random_mpi, a FORTRAN90 code which demonstrates one way to generate the same sequence of random numbers for both sequential execution and parallel execution under MPI.
A simpler approach to random numbers would simply let each processor choose a seed. Or the master processor could choose distinct seeds. However, this is not ideal since it will not match the sequential program and it does not avoid the possibility that two of the random sequences will quickly overlap because of a bad choice of seed.
Notice that if we have 10 processors available under MPI, we do not want each processor to generate the same random number sequence. Instead, we want each of the processors to generate a part of the sequence, so that all the parts together make up the same set of values that a sequential program would have computed.
We assume we are using a linear congruential random number generator or "LCRG", which takes an integer input and returns a new integer output:
U = ( A * V + B ) mod CWe assume that we want the MPI program to produce the same sequence of random values as a sequential program would - but we want each processor to compute one part of that sequence.
We do this by computing a new LCRG which can compute every P'th entry of the original one.
Our LCRG works with integers, but it is easy to turn each integer into a real number between [0,1].
The particular scheme for computing the parameters of the new LCRG is implemented in the UNIFORM library.
The computer code and data files described and made available on this web page are distributed under the MIT license
random_mpi is available in a C version and a C++ version and a FORTRAN90 version.
COMMUNICATOR_MPI, a FORTRAN90 code which creates new communicators involving a subset of initial set of MPI processes in the default communicator MPI_COMM_WORLD.
HEAT_MPI, a FORTRAN90 code which solves the 1D Time Dependent Heat Equation using MPI.
HELLO_MPI, a FORTRAN90 code which prints out "Hello, world!" using the MPI parallel programming environment.
mpi_test, FORTRAN90 examples which illustrate the use of the MPI application code interface for carrying out parallel computations in a distributed memory environment.
PRIME_MPI, a FORTRAN90 code which counts the number of primes between 1 and N, using MPI for parallel execution.
QUAD_MPI, a FORTRAN90 code which approximates an integral using a quadrature rule, and carries out the computation in parallel using MPI.
RING_MPI, a FORTRAN90 code which uses the MPI parallel programming environment, and measures the time necessary to copy a set of data around a ring of processes.
SATISFY_MPI, a FORTRAN90 code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using MPI to carry out the calculation in parallel.
SEARCH_MPI, a FORTRAN90 code which searches integers between A and B for a value J such that F(J) = C, using MPI for parallel execution.
UNIFORM, a FORTRAN90 code which computes elements of a uniform pseudorandom sequence.
WAVE_MPI, a FORTRAN90 code which uses finite differences and MPI to estimate a solution to the wave equation.