I'm a newbie in Matlab and trying get rid of Java/C++ customs.
The question is "how I can get rid of these for loops."
I tried to use nchoosek(n0,2) to get rid of one of the loops but another problem arose.(performance of nchoosek)
<Matlab code>
for j=2:n0
for i=1:j-1
%wij is the number of rows of A that have 1 at both column i and column j
%summing col i and j to find #of common 1's
wij = length(find((A(:,i)+A(:,j))==2));
%store it
W(1,j)=wij;
%testing whether the intersection of any two columns is too large
if wij>= (1+epsilon)*u2;
%create and edge between col i j
end
end
end
</matlab Code>
I assume that A is an array with only 0 and 1.
Then you can create a nCol-by-nCol array B with the "distance" between colums by writing
B = A'*A; %'# B(i,j) = length(find((A(:,i)+A(:,j))==2))
%# threshold
largeIntersection = B >= u2;
%# find i,j of large intersections
[largeIJ(:,1),largeIJ(:,2)] = find(largeIntersection);
%# make sure we only get unique i,j pairs
largeIJ = unique(sort(largeIJ,2),'rows');
Related
I am working in MATLAB with a signal data that consist of consecutive dips as shown below. I am trying to write a code which sorts the contents of each dip into a separate group. How should the general structure of such a code look like?
The following is my data. I am only interested in the portion of the signal that lies below a certain threshold d (the red line):
And here is the desired grouping:
Here is an unsuccessful attempt:
k=0; % Group number
for i = 1 : length(signal)
if signal(i) < d
k=k+1;
while signal(i) < d
NewSignal(i, k) = signal(i);
i = i + 1;
end
end
end
The code above generated 310 groups instead of the desired 12 groups.
Any explanation would be greatly appreciated.
Taking Benl generated data you can do the following:
%generate data
x=1:1000;
y=sin(x/20);
for ii=1:9
y=y+-10*exp(-(x-ii*100).^2./10);
end
y=awgn(y,4);
%set threshold
t=-4;
%threshold data
Y = char(double(y<t) + '0'); %// convert to string of zeros and ones
%search for start and ends
This idea is taken from here
[s, e] = regexp(Y, '1+', 'start', 'end');
%and now plot and see that each pair of starts and end
% represents a group
plot(x,y)
hold on
for k=1:numel(s)
line(s(k)*ones(2,1),ylim,'Color','k','LineStyle','--')
line(e(k)*ones(2,1),ylim,'Color','k','LineStyle','-')
end
hold off
legend('Data','Starts','Ends')
Comments: First of all I choose an arbitrary threshold, it is up to you to find the "best" one in your data. Additionally I didn't group the data explicitly but rather this approach gives you the start and end of each epoch with a dip (you might call it group). So you could say that each index is the grouping index. Finally I did not debug this approach for corner cases, when dips fall on starts and ends...
In MATLAB you cannot change the loop index of a for loop. A for loop:
for i = array
loops over each column of array in turn. In your code, 1 : length(signal) is an array, each of its elements is visited in turn. Inside this loop there is a while loop that increments i. However, when this while loop ends and the next iteration of the for loop runs, i is reset to the next item in the array.
This code therefore needs two while loops:
i = 1; % Index
k = 0; % Group number
while i <= numel(signal)
if signal(i) < d
k = k + 1;
while signal(i) < d
NewSignal(i,k) = signal(i);
i = i + 1;
end
end
i = i + 1;
end
Easy, the function you're looking for is bwlabel, which when combined with logical indexing makes this simple.
To start I made some fake data which resembled your data
x=1:1000;
y=sin(x/20);
for ii=1:9
y=y+-10*exp(-(x-ii*100).^2./10);
end
y=awgn(y,4);
plot(x,y)
Then set your threshold and use 'bwlabel'
d=-4;% set the threshold
groupid=bwlabel(y<d);
bwlabel labels connected groups in a black and white image, what we've effectively done here is make a black and white (logical 0 & 1) 1D image in the logical vector y<d. bwlabel returns the number of the region at the index of the region. We're not interested in the 0 region, so to get the x values or y values of the nth region, simply use x(groupid==n), for example with my test data
x_4=x(groupid==4)
y_4=y(groupid==4)
x_4 = 398 399 400 401 402
y_4 = -5.5601 -7.8280 -9.1965 -7.9083 -5.8751
I have 200 vectors; each one has a length of 10000.
I want to fill a matrix such that each line represents a vector.
If your vectors are already stored in an array then you can use vcat( ) here:
A = [rand(10000)' for idx in 1:200]
B = vcat(A...)
