here - Paramotopy
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1. Input Files The input file format for Paramotopy is fairly simple Extra white space on a single line is acceptable but there must be no extra blank lines Illustrative examples appear in Files 1 2 3 The input file consists of 1 Declare the numbers of functions a variable groups b parameters c and constants d in one line separated by spaces e g abcd Functions declaration without any name declarations or terminating semi colons Variable groups come next with each group getting its own line variables are comma sepa rated and there is no terminating character Constant declaration with the word constant appearing before a comma separated semi colon terminated line containing the constant names Each constant gets its own line with name value being the format 5 Finally the type of solve is indicated e 0 indicates the computer will supply a mesh The final lines tell the name of each pa rameter starting point of discretization ending point of discretization and number of discretization points The format for a line of parameter declaration is name abcde where startpoint a b endpoint c di and e indicates the number of discretization points which must be an integer See File 2 e 1 asserts the user supplies a text file containing parameter values the next line is the name of the file and the final lines simply indicate the parameter names See File 3 nfunct nvargrp nparam nconst2. Ask the user what to do e Generation of random values at new folder during program If while running the program the user wishes to start a new run should Paramotopy Keep the random values currently in use or Make a new set of random values e Set temp file location use ramdisk for temp files Bertini uses hard disk IO to communicate with itself and other processes This can overwhelm the hard disk uses read write cycles reducing the lifetime of a hard drive and injures per formance Using a location in memory as a hard disk otherwise known as a ramdisk will grant you enormous performance gains Two locations are scanned for existence by default dev shm and tmp If either are found the user is prompted for confirmation The user may also choose a custom location However at present time the name of the temporary file location root directory must be the same across all computers used Note Paramotopy does not guarantee that the chosen location is usable in the desired fashion the user must ensure that the temporary location is read writable e Max Data File Size The text files produced by Paramotopy grow in time of course To ensure that you don t produce unwieldly files change the maximum file size for data files The default is 64MB This maximum is not a hard maximum in the sense that a new file is started only after the max is achieved e Deletion of tmp files Step2 involves creation of many temporary fil
3. as per the license agreement For installation of dependencies on a Mac consider using Homebrew In addition Paramotopy relies on a suitably compiled version of Bertini which has the following dependencies e mpfr e gmp e Bison e Flex e MPICH2 When Bertini is compiled for use with Paramotopy it must be compiled in two ways into an executable and a library When compiled into the executable it must have the flag D HAVE MPI for use with Paramotopy In contrast the library must not have the D HAVE MPI flag In addition we redefine main to be bertini main via the command Dmain bertini main Compilation is a little different of every machine of course and a future milestone is to use something like configure to handle setting everything up properly for start to finish with minimal user input If you would like to help with this please contact the authors As it stands now Paramotopy is compiled using a Makefile Various options are available in the makefile e TIMING choose YES or NO Conditional compilation using ifdef in the code turns on or off timing statements for Step2 e OPT Sets available compiler options such as the 0 optimization flag and compiler warning levels These are left user set as every compiler has different options e VERBOSE Chooses whether Step2 ought to be compiled with ifdefs for extra output to the screen Additionally the user before compiling or in the process of must set
