minbraz / parmap

# parmap

We (Mindaugas Bražėnas, Gábor Horváth, Mikós Telek) have developed three parallel algorithms for fitting MAPs of ER-CHMM structure class. The procedures are implemented to be executed on GPU card using CUDA library. More details will be available in a paper 'Parallel algorithms for fitting Markov Arrival Processes'.

To build the program and and launch it, execute

$ mkdir build
$ cd build
$ cmake ..
$ make
$ ./prog

Upon start, the program performs some tests to check the code. Your these tests if you are modifying the source code.

/ Testing code ... 

  test_sole_gauss ... PASSED
  test_matrix_inverse ... PASSED
  test_erchmm_structure_generation ... PASSED
  test_stationary_prob_computation ... PASSED
  test_stationary_prob_computation_for_general_map ... PASSED
  test_erchmm_mean_computation ... PASSED
  test_interarrival_generation ... PASSED
  test_erchmm_to_general_map ... PASSED
  test_erchmm_generation ... PASSED
  test_em P_1 ... PASSED
  test_em P_2 ... PASSED
  test_em P_2_D ... PASSED
  test_em P_3 ... PASSED
  test_em P_3_D ... PASSED

/ All tests passed.

If all the tests passes, program shows available options:

Available options: 
  gen - generate ER-CHMM parameters
  sim - simulate ER-CHMM process
  llh - compute log-likelihood
  fit - perform fitting
  cnv - convert ER-CHMM parameters to MAP
  res - perform paper research
  q   - quit
Select your option : 

Next, we will go through a few of these options.

Generation of ER-CHMM parameters

Select your option : gen

/ ER-CHMM parameter generation /

Enter ER-CHMM file name ( erchmm.txt ) : 
  >> file name : 'erchmm.txt'

Enter number of states in each branch ( 1, 2, 3 ) : 3,1
  >> structure : 3, 1

Enter sample mean ( 1.0 ) : 2.0
  >> sample mean : 2.000000

The generated ER-CHMM parameters are written to 'erchmm.txt'

The Erlang branch transition rates are assigned value of 1, and then rescaled to match the given sample mean. The contents of generated file 'erchmm.txt':

# number of branches
2
# structure
3, 1
# lambda 
0.9862176464158663
0.9862176464158663
# P 
0.1395971306464416, 0.8604028693535585
0.8142417799836712, 0.1857582200163287

Interarrival generation

Select your option : sim

/ ER-CHMM simulation / 

Enter ER-CHMM file name ( erchmm.txt ) : 
  >> file name : 'erchmm.txt'

Enter file for saving interarrivals into ( interarrivals.bin ) : 
  >> file name : 'interarrivals.bin'

Enter number of interarrivals ( 100000 ) :  
  >> number of interarrivals : 100000

  The generated interarrivals (mean : 1.996757) are written to 'interarrivals.bin'.

The generated interarrivals, obtained by simulating ER-CHMM process, are written into a binary file. The first 32bit interger denotes number of interarrivals, then follows an array of interarrival values (32bit single precision floating point numbers).

Fitting We have implemented various ways to select initial ER-CHMM parameters for fitting. Here the most general will be shown.

Select your option : fit


/ Fitting / 

Enter interarrivals file ( interarrivals.bin ) : 
  >> file name : 'interarrivals.bin'

Number of interarrivals : 100000

Initial ER-CHMM parameters : 
  ff - from file
  rg - randomly generated 
Enter your choice ( ff ) : rg
  >> option : rg

Randomly generated ER-CHMM parameters : 
  st - for given structure 
  ss - for given number of states (multiple structures) 
Enter your choice ( st ) : ss
  >> option : ss

Enter number of states ( 5 ) : 
  >> number of states : 5

Enter range for number of branches, R ( 2, 5 ) : 2, 4
  >> range : [ 2, 4 ]

