collatz_parfor, a MATLAB code using the parfor() statement for parallel execution, to find the longest Collatz sequence in the range 1 through N.
A Collatz sequence starting at the integer I computes the next term by halving the number if it is even, or tripling and adding 1 if it is odd. The sequence stops when the value 1 is reached.
The number of steps required to reach 1 varies greatly. No formula has been determined, and in fact, it hasn't actually been proved that the value of 1 will always be reached.
An interesting question, suitable for parallel execution, is to ask for the length of the longest Collatz sequence between 1 and N.
Depending on the situation, the function could be executed in parallel:
The basic calculation is done by collatz_parfor and has the form:
j_max = collatz_parfor ( n )where
The computer code and data files described and made available on this web page are distributed under the MIT license
collatz_parfor is available in a MATLAB version.
collatz, a MATLAB code which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");
collatz_recursive, a MATLAB code which demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
heated_plate_parfor, a MATLAB code which solves the steady (time independent) heat equation in a 2D rectangular region, using parfor() to run in parallel.
hello_parfor, a MATLAB code which prints out "Hello, world!" multiple times, using parfor() for parallel execution.
high_card_parfor, a MATLAB code which uses the parfor() statement to compute in parallel the statistics for a card game in which you are required to guess the location of the highest card.
matlab_parallel, a MATLAB code which illustrates "local" parallel programming on a single computer with MATLAB's Parallel Computing Toolbox.
matlab_random_parallel, a MATLAB code which uses random number generator (RNG) functions when using parallel features such as parfor or spmd.
matrix_assemble_parfor, a MATLAB code which demonstrates the parfor parallel programming feature by assembling the Hilbert matrix in a parallel loop.
md_parfor, a MATLAB code which carries out a molecular dynamics simulation, running in parallel using the parfor() feature.
ode_sweep_parfor, a MATLAB code which demonstrates how parfor() can be used to parallelize the computation of a grid of solutions to a parameterized system of ODE's.
prime_parfor, a MATLAB code which counts the number of primes between 1 and N; running in parallel using the parfor() feature.
quad_parfor, a MATLAB code which estimates an integral using quadrature; running in parallel using the parfor() feature.
satisfy_parfor, a MATLAB code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, running in parallel using the parfor() feature.
sparse_parfor, a MATLAB code which demonstrates how a sparse matrix can be constructed by evaluating individual blocks in parallel with the parfor() command, and then assembled (on a single processor) using the sparse() command.
trapz_parfor, a MATLAB code which shows how a parfor() loop can be used to call the trapz() function, to compute several integral approximations in parallel.