4. lt all four must be present functionl function2 no terminating semicolon T do not name functions function n no sign vargroupl vargroup2 constant cl c2 ck note semicolon omit if nconst 0 cl 0 1234 semicolon and equal sign c2 0 9 I capital I for sqrt 1 ck 1 1 I 0 or 1 choose mesh or userdefined filename only if userdefined pl 0010 10 or pl declare mesh discretization p2 0010 64 or p2 or parameter name pj 0010 13 Or pj File 1 Generic Paramotopy input file Paramotopy has minimal error correction in this portion of the program so an error in an input file is likely to cause a fairly benign will not corrupt data program crash If the program is able to parse the input file without errors it will display information to the screen and the user may check everything has been imported correctly More syntax checking will be added later 171221 2 Fa k1 xa xb k2 c k4 ax f k5 f Daxa 3 Fb k1 xa xb k2 c k8 g k9 b f Db b 4 Fe k2 a xb k2 c k3 c k6 c e k7 g Dexc s Fd k3 c Ddxd e Fe k4 xaxe k5 x f k6 c e k7 g Dexe 7 Ff k4 a xe k5 f k8 g k9 b f Dfx f s Fg k6 c e k7 g k8 g k9 bx f Dg g oja b c d e f g 10 constant k3 k1 k5 k6 k7 k8 k9 Fa Fb Fc Fd Fe Ff Fg Da Db Dc Dd De Df Dg 11 k3 80349 12 k1 980389 13 k5 2 8034 14 k6 2 8018
5. 0203 c6 s5 0 4331 s5 s6 0 4318 cl xc2 0 1501 s1 0 0203 cl c2 c3 0 4331 cl c2 s3 0 4331 cl1 c3x s2 0 0203 cl xs2 s3 x 0 1501l cl 0 4318xc2xs1 0 0203 c2 c3 sl 0 4331 c2 slxs3 0 4331 c3x s1x s2 0 0203 s1 s2 s3 y 0 4331 c2 c3 0 4318 s2 0 0203 c2 s3 0 0203 c3 s2 0 4331 s2 s3 z s1 24 c1 2 1 s2 24 c2 2 1 s3 2 c3 2 1 s4 24 c4 2 1 s5 2 c5 2 1 s6 2 c6 2 1 1 cl1 s2 c2 s3 c3 84 c4 8s5 c5 86 c6 1 robomc 10000 a delta x y Z File 3 Paramotopy input file demonstrating use of user defined parameter file Line 1 indicates 12 equations lines 2 13 in 1 variable group line 14 with five parameters named on lines 17 21 and zero constant declarations Line 15 s 1 indicates Paramotopy should look for the file on the next line titled robomc_10000 The name of the file is arbitrary but should be at the same path at the input file The parameters are named a delta x y z oO 0 YN O Oc bh OQ NY RK BPR Be Be Be RB B RB H oO sy oana amp WN FO m 3 1 Monte Carlo Input Paramotopy enables the user to supply their own plain text file of parameter points over which to solve a parametrized family of polynomials The first line is an integer indicating the number of parameter points The remainder of the file gives the actual parameter values as one point per line with parameter real complex pairs separated by spaces See File 3
6. 15 k7 2 168776 16 k8 2 7982 17 k9 58973 18 Fa 4264 19 Fb 5284 20 Fc 1687 21 Fd 167896 22 Fe 5673 23 Ff 69386 24 Fg 79827 25 Da 0692 26 Db 08762 27 Dc 2897 23 Dd 0828 29 De 26967 30 Df 4238 31 Dg 5872 32 0 33 k4 0 0 10 40 34 k2 0010 50 File 2 Paramotopy input file demonstrating use of computer generated mesh and constant declaration Line 1 indicates 7 equations lines 2 8 in 1 variable group line 9 with five parameters lines 33 34 and 21 constant declarations 10 31 On line 32 0 tells Paramotopy to make a mesh from the parameters discretized in lines 33 34 Parameter k4 will be broken into 40 points on the complex line segment 0 Oi to 1 0i Similarly k2 will be broken into 50 points so a solve using this input file would have 2000 points total in the Step2 run a 10 11 12 13 14 15 16 17 18 19 20 21 12 15 0 0 4318 clxc2 0 2435xs1 0 0934xaxsl 0 0203 a cl s2 s3 0 0203 axcl xc2x c3 0 4318 c4 c5 0 1501 s4 0 0203 c4 c5 c6 0 4331 c4 c5 s6 0 4331 c4 c6 s5 0 0203 c4 s5 s6 delta 0 2435 cl 0 0934 axcl 0 4318 c2 sl 0 0203 a sl1 s2 s3 0 0203 axc2 c3 sl 0 1501 c4 0 4318 c5 s4 0 0203 c5x xc6 s4 0 4331 c5 s4 s6 0 4331 c6 s4 s5 0 0203 s4 s5 s6 0 0203 axc2 s3 0 4318 s2 0 0203 a c3 s2 0 4331 c5 c6 0 4318 s5 0 0203 c5 s6 0
7. as well Note that lines 4 10 and 14 20 are unmodified Bertini output complete with whitespace Paramotopy has a method implemented in Data Management which gathers and orders the data produced in a run as well as incorporating the re solved data generated in Failed Path Analysis Note that this method so far only gathers failed paths and solutions data file types The others have yet to be implemented The data gathering requires but does not check for free disk space available for at least the amount occupied by the generated data in bfiles filename run step2 DataGathered c The author Daniel Brake has some generic MATLAB code which can do basic parsing of some file types as well as data display methods If you need help with any aspect don t hesitate to ask Contact info in Section 1 1 18 6 Troubleshooting Known Problems e Stepl fails Are all the settings properly spelled and allowed Was the calling sequence correct Do you have the parallel version of Bertini installed Iry running Bertini on the created input file e Step2 fails Are all settings spelled properly and allowed Was the calling sequence correct Did Paramotopy correctly parse your input file Did the temporary files write to an acceptable location Try running Bertini on the created input file Bertini might provide a useful error report Turn off stifling of output so that you can read any generated error mes
