I have the following code:
A = rand(N1,N2);
b = rand(1,N1);
B = zeros(N1,N2);
for i=1:N1
for j=1:N2
B(i,j) = A(i,j)*b(i);
end
end
The question is how to write it in vector operation form? Something like B(:,:) = A(:,:).*b(:).
Simple use for bsxfun:
B = bsxfun(#times, A, b')
You can also try:
B = A*.(repmat(b,N2,1))';
Here, firstly you produce N2 repeated version of vector b and multiply it with A in an elementwise manner
Related
Aiming at optimizing following nested loop, the problem is how to deal with need for row-wise sum.
for i=1:N
for j=1:N
F(i,i)=(exp(-B(j,j))) * P(i,j)+ F(i,i);
end
end
Specifically, I want to eliminate loops and it looks achievable according to this solution but the problem is how to store changing value of F in each iteration.
I come up with this idea :
for j=1:N
F(:)=(exp(-B(j,j))) * P(:,j)+ F(:);
end
Using this solution, F will be overwritten in every iteration!! Any idea?
I think your code can be simplified to the code like below
F = diag(P*exp(-diag(B)));
Example
N = 3;
B = rand(N,N);
P = rand(N,N);
F = zeros(N);
for i=1:N
for j=1:N
F(i,i)=(exp(-B(j,j))) * P(i,j)+ F(i,i);
end
end
d = isequal(F,diag(P*exp(-diag(B)))); % check if F is identical to diag(P*exp(-diag(B)))
such that
>> d
d = 1 % indicating that they are identical
I have a series of arrays of equal length, and want to make a matrix for each data point of these, and perform some sort of operation such a multiplying the matrices.
a=ones(1,10);
b=3*ones(1,10);
c=zeros(1,10);
for i=1:10
A(i)=[a(i) a(i);
b(i) b(i)];
B(i)=[c(i) c(i)];
C(i)=B(i)*A(i);
end
Is this possible without using cells?
A = zeros(2,2,length(a));
B = zeros(length(a),:);
C = zeros(size(B));
for i=1:10
A(:,:,i)=[a(i) a(i);
b(i) b(i)];
B(i,:)=[c(i) c(i)];
C(i,:)=B(i,:)*A(:,:,i);
end
Note you can make A and B without loops:
aa = permute(A, [3,2,1]);
bb = permute(B, [3,2,1]);
A = [aa,aa;bb,bb];
B = [c.', c.'];
For those super experts out there, I was wondering if you see a quick way to convert the following "for" loop into a one-line vector calculation that is more efficient.
%Define:
%A size (n,1)
%B size (n,m)
%C size (n,1)
B = [2 200; 3 300; 4 400];
C = [1;2;1];
for j=1:n
A(j) = B( j, C(j) );
end
So to be clear, is there any alternative way to express A, as a function of B and C, without having to write a loop?
Yes, there is:
A = B(sub2ind([n,m], (1:n).', C));
It depends on functions A, B, and C, but this might work:
j = 1:n;
A = B(j, C(j));
I have three matrices in Matlab, A which is n x m, B which is p x m and C which is r x n.
Say we initialize some matrices using:
A = rand(3,4);
B = rand(2,3);
C = rand(5,4);
The following two are equivalent:
>> s=0;
>> for i=1:3
for j=1:4
s = s + A(i,j)*B(:,i)*C(:,j)';
end;
end
>> s
s =
2.6823 2.2440 3.5056 2.0856 2.1551
2.0656 1.7310 2.6550 1.5767 1.6457
>> B*A*C'
ans =
2.6823 2.2440 3.5056 2.0856 2.1551
2.0656 1.7310 2.6550 1.5767 1.6457
The latter being much more efficient.
I can't find any efficient version for the following variant of the loop:
s=0;
for i=1:3
for j=1:4
x = A(i,j)*B(:,i)*C(:,j)';
s = s + x/sum(sum(x));
end;
end
Here, the matrices being added are normalized by the sum of their values after each step.
Any ideas how to make this efficient like the matrix multiplication above? I thought maybe accumarray could help, but not sure how.
You can do it efficiently with bsxfun:
aux1 = bsxfun(#times, permute(B,[1 3 2]), permute(C,[3 1 4 2]));
aux2 = sum(sum(aux1,1),2);
s = sum(sum(bsxfun(#rdivide, aux1, aux2),3),4);
Note that, because of the normalization, the result is independent of A, assuming it doesn't contain any zero entries (if it does the result is undefined).
I'm fairly new to MATLAB. Normal matrix multiplication of a M x K matrix by an K x N matrix -- C = A * B -- has c_ij = sum(a_ik * b_kj, k = 1:K). What if I want this to be instead c_ij = sum(op(a_ik, b_kj), k = 1:K) for some simple binary operation op? Is there any nice way to vectorize this in MATLAB (or maybe even a built-in function)?
EDIT: This is currently the best I can do.
% A is M x K, B is K x N
% op is min
C = zeros(M, N);
for i = 1:M:
C(i, :) = sum(bsxfun(#min, A(i, :)', B));
end
Listed in this post is a vectorized approach that persists with bsxfun by using permute to create singleton dimensions as needed by bsxfun to let the singleton-expansion do its work and thus essentially replacing the loop in the original post. Please be reminded that bsxfun is a memory hungry implementation, so expect speedup with it only until it is stretched too far. Here's the final solution code -
op = #min; %// Edit this with your own function/ operation
C = sum(bsxfun(op, permute(A,[1 3 2]),permute(B,[3 2 1])),3)
NB - The above solution was inspired by Removing four nested loops in Matlab.
if the operator can operate element-by-element (like .*):
if(size(A,2)~=size(B,1))
error(blah, blah, blah...);
end
C = zeros(size(A,1),size(B,2));
for i = 1:size(A,1)
for j = 1:size(B,2)
C(i,j) = sum(binaryOp(A(i,:)',B(:,j)));
end
end
You can always write the loops yourself:
A = rand(2,3);
B = rand(3,4);
op = #times; %# use your own function here
C = zeros(size(A,1),size(B,2));
for i=1:size(A,1)
for j=1:size(B,2)
for k=1:size(A,2)
C(i,j) = C(i,j) + op(A(i,k),B(k,j));
end
end
end
isequal(C,A*B)
Depending on your specific needs, you may be able to use bsxfun in 3D to trick the binary operator. See this answer for more infos: https://stackoverflow.com/a/23808285/1121352
Another alternative would be to use cellfun with a custom function:
http://matlabgeeks.com/tips-tutorials/computation-using-cellfun/