This is the ParaDRAM class for generating instances of serial and parallel Delayed-Rejection Adaptive Metropolis-Hastings Markov Chain Monte Carlo sampler of the ParaMonte MATLAB library.
More...

Inheritance diagram for Paradram:

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Collaboration diagram for Paradram:

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Public Member Functions
function	Paradram ()
	Generate and return an instance of the serial and parallel Delayed-Rejection Adaptive Metropolis-Hastings Markov Chain Monte Carlo sampler of the ParaMonte MATLAB library. More...

function	getppm (in self)
	Generate and return the relevant Post-Processing Message (ppm) for the current ParaMonte sampler to be displayed on the MATLAB command line after the sampling is complete. More...

function	readChainMarkov (in self, in pattern, in sep)
	Return a list of objects of class pm.sampling.FileContentsChainDRAM containing the content(s) of the ParaMonte simulation output chain file(s) whose path(s) match the specified input `pattern` or the simulation specification sampler.spec.outputFileName. More...

function	run (in self, in getLogFunc, in ndim)
	Run the ParaDRAM sampler and return nothing. More...

Detailed Description

This is the ParaDRAM class for generating instances of serial and parallel Delayed-Rejection Adaptive Metropolis-Hastings Markov Chain Monte Carlo sampler of the ParaMonte MATLAB library.

For more information, see the documentation of the class constructor pm.sampling.Paradram::Paradram.

Note: See the documentation of the class constructor for usage interface and examples.

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin

Definition at line 17 of file Paradram.m.

Constructor & Destructor Documentation

◆ Paradram()

function Paradram::Paradram ( )

Generate and return an instance of the serial and parallel Delayed-Rejection Adaptive Metropolis-Hastings Markov Chain Monte Carlo sampler of the ParaMonte MATLAB library.

This function is the constructor of the pm.sampling.Paradram sampler class.
Once you assign the desired simulation specifications to the corresponding attributes within the component spec of an object of class pm.sampling.Paradram, call the ParaDRAM sampler via the object method pm.sampling.Paradram.run().

While the constructor of this class does not take any input arguments, all ParaDRAM simulation specifications can be set after creating the object.

Returns: sampler : The output scalar object of class pm.sampling.Paradram.

Possible calling interfaces ⛓

: sampler = pm.sampling.Paradram();

Warning: When using the ParaMonte MATLAB library functionalities, particularly ParaMonte samplers in parallel, it would be best to close any such aggressive software/applications as Dropbox, ZoneAlarm, ... that interfere with your ParaMonte MATLAB library output files, potentially causing the tasks to fail and crash before successful completion.
These situations scarcely happen.

Note: On Windows systems, when restarting an old interrupted ParaDRAM simulation, ensure your MATLAB session is also restarted before the simulation restart.
This may be needed as Windows frequently locks access to some or all simulation output files.; To unset an already-set input simulation specification, simply set the simulation attribute to empty double [] or re-instantiate an object of class pm.sampling.Paradram.run().

See also: ParaDRAM simulation specifications listing
ParaDRAM simulation restart functionality
ParaDRAM simulation output files

ParaDRAM Simulation Specifications

The ParaDRAM simulation specifications have lengthy comprehensive descriptions that appear in full in the output report files of every ParaDRAM simulation.

The best way to learn about individual ParaDRAM simulation attributes is to a run a minimal serial simulation as given in the above.
You can also use the sampler.spec.doc() method:

sampler = pm.sampling.Paradram();

sampler.spec.doc()

Example Usage: Serial

First, ensure the ParaMonte +pm package (i.e., folder) is available in your MATLAB paths.

Here is a MATLAB script main.m for a serial ParaDRAM simulation.
Copy and paste the following code into your MATLAB session:

ndim = 4;
sampler = pm.sampling.Paradram();
sampler.run ( @(x) - sum(x.^2)  ... getLogFunc: the natural log of the objective function.
            , ndim              ... ndim: the number of dimensions of the objective function.
            );
samples = sampler.readSample();
sample = samples{1};
tile = pm.vis.TileLine(sample.df);
tile.make("coly", sample.slfc + 1 : sample.slfc + ndim, "colc", "sampleLogFunc");

The mathematical objective function in the above example is a is a multivariate Normal distribution centered at the origin, whose natural logarithm is returned by the lambda (Anonymous) function defined as a function handle input to the ParaDRAM sampler.

Running this code will generate a set of simulation output files (in the current working directory of MATLAB).
Among these, the file suffixed with "_report.txt" contains the full description of all input specifications of the ParaDRAM simulation as well as other information about the simulation results.

Example Usage: Thread-Parallel

First, ensure the ParaMonte +pm package (i.e., folder) is available in your MATLAB paths.

Threading parallelism is possible as of ParaMonte MATLAB version 3.0.0.
However, only singleChain ParaDRAM simulations are supported.

Here is a MATLAB script main.m for a thread-parallel ParaDRAM simulation.
Copy and paste the following code and paste into your MATLAB session:

sampler = pm.sampling.Paradram();
sampler.spec.parallelismNumThread = 0; % use all available threads.
sampler.run ( @(x) - sum(x.^2)  ... getLogFunc: the natural log of the objective function.
            , 4                 ... ndim:       the number of dimensions of the objective function.
            );
samples = sampler.readSample();
sample = samples{1};
sample.vis.tile.line.make();
sample.vis.triplex.lshc2.make(); % Make a corner scatter/density-contour plot.

The statement sample.vis.tile.line.make(); in the above is equivalent to the following set of lines:

tile = pm.vis.TileLine(sample.df);

tile.make("coly", sample.slfc + 1 : sample.slfc + 4, "colc", "sampleLogFunc");

The mathematical objective function in the above example is a is a multivariate Normal distribution centered at the origin, whose natural logarithm is returned by the lambda (Anonymous) function defined as a function handle input to the ParaDRAM sampler.

Running this code will generate a set of simulation output files (in the current working directory of MATLAB).
Among these, the file suffixed with "_report.txt" contains the full description of all input specifications of the ParaDRAM simulation as well as other information about the simulation results.

Specifying 0 as the number of threads will lead to using all available CPU threads for thread-parallel ParaDRAM simulation.

Note: Benefits of thread-parallelism
Thread-parallel simulations offer a much more flexible and easier approach to benefiting from parallelism without going through the hassle of MPI-parallel simulations.
But they can still potentially offer much faster speed than serial simulations.
The actual speedup depends on a lot of factors.
Moreover, the number of threads is limited to maximum number of physical cores available on your system.
As such, thread-parallel simulations are not scalable.
If you need scalability, checkout MPI-parallelism below.

Example Usage: MPI-Parallel

First, ensure the ParaMonte +pm package (i.e., folder) is available in your MATLAB paths.

MPI-parallel simulations can be slightly more cumbersome than thread-parallel simulations described above because MPI-parallel simulations cannot be performed from within a MATLAB GUI session and require launching MATLAB via a compatible mpiexec launcher.

Ensure you need and will get a speedup by running the an MPI-parallel simulation.
Typically, your simulation may then benefit from parallelism only if a single evaluation of the objective function takes longer than a few milliseconds.
Ensure the required MPI libraries are installed on your system (You can skip this step if you know that you already have a compatible MPI library installed on your system).
On the MATLAB command line type the following,

pm.lib.verify();

This will verify the existence of a valid MPI library on your system and, if missing, will guide you to install the MPI library on your system.
Once the MPI installation is verified, copy and paste the following code into your MATLAB session:
fid = fopen("main_mpi.m", "w");

sourceCode = ...

"sampler = pm.sampling.Paradram();" + newline + ...

"%sampler.mpiname = ''; % set this to an explicit MPI library name if needed." + newline + ...

"sampler.run( @(x) - sum(x.^2) ... getLogFunc: the natural log of the objective function." + newline + ...

" , 4 ... ndim: the number of dimensions of the objective function" + newline + ...

