I need to write a Perl routine that will generate the n choose k combinations of a given set. I don't need to count how many sets there are, I have to be able to print them out. I'm pretty stumped.
Any advice is appreciated.
Regards.
There's a module called Math::Combinatorics that produces combinations (nCr), permutations (nPr), and derangements of any set of things that you provide to it.
If you want combinations without repetition, you can generate all binary numbers to length k, select those that have n 1's and apply them to the set in a fixed order: 0 means not selected, 1 means selected. To get a binary number, use sprintf '%05b'; to count 1's use tr/1//.
Related
I am working on a code in Least Square Non Negative solution recovery context on Matlab, and I need (with no more details because it's not that important for this question) to know the number of non zero elements in my matrices and arrays.
The function NNZ on matlab does exactly what I want, but it happens that I need more information about what Matlab thinks of a "zero element", it could be 0 itself, or the numerical zero like 1e-16 or less.
Does anybody has this information about the NNZ function, cause I couldn't get the original script
Thanks.
PS : I am not an expert on Matlab, so accept my apologies if it's a really simple task.
I tried "open nnz", on Matlab but I only get a small script of commented code lines...
Since nnz counts everything that isn't an exact zero (i.e. 1e-100 is non-zero), you just have to apply a relational operator to your data first to find how many values exceed some tolerance around zero. For a matrix A:
n = nnz(abs(A) > 1e-16);
Also, this discussion of floating-point comparison might be of interest to you.
You can add in a tolerance by doing something like:
nnz(abs(myarray)>tol);
This will create a binary array that is 1 when abs(myarray)>tol and 0 otherwise and then count the number of non-zero entries.
How could I correlate the first (also second and third, etc) line of each function together? I meant I want to pick up the value of the first line of function 1, first line of function 2 and so on... Specially number of these lines (between two #...#) are not always equal.
Let's say the values between (# -#) is one matrix. I see that the problem is I need to break them down into different matrix and then equalize all these matrix to the same size by adding NaN values and then reconstruct them again. That is what I think but I dont know how to ask Matlab do these tasks.
Would you please give me a help?
Thank you very much !!
I need to generate m unique random numbers in range 1 to n. Currently what I have implemented is:
round(rand(1,m)*(n-1)+1)
However, some numbers are repeated in the array. How can I get only unique numbers?
You can use randperm.
From the description:
p = randperm(n,k) returns a row vector containing k unique integers
selected randomly from 1 to n inclusive.
Thus, randperm(6,3)
might be the vector
[4 2 5]
Update
The two argument version of randperm only appeared in R2011b, so if you are using an earlier version of MATLAB then you will see that error. In this case, use:
A = randperm(n);
A = A(1:m);
As pointed out above, in Matlab versions older than R2011b randperm only accepts one input argument. In that case the easiest approach, assuming you have the Statistics Toolbx, is to use randsample:
randsample(n,m)
The randperm approach described by #Stewie appears to be the way to go in most cases. However if you can only use Matlab with 1 input argument and n is really large, it may not be feasible to use randperm on all numbers and select the first few. In this case here is what you can do:
Generate an integer between 1 and n
Generate an integer between 1 and n-1, this is the choice out of the available integers.
Repeat until you have m numbers
This can be done with randi and could even be vectorized by just drawing a lot of random numbers at each step until the unique amount is correct.
Use Shuffle, from the MATLAB File Exchange.
Index = Shuffle(n, 'index', m);
This can be done by sorting a random vector of floats:
[i,i]=sort(rand(1,range));
output=i(1:m);
I would like to be able to load long list of positive integer ranges and create a new "summary" range list that is the union of the intersections of each pairs of ranges. And, I want to do this in Perl. For example:
Sample ranges: (1..30) (45..90) (15..34) (92..100)
Intersection of ranges: (15..30)
The only way I could think of was using a bunch of nested if statements to determine the starting point of sample A, sample B, sample C, etc. and figure out the overlap this way, but it's not possible to do that with hundreds of sample, each containing numerous ranges.
Any suggestions are appreciated!
The first thing you should do when you need to do some thing is take a look at CPAN to see what tools are available of if someone has solved your problem for you already.
Set::IntSpan and Set::IntRange are on the first page of results for "set" on CPAN.
What you want is the union of the intersection of each pair of ranges, so the algorithm is as follows:
Create an empty result set.
Create a set for each range.
For each set in the list,
For each later set in the list,
Find the intersection of those two sets.
Find the union of the result set and this intersection. This is the new result set.
Enumerate the elements of the result set.
I don't have code to share, but I would expand each range into hash, or use a Set module, and then use intersection operations on the sets.
I have created a vector containing zeros and 1's using the following command in a for loop.
G(:,i)=rand(K,1)<rand;
Since this is part of a larger problem at a particular stage I need to count the number of 1's that are present in each column.
I have tried to find the count using a for loop which is very messy and takes too long.
I found that histc can be used for this but I get an error
histc(G(:,1),1)
First input must be non-sparse numeric array.
Is there a better way to do this or am I missing something here ?
If you have a matrix G containing zeroes and ones, and you want to know how many ones are in each column, all you need is SUM:
nZeroes = sum(G);
This will give you a vector containing a total for each column in G.