I have two vectors and , each of them has three coordinates which have sizes 80x80x2000.
I want to calculate the cross product in MATLAB of these two vectors for each time moment. I know that I can extract individually coordinates in nested loops but is it possible to make it avoiding any loops?
here is the sample code with loops
m1x = cat(3, [1 2; 3 4], [5 6; 7 8]);
m1y = cat(3, [9 10; 11 12], [13 14; 15 16]);
m1z = cat(3, [17 18; 19 20], [21 22; 23 24]);
m2x = cat(3, [5 6; 2 6], [1 3; 7 9]);
m2y = cat(3, [6 7; 3 5], [2 11; 2 6]);
m2z = cat(3, [3 9; 0 1], [4 2; 3 15]);
result_x(2,2,2)=0; result_y(2,2,2)=0; result_z(2,2,2)=0;
for t=1:2
for i=1:2
for j=1:2
a = [m1x(i,j,t); m1y(i,j,t); m1z(i,j,t);];
b = [m2x(i,j,t); m2y(i,j,t); m2z(i,j,t);];
c = cross(a,b);
result_x(i,j,t) = c(1);
result_y(i,j,t) = c(2);
result_z(i,j,t) = c(3);
end;
end;
end;
so finally I have three components x,y and z of resulting vector for each moment of time
For example, if you have matrices A and B, such that each one has t (time) rows and 3 columns (x, y, z) or if you can reshape them to arrive at this configuration, you can use:
C=cross(A,B);
and each row t in C will be the cross-product of the corresponding rows in A and B. Example:
>> A=[rand(2000,1),rand(2000,1),rand(2000,1)];
>> B=[rand(2000,1),rand(2000,1),rand(2000,1)];
>> C=cross(A,B);
>> C(1,:)
ans =
0.0090 -0.0435 0.0756
>> cross(A(1,:),B(1,:))
ans =
0.0090 -0.0435 0.0756
Related
I have the following three-dimensional matrix X of size 2*2*3:
X = zeros(2, 2, 3);
X(:,:,1) = [1 2; 3 4];
X(:,:,2) = [5 6; 7 8];
X(:,:,3) = [9 10; 11 12];
I want to automatically reshape X to a two-dimensional matrix of size 6*2 such that I should obtain:
X_reshaped = [1 2; 3 4; 5 6; 7 8; 9 10; 11 12].
In MATLAB, I am trying to write X_reshaped = reshape(X, [size(X,1)*size(X,3), size(X,2)]), but this doesn't give me the desired X_reshaped as above.
Any help will be very appreciated!
Using the permute() function will allow the array to be reshaped so that the elements are stored in pairs along the first dimension. This allows the reshape() function to access those pairs accordingly by default.
X = zeros(2, 2, 3);
X(:,:,1) = [1 2; 3 4];
X(:,:,2) = [5 6; 7 8];
X(:,:,3) = [9 10; 11 12];
reshape(permute(X,[1 3 2]),[6 2])
This problem is a succession of my previous problem:
1) Extract submatrices, 2) vectorize and then 3) put back
Now, I have two patients, named Ann and Ben.
Indeed the matrices A and B are data for Ann and the matrix C is data for Ben:
Now, I need to design a matrix M such that y = M*x where
y = [a11, a21, a12, a22, b11, b21, b12, b22]' which is a vector, resulting from concatenation of the top-left sub-matrices, Ann and Ben;
x = [2, 5, 4, 6, 7, 9, 6, 2, 9, 3, 4, 2]' which is a vector, resulting from concatenation of sub-matrices A, B and C.
Here, the M is a 8 by 12 matrix that
a11 = 2 + 7, a21 = 5 + 9, .., a22 = 6 + 2 and b11 = 9, ..b22 = 2.
I design the M manually by:
M=zeros(8,12)
M(1,1)=1; M(1,5)=1; % compute a11
M(2,2)=1; M(2,6)=1; % compute a21
M(3,3)=1; M(3,7)=1; % compute a12
M(4,4)=1; M(4,8)=1; % compute a22
M(5,9)=1; % for setting b11 = 9, C(1,1)
M(6,10)=1; % for setting b21 = 3, C(2,1)
M(7,11)=1; % for setting b12 = 4, C(1,2)
M(8,12)=1 % for setting b22 = 2, C(2,2)
Obviously, in general for M(i,j), i means the 8 linear-index position of vector y and j means linear-index position of vector x.
However, I largely simplified my original problem that I want to construct this M automatically.
Thanks in advance for giving me a hand.
Here you have my solution. I have essentially build the matrix M automatically (from the proper indexes) as you suggested.