" );";

fprintf(fid, "%s\n", sourceCode);

fclose(fid);
This will generate a main_mpi.m MATLAB script file in the current working directory of your MATLAB session.
Now, you can execute this MATLAB script file (main_mpi.m) in parallel.
To do so, you need to call MATLAB on a command-line, out of MATLAB GUI.
1. On Windows:
  From within command prompt that recognizes both MATLAB and mpiexec, ideally, the Intel dedicated command-prompt that is shipped with Intel MPI library, type the following,
  mpiexec -localonly -n 3 matlab -batch "main_mpi"
  
  Note
  In the above MPI launcher command for Windows OS, we assumed that you would be using the Intel MPI library, hence, the reason for the extra flag -localonly.
  This flag runs the parallel code only on one node, but in doing so, it avoids the use of Hydra service and its registration.
  If you are not on a Windows cluster, (e.g., you are using your personal device), then we recommend specifying this flag.
2. On macOS/Linux:
  From within a Bash terminal that recognizes both MATLAB and mpiexec, type the following,
  mpiexec -n 3 matlab -batch "main_mpi"
  
  Note
  In both cases in the above, the script main_mpi.m will run on 3 processors.
  Feel free to change the number of processors to any number desired.
  But do not request more than the available number of physical cores on your system.

Warning: Do not add postprocessing codes (such as reading and plotting the output samples) in your MPI-parallel code.
There is no point in doing so, since MATLAB will run in -batch mode for parallel simulations, disabling all plotting capabilities.
Moreover, if you read and postprocess the output files in parallel mode, the task will be done by all parallel processes, potentially overwriting external IO activities of each other.
Only perform the sampling as described above in MPI-parallel mode.

Example usage ⛓

: 1cd(fileparts(mfilename('fullpath'))); % Change working directory to source code directory.

2addpath('../../../../'); % Add the ParaMonte library root directory to the search path.

3

4%%%%

5%%%% Setup the sampler.

6%%%%

7

8sampler = pm.sampling.Paradram();

9sampler.spec.outputStatus = "retry";

10sampler.spec.proposalStart = [-5, 5];

11sampler.spec.outputFileName = "himmelblau";

12sampler.spec.randomSeed = 28457353; % make sampling reproducible.

13%sampler.spec.outputChainSize = 30000; % Use a small chain size for illustration.

14sampler.spec.parallelismNumThread = []; % Set this to a positive number to request that many parallel threads for the sampling.

15sampler.spec.outputRestartFileFormat = "ascii";

16

17%%%% Set ``mpiname`` to your choice of MPI library

18%%%% ("intel", "openmpi", "mpich", ...) for MPI-parallel applications below.

19%%%% This setting is optional for most MPI-parallel simulations because the

20%%%% ParaMonte library will automatically infer the MPI library usage and type.

21%%%% If the sampler has trouble finding the right MPI-library, help the sampler

22%%%% find the invoke right MPI library build of the ParaMonte library by

23%%%% explicitly specifying its name blow.

24

25% sampler.mpiname = ''; % default

26% sampler.mpiname = "openmpi";

27% sampler.mpiname = "intel";

28% sampler.mpiname = "mpich";

29

30%%%% Developer Warning:

31%%%% Enable `silent` mode when generating

32%%%% the ParaMonte MATLAB documentation for a cleaner doc.

33

34sampler.silent = true;

35

36%%%%

37%%%% Run the sampler.

38%%%%

39

40if true % set to ``false`` to only post-process an existing simulation in the current folder.

41 sampler.run ( @(x) pm.stats.dist.himmelblau.getLogUDF(x(1), x(2)) ...

42 , 2 ...

43 );

44end

45

46%%%%

47%%%% Ensure postprocessing is done by only one parallel process if distributed (MPI) parallelism is enabled.

48%%%%

49

50if pm.lib.mpi.runtime.rankp1() == 1

51

52 %%%%

53 %%%% Postprocess the output chain file.

54 %%%%

55

56 chain = sampler.readChain();

57 chain = chain{1};

58

59 %%%%

60 %%%% Make plots of proposal adaptation.

61 %%%%

62

63 p = pm.vis.PlotScatter(chain.df, "coly", "proposalAdaptation");

64 p.make("axes", {"yscale", "log"});

65 p.savefig("Paradram.himmelblau.proposalAdaptation.png", "-m3");

66

67 chain.vis.proposalAdaptation.line.make()

68 chain.vis.proposalAdaptation.line.savefig("Paradram.himmelblau.proposalAdaptation.line.png", "-m3");

69

70 chain.vis.proposalAdaptation.scatter.make()

71 chain.vis.proposalAdaptation.scatter.savefig("Paradram.himmelblau.proposalAdaptation.scatter.png", "-m3");

72

73 %%%%

74 %%%% Make triplet (corner) plots from the chain file.

75 %%%%

76

77 chain.vis.triplex.lshc2.make();

78 chain.vis.triplex.lshc2.savefig("Paradram.himmelblau.triplex.lshc2.png", "-m3");

79

80 chain.vis.triplex.lshc3.make();

81 chain.vis.triplex.lshc3.savefig("Paradram.himmelblau.triplex.lshc3.png", "-m3");

82

83 chain.vis.triplex.lshcf.make();

84 chain.vis.triplex.lshcf.savefig("Paradram.himmelblau.triplex.lshcf.png", "-m3");

85

86 %%%%

87 %%%% The number `chain.slfc` corresponds to the data column with header "sampleLogFunc"`.

88 %%%%

89

90 p = pm.vis.PlotLineScatter(chain.df, "colx", chain.slfc + 1, "coly", chain.slfc + 2);

91 p.make("colc", "sampleLogFunc");

92 p.savefig("Paradram.himmelblau.domain.2d.png", "-m3");

93

94 p = pm.vis.PlotScatter3(chain.df, "colx", chain.slfc + 1, "coly", chain.slfc + 2, "colz", chain.slfc, "colc", chain.slfc);

95 p.make();

96 p.savefig("Paradram.himmelblau.domain.3d.png", "-m3");

97

98 p = pm.vis.TileLine(chain.df, "tileshape", [2, 1]);

99 p.make("coly", chain.slfc + [1 : 2], "colc", "sampleLogFunc");

100 p.savefig("Paradram.himmelblau.traceplot.png", "-m3");

101

102 %%%%

103 %%%% Postprocess the output restart file.

104 %%%%

105

106 restart = sampler.readRestart();

107 restart = restart{1};

108

109 p = pm.vis.PlotEllipse3(restart.proposalCov, restart.proposalMean, transpose(restart.uniqueStateVisitCount));

110 p.make("axes", {"zscale", "log"});

111 p.savefig("Paradram.himmelblau.proposalCov.png", "-m3");

112

113 %%%%

114 %%%% Postprocess the output report file.

115 %%%%

116

117 report = sampler.readReport();

118 report = report{1};

119

120 for parcond = ["sameeff", "zeroeff"]

121 report.stats.parallelism.speedup.scaling.strong.(parcond).vis.lineScatter.make();

122 report.stats.parallelism.speedup.scaling.strong.(parcond).vis.lineScatter.savefig("Paradram.himmelblau.parallelism.speedup.scaling.strong." + parcond + ".png", "-m3");

123 %p = pm.vis.PlotLineScatter(report.stats.parallelism.speedup.scaling.strong.(parcond).df, "colx", "1", "coly", "2", "colc", "2");

124 %p.make("axes", {"xscale", "log"}, "plot", {"linewidth", 2}, "scatter", {"size", 7});

125 %p.savefig("Paradram.himmelblau.parallelism.speedup.scaling.strong." + parcond + ".png", "-m3");

126 end

127

128end

name
function name(in vendor)
Return the MPI library name as used in naming the ParaMonte MATLAB shared library directories.

find
function find(in vendor)
Return a list of scalar MATLAB strings containing the paths to all detected mpiexec binaries installe...

parallel
function parallel()
Return a scalar MATLAB logical that is true if and only if the current installation of MATLAB contain...

root
function root()
Return a scalar MATLAB string containing the root directory of the ParaMonte library package.

Example output ⛓
1 ParaDRAM - NOTE: Setting up the MATLAB programming language environment for a ParaDRAM simulation...