8. to disk only when a threshold is reached To change this threshold change this buffer size e Manually set location of bertini executable Paramotopy automatically scans the current directory and PATH for Bertini at startup in that order and chooses the first instance of Bertini it finds If the user wishes to manually change the location for Bertini they should this option e Manually set location of step2 executable Same as for Bertini 4 7 FileIO files current settings name customtmplocation deletetmpfilesatend newfilethreshold 67108864 newrandom newfolder 9 previousdatamethod 1 saveprogresseverysomany 1 tempfilelocation writemeshtomc 9 Files amp c 1 Which folder to load at startup 2 Generation of random values when creating new folder 3 Set temp file location Use ramdisk for temp files 4 Max data file Size New file threshold 5 Deletion of temp files at end of run 6 Generation of mc mesh file for non user def runs F3 0 go back Figure 13 File IO menu e Load Data Folder Method At launch of Paramotopy if not supplied with an argument of the filename to load Paramotopy will ask the user for the filename Each filename gets its own folder for storing data and in this folder will be another folder containing the data for a run At launch Paramotopy will do one of the following Reload data from the most recent run Make a new run folder and make new start point 15
9. Paramotopy Parallel Parameter Homotopy via Bertini Daniel Brake and Matt Niemerg with Dan Bates Manual prepared by Daniel Brake Colorado State University Mathematics August 3 2015 Contents 1 Introduction Ll dntnBb 2 fans Rie Pe ba men 12 License 22 2 os 2 Getting Started 2 1 Compilation and Installation 2 2 Using Paramotopy 3 Input Files 3 1 Monte Carlo Input 4 Options amp Configuration 4 1 Stepl and Step2 Bertini Settings 4 2 Solver Modes 43 Path Failure oss 44 Parallelism 45 File Saving 4 6 System Settings Ay qeelO o ae we oe ke Se vu 4 8 Meta Settings 5 Data Gathering 6 Troubleshooting Known Problems Index m mM 10 10 11 11 14 14 15 16 18 19 20 1 Introduction The Paramotopy program is a compiled linux unix wrapper around Bertini which permits rapid parallel solving of parameterized polynomial systems It consists of two executable programs Paramotopy and Step2 and further depends on having a copy of the parallel version of Bertini Paramotopy is called from the command line and in turn calls Bertini and step2 Briefly homotopy continuation is the tracking of solutions from one system to another through continuous deformation a simplified example appears in Figure 1 Using a combination of pre diction and correction Bertini follows solutions through such a deformation First it obtains the s
10. an environment variable MACHINENAME to have the value of the name of their machine Then in the Makefile the user sets such things as the location of the necessary libraries and other machine specific parameters Simply issuing the make command should be enough to compile the programs once initial con figuration is completed 2 2 Using Paramotopy K ie koe ok ok ck ok ke ok oe ke OR ok kK k ok oe ke oe oe oe ok ok oe e ke e o Welcome to Paramotopy parametrized system analysis software by daniel brake and matthew niemerg with dan bates www paramotopy com danielthebrake8gmail com matthew niemerg gmail com OR k k k E k k k k k k k k k k k k k EE KEKE k Figure 3 The welcome screen If you do not supply the filename as the first argument to Paramotopy from the command line it will immediately prompt you for the name You cannot use the program without an input file Your choices 1 Parse an appropriate input file 2 Data Management 3 unprogrammed 4 Manage start point load save new 5 Write Step 1 6 Run Step 1 7 Run Step 2 8 Failed Path Analysis 99 Preferences 0 Quit the program Enter the integer value of your choice Figure 4 Main menu describing the available choices Use numeric input or whatever it prompts for If you just loaded the program it will describe what directory it is working in on WY O OG RB OQ Ww eR e e e Be Be BR BR p N OQ ow R DO NF o m 3