A = [2 4 8;
5 6 3;
10 3 6];
B = [7 6 3;
9 2 9;
10 2 3];
C = [9 4 7;
3 2 5;
10 3 4];
% All matrices in the same array
concat = cat(3, A, B, C);
concat_sub = concat(1:2,1:2,:);
x = concat_sub(:);
n = numel(x)/3; %Number of elements in each subset
M2 = zeros(12,8); %Transpose of the M matrix (it could be implemented directly over M but that was my first approach)
% The indexes you need
idx1 = 1:13:12*n; % Indeces for A
idx2 = 5:13:12*2*n; % Indices for B and C
M2([idx1 idx2]) = 1;
M = M2';
y = M*x
I have taken advantage of the shape that the matrix M shold take:
You can index into things and extract what you want without multiplication. For your example:
A = [2 4 8; 5 6 3; 10 3 6];
B = [7 6 3; 9 2 9; 10 2 3];
C = [9 4 7;3 2 5; 10 3 4];
idx = logical([1 1 0;1 1 0; 0 0 0]);
Ai = A(idx);
Bi = B(idx);
Ci = C(idx);
output = [Ai; Bi; Ci];
y = [Ai + Bi; Ci]; % desired y vector
This shows each step individually but they can be done in 2 lines. Define the index and then apply it.
idx = logical([1 1 0;1 1 0;0 0 0]);
output = [A(idx); B(idx); C(idx)];
y = [Ai + Bi; Ci]; % desired y vector
Also you can use linear indexing with idx = [1 2 4 5]' This will produce the same subvector for each of A B C. Either way works.
idx = [1 2 4 5]';
or alternatively
idx = [1;2;4;5];
output = [A(idx); B(idx); C(idx)];
y = [Ai + Bi; Ci]; % desired y vector
Either way works. Check out doc sub2ind for some examples of indexing from MathWorks.
I have a cell array A of size 10x10 (say). Each cell in turn contains a 5x20 matrix. I want to select (i,j) element from each cell, where (i,j) are indices within a loop. I can run 4 for loops and easily get the answer. It may even be faster as it has been discussed many times that loops could be faster than cellfun, structfun etc.
Still, is there any solution using cellfun which I can use in a loop over (i,j) and extract (i,j) element in each cell? I tried writing a function which will act as handle to cellfun but I couldn't access two-leves down i.e. A{eachCellRow,eachCellCol}(i,j).
Example:
If A={[1 2;5 6], [3 4; 6 7]; [3 4; 6 7], [9 8; 5 6]};
Then for i=1, j=1 and i=2, j=1 output should be:
B=[1 3; 3 9] and B=[5 6; 6 5]
CELL2MAT gets all the data from a cell array that consists of numeric data only, into a numeric array. So, that helped us here. For your original problem, try this -
celldim_i = 10;
celldim_j = 10;
block_size_i = 5;
block_size_j = 20;
search_i = i; %// Edit to your i
search_j = j; %// Edit to your j
A_mat = cell2mat(A);
out = A_mat(search_i+block_size_i*(0:celldim_i-1),search_j+block_size_j*(0:celldim_j-1))
The easy to use cellfun one-liner would be:
ii = 2;
jj = 1;
A = {[1 2;5 6], [3 4; 6 7]; [3 4; 6 7], [9 8; 5 6]};
B = cell2mat( cellfun( #(x) x(ii,jj), A, 'uni', 0) )
gives:
B =
5 6
6 5
Advantage over Divakar's Solution: it works also for inconsistent matrix sizes in A.
And if you want to avoid also the outer loop, another fancy two-liner:
dim = [2 2];
[II, JJ] = meshgrid( 1:dim(1), 1:dim(2) );
C = cellfun( #(y) ...
{ cell2mat( cellfun( #(x) x( real(y), imag(y) ), A, 'uni', 0) ) },...
num2cell( II(:)+1i*JJ(:) ))
gives:
>> celldisp(C)
C{1} = % ii = 1 , jj = 1
1 3
3 9
C{2} = % ii = 1 , jj = 2
2 4
4 8
C{3} = % ii = 2 , jj = 1
5 6
6 5
C{4} = % ii = 2 , jj = 2
6 7
7 6
If memory is not an issue, you can concat all matrices along a third dim; and then indexing is very easy:
%// Example data
A = {[1 2;5 6], [3 4; 6 7]; [3 4; 6 7], [9 8; 5 6]};
ii = 2;
jj = 1;
%// Compute the result B
A2 = cat(3,A{:}); %// concat along third dim
B = reshape(A2(ii,jj,:),size(A{1})); %// index A2 and reshape
I have the following data:
A = [1 2 ; 3 2; 4 7; 10 2; 6 7; 10 9]
B = [1 2 3; 4 4 9; 1 8 0; 3 7 9; 3 6 8]
C = [4; 10; 6; 3; 1]
A =
1 2
3 2
4 7
10 2
6 7
10 9
B =
1 2 3
4 4 9
1 8 0
3 7 9
3 6 8
C.' =
4 10 6 3 1
For each unique value in A(:,2) I need to take the corresponding values in A(:,1),
look for their value in C, then take the relevant rows in B and compute their mean.
