combination of filters?
If it is a sungle result than there is an easy way.
If you use linear filters (like convolutions) then apply filters one on another. Finally apply the resulting filter on the image. Thus image will be convolved only once.
If you filters are symmetric (x and y direction) then instead of applying the 9x9 filter apply 9x1 on y direction and 1x9 on x direction. Works a bit faster.
Finally, you can try using Mex file