2 ParaDRAM - NOTE:

3 ParaDRAM - NOTE: The user-specified internal input file for ParaDRAM specifications detected.

4 ParaDRAM - NOTE: All ParaDRAM simulation specifications will be read from the specified internal namelist file...

5

6 ParaDRAM - NOTE: Variable `outputFileName` detected among the user-supplied specifications of the ParaDRAM sampler:

7 ParaDRAM - NOTE: "himmelblau"

8 ParaDRAM - NOTE:

9 ParaDRAM - NOTE: Path to the current working directory:

10 ParaDRAM - NOTE: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/himmelblau"

11 ParaDRAM - NOTE:

12 ParaDRAM - NOTE: Generating the requested directory for the ParaDRAM simulation output files:

13 ParaDRAM - NOTE: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/himmelblau"

14 ParaDRAM - NOTE:

15 ParaDRAM - NOTE: 1 count of preexisting complete simulation runs with the same name prefix were detected.

16 ParaDRAM - NOTE:

17 ParaDRAM - NOTE: The last complete simulation run #1 will be overwritten as requested.

18 ParaDRAM - NOTE: Starting a fresh simulation run #1...

19 ParaDRAM - NOTE:

20 ParaDRAM - NOTE: Running the simulation in serial on 1 process...

21 ParaDRAM - NOTE:

22 ParaDRAM - NOTE: Generating the new output report file:

23 ParaDRAM - NOTE:

24 ParaDRAM - NOTE: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/himmelblau/himmelblau_run1_pid1_report.txt"

25 ParaDRAM - NOTE:

26 ParaDRAM - NOTE: Please see the output *_pid1_report.txt and *_pid1_progress.txt files for further realtime simulation details...

