QCDMAPT: Program package for Analytic approach to QCD

A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in detail. The package includes both the calculated explicit expressions for relevant spectral functions up to the four-loop level and the subroutines for necessary integrals.

Program summary

Program title: QCDMAPTCatalogue identifier: AEGP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2579No. of bytes in distributed program, including test data, etc.: 180 052Distribution format: tar.gzProgramming language: Maple 9 and higherComputer: Any which supports Maple 9Operating system: Any which supports Maple 9Classification: 11.1, 11.5, 11.6Nature of problem: Subroutines helping computations within Analytic approach to QCD.Solution method: A program package for Maple is provided. It includes both the explicit expressions for relevant spectral functions and the subroutines for basic integrals used in the framework of Analytic approach to QCD.Running time: Template program running time is about a minute (depends on CPU).     

QCDF90: a set of Fortran 90 modules for a high-level, efficient implementation of QCD simulations

We present a complete set of Fortran 90 modules that can be used to write very compact, efficient, and high level QCD programs. The modules define fields (gauge, fermi, generators, complex, and real fields) as abstract data types, together with simpler objects such as SU (3) matrices or color vectors. Overloaded operators are then defined to perform all possible operations between the fields that may be required in a QCD simulation. QCD programs written using these modules need not have cumbersome subroutines and can be very simple and transparent. This is illustrated with two simple example programs.     

FDCHQHP: A Fortran package for heavy quarkonium hadroproduction

FDCHQHP is a Fortran package to calculate the transverse momentum (_pt$p_t$) distribution of yield and polarization for heavy quarkonium hadroproduction at next-to-leading-order (NLO) based on non-relativistic QCD(NRQCD) framework. It contains the complete color-singlet and color-octet intermediate states in present theoretical level, and is available to calculate different polarization parameters in different frames. As the LHC running now and in the future, it supplies a very useful tool to obtain theoretical prediction on the heavy quarkonium hadroproduction.     

TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95

We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula. TaylUR makes heavy use of operator overloading and other Fortran 95 features such as elemental functions.

Program summary

Program title: TaylURCatalogue identifier:ADXR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language:Fortran 95Computer:Any computer with a conforming Fortran 95 compilerOperating system:Any system with a conforming Fortran 95 compilerNo. of lines in distributed program, including test data, etc.:6286No. of bytes in distributed program, including test data, etc:14 994Distribution format:tar.gzNature of problem:Problems that require potentially high orders of derivatives with respect to some variables, such as e.g. expansions of Feynman diagrams in particle masses in perturbative Quantum Field Theory, and which cannot be treated using existing Fortran modules for automatic differentiation [C.W. Straka, ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables, Comput. Phys. Comm. 168 (2005) 123-139, arXiv:cs.MS/0503014; S. Stamatiadis, R. Prosmiti, S.C. Farantos, auto_deriv: Tool for automatic differentiation of a FORTRAN code, Comput. Phys. Comm. 127 (2000) 343-355].Solution method:Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula.Restrictions:Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders.Unusual features:No mixed higher-order derivatives are computed. The complex conjugation operation assumes all independent variables to be real.Running time:The running time of TaylUR operations depends linearly on the number of variables. Its dependence on the Taylor expansion order varies from linear (for linear operations) through quadratic (for multiplication) to exponential (for elementary function calls).     

MathQCDSR: A Mathematica package for QCD sum rules calculations

We present a software package written in Mathematica for standard QCD sum rules calculations. Two examples are given to demonstrate how to use the package. One is for the mass spectrum of octet baryons from two-point correlation functions; the other for the magnetic moments of octet baryons in the external-field method. The free package FeynCalc is used to handle the gamma-matrix algebra. In addition to two notebooks for the construction of the QCD sum rules, two corresponding notebooks are provided for a Monte Carlo-based numerical analysis, complete with in-line graphical display of sum rule matching, error distributions, and scatter plots for correlations.