Number of generated structures : 5
  [ 1 ] : 4, 1
  [ 2 ] : 3, 2
  [ 3 ] : 3, 1, 1
  [ 4 ] : 2, 2, 1
  [ 5 ] : 2, 1, 1, 1

Enter number of iterations ( 100 ) : 
  >> number of iterations : 100

Enter number of partitions ( 7680 ) : 
  >> number of partitions : 7680

Enter EM algorithm implementations, available : 
  ser - serial implementation
  p1 - parallel implementation with one pass
  p2, p2d - parallel implementation with two passes
  p3, p3d - parallel implementation with three passes
Enter your choice ( ser, p3d ) : ser, p2, p3d      
  >> options : ser, p2, p3d


/ Fitting has been started. / 

Fitting research for [L1-R2-ser-4-1] :
Setting up initial ER-CHMM ...... done.
Allocating memory ...... done.
Fitting ...... done.
Computing log-likelihood ... ... done.
Collecting results ...... done.
Deallocating memory ...... done.
Fitting research for [L7680-R2-p2-4-1] :
Setting up initial ER-CHMM ...... done.
Allocating memory ...... done.
Fitting ...... done.
Computing log-likelihood ... ... done.
Collecting results ...... done.
Deallocating memory ...... done.

  [ ... omitted some lines here ... ] 

Fitting research for [L7680-R4-p3d-2-1-1-1] :
Setting up initial ER-CHMM ...... done.
Allocating memory ...... done.
Fitting ...... done.
Computing log-likelihood ... ... done.
Collecting results ...... done.
Deallocating memory ...... done.


/ Fitting is done. / 

The results are written into several files.

'info.txt' - contains information about each fitting procedure. Memory usage is in megabytes, and runtime is measured in seconds.

tag; L; R; impl; struct; llh; mean; runtime; cpu mem; gpu mem; total mem
L1-R2-ser-4-1; 1; 2; ser; 4, 1; -1.628860e+05; 1.996752e+00; 2.110; 3.433; 0.000; 3.433
L7680-R2-p2-4-1; 7680; 2; p2; 4, 1; -1.628860e+05; 1.996749e+00; 0.142; 1.063; 1.063; 2.126
L7680-R2-p3d-4-1; 7680; 2; p3d; 4, 1; -1.628860e+05; 1.996756e+00; 0.091; 0.899; 3.951; 4.850
L1-R2-ser-3-2; 1; 2; ser; 3, 2; -1.676135e+05; 1.996752e+00; 2.221; 3.433; 0.000; 3.433
L7680-R2-p2-3-2; 7680; 2; p2; 3, 2; -1.676135e+05; 1.996748e+00; 0.143; 1.063; 1.063; 2.126
L7680-R2-p3d-3-2; 7680; 2; p3d; 3, 2; -1.676135e+05; 1.996751e+00; 0.091; 0.899; 3.951; 4.850
L1-R3-ser-3-1-1; 1; 3; ser; 3, 1, 1; -1.624684e+05; 1.996753e+00; 2.594; 4.578; 0.000; 4.578
L7680-R3-p2-3-1-1; 7680; 3; p2; 3, 1, 1; -1.624684e+05; 1.996754e+00; 0.261; 1.908; 1.907; 3.815
L7680-R3-p3d-3-1-1; 7680; 3; p3d; 3, 1, 1; -1.624684e+05; 1.996753e+00; 0.111; 1.254; 5.450; 6.703
L1-R3-ser-2-2-1; 1; 3; ser; 2, 2, 1; -1.633232e+05; 1.996753e+00; 2.580; 4.578; 0.000; 4.578
L7680-R3-p2-2-2-1; 7680; 3; p2; 2, 2, 1; -1.633232e+05; 1.996756e+00; 0.259; 1.908; 1.907; 3.815
L7680-R3-p3d-2-2-1; 7680; 3; p3d; 2, 2, 1; -1.633232e+05; 1.996753e+00; 0.112; 1.254; 5.450; 6.703
L1-R4-ser-2-1-1-1; 1; 4; ser; 2, 1, 1, 1; -1.633241e+05; 1.996753e+00; 3.117; 5.722; 0.000; 5.722
L7680-R4-p2-2-1-1-1; 7680; 4; p2; 2, 1, 1, 1; -1.633241e+05; 1.996750e+00; 0.484; 3.352; 3.352; 6.703
L7680-R4-p3d-2-1-1-1; 7680; 4; p3d; 2, 1, 1, 1; -1.633241e+05; 1.996751e+00; 0.141; 1.717; 7.057; 8.774