Julia stores matrices in column-major order so you are going to have to adapt a bit to that
If you have 200 vectors of length 100000 you should make first an empty vector, a = [], this will be your matrix
Then you have to vcat the first vector to your empty vector, like so
v = your vectors, however they are defined
a = []
a = vcat(a, v[1])
Then you can iterate through vectors 2:200 by
for i in 2:200
a = hcat(a,v[i])
end
And finally transpose a
a = a'
Alternatively, you could do
a = zeros(200,10000)
for i in 1:length(v)
a[i,:] = v[i]
end
but I suppose that wont be as fast, if performance is at all an issue, because as I said, julia stores in column major order so access will be slower
EDIT from reschu's comment
a = zeros(10000,200)
for i in 1:length(v)
a[:,i] = v[i]
end
a = a'
I am find the rank of binary matrix in GF(2)( Galois Field). The rank function in matlab cannot find it. For example, Given a matrix 400 by 400 as here. If you use the rank function as
rank(A)
ans=357
However, the correct ans. in GF(2) must be 356 by this code
B=gf(A);
rank(B);
ans=356;
But this way spends a lot a time (about 16s). Hence, I used Gaussian elimination to find the rank in GF(2) with small time. But, it does not works well. Sometime, it returns the true value, but sometime it returns wrong. Please see my code and let me know the problem in my code. Note that, it spend very small time compare with above code
function rankA =GaussEliRank(A)
tic
mat = A;
[m n] = size(A); % read the size of the original matrix A
for i = 1 : n
j = find(mat(i:m, i), 1); % finds the FIRST 1 in i-th column starting at i
if isempty(j)
mat = mat( sum(mat,2)>0 ,:);
rankA=rank(mat);
return;
else
j = j + i - 1; % we need to add i-1 since j starts at i
temp = mat(j, :); % swap rows
mat(j, :) = mat(i, :);
mat(i, :) = temp;
% add i-th row to all rows that contain 1 in i-th column
% starting at j+1 - remember up to j are zeros
for k = find(mat( (j+1):m, i ))'
mat(j + k, :) = bitxor(mat(j + k, :), mat(i, :));
end
end
end
%remove all-zero rows if there are some
mat = mat( sum(mat,2)>0 ,:);
if any(sum( mat(:,1:n) ,2)==0) % no solution because matrix A contains
error('No solution.'); % all-zero row, but with nonzero RHS
end
rankA=sum(sum(mat,2)>0);
end
Let use the gfrank function. It is suitable for your matrix.
Use:
gfrank(A)
ans=
356
More detail: How to find the row rank of matrix in Galois fields?
input: C matrix 2xN (2D points)
output: C matrix 2xM (2D points) with equal or less points.
Lets say we have C matrix 2xN that contains several 2D points, and it looks something like that:
What we want is to group "close" points to one point, measured by the average of the other points.
For example, in the second image, every group of blue circle will be one point, the point coordinate will be the average point off all points in the blue circle.
also by saying "close", I mean that: their distance one to each other will be smaller then DELTA (known scalar). So wanted output is:
About running time of the algorithm, I don't have upper-limit request but I call that method several times...
What i have tried:
function C = ReduceClosePoints(C ,l_boundry)
x_size = abs(l_boundry(1,1)-l_boundry(1,2)); %220
DELTA = x_size/10;
T = [];
for i=1:size(C,2)
sum = C(:,i);
n=1;
for j=1:size(C,2)
if i~=j %not in same point
D = DistancePointToPoint(C(:,i),C(:,j));
if D < DELTA
sum = sum + C(:,j);
n=n+1;
end
end
end
sum = sum./n; %new point -> save in T matrix
T = [T sum];
end
C = T;
end
I am using Matlab.
Thank you
The simplest way to remove the duplicates from the output is in the final step, by replacing:
C = T;
with:
C = unique(T', 'rows')';
Note that unique() in matrix context only works row-wise, so we have to transpose twice.
I forgot to remove points that i have tested before.
If that code will be useful to someone use that code:
function C = ReduceClosePoints(C ,l_boundry)
x_size = abs(boundry(1,1)-boundry(1,2)); %220 / 190
DELTA = x_size/10;
i=1;
while i~=size(C,2)+1
sum = C(:,i);
n=1;
j=i;
while j~=size(C,2)+1
if i~=j %not same point
D = DistancePointToPoint(C(:,i),C(:,j));
if D < DELTA
sum = sum + C(:,j);
n=n+1;
C(:,j) = [];
j=j-1;
end
end
j=j+1;
end
C(:,i) = sum./n; %change to new point
i=i+1;
end
end
Statement of Problem:
I have an array M with m rows and n columns. The array M is filled with non-zero elements.
I also have a vector t with n elements, and a vector omega
with m elements.
The elements of t correspond to the columns of matrix M.
The elements of omega correspond to the rows of matrix M.