11. e indicates one parameter point and each real complex pair is separated by a space 4 Options amp Configuration Persistent configuration of Paramotopy is maintained through the HOME paramotopy paramotopyprefs xml file located in the home directory The following sections describe what the settings affect Note that since the preferences file is merely text the user could manually hack it with a text editor Preferences Main Menu Bertini settings Solver Modes Path failure resolution Parallelism Set files to save System Settings File IO MetaSettings return to paramotopy Figure 5 The Paramotopy main menu Interaction is via mainly numeric input at the console 4 1 Stepl and Step2 Bertini Settings Separate settings categories are present for both the Step1 and Step2 runs and persist from run to run and session to session These are written directly into the input files for Bertini and there is no error checking if the user sets a setting to one disallowed or misspells a name the Bertini calls in Stepl or Step2 will just ignore the setting Step1Settings current settings name value FINALTOL 1e 11 IMAGTHRESHOLD 0 0001 PRINTPATHMODULUS 20 SECURITYLEVEL TRACKTOLBEFOREEG 1e 05 TRACKTOLDURINGEG 1e 06 USERHOMOTOPY 0 Basic Step1 Settings 1 Change Setting 2 Remove Setting 3 Add Setting 4 Reset to Default Settings 0 Go Back Figure 6 Step1 Settings All settings are direct Bertini co
12. e mode If off then a single processor will be used for all portions of the program e Number of Files to send to workers at a time to minimize network traffic it is advisable to distribute the work in chunks Setting this value close to one will kill performance while setting it near the total number of parameter points will send all the work to a single processor It is up to the user to find balance though one rule of thumb would be to set this to total files kx processors with k perhaps 5 or 10 meaning that 5 or 10 batches would be sent to each processor through out the computation e Machinefile some MPI installations require a machine file for process distribution e Architecture calling set the call to start an MPI process on your machine Two defaults are built in mpiexec aprun You may also use your own although there is no error checking for whether your custom command exists or functions properly We will soon add the feature of custom calling sequences for more complex command strings e Number of processors used Set the number of processors for Step1 Step2 and rerunning of failed paths realized as Step2 13 runs There should be at least two processors for this mode as Paramotopy currently uses the master slave model with a single master If you wish to use only one process switch off parallel mode 4 5 File Saving SaveFiles current settings name value failed paths main data midpath da
13. empt to re solve adjust settings and delete files and start over for Step2 runs If tolerance tightening is enabled at each iteration of resolve the finaltol tracktolbeforeeg and tracktolduringeg values are decreased by a factor of ten e Set Num Iterations Path Failure mode will automatically try to re solve failed paths up to this number of times before returning back to the user for input e Reset to Default Settings Reset PathFailure settings to default hardcoded values 12 4 4 Parallelism Parallelism is achieved using MPICH2 Paramotopy itself acts as a gateway to the Step2 program where all the real work is done The gateway allows the user to load input files make new data folders change settings run Bertini for Step1 call Step2 and perform Failed Path Analysis on a completed Step2 run The gateway model was used because Bertini uses MPI itself and MPI Init O MPI Finalize can only be called once within a program Therefore Step2 uses the nonparallel version whereas Step1 can call either one parallelism current settings name value architecture mpiexec numfilesatatime 400 numprocs 4 parallel 1 usemachine 0 Parallelism 1 Switch Parallel On Off and consequential others 2 Number of Files to send to workers at a time 3 Machinefile 4 Architecture calling 5 Number of processors used 0 go back Figure 10 Parallelism menu e Switch Parallel On Off turn on or off parallel solv