27

28 Accepted/Total Func. Call Dynamic/Overall Acc. Rate Elapsed/Remained Time [s]

29 ========================= ========================= =========================

30

31 356 / 1000 0.3560 / 0.3560 0.0103 / 2.8759

32 635 / 2000 0.2790 / 0.3175 0.0157 / 2.4633

33 899 / 3000 0.2640 / 0.2997 0.0207 / 2.2817

34 1167 / 4000 0.2680 / 0.2918 0.0259 / 2.1906

35 1469 / 5000 0.3020 / 0.2938 0.0307 / 2.0596

36 1796 / 6000 0.3270 / 0.2993 0.0356 / 1.9476

37 2060 / 7000 0.2640 / 0.2943 0.0402 / 1.9123

38 2308 / 8000 0.2480 / 0.2885 0.0452 / 1.9128

39 2586 / 9000 0.2780 / 0.2873 0.0499 / 1.8806

40 2859 / 10000 0.2730 / 0.2859 0.0547 / 1.8571

41 3051 / 11000 0.1920 / 0.2774 0.0594 / 1.8886

42 3338 / 12000 0.2870 / 0.2782 0.0645 / 1.8667

43 3654 / 13000 0.3160 / 0.2811 0.0694 / 1.8293

44 3900 / 14000 0.2460 / 0.2786 0.0740 / 1.8226

45 4157 / 15000 0.2570 / 0.2771 0.0786 / 1.8128

46 4422 / 16000 0.2650 / 0.2764 0.0833 / 1.7999

47 4608 / 17000 0.1860 / 0.2711 0.0879 / 1.8204

48 4859 / 18000 0.2510 / 0.2699 0.0929 / 1.8191

49 5118 / 19000 0.2590 / 0.2694 0.0985 / 1.8255

50 5395 / 20000 0.2770 / 0.2697 0.1032 / 1.8100

51 5621 / 21000 0.2260 / 0.2677 0.1079 / 1.8117

52 5826 / 22000 0.2050 / 0.2648 0.1124 / 1.8166

53 6104 / 23000 0.2780 / 0.2654 0.1171 / 1.8013

54 6346 / 24000 0.2420 / 0.2644 0.1217 / 1.7953

55 6600 / 25000 0.2540 / 0.2640 0.1264 / 1.7887

56 6799 / 26000 0.1990 / 0.2615 0.1309 / 1.7944

57 7059 / 27000 0.2600 / 0.2614 0.1356 / 1.7858

58 7346 / 28000 0.2870 / 0.2624 0.1402 / 1.7686

59 7571 / 29000 0.2250 / 0.2611 0.1448 / 1.7675

60 7869 / 30000 0.2980 / 0.2623 0.1495 / 1.7501

61 8168 / 31000 0.2990 / 0.2635 0.1542 / 1.7340

62 8421 / 32000 0.2530 / 0.2632 0.1588 / 1.7269

63 8751 / 33000 0.3300 / 0.2652 0.1636 / 1.7059

64 8970 / 34000 0.2190 / 0.2638 0.1687 / 1.7119

65 9225 / 35000 0.2550 / 0.2636 0.1735 / 1.7072

66 9403 / 36000 0.1780 / 0.2612 0.1780 / 1.7148

67 9604 / 37000 0.2010 / 0.2596 0.1827 / 1.7198

68 9799 / 38000 0.1950 / 0.2579 0.1874 / 1.7247

69 9993 / 39000 0.1940 / 0.2562 0.1918 / 1.7280

70 10186 / 40000 0.1930 / 0.2546 0.1964 / 1.7313

71 10454 / 41000 0.2680 / 0.2550 0.2011 / 1.7222

72 10701 / 42000 0.2470 / 0.2548 0.2056 / 1.7157

73 10965 / 43000 0.2640 / 0.2550 0.2102 / 1.7071

74 11197 / 44000 0.2320 / 0.2545 0.2152 / 1.7071

75 11390 / 45000 0.1930 / 0.2531 0.2203 / 1.7136

76 11642 / 46000 0.2520 / 0.2531 0.2252 / 1.7092

77 11838 / 47000 0.1960 / 0.2519 0.2299 / 1.7119

78 12067 / 48000 0.2290 / 0.2514 0.2346 / 1.7098

79 12340 / 49000 0.2730 / 0.2518 0.2395 / 1.7013

80 12582 / 50000 0.2420 / 0.2516 0.2443 / 1.6970

81 12855 / 51000 0.2730 / 0.2521 0.2491 / 1.6887

82 13126 / 52000 0.2710 / 0.2524 0.2538 / 1.6799

83 13245 / 53000 0.1190 / 0.2499 0.2583 / 1.6918

84 13426 / 54000 0.1810 / 0.2486 0.2628 / 1.6948

85 13655 / 55000 0.2290 / 0.2483 0.2675 / 1.6914

86 13888 / 56000 0.2330 / 0.2480 0.2721 / 1.6874

87 14100 / 57000 0.2120 / 0.2474 0.2768 / 1.6865

88 14340 / 58000 0.2400 / 0.2472 0.2815 / 1.6813

89 14515 / 59000 0.1750 / 0.2460 0.2859 / 1.6839

90 14686 / 60000 0.1710 / 0.2448 0.2905 / 1.6878

91 15024 / 61000 0.3380 / 0.2463 0.2955 / 1.6715

92 15313 / 62000 0.2890 / 0.2470 0.3003 / 1.6610

93 15602 / 63000 0.2890 / 0.2477 0.3052 / 1.6507

94 15849 / 64000 0.2470 / 0.2476 0.3099 / 1.6452

95 16136 / 65000 0.2870 / 0.2482 0.3147 / 1.6356

96 16405 / 66000 0.2690 / 0.2486 0.3196 / 1.6284

97 16644 / 67000 0.2390 / 0.2484 0.3244 / 1.6244

98 16862 / 68000 0.2180 / 0.2480 0.3290 / 1.6222

99 17155 / 69000 0.2930 / 0.2486 0.3339 / 1.6126

100 17387 / 70000 0.2320 / 0.2484 0.3386 / 1.6090

101 17657 / 71000 0.2700 / 0.2487 0.3433 / 1.6012

102 17935 / 72000 0.2780 / 0.2491 0.3481 / 1.5928

103 18230 / 73000 0.2950 / 0.2497 0.3531 / 1.5837

104 18508 / 74000 0.2780 / 0.2501 0.3579 / 1.5757

105 18703 / 75000 0.1950 / 0.2494 0.3624 / 1.5751

106 18977 / 76000 0.2740 / 0.2497 0.3673 / 1.5682

107 19277 / 77000 0.3000 / 0.2504 0.3720 / 1.5579

108 19533 / 78000 0.2560 / 0.2504 0.3769 / 1.5528

109 19640 / 79000 0.1070 / 0.2486 0.3814 / 1.5605

110 19874 / 80000 0.2340 / 0.2484 0.3861 / 1.5564

111 20150 / 81000 0.2760 / 0.2488 0.3908 / 1.5487

112 20417 / 82000 0.2670 / 0.2490 0.3957 / 1.5422

113 20670 / 83000 0.2530 / 0.2490 0.4004 / 1.5366

114 20976 / 84000 0.3060 / 0.2497 0.4052 / 1.5266

115 21213 / 85000 0.2370 / 0.2496 0.4100 / 1.5229

116 21553 / 86000 0.3400 / 0.2506 0.4150 / 1.5105

117 21785 / 87000 0.2320 / 0.2504 0.4196 / 1.5067

118 22023 / 88000 0.2380 / 0.2503 0.4244 / 1.5026

119 22326 / 89000 0.3030 / 0.2509 0.4293 / 1.4935

120 22507 / 90000 0.1810 / 0.2501 0.4338 / 1.4935

121 22769 / 91000 0.2620 / 0.2502 0.4385 / 1.4873

122 22951 / 92000 0.1820 / 0.2495 0.4430 / 1.4872

123 23283 / 93000 0.3320 / 0.2504 0.4479 / 1.4759

124 23582 / 94000 0.2990 / 0.2509 0.4527 / 1.4670

125 23763 / 95000 0.1810 / 0.2501 0.4573 / 1.4670

126 24022 / 96000 0.2590 / 0.2502 0.4622 / 1.4619

127 24271 / 97000 0.2490 / 0.2502 0.4671 / 1.4573

128 24485 / 98000 0.2140 / 0.2498 0.4717 / 1.4549

129 24679 / 99000 0.1940 / 0.2493 0.4763 / 1.4537

130 24989 / 100000 0.3100 / 0.2499 0.4811 / 1.4442

131 25203 / 101000 0.2140 / 0.2495 0.4857 / 1.4415

132 25435 / 102000 0.2320 / 0.2494 0.4903 / 1.4374

133 25665 / 103000 0.2300 / 0.2492 0.4950 / 1.4338

134 25880 / 104000 0.2150 / 0.2488 0.4995 / 1.4306

135 26120 / 105000 0.2400 / 0.2488 0.5041 / 1.4259

136 26397 / 106000 0.2770 / 0.2490 0.5089 / 1.4189

137 26720 / 107000 0.3230 / 0.2497 0.5137 / 1.4087

138 27034 / 108000 0.3140 / 0.2503 0.5185 / 1.3994

139 27269 / 109000 0.2350 / 0.2502 0.5232 / 1.3954

140 27541 / 110000 0.2720 / 0.2504 0.5278 / 1.3886

141 27819 / 111000 0.2780 / 0.2506 0.5328 / 1.3824

142 28077 / 112000 0.2580 / 0.2507 0.5376 / 1.3770

143 28297 / 113000 0.2200 / 0.2504 0.5422 / 1.3740

144 28539 / 114000 0.2420 / 0.2503 0.5469 / 1.3695

145 28800 / 115000 0.2610 / 0.2504 0.5516 / 1.3637

146 29039 / 116000 0.2390 / 0.2503 0.5563 / 1.3595

147 29196 / 117000 0.1570 / 0.2495 0.5608 / 1.3599

148 29427 / 118000 0.2310 / 0.2494 0.5654 / 1.3560

149 29683 / 119000 0.2560 / 0.2494 0.5701 / 1.3506

150 29993 / 120000 0.3100 / 0.2499 0.5750 / 1.3421

151 30213 / 121000 0.2200 / 0.2497 0.5798 / 1.3392

152 30524 / 122000 0.3110 / 0.2502 0.5846 / 1.3306

153 30825 / 123000 0.3010 / 0.2506 0.5893 / 1.3225

154 30960 / 124000 0.1350 / 0.2497 0.5937 / 1.3239

155 31267 / 125000 0.3070 / 0.2501 0.5985 / 1.3157

156 31570 / 126000 0.3030 / 0.2506 0.6033 / 1.3077

157 31818 / 127000 0.2480 / 0.2505 0.6079 / 1.3027

158 32066 / 128000 0.2480 / 0.2505 0.6125 / 1.2976

159 32393 / 129000 0.3270 / 0.2511 0.6174 / 1.2886

160 32604 / 130000 0.2110 / 0.2508 0.6220 / 1.2858

161 32809 / 131000 0.2050 / 0.2505 0.6266 / 1.2831

162 33021 / 132000 0.2120 / 0.2502 0.6313 / 1.2805

163 33332 / 133000 0.3110 / 0.2506 0.6361 / 1.2723

164 33511 / 134000 0.1790 / 0.2501 0.6406 / 1.2710