Goal of Algorithm:
Define chi as the multiplication of vector t and omega. I need to obtain a 1D vector a, where each element of a is a function of chi.
Each element of chi is unique (i.e. every element is different).
Using mathematics notation, this can be expressed as a(chi)
Each element of vector a corresponds to an element or elements of M.
Matlab code:
Here is a code snippet showing how the vectors t and omega are generated. The matrix M is pre-existing.
[m,n] = size(M);
t = linspace(0,5,n);
omega = linspace(0,628,m);
Conceptual Diagram:
This appears to be a type of integration (if this is the right word for it) along constant chi.
Reference:
Link to reference
The algorithm is not explicitly stated in the reference. I only wish that this algorithm was described in a manner reminiscent of computer science textbooks!
Looking at Figure 11.5, the matrix M is Figure 11.5(a). The goal is to find an algorithm to convert Figure 11.5(a) into 11.5(b).
It appears that the algorithm is a type of integration (averaging, perhaps?) along constant chi.
It appears to me that reshape is the matlab function you need to use. As noted in the link:
B = reshape(A,siz) returns an n-dimensional array with the same elements as A, but reshaped to siz, a vector representing the dimensions of the reshaped array.
That is, create a vector siz with the number m*n in it, and say A = reshape(P,siz), where P is the product of vectors t and ω; or perhaps say something like A = reshape(t*ω,[m*n]). (I don't have matlab here, or would run a test to see if I have the product the right way around.) Note, the link does not show an example with one number (instead of several) after the matrix parameter to reshape, but I would expect from the description that A = reshape(t*ω,m*n) might also work.
You should add a pseudocode or a link to the algorithm you want to implement. From what I could understood I have developed the following code anyway:
M = [1 2 3 4; 5 6 7 8; 9 10 11 12]' % easy test M matrix
a = reshape(M, prod(size(M)), 1) % convert M to vector 'a' with reshape command
[m,n] = size(M); % Your sample code
t = linspace(0,5,n); % Your sample code
omega = linspace(0,628,m); % Your sample code
for i=1:length(t)
for j=1:length(omega) % Acces a(chi) in the desired order
chi = length(omega)*(i-1)+j;
t(i) % related t value
omega(j) % related omega value
a(chi) % related a(chi) value
end
end
As you can see, I also think that the reshape() function is the solution to your problems. I hope that this code helps,
The basic idea is to use two separate loops. The outer loop is over the chi variable values, whereas the inner loop is over the i variable values. Referring to the above diagram in the original question, the i variable corresponds to the x-axis (time), and the j variable corresponds to the y-axis (frequency). Assuming that the chi, i, and j variables can take on any real number, bilinear interpolation is then used to find an amplitude corresponding to an element in matrix M. The integration is just an averaging over elements of M.
The following code snippet provides an overview of the basic algorithm to express elements of a matrix as a vector using the spectral collapsing from 2D to 1D. I can't find any reference for this, but it is a solution that works for me.
% Amp = amplitude vector corresponding to Figure 11.5(b) in book reference
% M = matrix corresponding to the absolute value of the complex Gabor transform
% matrix in Figure 11.5(a) in book reference
% Nchi = number of chi in chi vector
% prod = product of timestep and frequency step
% dt = time step
% domega = frequency step
% omega_max = maximum angular frequency
% i = time array element along x-axis
% j = frequency array element along y-axis
% current_i = current time array element in loop
% current_j = current frequency array element in loop
% Nchi = number of chi
% Nivar = number of i variables
% ivar = i variable vector
% calculate for chi = 0, which only occurs when
% t = 0 and omega = 0, at i = 1
av0 = mean( M(1,:) );
av1 = mean( M(2:end,1) );
av2 = mean( [av0 av1] );
Amp(1) = av2;
% av_val holds the sum of all values that have been averaged
av_val_sum = 0;
% loop for rest of chi
for ccnt = 2:Nchi % 2:Nchi
av_val_sum = 0; % reset av_val_sum
current_chi = chi( ccnt ); % current value of chi
% loop over i vector
for icnt = 1:Nivar % 1:Nivar
current_i = ivar( icnt );
current_j = (current_chi / (prod * (current_i - 1))) + 1;
current_t = dt * (current_i - 1);
current_omega = domega * (current_j - 1);
% values out of range
if(current_omega > omega_max)
continue;
end
% use bilinear interpolation to find an amplitude
% at current_t and current_omega from matrix M
% f_x_y is the bilinear interpolated amplitude
% Insert bilinear interpolation code here
% add to running sum
av_val_sum = av_val_sum + f_x_y;
end % icnt loop
% compute the average over all i
av = av_val_sum / Nivar;
% assign the average to Amp
Amp(ccnt) = av;
end % ccnt loop