Program summary

Program title: MathQCDSRCatalogue identifier: AEJA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 93 897No. of bytes in distributed program, including test data, etc.: 631 481Distribution format: tar.gzProgramming language: MathematicaComputer: PCs and WorkstationsOperating system: Any OS that supports Mathematica. The package has been tested under Windows XP, Macintosh OS X, and LinuxClassification: 11.5External routines: FeynCalc (http://www.feyncalc.org/). It is a freely available Mathematica package for high-energy physics calculations. Here it is used primarily to handle gamma-matrix algebra.Nature of problem: The QCD sum rule method is a nonperturbative approach to solving quantum chromodynamics (QCD), the fundamental theory of the strong force. The approach establishes a direct link between hadron phenomenology and the QCD vacuum structure via a few QCD parameters called vacuum condensates and susceptibilities. It has been widely applied in nuclear and particle physics to gain insight into various aspects of strong-interaction physics.Solution method: First, QCD sum rules are constructed by evaluating correlation functions from two perspectives. On the quark level, it leads to a function of QCD parameters and the Borel mass parameter M. On the hadronic level, it leads to a function of phenomenological parameters and the same M. By numerically matching the two sides over a range in M, the phenomenological parameters can be extracted. The construction involves a large amount of gamma-matrix algebra, Fourier transform, and Borel transform. The matching usually involves searching for minimum χ². We employ a Monte Carlo-based procedure to perform the analysis which allows for realistic error estimates.Restrictions: The package deals with only standard (SVZ) QCD sum rule calculations. It can be easily adapted to handle other variants of the method (like finite-energy sum rules). Due to the use of FeynCalc, two of the notebooks (qcdsr2pt-construction.nb and qcdsr3pt-construction.nb) only run on version 6.0 of Mathematica. The other two can run on any version.Additional comments: The package consists of the following 4 notebooks:

• • 

  qcdsr2pt-construction.nb – This notebook constructs the QCD sum rules for octet baryon masses and outputs them, one particle at a time, to disk in plain text for analysis. For reference, we include all the output files (named Mass-*.txt) as part of the package, totaling 8 files in about 20 lines. The user should generate the outputs on their own computer and check against the supplied ones.

• • 

  qcdsr2pt-analysis.nb – This notebook reads and analyzes the QCD sum rules produced by qcdsr2pt-construction.nb. The user can save the graphics in the analysis to disk in a variety of formats.

• • 

  qcdsr3pt-construction.nb – This notebook constructs the QCD sum rules for the octet baryon magnetic moments and outputs them, one particle at a time, to disk in plain text for analysis. Again, for reference, we include all the output files (named Mag-*.txt), totaling 24 files in about 400 lines. The user should generate the outputs on their own computer and check against the supplied ones to make sure the program is running properly.

• • 

  qcdsr3pt-analysis.nb – This notebook reads and analyzes the QCD sum rules produced by qcdsr3pt-construction.nb. The user can save the graphics in the analysis to disk in a variety of formats.

Each notebook can be run separately, apart from the simple interface between the construction and analysis programs via plain text files written to disk.Running time: For mass calculations, qcdsr2ptconstruction.nb and qcdsr2pt-analysis.nb take about a minute each to run on a laptop. For magnetic moment calculations, qcdsr3pt-construction.nb can take up to 10 minutes for a given particle, and qcdsr3pt-analysis.nb typically a few minutes, depending on the number of Monte Carlo samples.     

TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives.