165 33802 / 135000 0.2910 / 0.2504 0.6454 / 1.2640

166 34088 / 136000 0.2860 / 0.2506 0.6502 / 1.2572

167 34336 / 137000 0.2480 / 0.2506 0.6549 / 1.2524

168 34618 / 138000 0.2820 / 0.2509 0.6596 / 1.2457

169 34876 / 139000 0.2580 / 0.2509 0.6645 / 1.2407

170 35163 / 140000 0.2870 / 0.2512 0.6692 / 1.2340

171 35389 / 141000 0.2260 / 0.2510 0.6738 / 1.2301

172 35604 / 142000 0.2150 / 0.2507 0.6785 / 1.2271

173 35829 / 143000 0.2250 / 0.2506 0.6833 / 1.2238

174 36056 / 144000 0.2270 / 0.2504 0.6880 / 1.2202

175 36295 / 145000 0.2390 / 0.2503 0.6927 / 1.2159

176 36536 / 146000 0.2410 / 0.2502 0.6976 / 1.2117

177 36779 / 147000 0.2430 / 0.2502 0.7023 / 1.2071

178 37064 / 148000 0.2850 / 0.2504 0.7070 / 1.2006

179 37320 / 149000 0.2560 / 0.2505 0.7118 / 1.1955

180 37614 / 150000 0.2940 / 0.2508 0.7167 / 1.1887

181 37884 / 151000 0.2700 / 0.2509 0.7214 / 1.1829

182 38082 / 152000 0.1980 / 0.2505 0.7261 / 1.1806

183 38302 / 153000 0.2200 / 0.2503 0.7307 / 1.1771

184 38552 / 154000 0.2500 / 0.2503 0.7354 / 1.1722

185 38815 / 155000 0.2630 / 0.2504 0.7401 / 1.1666

186 39030 / 156000 0.2150 / 0.2502 0.7449 / 1.1636

187 39266 / 157000 0.2360 / 0.2501 0.7498 / 1.1597

188 39504 / 158000 0.2380 / 0.2500 0.7548 / 1.1559

189 39804 / 159000 0.3000 / 0.2503 0.7598 / 1.1491

190 40080 / 160000 0.2760 / 0.2505 0.7652 / 1.1440

191 40325 / 161000 0.2450 / 0.2505 0.7698 / 1.1393

192 40580 / 162000 0.2550 / 0.2505 0.7745 / 1.1341

193 40815 / 163000 0.2350 / 0.2504 0.7791 / 1.1298

194 41088 / 164000 0.2730 / 0.2505 0.7838 / 1.1238

195 41307 / 165000 0.2190 / 0.2503 0.7884 / 1.1202

196 41567 / 166000 0.2600 / 0.2504 0.7931 / 1.1149

197 41877 / 167000 0.3100 / 0.2508 0.7979 / 1.1075

198 42097 / 168000 0.2200 / 0.2506 0.8026 / 1.1040

199 42336 / 169000 0.2390 / 0.2505 0.8072 / 1.0995

200 42597 / 170000 0.2610 / 0.2506 0.8119 / 1.0941

201 42823 / 171000 0.2260 / 0.2504 0.8167 / 1.0904

202 43088 / 172000 0.2650 / 0.2505 0.8214 / 1.0849

203 43337 / 173000 0.2490 / 0.2505 0.8261 / 1.0801

204 43600 / 174000 0.2630 / 0.2506 0.8307 / 1.0746

205 43877 / 175000 0.2770 / 0.2507 0.8354 / 1.0686

206 44222 / 176000 0.3450 / 0.2513 0.8404 / 1.0600

207 44474 / 177000 0.2520 / 0.2513 0.8451 / 1.0551

208 44749 / 178000 0.2750 / 0.2514 0.8499 / 1.0493

209 45003 / 179000 0.2540 / 0.2514 0.8545 / 1.0443

210 45288 / 180000 0.2850 / 0.2516 0.8592 / 1.0380

211 45573 / 181000 0.2850 / 0.2518 0.8639 / 1.0318

212 45800 / 182000 0.2270 / 0.2516 0.8686 / 1.0279

213 46022 / 183000 0.2220 / 0.2515 0.8732 / 1.0242

214 46281 / 184000 0.2590 / 0.2515 0.8779 / 1.0190

215 46527 / 185000 0.2460 / 0.2515 0.8827 / 1.0144

216 46827 / 186000 0.3000 / 0.2518 0.8874 / 1.0077

217 47101 / 187000 0.2740 / 0.2519 0.8922 / 1.0020

218 47353 / 188000 0.2520 / 0.2519 0.8968 / 0.9971

219 47594 / 189000 0.2410 / 0.2518 0.9015 / 0.9926

220 47798 / 190000 0.2040 / 0.2516 0.9061 / 0.9895

221 48016 / 191000 0.2180 / 0.2514 0.9106 / 0.9858

222 48251 / 192000 0.2350 / 0.2513 0.9153 / 0.9816

223 48490 / 193000 0.2390 / 0.2512 0.9198 / 0.9771

224 48784 / 194000 0.2940 / 0.2515 0.9245 / 0.9706

225 49047 / 195000 0.2630 / 0.2515 0.9292 / 0.9653

226 49291 / 196000 0.2440 / 0.2515 0.9339 / 0.9608

227 49570 / 197000 0.2790 / 0.2516 0.9387 / 0.9550

228 49727 / 198000 0.1570 / 0.2511 0.9432 / 0.9536

229 50000 / 199000 0.2730 / 0.2513 0.9479 / 0.9479

230 50189 / 200000 0.1890 / 0.2509 0.9523 / 0.9452

231 50391 / 201000 0.2020 / 0.2507 0.9579 / 0.9431

232 50612 / 202000 0.2210 / 0.2506 0.9628 / 0.9395

233 50873 / 203000 0.2610 / 0.2506 0.9674 / 0.9342

234 51131 / 204000 0.2580 / 0.2506 0.9722 / 0.9292

235 51500 / 205000 0.3690 / 0.2512 0.9770 / 0.9201

236 51778 / 206000 0.2780 / 0.2513 0.9817 / 0.9143

237 52007 / 207000 0.2290 / 0.2512 0.9863 / 0.9101

238 52358 / 208000 0.3510 / 0.2517 0.9912 / 0.9019

239 52676 / 209000 0.3180 / 0.2520 0.9960 / 0.8948

240 52923 / 210000 0.2470 / 0.2520 1.0006 / 0.8901

241 53100 / 211000 0.1770 / 0.2517 1.0051 / 0.8878

242 53294 / 212000 0.1940 / 0.2514 1.0095 / 0.8847

243 53569 / 213000 0.2750 / 0.2515 1.0142 / 0.8791

244 53778 / 214000 0.2090 / 0.2513 1.0187 / 0.8756

245 53994 / 215000 0.2160 / 0.2511 1.0235 / 0.8720

246 54251 / 216000 0.2570 / 0.2512 1.0281 / 0.8670

247 54470 / 217000 0.2190 / 0.2510 1.0327 / 0.8632

248 54667 / 218000 0.1970 / 0.2508 1.0374 / 0.8603

249 54938 / 219000 0.2710 / 0.2509 1.0420 / 0.8547

250 55126 / 220000 0.1880 / 0.2506 1.0464 / 0.8518

251 55390 / 221000 0.2640 / 0.2506 1.0511 / 0.8466

252 55642 / 222000 0.2520 / 0.2506 1.0559 / 0.8418

253 55930 / 223000 0.2880 / 0.2508 1.0605 / 0.8356

254 56148 / 224000 0.2180 / 0.2507 1.0650 / 0.8318

255 56322 / 225000 0.1740 / 0.2503 1.0695 / 0.8294

256 56611 / 226000 0.2890 / 0.2505 1.0742 / 0.8233

257 56925 / 227000 0.3140 / 0.2508 1.0789 / 0.8164

258 57148 / 228000 0.2230 / 0.2506 1.0837 / 0.8126

259 57413 / 229000 0.2650 / 0.2507 1.0883 / 0.8073

260 57623 / 230000 0.2100 / 0.2505 1.0929 / 0.8038

261 57871 / 231000 0.2480 / 0.2505 1.0985 / 0.7997

262 58118 / 232000 0.2470 / 0.2505 1.1031 / 0.7950

263 58444 / 233000 0.3260 / 0.2508 1.1079 / 0.7878

264 58673 / 234000 0.2290 / 0.2507 1.1125 / 0.7836

265 58946 / 235000 0.2730 / 0.2508 1.1173 / 0.7781

266 59136 / 236000 0.1900 / 0.2506 1.1217 / 0.7751

267 59408 / 237000 0.2720 / 0.2507 1.1263 / 0.7696

268 59631 / 238000 0.2230 / 0.2506 1.1309 / 0.7656

269 59917 / 239000 0.2860 / 0.2507 1.1355 / 0.7596

270 60192 / 240000 0.2750 / 0.2508 1.1403 / 0.7541

271 60465 / 241000 0.2730 / 0.2509 1.1450 / 0.7487

272 60778 / 242000 0.3130 / 0.2511 1.1499 / 0.7421

273 61071 / 243000 0.2930 / 0.2513 1.1546 / 0.7360

274 61365 / 244000 0.2940 / 0.2515 1.1593 / 0.7299

275 61524 / 245000 0.1590 / 0.2511 1.1636 / 0.7277

276 61811 / 246000 0.2870 / 0.2513 1.1683 / 0.7218

277 62094 / 247000 0.2830 / 0.2514 1.1730 / 0.7161

278 62329 / 248000 0.2350 / 0.2513 1.1779 / 0.7119

279 62518 / 249000 0.1890 / 0.2511 1.1823 / 0.7089

280 62763 / 250000 0.2450 / 0.2511 1.1868 / 0.7041

281 63014 / 251000 0.2510 / 0.2511 1.1914 / 0.6993

282 63185 / 252000 0.1710 / 0.2507 1.1959 / 0.6968

283 63436 / 253000 0.2510 / 0.2507 1.2007 / 0.6920

284 63706 / 254000 0.2700 / 0.2508 1.2054 / 0.6867

285 63862 / 255000 0.1560 / 0.2504 1.2098 / 0.6846

286 64162 / 256000 0.3000 / 0.2506 1.2146 / 0.6784

287 64542 / 257000 0.3800 / 0.2511 1.2195 / 0.6700

288 64857 / 258000 0.3150 / 0.2514 1.2243 / 0.6634

289 65075 / 259000 0.2180 / 0.2513 1.2289 / 0.6595

290 65382 / 260000 0.3070 / 0.2515 1.2336 / 0.6532

291 65621 / 261000 0.2390 / 0.2514 1.2383 / 0.6487

292 65808 / 262000 0.1870 / 0.2512 1.2428 / 0.6457

293 66007 / 263000 0.1990 / 0.2510 1.2474 / 0.6424

294 66342 / 264000 0.3350 / 0.2513 1.2523 / 0.6353

295 66534 / 265000 0.1920 / 0.2511 1.2567 / 0.6321

296 66814 / 266000 0.2800 / 0.2512 1.2614 / 0.6265

297 67047 / 267000 0.2330 / 0.2511 1.2660 / 0.6222

