Walker: Integrating the skew-normal SDE
This example runs Walker to integrate the skew-normal SDE (see DiffEq/SkewNormal.h) using constant coefficients.
Control file
title "Example problem" walker term 10.0 # Max time dt 0.001 # Time step size npar 10000 # Number of particles ttyi 1000 # TTY output interval rngs mkl_r250 seed 1 end end skew-normal depvar m init zero coeff const ncomp 2 T 1.0 3.5 end sigmasq 0.04 0.25 end lambda 100.0 -50.0 end rng mkl_r250 end statistics interval 2 <m1m1> <m2m2> end pdfs interval 10 filetype txt policy overwrite centering elem format scientific precision 4 p1( M1 : 1.0e-2 ) p2( M2 : 1.0e-2 ) end end
Example run on 4 CPUs
./charmrun +p4 Main/walker -v -c ../../tmp/test.q -u 0.9Output
Running on 4 processors: Main/walker -v -c ../../tmp/skew.q -u 0.9
charmrun> /usr/bin/setarch x86_64 -R mpirun -np 4 Main/walker -v -c ../../tmp/skew.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 07:41:35 2015
Work directory : /home/jbakosi/code/quinoa/build/clang
Executable (rel. to work dir) : Main/walker
Command line arguments : '-v -c ../../tmp/skew.q -u 0.9'
Output : verbose (quiet: omit -v)
Control file : ../../tmp/skew.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):
----------------------------------------
< Skew-Normal >
kind : stochastic
dependent variable : m
initialization policy : Z
coefficients policy : C
start offset in particle array : 0
number of components : 2
random number generator : MKL R250
coeff T [2] : { 1 3.5 }
coeff sigmasq [2] : { 0.04 0.25 }
coeff lambda [2] : { 100 -50 }
* Output filenames:
-------------------
Statistics : stat.txt
PDF : pdf
* Discretization parameters:
----------------------------
Number of time steps : 18446744073709551615
Terminate time : 10
Initial time step size : 0.001
* Output intervals:
-------------------
TTY : 1000
Statistics : 2
PDF : 10
* Statistical moments and distributions:
----------------------------------------
Estimated statistical moments : <M1> <M2> <m1m1> <m2m2>
PDFs : p1(M1:0.01) p2(M2:0.01)
PDF output file type : txt
PDF output file policy : overwrite
PDF output file centering : elem
Text floating-point format : scientific
Text precision in digits : 4
* Load distribution:
--------------------
Virtualization [0.0...1.0] : 0.9
Load (number of particles) : 10000
Number of processing elements : 4
Number of work units : 40 (39*250+250)
* 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-03 000:00:02 000:00:26 SP
2000 2.000000e+00 1.000000e-03 000:00:05 000:00:23 SP
3000 3.000000e+00 1.000000e-03 000:00:08 000:00:20 SP
4000 4.000000e+00 1.000000e-03 000:00:11 000:00:17 SP
5000 5.000000e+00 1.000000e-03 000:00:14 000:00:14 SP
6000 6.000000e+00 1.000000e-03 000:00:18 000:00:12 SP
7000 7.000000e+00 1.000000e-03 000:00:21 000:00:09 SP
8000 8.000000e+00 1.000000e-03 000:00:24 000:00:06 SP
9000 9.000000e+00 1.000000e-03 000:00:27 000:00:03 SP
10000 1.000000e+01 1.000000e-03 000:00:30 000:00:00 SP
Normal finish, maximum time reached: 10.000000
* Timers (h:m:s):
-----------------
Initial conditions : 0:0:0
Migration of global-scope data : 0:0:0
Total runtime : 0:0:30
[Partition 0][Node 0] End of program
Results
The left figure shows the first two moments indicating convergence to a statistically stationary state. The right one shows the estimated PDFs with their analytical solution (see DiffEq/SkewNormal.h).
Gnuplot commands to reproduce the above plots:
plot "stat.txt" u 2:3 w l t "<M1>", "stat.txt" u 2:4 w l t "<M2>", "stat.txt" u 2:5 w l t "<m1m1>", "stat.txt" u 2:6 w l t "<m2m2>" plot "pdf_p1.txt" w p, "pdf_p2.txt" w p, exp(-x*x/2/0.2/0.2)*(1+erf(100.0*x/sqrt(2)))/0.2/sqrt(2*pi) lt 1, exp(-x*x/2/0.5/0.5)*(1+erf(-50.0*x/sqrt(2)))/0.5/sqrt(2*pi) lt 2