New version program summary

Program title: TaylURCatalogue identifier: ADXR_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPLv2No. of lines in distributed program, including test data, etc.: 6750No. of bytes in distributed program, including test data, etc.: 19 162Distribution format: tar.gzProgramming language: Fortran 95Computer: Any computer with a conforming Fortran 95 compilerOperating system: Any system with a conforming Fortran 95 compilerClassification: 4.12, 4.14Catalogue identifier of previous version: ADXR_v2_0Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 710Does the new version supersede the previous version?: YesNature of problem: Problems that require potentially high orders of partial derivatives with respect to several variables or derivatives of complex-valued functions, such as e.g. momentum or mass expansions of Feynman diagrams in perturbative QFT, and which previous versions of this TaylUR [1,2] cannot handle due to their lack of support for mixed partial derivatives.Solution method: Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few partial derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using multivariate forms [3] of Leibniz's rule where ν=(ν₁,…,νd), , , Dνf=^∂|ν|f/(ν₁^∂x₁?νd^∂xd), and μ<ν iff either |μ|<|ν| or |μ|=|ν|,μ₁=ν₁,…,μk=νk,μk+1<νk+1 for some k∈{0,…,d−1}, and of Fàa di Bruno's formula where the sum is over , . An indexed storage system is used to store the higher-order derivative tensors in a one-dimensional array. The relevant indices (k₁,…,ks;λ₁,…,λs) and the weights occurring in the sums in Leibniz's and Fàa di Bruno's formula are precomputed at startup and stored in static arrays for later use.Reasons for new version: The earlier version lacked support for mixed partial derivatives, but a number of projects of interest required them.Summary of revisions: The internal representation of a taylor object has changed to a one-dimensional array which contains the partial derivatives in ascending order, and in lexicographic order of the corresponding multiindex within the same order. The necessary mappings between multiindices and indices into the taylor objects' internal array are computed at startup. To support the change to a genuinely multivariate taylor type, the DERIVATIVE function is now implemented via an interface that accepts both the older format derivative(f,mu,n) and also a new format derivative(f,mu(:))=Dμf that allows access to mixed partial derivatives. Another related extension to the functionality of the module is the HESSIAN function that returns the Hessian matrix of second derivatives of its argument. Since the calculation of all mixed partial derivatives can be very costly, and in many cases only some subset is actually needed, a masking facility has been added. Calling the subroutine DEACTIVATE_DERIVATIVE with a multiindex as an argument will deactivate the calculation of the partial derivative belonging to that multiindex, and of all partial derivatives it can feed into. Similarly, calling the subroutine ACTIVATE_DERIVATIVE will activate the calculation of the partial derivative belonging to its argument, and of all partial derivatives that can feed into it. Moreover, it is possible to turn off the computation of mixed derivatives altogether by setting Diagonal_taylors to .TRUE.. It should be noted that any change of Diagonal_taylors or Taylor_order invalidates all existing taylor objects. To aid the better integration of TaylUR into the HPSrc library [4], routines SET_DERIVATIVE and SET_ALL_DERIVATIVES are provided as a means of manually constructing a taylor object with given derivatives.Restrictions: Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders.Unusual features: These are the same as in previous versions, but are enumerated again here for clarity. The complex conjugation operation assumes all independent variables to be real. The functions REAL and AIMAG do not convert to real type, but return a result of type taylor (with the real/imaginary part of each derivative taken) instead. The user-defined functions VALUE, REALVALUE and IMAGVALUE, which return the value of a taylor object as a complex number, and the real and imaginary part of this value, respectively, as a real number are also provided. Fortran 95 intrinsics that are defined only for arguments of real type (ACOS, AINT, ANINT, ASIN, ATAN, ATAN2, CEILING, DIM, FLOOR, INT, LOG10, MAX, MAXLOC, MAXVAL, MIN, MINLOC, MINVAL, MOD, MODULO, NINT, SIGN) will silently take the real part of taylor-valued arguments unless the module variable Real_args_warn is set to .TRUE., in which case they will return a quiet NaN value (if supported by the compiler) when called with a taylor argument whose imaginary part exceeds the module variable Real_args_tol. In those cases where the derivative of a function becomes undefined at certain points (as for ABS, AINT, ANINT, MAX, MIN, MOD, and MODULO), while the value is well defined, the derivative fields will be filled with quiet NaN values (if supported by the compiler).Additional comments: This version of TaylUR is released under the second version of the GNU General Public License (GPLv2). Therefore anyone is free to use or modify the code for their own calculations. As part of the licensing, it is requested that any publications including results from the use of TaylUR or any modification derived from it cite Refs. [1,2] as well as this paper. Finally, users are also requested to communicate to the author details of such publications, as well as of any bugs found or of required or useful modifications made or desired by them.Running time: The running time of TaylUR operations grows rapidly with both the number of variables and the Taylor expansion order. Judicious use of the masking facility to drop unneeded higher derivatives can lead to significant accelerations, as can activation of the Diagonal_taylors variable whenever mixed partial derivatives are not needed.Acknowledgments: The author thanks Alistair Hart for helpful comments and suggestions. This work is supported by the Deutsche Forschungsgemeinschaft in the SFB/TR 09.References:

[1]

G.M. von Hippel, TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 174 (2006) 569.