298 67282 / 268000 0.2350 / 0.2511 1.2705 / 0.6178

299 67613 / 269000 0.3310 / 0.2513 1.2752 / 0.6109

300 67798 / 270000 0.1850 / 0.2511 1.2797 / 0.6078

301 68054 / 271000 0.2560 / 0.2511 1.2843 / 0.6029

302 68215 / 272000 0.1610 / 0.2508 1.2887 / 0.6005

303 68377 / 273000 0.1620 / 0.2505 1.2931 / 0.5980

304 68655 / 274000 0.2780 / 0.2506 1.2977 / 0.5925

305 68873 / 275000 0.2180 / 0.2504 1.3024 / 0.5886

306 69164 / 276000 0.2910 / 0.2506 1.3070 / 0.5827

307 69403 / 277000 0.2390 / 0.2506 1.3114 / 0.5782

308 69588 / 278000 0.1850 / 0.2503 1.3159 / 0.5751

309 69815 / 279000 0.2270 / 0.2502 1.3203 / 0.5709

310 70098 / 280000 0.2830 / 0.2503 1.3250 / 0.5652

311 70264 / 281000 0.1660 / 0.2500 1.3293 / 0.5626

312 70509 / 282000 0.2450 / 0.2500 1.3338 / 0.5579

313 70709 / 283000 0.2000 / 0.2499 1.3382 / 0.5543

314 70971 / 284000 0.2620 / 0.2499 1.3428 / 0.5492

315 71186 / 285000 0.2150 / 0.2498 1.3472 / 0.5453

316 71441 / 286000 0.2550 / 0.2498 1.3517 / 0.5404

317 71643 / 287000 0.2020 / 0.2496 1.3562 / 0.5368

318 71873 / 288000 0.2300 / 0.2496 1.3607 / 0.5325

319 72164 / 289000 0.2910 / 0.2497 1.3654 / 0.5267

320 72506 / 290000 0.3420 / 0.2500 1.3701 / 0.5195

321 72749 / 291000 0.2430 / 0.2500 1.3747 / 0.5149

322 73005 / 292000 0.2560 / 0.2500 1.3793 / 0.5100

323 73244 / 293000 0.2390 / 0.2500 1.3840 / 0.5056

324 73436 / 294000 0.1920 / 0.2498 1.3885 / 0.5023

325 73667 / 295000 0.2310 / 0.2497 1.3930 / 0.4979

326 73860 / 296000 0.1930 / 0.2495 1.3976 / 0.4946

327 74108 / 297000 0.2480 / 0.2495 1.4022 / 0.4899

328 74297 / 298000 0.1890 / 0.2493 1.4066 / 0.4866

329 74581 / 299000 0.2840 / 0.2494 1.4113 / 0.4810

330 74866 / 300000 0.2850 / 0.2496 1.4160 / 0.4754

331 75198 / 301000 0.3320 / 0.2498 1.4208 / 0.4686

332 75489 / 302000 0.2910 / 0.2500 1.4254 / 0.4628

333 75784 / 303000 0.2950 / 0.2501 1.4300 / 0.4570

334 76039 / 304000 0.2550 / 0.2501 1.4347 / 0.4521

335 76337 / 305000 0.2980 / 0.2503 1.4393 / 0.4462

336 76626 / 306000 0.2890 / 0.2504 1.4440 / 0.4405

337 76868 / 307000 0.2420 / 0.2504 1.4486 / 0.4359

338 77156 / 308000 0.2880 / 0.2505 1.4535 / 0.4303

339 77399 / 309000 0.2430 / 0.2505 1.4581 / 0.4258

340 77652 / 310000 0.2530 / 0.2505 1.4626 / 0.4209

341 77849 / 311000 0.1970 / 0.2503 1.4671 / 0.4175

342 78124 / 312000 0.2750 / 0.2504 1.4719 / 0.4121

343 78329 / 313000 0.2050 / 0.2503 1.4765 / 0.4085

344 78594 / 314000 0.2650 / 0.2503 1.4812 / 0.4034

345 78886 / 315000 0.2920 / 0.2504 1.4859 / 0.3977

346 79202 / 316000 0.3160 / 0.2506 1.4906 / 0.3914

347 79419 / 317000 0.2170 / 0.2505 1.4952 / 0.3875

348 79662 / 318000 0.2430 / 0.2505 1.4998 / 0.3829

349 79950 / 319000 0.2880 / 0.2506 1.5046 / 0.3773

350 80151 / 320000 0.2010 / 0.2505 1.5090 / 0.3737

351 80348 / 321000 0.1970 / 0.2503 1.5135 / 0.3702

352 80659 / 322000 0.3110 / 0.2505 1.5182 / 0.3640

353 80934 / 323000 0.2750 / 0.2506 1.5228 / 0.3587

354 81219 / 324000 0.2850 / 0.2507 1.5275 / 0.3532

355 81496 / 325000 0.2770 / 0.2508 1.5322 / 0.3479

356 81713 / 326000 0.2170 / 0.2507 1.5368 / 0.3439

357 82051 / 327000 0.3380 / 0.2509 1.5415 / 0.3372

358 82304 / 328000 0.2530 / 0.2509 1.5461 / 0.3324

359 82533 / 329000 0.2290 / 0.2509 1.5507 / 0.3282

360 82801 / 330000 0.2680 / 0.2509 1.5553 / 0.3231

361 82986 / 331000 0.1850 / 0.2507 1.5597 / 0.3198

362 83252 / 332000 0.2660 / 0.2508 1.5645 / 0.3147

363 83478 / 333000 0.2260 / 0.2507 1.5689 / 0.3105

364 83690 / 334000 0.2120 / 0.2506 1.5734 / 0.3066

365 83855 / 335000 0.1650 / 0.2503 1.5779 / 0.3038

366 84177 / 336000 0.3220 / 0.2505 1.5826 / 0.2975

367 84585 / 337000 0.4080 / 0.2510 1.5875 / 0.2893

368 84866 / 338000 0.2810 / 0.2511 1.5921 / 0.2839

369 85089 / 339000 0.2230 / 0.2510 1.5968 / 0.2798

370 85304 / 340000 0.2150 / 0.2509 1.6013 / 0.2759

371 85510 / 341000 0.2060 / 0.2508 1.6058 / 0.2721

372 85679 / 342000 0.1690 / 0.2505 1.6101 / 0.2691

373 86018 / 343000 0.3390 / 0.2508 1.6150 / 0.2625

374 86259 / 344000 0.2410 / 0.2508 1.6195 / 0.2580

375 86460 / 345000 0.2010 / 0.2506 1.6239 / 0.2543

376 86584 / 346000 0.1240 / 0.2502 1.6282 / 0.2523

377 86880 / 347000 0.2960 / 0.2504 1.6329 / 0.2466

378 87133 / 348000 0.2530 / 0.2504 1.6375 / 0.2418

379 87418 / 349000 0.2850 / 0.2505 1.6421 / 0.2363

380 87646 / 350000 0.2280 / 0.2504 1.6467 / 0.2321

381 87950 / 351000 0.3040 / 0.2506 1.6513 / 0.2262

382 88253 / 352000 0.3030 / 0.2507 1.6560 / 0.2204

383 88535 / 353000 0.2820 / 0.2508 1.6606 / 0.2150

384 88836 / 354000 0.3010 / 0.2509 1.6653 / 0.2093

385 89149 / 355000 0.3130 / 0.2511 1.6700 / 0.2033

386 89356 / 356000 0.2070 / 0.2510 1.6745 / 0.1995

387 89590 / 357000 0.2340 / 0.2510 1.6790 / 0.1951

388 89876 / 358000 0.2860 / 0.2511 1.6837 / 0.1897

389 90163 / 359000 0.2870 / 0.2512 1.6884 / 0.1842

390 90407 / 360000 0.2440 / 0.2511 1.6929 / 0.1796

391 90703 / 361000 0.2960 / 0.2513 1.6975 / 0.1740

392 90949 / 362000 0.2460 / 0.2512 1.7020 / 0.1694

393 91236 / 363000 0.2870 / 0.2513 1.7067 / 0.1639

394 91515 / 364000 0.2790 / 0.2514 1.7113 / 0.1587

395 91738 / 365000 0.2230 / 0.2513 1.7158 / 0.1545

396 91993 / 366000 0.2550 / 0.2513 1.7205 / 0.1498

397 92280 / 367000 0.2870 / 0.2514 1.7251 / 0.1443

398 92533 / 368000 0.2530 / 0.2514 1.7297 / 0.1396

399 92792 / 369000 0.2590 / 0.2515 1.7342 / 0.1347

400 93077 / 370000 0.2850 / 0.2516 1.7388 / 0.1293

401 93286 / 371000 0.2090 / 0.2514 1.7434 / 0.1255

402 93524 / 372000 0.2380 / 0.2514 1.7482 / 0.1211

403 93795 / 373000 0.2710 / 0.2515 1.7528 / 0.1160

404 94045 / 374000 0.2500 / 0.2515 1.7574 / 0.1113

405 94276 / 375000 0.2310 / 0.2514 1.7619 / 0.1070

406 94511 / 376000 0.2350 / 0.2514 1.7666 / 0.1026

407 94815 / 377000 0.3040 / 0.2515 1.7713 / 0.0969

408 95049 / 378000 0.2340 / 0.2515 1.7759 / 0.0925

409 95290 / 379000 0.2410 / 0.2514 1.7804 / 0.0880

410 95574 / 380000 0.2840 / 0.2515 1.7850 / 0.0827

411 95826 / 381000 0.2520 / 0.2515 1.7896 / 0.0780

412 96069 / 382000 0.2430 / 0.2515 1.7941 / 0.0734

413 96280 / 383000 0.2110 / 0.2514 1.7986 / 0.0695

414 96638 / 384000 0.3580 / 0.2517 1.8034 / 0.0627

415 96877 / 385000 0.2390 / 0.2516 1.8079 / 0.0583

416 97117 / 386000 0.2400 / 0.2516 1.8124 / 0.0538

417 97455 / 387000 0.3380 / 0.2518 1.8172 / 0.0475

418 97678 / 388000 0.2230 / 0.2517 1.8217 / 0.0433

419 97920 / 389000 0.2420 / 0.2517 1.8263 / 0.0388

420 98047 / 390000 0.1270 / 0.2514 1.8305 / 0.0365

421 98261 / 391000 0.2140 / 0.2513 1.8351 / 0.0325

422 98484 / 392000 0.2230 / 0.2512 1.8396 / 0.0283

423 98728 / 393000 0.2440 / 0.2512 1.8443 / 0.0238

424 98936 / 394000 0.2080 / 0.2511 1.8490 / 0.0199

425 99032 / 395000 0.0960 / 0.2507 1.8535 / 0.0181

426 99221 / 396000 0.1890 / 0.2506 1.8581 / 0.0146

427 99415 / 397000 0.1940 / 0.2504 1.8627 / 0.0110

428 99662 / 398000 0.2470 / 0.2504 1.8677 / 0.0063

429 99894 / 399000 0.2320 / 0.2504 1.8724 / 0.0020

430 100000 / 399632 0.1060 / 0.2502 1.8752 / 0.0000

431