14. es Each worker creates a folder in which to initialize Bertini named init where is the id number assigned by MPI Then each worker creates another folder named work with the same naming scheme in which it produces the data All Bertini data is created in this folder Switching this settings will toggle whether these folders ought to be deleted at the end of a successful run e Generation of mc mesh file for non user def runs User can choose whether step2 ought to create a text file containing all the parameter values for all points during a computer generated mesh run This file is usable in a user defined run However this file can be very large and eats hard drive write throughput so we have provided the option to not create this file 4 8 Meta Settings Meta Settings 1 Load a set of settings 2 Save current settings as default E Go Back Figure 14 Meta Settings menu e Load a set of settings Scans HOME paramotopy for xm1 files for settings and offers you a choice to load 16 e Save current settings as default Saves what you have in memory for settings right now as the default for future filenames 17 5 Data Gathering Paramotopy is capable of producing immense amounts of data Probably the two most useful files you can choose to save are nonsingular solutions and real solutions Both are easy to have a machine parse with predictable numbers of lines per parameter point At some points in pa
15. for an example of such a Paramotopy input file and File 4 for an example of the user defined file 10000 10 1 56133 0 0 156326 0 0 611479 0 0 430234 0 10 1 56133 0 0 423045 0 0 178196 0 0 498284 0 10 1 56133 0 0 683401 0 0 0113754 0 0 35804 0 10 1 56133 0 0 560595 0 0 178767 0 0 0282532 0 10 1 56133 0 0 391407 0 0 00876144 0 0 464572 0 10 1 56133 0 0 218755 0 0 530148 0 0 429091 0 10 1 56133 0 0 277281 0 0 620464 0 0 18738 0 10 1 56133 0 0 436947 0 0 116395 0 0 503699 0 10 1 56133 0 0 464191 0 0 185408 0 0 365677 0 10 1 56133 0 0 183529 0 0 348453 0 0 344025 0 10 1 56133 0 0 327672 0 0 047893 0 0 608647 0 10 1 56133 0 0 0981337 0 0 505425 0 0 0346073 0 10 1 56133 0 0 595407 0 0 204762 0 0 601097 0 10 1 56133 0 0 798536 0 0 1768 0 0 193611 0 10 1 56133 0 0 501227 0 0 465084 0 0 515747 0 10 1 56133 0 0 234762 0 0 466421 0 0 370907 0 10 1 56133 0 0 0867984 0 0 540995 0 0 518395 0 10 1 56133 0 0 477477 0 0 125201 0 0 561676 0 File 4 User defined parameter point file This file is named in the input file this is robomc_10000 as mentioned in File 3 and must be placed in the same directory doing otherwise is untested The first line of the file must be an integer indicating the number of parameter points which follow in this case 10000 This integer must be at most the number of parameter points in the file though it can be fewer For the remainder of the file each lin
16. nfig options 10 Options are to change delete and add a setting User may also reset all of that Step s settings and reset to default which are the Bertini default values as well Note that each setting has a type being either a string integer or double value Doubles may use the 1e 4 format for convenience While capitalization does not matter in Bertini Paramotopy is currently case sensitive so deleting or changing a setting requires the same capitalization as displayed 4 2 Solver Modes mode current settings name value main mode 0 standardstep2 1 startfilename nonsingular solutions Solver Mode Settings 1 Brute force vs Search 2 Standard step2 run 3 File to use for step2 start file go back Figure 7 Choose from a suite of modes and configuration options e Brute force vs Search choose whether to solve across the mesh or sampler you feed in or to search for solutions with a particular property e Standard step2 run choose to run a total degree solve each parameter point or use coefficient parameter homotopy as usual e Set the file to use for step2 start file User may select to use either the nonsingular_solutions or finite_solutions output from Stepl as the start file for Step2 solves 4 3 Path Failure Paramotopy detects failed paths that occur during a run and has methods for resolving the system repeatedly if necessary to get the proper solution set e Choose random sta
