I have read through a lot of julia-posts, but haven't found anything concerning this very special problem.
We are iterating eigenvalues and corresponding eigenvectors via Power-Iteration.
The algorithm is working and calculating the approximate eigenvalue, but we are asked to save the values of our approximate values after each iteration in a seperate vector.
I tried:
collect(lambda_k)
in a while loop:
l_end = []
push!(l_end,lambda_k)
But it doesn't work, are you able to help me?
Greetings!
Mass_Matics
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I've been staring at the following underlined statement from this book for hours, and I cannot for the life of me figure out how it can be right:
For some definitions:
is an r x r matrix (we may ignore its contents for this purpose).
A is an N x r matrix defined as the following matrix of column vectors, where each vector is N elements long:
First of all I'm convinced that when they write:
they really mean:
otherwise it simply would not make sense from the start. My confusion is when they say is a linear combination of the column vectors of A.
At first I thought maybe it just wasn't obvious to me, so I started doing the calculations as an exercise.
My calculation (please don't make me type all this into a text equation editor):
I THINK my calculation is correct, but there was a lot to keep track of, so...
I did not do the multiplication with because it's trivial, and it doesn't solve the problem.
How can the products of different elements (complex conjugated no less) of the vectors in A end up as a linear combination of the columns of A?
Am I forgetting something fundamental here? Maybe something to do with the fact that is an eigenvector of ...?
I have to solve a problem with permutations. The function takes vector a with n elements as a parameter. I declare b as #variable - there should be the permutation 1:n that gives the best result after finding the solution of a problem.
The error appears when I want to create #constraint. I have to use a[b[1]], so it takes the first element from vector which is a variable. It gives my error, that I can't use type VariableRef as a index of an array. But how can I get around this when I have to use it?
I sounds as if you have two optimisation problems one of which is an integer programming problem. You might think about separating the two.
(Sorry for not writing a comment, my reputation is still too low ;-) )
I scripted a simple for-loop to iterate over each row of a data set to calculate the distance between two coordinates. The code uses the 'geosphere' package and the 'distm' function which takes two sets of coordinates and returns the distance in meters (which I convert to miles by multiplying by 0.00062137).
Here is my loop:
##For loop to find distance in miles for each coordinate pair
miles <- 0
for (i in i:3303) {
miles[i] <- distm(x = c(clean.zips[i,4], clean.zips[i,3]), y = c(clean.zips[i,7], clean.zips[i,6]))[,1] * 0.00062137
}
However, when I run it I receive an error:
Error: object 'i' not found
The thing is, I've run this code before and it worked. Other times, I get this error. I'm not changing any code, it just seems to randomly work only some of the times. I feel the loop must be constructed correctly if it does what I want on occasion, but why would it only work sometimes?
OK, I'm not certain what justifies the down votes on this, but guess I apologize to whomever thought that necessary.
The issue seems to have just been starting the indexing with an actual numeric value like Zheyuan suggested (i.e. using '1:3303' rather than 'i:3303'). I feel like I've created loops before using 'i in i:xxx' without first defining 'i' but maybe not. Anyway, it's solved and thank you!
I am trying to find an efficient way to create a new array by repeating each element of an old array a different, specified number of times. I have come up with something that works, using array comprehensions, but it is not very efficient, either in memory or in computation:
LENGTH = 1e6
A = collect(1:LENGTH) ## arbitrary values that will be repeated specified numbers of times
NumRepeats = [rand(20:100) for idx = 1:LENGTH] ## arbitrary numbers of times to repeat each value in A
B = vcat([ [A[idx] for n = 1:NumRepeats[idx]] for idx = 1:length(A) ]...)
Ideally, what I would like would be a structure akin to the sparse matrix apparatus that Julia has but that would instead store data efficiently based on the indices where repeated values occur. Barring that, I would at least like an efficient way to create a vector such as B in the example above. I looked into the repeat() function, but as far as I can tell from the documentation and my experimentation with the function, it is just for repeating slices of an array the same number of times for each slice. What is the best way to approach this?
Sounds like you're looking for run-length encoding. There's an RLEVectors.jl package here: https://github.com/phaverty/RLEVectors.jl. Not sure how usable it is. You could also make your own data type fairly easily.
Thanks for trying RLEVectors.jl. Some features and optimizations had been languishing on master without a version bump. It can definitely be mixed with other vectors for element-wise arithmetic. I'll put the linear algebra operations on the feature request list. Any additional feature suggestions would be most welcome.
RLEVectors.jl has a rep function that works like R's and RLEVectors.inverse_ree is like StatsBase.inverse_rle, but it works on run ends rather than lengths.
I have a large sparse matrix, and I want to permute its rows or columns to turn the original matrix into a block diagonal matrix. Anyone knows which functions in R or MATLAB can do this? Thanks a lot.
I'm not really set up to test this, but for a matrix m I would try:
p = symrcm(m);
block_m = m(p,p);
If that doesn't work, look through the other functions listed in help sparfun to see if any will help you out.
The seriation package in R has a number of tools for problems related to this one.
Not exactly sure if this is what you want, but in MATLAB this is what I have used in the past. Probably not the most elegant solution.
I go from sparse to full and then chop the thing into square blocks.
A=full(A);
Then:
blockedmatrix = mat2cell(A, (n*ones(1,size(A,1)/n)), ...
(n*ones(1,size(A,1)/n))); %found somewhere on internetz
This returns a cell, where each entry is of size nxn.
It's easy to extract the blocks of interest, manipulate them, and then restore them to a matrix with cell2mat.
Maybe a bit late to the game, but since there are available commands, here is a simple one. If you have a matrix H and the block diagonal form is needed, you can obtain it through the following lines (MATLAB):
[p,q] = dmperm(H);
H(p,q)
which is equivalent to Dulmage - Mendelsohn permutation.