The result should be length(unique(A(:,2)) x size(B,2);
The expected result for this example:
Value "2": mean of rows 2, 4 and 5 from B
Explanation: Indices 1, 3 and 10 that correspond to value "2" in A are
at indices 2, 4, 5 in C.
Correspondingly:
Value "7": mean of rows 1 and 3 from B.
Value "9": mean of row 2 from B.
I compute it now by applying unique on A and iterating each value, searching the right indices. My data set is quite large, so it takes quite a time. How can I avoid the loops?
Let's do what you say in the question step by step:
For each unique value in A(:, 2):
[U, ia, iu] = unique(A(:, 2));
Take the corresponding values in A(:, 1) and look for their value in C:
[tf, loc] = ismember(A(:, 1), C);
It's also recommended to make sure, just in case, that all values are actually found in C:
assert(all(tf))
Then take the relevant rows in B and compute their mean:
[X, Y] = meshgrid(1:size(B, 2), iu);
result = accumarray([Y(:), X(:)], reshape(B(loc, :), 1, []), [], #mean);
Hope this helps! :)
Example
%// Sample input
A = [1 2 ; 3 2; 4 7; 10 2; 6 7; 10 9];
B = [1 2 3; 4 4 9; 1 8 0; 3 7 9; 3 6 8];
C = [4; 10; 6; 3; 1];
%// Compute means
[U, ia, iu] = unique(A(:, 2));
[tf, loc] = ismember(A(:, 1), C);
[X, Y] = meshgrid(1:size(B, 2), iu);
result = accumarray([Y(:), X(:)], reshape(B(loc, :), [], 1), [], #mean);
The result is:
result =
3.3333 5.6667 8.6667
1.0000 5.0000 1.5000
4.0000 4.0000 9.0000
Here is another solution without arrayfun and accumarray using good old-fashion matrix multiplication:
r = bsxfun(#eq, A(:,1), C')*(1:numel(C))';
[~,m,n] = unique(A(:,2));
f=histc(n, 1:numel(m));
result = diag(1./f)*bsxfun(#eq, 1:numel(m), n).'*B(r,:);
I ran a benchmark against other two solutions and it appears to be faster than both. For 1000 repetitions:
This method takes 0.205650 seconds.
Eitan T's solution takes 0.546976 seconds.
matlabit's solution takes 1.619039 seconds.
Here is the benchmark code:
N = 1e3;
tic
for k=1:N,
r = bsxfun(#eq, A(:,1), C')*(1:numel(C))'; % faster than [~,r] = ismember(A(:,1), C)
[~,m,n] = unique(A(:,2));
f=histc(n, 1:numel(m));
result2 = diag(1./f)*bsxfun(#eq, 1:numel(m), n).'*B(r,:);
end
toc
tic
for k=1:N,
[U, ia, iu] = unique(A(:, 2));
[tf, loc] = ismember(A(:, 1), C);
[X, Y] = meshgrid(1:size(B, 2), iu);
result1 = accumarray([Y(:), X(:)], reshape(B(loc, :), [], 1), [], #mean);
end
toc
tic
for k=1:N,
D = [arrayfun(#(x) find(C == x,1,'first'), A(:,1) ), A(:,2)];
data = [B(D(:,1),:), D(:,2)];
st = grpstats(data(:,1:3),data(:,4:4),{'mean'});
end
toc
Thanks,
I also thought of:
D = [arrayfun(#(x) find(C == x,1,'first'), A(:,1) ), A(:,2)];
data = [B(D(:,1),:), D(:,2)];
st = grpstats(data(:,1:3),data(:,4:4),{'mean'});
A = [1 3 5 8]
B = [1 2 3 4 5 6 7 8]
I would like to create a vector C which returns the rownumber of the element in vector A with the smallest non-negative difference to each element in vector B.
So, given the example above, it should return:
C = [1 2 2 3 3 4 4 4]
I'm sure there are many ways to do this. Here's one:
A = [1 3 5 8]
B = [1 2 3 4 5 6 7 8]
%create matrices of the values to subtract
[a,b] = meshgrid(A,B);
%subtract
aLessB = a-b;
%make sure we don't use the negative values
aLessB(aLessB < 0) = Inf;
%sort the subtracted matrix
[dum, idx] = sort(aLessB, 2, 'ascend');
idx(:,1) is the solution you are looking for.
An alternative solution:
D = bsxfun(#minus, A', B);
D(D < 0) = Inf;
[~, C] = min(D, [], 1);