[2]

G.M. von Hippel, New version announcement for TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 176 (2007) 710.

[3]

G.M. Constantine, T.H. Savits, A multivariate Faa di Bruno formula with applications, Trans. Amer. Math. Soc. 348 (2) (1996) 503.

[4]

A. Hart, G.M. von Hippel, R.R. Horgan, E.H. Müller, Automated generation of lattice QCD Feynman rules, Comput. Phys. Comm. 180 (2009) 2698, doi:10.1016/j.cpc.2009.04.021, arXiv:0904.0375.

     

New version of PLNoise: a package for exact numerical simulation of power-law noises

In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/fα noises with 0<α?2. Here I extend the algorithm to generate 1/fα noises with 2<α?4 (black noises). The method is exact in the sense that it produces a sampled process with a theoretically guaranteed range-limited power-law spectrum for any arbitrary sequence of sampling intervals, i.e. the sampling times may be unevenly spaced.

Program summary

Title of program: PLNoiseCatalogue identifier:ADXV_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v2_0.htmlLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language used: ANSI CComputer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4Operating system: All operating systems capable of running an ANSI C compilerRAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2⋅¹⁰⁴, the RAM taken by the list is 200 KbytesExternal routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press., Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine.No. of lines in distributed program, including test data, etc.:2975No. of bytes in distributed program, including test data, etc.:194 588Distribution format:tar.gzCatalogue identifier of previous version: ADXV_v1_0Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212Does the new version supersede the previous version?: YesNature of problem: Exact generation of different types of colored noise.Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701], possibly followed by an integration step to produce noise with spectral index >2.Reasons for the new version: Extension to 1/fα noises with spectral index 2<α?4: the new version generates both noises with spectral with spectral index 0<α?2 and with 2<α?4.Summary of revisions: Although the overall structure remains the same, one routine has been added and several changes have been made throughout the code to include the new integration step.Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing.Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy.Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 3 in the long write-up, the generation routine took on average about 75 μs for each sample.     

tweezercalib 2.0: Faster version of MatLab package for precise calibration of optical tweezers

We present a vectorized version of the MatLab (MathWorks Inc.) package tweezercalib for calibration of optical tweezers with precision. The calibration is based on the power spectrum of the Brownian motion of a dielectric bead trapped in the tweezers. Precision is achieved by accounting for a number of factors that affect this power spectrum, as described in vs. 1 of the package [I.M. Toli?-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Matlab program for precision calibration of optical tweezers, Comput. Phys. Comm. 159 (2004) 225-240]. The graphical user interface allows the user to include or leave out each of these factors. Several “health tests” are applied to the experimental data during calibration, and test results are displayed graphically. Thus, the user can easily see whether the data comply with the theory used for their interpretation. Final calibration results are given with statistical errors and covariance matrix.