17. olutions to the initial system Taking discrete steps in complex valued time each solution path is tracked individually If suitable options are chosen in the configuration of the run precision will be automatically adjusted to compensate for loss of accuracy near system singularities due to poorly conditioned matrices Additionally Bertini has various endgame schemes for bringing the paths to successful completion as well as determining whether paths crossed or other problems happened along the way Nearly all these options may be accessed through Paramotopy For a thorough description of the Bertini program including many capabilities not used within Paramotopy see the Bertini User s Manual Paramotopy is implemented to make use of both the basic zero dimensional solve Bertini per forms by default as well as exploiting the userhomotopy mode An illustration of the scheme is in Figure 2 First Paramotopy performs what we define here to be a Stepl run Bertini finds all zero dimensional solutions to the system supplied to it for a set of complex parameter values randomly determined for this solve there will likely be superfluous paths Second Paramotopy tracks all meaningful solutions found in Stepl from nonsingular solutions to each parameter point at which the user wishes to solve this is called Step2 Performing the second step in this way will eliminate the extra paths from Stepl With respect to the soundness and reliabilit
18. rameter space polynomial systems will be faster to solve than others Combined with the use of a parallel machine this will result in data files which are out of order Whatever data collection method you use you must deal with this fact Data collection is achieved by simply copying the Bertini output file into memory and then along with the index of the parameter point and the parameter values into a collective output file The format is essentially what appears in File 5 Pri Pil Pr2 Pi2 0 00000000 2 0 200890604423765803e 40 0 860954559733244710586e 41 0 8394559733244710586e 41 0 21882676674265533030607e 40 o 0 Nn ont wre 0 000000000000000e 00 7 589415207398531e 19 1 589415207398531e 19 9 351243737687476e 19 m o m m 1 0 555556 0000000 2 m N m w m I 15 16 7 318364664277155e 19 9 520650327138336e 19 171 218033378151684e 18 0 000000000000000 e 00 18 19 0 8121868223093549866e 18 0 8704335463135312587e 18 20 0 1229193841385923155e 17 0 1420916030667911630e 19 File 5 Example output file from Paramotopy The first line of each file created by Paramotopy declares the names of the parameters Each parameter point gets its own section with the index lines 2 12 parameter values lines 3 13 and copied Bertini output This is an example of real solutions output so lines 4 14 indicate the number of solutions which follow The actual solutions appear
19. rt point Method When resolving points with failed paths Paramotopy can optionally choose a new start point before solving the set of fails To be developed is a variety of methods for choosing this start point e g specifying a distance from the original start point etc e Change security level ensure securitylevel 1 is turned on for more secure solution of failed paths e Tolerance Tightening When Failed Path Analysis is entered in Paramotopy the settings are those currently used 11 PathFailure current settings name value maxautoiterations 4l newrandommethod tightentolerances Path Failure Settings 1 Choose random start point Method 2 Tolerance Tightening 3 Set Num Iterations 5 Manage Bertini Settings 7 Reset fully to Default path failure Settings 0 Go Back Figure 8 Path Failure Settings menu The path failure analysis section of the program utilizes the Bertini preferences from the Stepl1 and Step2 sections optionally changing them with successive runs There were 84 points with path failures out of 2000 total points current iteration 0 PathFailure current settings name value maxautoiterations 3 newrandommethod 1 tightentolerances 1 turnon securitylevell 0 Path Failure Menu 1 ReRun Failed Paths 2 Clear Failed Path Data start over 3 Change path failure settings resets tolerance tightening 0 Go Back Figure 9 Path Failure Re solve menu User can continue to att
20. sages A list of known problems e There cannot be any spaces in folder or input file names 19 Index MACHINENAME 4 bertini location 15 mc mesh file 16 step2 location 15 bertini settings 10 choosing saved files 14 computer generated mesh 6 data file format 18 data file size 16 data gathering 18 failed path analysis 11 failed paths menu 12 file distribution 13 file I O menu 15 general settings menu 14 input file format 6 machinefile 13 main menu option 1 6 main menu option 2 18 meta settings 16 mode menu 11 monte carlo samplings 9 new run folders 16 parallelism preferences 13 preferences location 10 ramdisk 16 read buffer 15 restoring previous runs 15 start file 11 stifle output 15 temp files 16 user defined parameter files 6 9 20