432

433 ParaDRAM - NOTE: Computing the statistical properties of the Markov chain...

434

435 ParaDRAM - NOTE: Computing the final refined i.i.d. sample size...

436

437 ParaDRAM - NOTE: Generating the output sample file:

438 ParaDRAM - NOTE: /home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/himmelblau/himmelblau_run1_pid1_sample.txt

439

440 ParaDRAM - NOTE: Computing the statistical properties of the final output sample...

441

442

443 ParaDRAM - NOTE: Mission Accomplished.

444

445| 50%

446| 100% done in 0.065191 seconds.

Paradram
This is the ParaDRAM class for generating instances of serial and parallel Delayed-Rejection Adaptive...
Definition: Paradram.m:18

Paradram::run
function run(in self, in getLogFunc, in ndim)
Run the ParaDRAM sampler and return nothing.

home
function home()
Return a MATLAB string containing the absolute path to the system home directory.

lib
function lib()
Return a scalar MATLAB string containing the path to the lib directory of the ParaMonte library packa...

Visualization of the example output ⛓

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin

Member Function Documentation

◆ getppm()

function Paradram::getppm ( in self )

Generate and return the relevant Post-Processing Message (ppm) for the current ParaMonte sampler to be displayed on the MATLAB command line after the sampling is complete.

This is a private dynamic method of the pm.sampling.Paradram sampler class.
This method is not meant to be used or accessed by the end users.

Parameters

[in] self : The input parent object of class pm.sampling.Sampler which is implicitly passed to this dynamic method (not by the user).

Note: This is an internal method of the class pm.sampling.Sampler.

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, September 1, 2012, 12:00 AM, National Institute for Fusion Studies, The University of Texas at Austin

◆ readChainMarkov()

function Paradram::readChainMarkov	(	in	self,
		in	pattern,
		in	sep
	)

Return a list of objects of class pm.sampling.FileContentsChainDRAM containing the content(s) of the ParaMonte simulation output chain file(s) whose path(s) match the specified input pattern or the simulation specification sampler.spec.outputFileName.

Parameters

[in]	self	: The input/output parent object of class pm.sampling.Paradram which is implicitly passed to this dynamic method (not by the user).
[in]	pattern	: See the documentation of the corresponding argument of the constructor of the method pm.sampling.Sampler.readChain. (optional, The default is set by pm.sampling.Sampler.readChain)
[in]	sep	: See the documentation of the corresponding argument of the constructor of the method pm.sampling.Sampler.readChain. (optional, The default is set by pm.sampling.Sampler.readChain)

Returns: chainMarkovList : The output cell array of objects of class pm.sampling.FileContentsChainDRAM, each of which corresponds to the contents of a unique chain file.
Try doc pm.sampling.FileContentsChainDRAM to see the documentation of the contents of the objects of the output list.

Possible calling interfaces ⛓

: sampler = pm.sampling.Paradram();

chainMarkovList = sampler.readChainMarkov();

chainMarkovList = sampler.readChainMarkov([]);

chainMarkovList = sampler.readChainMarkov(pattern);

chainMarkovList = sampler.readChainMarkov([], []);

chainMarkovList = sampler.readChainMarkov(pattern, []);

chainMarkovList = sampler.readChainMarkov(pattern, sep);

Warning: Avoid using this routine for very large compact chains.
Reading the full Markov chain of large-scale simulation problems can be extremely memory-intensive without any potential benefits.; This method is to be only used for post-processing of the output chain file(s) of an already finished simulation. It is not meant to be called by all processes in parallel mode, although it is possible.

Note: This routine is identical to pm.sampling.Sampler.readChain method, except for the fact that upon reading the output chain files, it will also convert the chain contents from the default efficient compact format stored in the file to the full verbose Markov chain format.

Example usage ⛓

: 1cd(fileparts(mfilename('fullpath'))); % Change working directory to source code directory.

2addpath('../../../../'); % Add the ParaMonte library root directory to the search path.

3

4sampler = pm.sampling.Paradram();

5sampler.spec.outputFileName = "./out/run";

6sampler.spec.outputChainSize = 3000;

7sampler.run ( @(x) -sum((x - [-5; 5]).^2) ...

8 , 2 ...

9 );

10chain = sampler.readChainMarkov();

11chain = chain{1};

12head(chain.df)

13

14p = pm.vis.PlotScatter(chain.df, "coly", "proposalAdaptation");

15p.make("axes", {"yscale", "log"});

16p.savefig("readChainMarkov.proposalAdaptation.png", "-m3");

17

18p = pm.vis.PlotLineScatter(chain.df, "colx", chain.slfc + 1, "coly", chain.slfc + 2);

19p.make("colc", "sampleLogFunc");

20p.savefig("readChainMarkov.domain.png", "-m3");

21

22p = pm.vis.TileLine(chain.df, "tileshape", [2, 1]);

23p.make("coly", chain.slfc + [1 : 2], "colc", "sampleLogFunc");

24p.savefig("readChainMarkov.traceplot.png", "-m3");

PlotScatter
This is the PlotScatter class for generating instances of 2-dimensional Scatter Plot visualizations b...
Definition: PlotScatter.m:30

1 ParaDRAM - NOTE: Setting up the MATLAB programming language environment for a ParaDRAM simulation...

2 ParaDRAM - NOTE:

3 ParaDRAM - NOTE: The user-specified internal input file for ParaDRAM specifications detected.

4 ParaDRAM - NOTE: All ParaDRAM simulation specifications will be read from the specified internal namelist file...

5

6 ParaDRAM - NOTE: Variable `outputFileName` detected among the user-supplied specifications of the ParaDRAM sampler:

7 ParaDRAM - NOTE: "./out/run"

8 ParaDRAM - NOTE:

9 ParaDRAM - NOTE: Path to the current working directory:

10 ParaDRAM - NOTE: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov"

11 ParaDRAM - NOTE:

12 ParaDRAM - NOTE: Generating the requested directory for the ParaDRAM simulation output files:

13 ParaDRAM - NOTE: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/./out/"

14 ParaDRAM - NOTE:

15 ParaDRAM - NOTE: 3 counts of preexisting complete simulation runs with the same name prefix were detected.

16 ParaDRAM - NOTE:

17 ParaDRAM - NOTE: Checking for simulation restart possibility...

18 ParaDRAM - NOTE:

19 ParaDRAM - NOTE: Starting a fresh simulation run #4 from the most recent completed simulation...

20 ParaDRAM - NOTE:

21 ParaDRAM - NOTE: Running the simulation in serial on 1 process...

22 ParaDRAM - NOTE:

23 ParaDRAM - NOTE: Generating the new output report file:

24 ParaDRAM - NOTE:

25 ParaDRAM - NOTE: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/./out/run_run4_pid1_report.txt"

26 ParaDRAM - NOTE:

27 ParaDRAM - NOTE: Please see the output *_pid1_report.txt and *_pid1_progress.txt files for further realtime simulation details...

