Walker: Integrating the Ornstein-Uhlenbeck SDE
This example runs Walker to integrate the Ornstein-Uhlenbeck SDE (see DiffEq/OrnsteinUhlenbeck.h) using constant coefficients.
Control file
title "Example problem" walker #nstep 1 # Max number of time steps term 5.0 # Max time dt 0.001 # Time step size npar 1000000 # Number of particles (this many only to have a reasonably # smooth bivariated PDF ttyi 1000 # TTY output interval rngs mkl_mrg32k3a seed 0 end end ornstein-uhlenbeck depvar r init raw coeff const ncomp 3 theta 1.0 2.0 3.0 end mu 0.0 0.5 1.0 end # Upper triangle of the square of the diffusion matrix 'sigma-square'. # Must be symmetric positive semi-definite. sigmasq 4.0 2.5 1.1 32.0 5.6 23.0 end rng mkl_mrg32k3a end statistics interval 2 <R> <rr> <R2> <r2r2> <R3> <r3r3> <r1r2> <r1r3> <r2r3> end pdfs interval 1000 filetype gmshbin policy overwrite centering node #format scientific #precision 4 f2( r1 r2 : 2.0e-1 2.0e-1 ) #; -2 2 -2 2 ) end end
Example run on 4 CPUs
./charmrun +p4 Main/walker -v -c ../../tmp/ou.q -u 0.9Output
Running on 4 processors: Main/walker -v -c ../../tmp/ou.q -u 0.9
charmrun> /usr/bin/setarch x86_64 -R mpirun -np 4 Main/walker -v -c ../../tmp/ou.q -u 0.9
Charm++> Running on MPI version: 3.0
Charm++> level of thread support used: MPI_THREAD_SINGLE (desired: MPI_THREAD_SINGLE)
Charm++> Running in non-SMP mode: numPes 4
Converse/Charm++ Commit ID: b8b2735
CharmLB> Load balancer assumes all CPUs are same.
Charm++> Running on 1 unique compute nodes (4-way SMP).
Charm++> cpu topology info is gathered in 0.000 seconds.
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\/ \/ \/ \/
< ENVIRONMENT >
------ o ------
* Build environment:
--------------------
Hostname : sprout
Executable : walker
Version : 0.1
Release : LA-CC-XX-XXX
Revision : e26d8f8514a11ade687ba460f42dfae5af53d4d6
CMake build type : DEBUG
Asserts : on (turn off: CMAKE_BUILD_TYPE=RELEASE)
Exception trace : on (turn off: CMAKE_BUILD_TYPE=RELEASE)
MPI C++ wrapper : /opt/openmpi/1.8/clang/system/bin/mpicxx
Underlying C++ compiler : /usr/bin/clang++-3.5
Build date : Fri Feb 6 06:39:01 MST 2015
* Run-time environment:
-----------------------
Date, time : Sat Feb 7 11:58:53 2015
Work directory : /home/jbakosi/code/quinoa/build/clang
Executable (rel. to work dir) : Main/walker
Command line arguments : '-v -c ../../tmp/ou.q -u 0.9'
Output : verbose (quiet: omit -v)
Control file : ../../tmp/ou.q
Parsed control file : success
< FACTORY >
---- o ----
* Particle properties data layout policy (CMake: LAYOUT):
---------------------------------------------------------
particle-major
* Registered differential equations:
------------------------------------
Unique equation types : 8
With all policy combinations : 18
Legend: equation name : supported policies
Policy codes:
* i: initialization policy: R-raw, Z-zero
* c: coefficients policy: C-const, J-jrrj
Beta : i:RZ, c:CJ
Diagonal Ornstein-Uhlenbeck : i:RZ, c:C
Dirichlet : i:RZ, c:C
Gamma : i:RZ, c:C
Generalized Dirichlet : i:RZ, c:C
Ornstein-Uhlenbeck : i:RZ, c:C
Skew-Normal : i:RZ, c:C
Wright-Fisher : i:RZ, c:C
< PROBLEM >
---- o ----
* Title: Example problem
------------------------
* Differential equations integrated (1):
----------------------------------------
< Ornstein-Uhlenbeck >
kind : stochastic
dependent variable : r
initialization policy : R
coefficients policy : C
start offset in particle array : 0
number of components : 3
random number generator : MKL MRG32K3A
coeff sigmasq [6, upper tri] : { 4 2.5 1.1 32 5.6 23 }
coeff theta [3] : { 1 2 3 }
coeff mu [3] : { 0 0.5 1 }
* Output filenames:
-------------------
Statistics : stat.txt
PDF : pdf
* Discretization parameters:
----------------------------
Number of time steps : 18446744073709551615
Terminate time : 5
Initial time step size : 0.001
* Output intervals:
-------------------
TTY : 1000
Statistics : 2
PDF : 1000
* Statistical moments and distributions:
----------------------------------------
Estimated statistical moments : <R1> <R2> <R3> <r1r1> <r1r2> <r1r3> <r2r2> <r2r3> <r3r3>
PDFs : f2(r1,r2:0.2,0.2)
PDF output file type : gmshbin
PDF output file policy : overwrite
PDF output file centering : node
Text floating-point format : default
Text precision in digits : 6
* Load distribution:
--------------------
Virtualization [0.0...1.0] : 0.9
Load (number of particles) : 1000000
Number of processing elements : 4
Number of work units : 40 (39*25000+25000)
* Time integration: Differential equations testbed
--------------------------------------------------
Legend: it - iteration count
t - time
dt - time step size
ETE - estimated time elapsed (h:m:s)
ETA - estimated time for accomplishment (h:m:s)
out - output-saved flags (S: statistics, P: PDFs)
it t dt ETE ETA out
---------------------------------------------------------------
1000 1.000000e+00 1.000000e-03 000:04:16 000:17:04 SP
2000 2.000000e+00 1.000000e-03 000:08:33 000:12:49 SP
3000 3.000000e+00 1.000000e-03 000:12:51 000:08:34 SP
4000 4.000000e+00 1.000000e-03 000:17:06 000:04:16 SP
5000 5.000000e+00 1.000000e-03 000:21:19 000:00:00 SP
Normal finish, maximum time reached: 5.000000
* Timers (h:m:s):
-----------------
Initial conditions : 0:0:0
Migration of global-scope data : 0:0:0
Total runtime : 0:21:19
[Partition 0][Node 0] End of program
Estimated moments
Left – time evolution of the means and the means of the invariant distribution, right – time evolution of the components of the covariance matrix and those of the invariant.
Gnuplot commands to reproduce the above plots:
plot "stat.txt" u 2:3 w l t "<R1>", "stat.txt" u 2:4 w l t "<R2>", "stat.txt" u 2:5 w l t "<R3>", 0 lt 1, 0.5 lt 2, 1.0 lt 3 plot "stat.txt" u 2:6 w l t "<r1r1>", "stat.txt" u 2:7 w l t "<r1r2>", "stat.txt" u 2:8 w l t "<r1r3>", "stat.txt" u 2:9 w l t "<r2r2>", "stat.txt" u 2:10 w l t "<r2r3>", "stat.txt" u 2:11 w l t "<r3r3>", 4.0/2 lt 1, 2.5/3 lt 2, 1.1/4 lt 3, 32.0/4 lt 4, 5.6/5 lt 5, 23.0/6 lt 6
Estimated bivariate PDF
Example visualization of the estimated bivariate PDF at the final time step using gmsh.