21. stem f x i paths diverge g x i V infinity ch cn convergent t 0 complex time end tel start Figure 1 Generic Homotopy Continuation f x p same number of f x p superfluous g x paths for each p m d paths meaningful gt cn many faster cn single costly cn parameter solves initial solve Figure 2 Parameter Homotopy with initial Step run The authors wish to thank the following e Boost e MTRand e Zube 1 2 License Paramotopy is free open source software with restrictions The license is available on the web at paramotopy com Disclaimer Paramotopy and all related code executables and other material are offered without warranty for any purpose implied or explicit Any opinions findings and conclusions or recommendations expressed in this material are those of the author s and do not necessarily reflect the views of the National Science Foundation 2 Getting Started 2 1 Compilation and Installation Paramotopy has the following library dependencies e Tinyxml lies internally to the program s folders as per the license agreement e MPICH2 e Boost regex system filesystem for file manipulation and a few others Make sure you have the entire boost library Minimum version is 1 49 e OpenMP for the most accurate timing available Seems standard on nix variants these days e M TRand lies internally to the program s folders
22. ta nonsingular solutions raw data raw solutions real solutions singular solutions Sreore0r Files to Save 1 Change Files to Save 0 Go Back Figure 11 Paramotopy can save each of the output files from Bertini for each point at which it solves the input system failed paths is always saved the rest are optional Bertini produces several output files which may be desirable to keep The file named failed paths is always saved to enable Failed Path Analysis All other files are optional Some are more useful than others for humans or computers For a more thorough description of the output of Bertini see the Bertini User s Manual 4 6 System Settings System current settings name value bertinilocation Users ofloveandhate bin buffersize 65536 step2location Users ofloveandhate bin stifle 0 System Settings 1 Stifle Step2 Output 2 Change Buffer Size 3 Set location of bertini executable 4 Set location of stage2 executable 0 go back Figure 12 System Settings menu 14 e Stifle Step2 Output Bertini produces an overwhelming amount of screen output Not only is this annoying but sending text to the screen overwhelms the network It is suggested to stifle only when you are confident in the success of your Step2 runs Stifling by redirection to dev null produces a significant speedup e Change Buffer Size to minimize writes to the hard drive each worker buffers its files in memory and writes
23. y of this method theory dictates that off a set of measure zero an algebraic system will have the same number of complex roots throughout its parameter space Therefore we are virtually guaranteed that for a randomly chosen point in parameter space we will find the full generic number of solutions Then for Step2 as we track from the random point to the specific points at which we wish to solve we will find all the solutions Paramotopy uses a compiled library of Bertini MPICH 2 for process distribution OpenMP for accurate timing measurements TinyXML for preference and information storage and Boost for filesystem operations System requirements and compilation information may be found in Section 2 In Section 3 is presented the format for the input files as well as information on configuring and using Paramotopy Specific descriptions of options are given in Section 4 and data output is described in Section 5 Coarse troubleshooting tips are in Section 6 1 1 Contact For assistance with Paramotopy please contact Daniel Brake at danielthebrake gmail com For help with Bertini contact Daniel Brake Dan Bates bates math colostate edu or one of the other Bertini authors Acknowledgements e This research utilized the CSU ISTeC Cray HPC System supported by NSF Grant CNS 0923386 e This material is based upon work supported by the National Science Foundation under Grants No DMS 1025564 and DMS 1115668 Target Start system 3 sy
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