A particular search is identified by a tag, for example, the tag L7680-R3-p2-3-1-1 is used for a parallel search ('P2') using 7680 partitions, ER-CHMM structure {3, 1, 1} with 3 branches.

In order to easier judge about runtimes, results are summarized in 'summary.txt' for every R:

L = 1, ser
-----------------------------
R; runtime (seconds); total mem; cpu mem; gpu mem
2; 2.166; 3.433; 3.433; 0.000
3; 2.587; 4.578; 4.578; 0.000
4; 3.117; 5.722; 5.722; 0.000

L = 7680, p2
-----------------------------
R; runtime (seconds); total mem; cpu mem; gpu mem
2; 0.142; 2.126; 1.063; 1.063
3; 0.260; 3.815; 1.908; 1.907
4; 0.484; 6.703; 3.352; 3.352

L = 7680, p3d
-----------------------------
R; runtime (seconds); total mem; cpu mem; gpu mem
2; 0.091; 4.850; 0.899; 3.951
3; 0.111; 6.703; 1.254; 5.450
4; 0.141; 8.774; 1.717; 7.057

Also, in order to analyse which structures are the best for fitting, the sorted tags are given in 'llh.txt' file:

tag; llh
L1-R3-ser-3-1-1; -1.6246840625000000e+05
L7680-R3-p3d-3-1-1; -1.6246840625000000e+05
L7680-R3-p2-3-1-1; -1.6246842187500000e+05
L1-R2-ser-4-1; -1.6288598437500000e+05
L7680-R2-p2-4-1; -1.6288598437500000e+05
L7680-R2-p3d-4-1; -1.6288598437500000e+05
L1-R3-ser-2-2-1; -1.6332318750000000e+05
L7680-R3-p2-2-2-1; -1.6332318750000000e+05
L7680-R3-p3d-2-2-1; -1.6332318750000000e+05
L1-R4-ser-2-1-1-1; -1.6332409375000000e+05
L7680-R4-p2-2-1-1-1; -1.6332409375000000e+05
L7680-R4-p3d-2-1-1-1; -1.6332409375000000e+05
L1-R2-ser-3-2; -1.6761348437500000e+05
L7680-R2-p2-3-2; -1.6761348437500000e+05
L7680-R2-p3d-3-2; -1.6761348437500000e+05

Finally, the initial ER-CHMM parameters used for fitting are written to 'initial-erchmm/' folder, and the resulting ER-CHMM parameters are written to 'result-erchmm/' folder.

Research To replicate all the results presented in the paper execute:

Select your option : res


/ Research computations for paper. / 

  ! The research can be interrupted (by closing application). The next time it will be launched it will resume the computations.


Research started. 

Checking for meta file './research/.meta' ...... found. Resuming research.
Reading meta file 'research/.meta' ...... done.
Reading ER-CHMM from './research/gen-erchmm.txt' ...... done.
Reading interarrivals from './research/interarrivals.bin' ...... done.
Reading meta file 'research/.meta' ...... done.

( step : 0 )

  [ ... omitted many lines here ... ]

All the research results are written to 'research/' folder. All the research computations, depending on hardware, can take a long time to complete, therefore we have implemented interruption handling. The computations can be stoped (forcefully) at any time and will be resume upon next launch.

mindaugas.brazenas at yahoo.com