28

29 Accepted/Total Func. Call Dynamic/Overall Acc. Rate Elapsed/Remained Time [s]

30 ========================= ========================= =========================

31

32 609 / 1000 0.6090 / 0.6090 0.0068 / 0.0268

33 1180 / 2000 0.5710 / 0.5900 0.0122 / 0.0188

34 1756 / 3000 0.5760 / 0.5853 0.0176 / 0.0125

35 2343 / 4000 0.5870 / 0.5857 0.0227 / 0.0064

36 2919 / 5000 0.5760 / 0.5838 0.0278 / 0.0008

37 3000 / 5143 0.0810 / 0.5833 0.0285 / 0.0000

38

39

40 ParaDRAM - NOTE: Computing the statistical properties of the Markov chain...

41

42 ParaDRAM - NOTE: Computing the final refined i.i.d. sample size...

43

44 ParaDRAM - NOTE: Generating the output sample file:

45 ParaDRAM - NOTE: /home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/./out/run_run4_pid1_sample.txt

46

47 ParaDRAM - NOTE: Computing the statistical properties of the final output sample...

48

49

50 ParaDRAM - NOTE: Mission Accomplished.

51

52

53Use the following object methods to read the generated basic output files:

54

55 sampler.readChain() % Return a list of the contents of the output chain file(s).

56 sampler.readSample() % Return a list of i.i.d. sample(s) from the output sample file(s).

57 sampler.readReport() % Return a list of summary report(s) from the output report file(s).

58 sampler.readRestart() % Return a list of the contents of the ASCII output restart file(s).

59 sampler.readProgress() % Return a list of the contents of the output progress file(s).

60

61Use the following object method to read the generated basic output chain file and and unroll the contents as a Markov Chain:

62

63 sampler.readChainMarkov() % Return a list of the unrolled contents of the output chain file(s) as Markov Chains.

64

65Beware that the chain unrolling significantly increases the chain size and can be very slow.

66It can potentially overflow the computer RAM for high-dimensional target density functions.

67

68For more information and examples on the usage, visit:

69

70 https://www.cdslab.org/paramonte

71

72

734 files were detected matching pattern: "./out/run"

74processing file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run4_pid1_chain.txt"

75reading file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run4_pid1_chain.txt"

76done in 0.035809 seconds.

77ncol = 9, nrow = 3000

78adding the stats components...computing the sample correlation matrix...done in 0.090981 seconds.

79computing the sample covariance matrix...done in 0.030562 seconds.

80computing the sample autocorrelation...done in 0.158750 seconds.

81done in 0.087075 seconds.

82computing the sample correlation matrix...done in 0.011630 seconds.

83computing the sample covariance matrix...done in 0.007385 seconds.

84computing the sample autocorrelation...done in 0.025510 seconds.

85adding the visualization components...done in 1.069900 seconds.

86adding the ParaDRAM-specific visualization components...adding DRAM-specific visualizations to the chain object...done in 0.042881 seconds.

87processing file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run3_pid1_chain.txt"

88reading file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run3_pid1_chain.txt"

89done in 0.021096 seconds.

90ncol = 9, nrow = 3000

91adding the stats components...computing the sample correlation matrix...done in 0.011638 seconds.

92computing the sample covariance matrix...done in 0.004599 seconds.

93computing the sample autocorrelation...done in 0.026851 seconds.

94done in 0.046436 seconds.

95computing the sample correlation matrix...done in 0.004680 seconds.

96computing the sample covariance matrix...done in 0.003281 seconds.

97computing the sample autocorrelation...done in 0.019620 seconds.

98adding the visualization components...done in 0.357770 seconds.

99adding the ParaDRAM-specific visualization components...adding DRAM-specific visualizations to the chain object...done in 0.021560 seconds.

100processing file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run2_pid1_chain.txt"

101reading file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run2_pid1_chain.txt"

102done in 0.034319 seconds.

103ncol = 9, nrow = 3000

104adding the stats components...computing the sample correlation matrix...done in 0.013120 seconds.

105computing the sample covariance matrix...done in 0.004514 seconds.

106computing the sample autocorrelation...done in 0.025124 seconds.

107done in 0.033488 seconds.

108computing the sample correlation matrix...done in 0.006302 seconds.

109computing the sample covariance matrix...done in 0.005268 seconds.

110computing the sample autocorrelation...done in 0.023764 seconds.

111adding the visualization components...done in 0.342800 seconds.

112adding the ParaDRAM-specific visualization components...adding DRAM-specific visualizations to the chain object...done in 0.027261 seconds.

113processing file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run1_pid1_chain.txt"

114reading file: "/home/amir/git/paramonte/external/paramonted/doxygen/bld/linux/amd64/csid/csvs/native/lib/mem/serial/matlab/checking/pkg/example/sampling/Paradram/readChainMarkov/out/run_run1_pid1_chain.txt"

115done in 0.012995 seconds.

116ncol = 9, nrow = 3000

117adding the stats components...computing the sample correlation matrix...done in 0.009447 seconds.

118computing the sample covariance matrix...done in 0.002928 seconds.

119computing the sample autocorrelation...done in 0.019611 seconds.

120done in 0.033839 seconds.

121computing the sample correlation matrix...done in 0.005856 seconds.

122computing the sample covariance matrix...done in 0.003767 seconds.

123computing the sample autocorrelation...done in 0.020161 seconds.

124adding the visualization components...done in 0.299970 seconds.

125adding the ParaDRAM-specific visualization components...adding DRAM-specific visualizations to the chain object...done in 0.020134 seconds.

126 processID delayedRejectionStage meanAcceptanceRate proposalAdaptation burninLocation sampleWeight sampleLogFunc sampleState1 sampleState2

127 _________ _____________________ __________________ __________________ ______________ ____________ _________________ ____________________ ___________________

128 1 0 0.250000009666267 0 1 1 -50 0 0

129 1 0 0.250000009666267 0 1 1 -50 0 0

130 1 0 0.250000009666267 0 1 1 -50 0 0

131 1 0 0.250000009666267 0 1 1 -50 0 0

132 1 0 0.342882473898846 0 1 1 -50.3362949891696 -0.32141397210834 -0.333584889057882

133 1 0 0.42093111931257 0.967499438460934 1 1 -50.2156223903078 -0.00626487809246379 -0.0277462070529085

134 1 0 0.42093111931257 0.967499438460934 1 1 -50.2156223903078 -0.00626487809246379 -0.0277462070529085

135 1 0 0.42093111931257 0.967499438460934 1 1 -50.2156223903078 -0.00626487809246379 -0.0277462070529085

136| 50%

137| 100% done in 0.050860 seconds.

list
function list()
Return a list of MATLAB strings containing the names of OS platforms supported by the ParaMonte MATLA...

Paradram::readChainMarkov
function readChainMarkov(in self, in pattern, in sep)
Return a list of objects of class pm.sampling.FileContentsChainDRAM containing the content(s) of the ...

Visualization of the example output ⛓

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Joshua Alexander Osborne, May 21 2024, 12:06 AM, University of Texas at Arlington
Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin

◆ run()

function Paradram::run	(	in	self,
		in	getLogFunc,
		in	ndim
	)

Run the ParaDRAM sampler and return nothing.

For example usage, see the documentation of the parent class of this method pm.sampler.Paradram.

Parameters

[in,out]	self	: The input/output parent object of class pm.sampling.Paradram which is implicitly passed to this dynamic method (not by the user).
[in]	getLogFunc	: The input MATLAB function handle or anonymous (lambda) function containing the implementation of the objective function to be sampled. This user-specified function must have the following interface, function logFunc = getLogFunc(state) end where, the input argument `state` is a vector of type MATLAB `double` of size `ndim` representing a single point from within the `ndim` dimensional domain of the mathematical object function to be explored. the output argument `logFunc` is a scalar of the same type as the input `state` containing the natural logarithm of the objective function at the specified input `state` within its domain.
[in]	ndim	: The input scalar positive-valued whole-number representing the number of dimensions of the domain of the user-specified objective function in the input `getLogFunc()`.

Possible calling interfaces ⛓

: sampler = pm.sampling.Paradram();

sampler.run(getLogFunc, ndim);

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, September 1, 2012, 12:00 AM, National Institute for Fusion Studies, The University of Texas at Austin

The documentation for this class was generated from the following file:

src/matlab/main/+pm/+sampling/@Paradram/Paradram.m

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Paradram()

ParaDRAM Simulation Specifications

Example Usage: Serial

Example Usage: Thread-Parallel

Example Usage: MPI-Parallel

Member Function Documentation

◆ getppm()

◆ readChainMarkov()

◆ run()