New version program summary

Title of program: tweezercalibCatalogue identifier: ADTV_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTV_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandReference in CPC to previous version: I.M. Toli?-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Comput. Phys. Comm. 159 (2004) 225Catalogue identifier of previous version: ADTVDoes the new version supersede the original program: YesComputer for which the program is designed and others on which it has been tested: General computer running MatLab (Mathworks Inc.)Operating systems under with the program has been tested: Windows2000, Windows-XP, LinuxProgramming language used: MatLab (Mathworks Inc.), standard licenseMemory required to execute with typical data: Of order four times the size of the data fileHigh speed storage required: noneNo. of lines in distributed program, including test data, etc.: 135 989No. of bytes in distributed program, including test data, etc.: 1 527 611Distribution format: tar. gzNature of physical problem: Calibrate optical tweezers with precision by fitting theory to experimental power spectrum of position of bead doing Brownian motion in incompressible fluid, possibly near microscope cover slip, while trapped in optical tweezers. Thereby determine spring constant of optical trap and conversion factor for arbitrary-units-to-nanometers for detection system.Method of solution: Elimination of cross-talk between quadrant photo-diode's output channels for positions (optional). Check that distribution of recorded positions agrees with Boltzmann distribution of bead in harmonic trap. Data compression and noise reduction by blocking method applied to power spectrum. Full accounting for hydrodynamic effects: Frequency-dependent drag force and interaction with nearby cover slip (optional). Full accounting for electronic filters (optional), for “virtual filtering” caused by detection system (optional). Full accounting for aliasing caused by finite sampling rate (optional). Standard non-linear least-squares fitting. Statistical support for fit is given, with several plots facilitating inspection of consistency and quality of data and fit.Summary of revisions: A faster fitting routine, adapted from [J. Nocedal, Y.x. Yuan, Combining trust region and line search techniques, Technical Report OTC 98/04, Optimization Technology Center, 1998; W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986], is applied. It uses fewer function evaluations, and the remaining function evaluations have been vectorized. Calls to routines in Toolboxes not included with a standard MatLab license have been replaced by calls to routines that are included in the present package. Fitting parameters are rescaled to ensure that they are all of roughly the same size (of order 1) while being fitted. Generally, the program package has been updated to comply with MatLab, vs. 7.0, and optimized for speed.Restrictions on the complexity of the problem: Data should be positions of bead doing Brownian motion while held by optical tweezers. For high precision in final results, data should be time series measured over a long time, with sufficiently high experimental sampling rate: The sampling rate should be well above the characteristic frequency of the trap, the so-called corner frequency. Thus, the sampling frequency should typically be larger than 10 kHz. The Fast Fourier Transform used works optimally when the time series contain n² data points, and long measurement time is obtained with n>12-15. Finally, the optics should be set to ensure a harmonic trapping potential in the range of positions visited by the bead. The fitting procedure checks for harmonic potential.Typical running time: SecondsUnusual features of the program: NoneReferences: The theoretical underpinnings for the procedure are found in [K. Berg-Sørensen, H. Flyvbjerg, Power spectrum analysis for optical tweezers, Rev. Sci. Ins. 75 (2004) 594-612].     

A new Fortran 90 program to compute regular and irregular associated Legendre functions

We present a modern Fortran 90 code to compute the regular and irregular associated Legendre functions for all x∈(−1,+1) (on the cut) and |x|>1 and integer degree (l) and order (m). The code applies either forward or backward recursion in (l) and (m) in the stable direction, starting with analytically known values for forward recursion and considering both a Wronskian based and a modified Miller's method for backward recursion. While some Fortran 77 codes existed for computing the functions off the cut, no Fortran 90 code was available for accurately computing the functions for all real values of x different from x=±1 where the irregular functions are not defined.

Program summary

Program title: Associated Legendre FunctionsCatalogue identifier: AEHE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 6722No. of bytes in distributed program, including test data, etc.: 310 210Distribution format: tar.gzProgramming language: Fortran 90Computer: Linux systemsOperating system: LinuxRAM: bytesClassification: 4.7Nature of problem: Compute the regular and irregular associated Legendre functions for integer values of the degree and order and for all real arguments. The computation of the interaction of two electrons, 1/|r₁−r₂|, in prolate spheroidal coordinates is used as one example where these functions are required for all values of the argument and we are able to easily compare the series expansion in associated Legendre functions and the exact value.Solution method: The code evaluates the regular and irregular associated Legendre functions using forward recursion when |x|<1 starting the recursion with the analytically known values of the first two members of the sequence. For values of the argument |x|<1, the upward recursion over the degree for the regular functions is numerically stable. For the irregular functions, backward recursion must be applied and a suitable method of starting the recursion is required. The program has two options; a modified version of Miller's algorithm and the use of the Wronskian relation between the regular and irregular functions, which was the method considered in [1]. Both approaches require the computation of a continued fraction to begin the recursion. The Wronskian method (which can also be described as a modified Miller's method) is a convenient method of computations when both the regular and irregular functions are needed.Running time: The example tests provided take a few seconds to run.References:

• [1] 

  A. Gil, J. Segura, A code to evaluate prolate and oblate spheroidal harmonics, Comput. Phys. Commun. 108 (1998) 267–278.

     

A new version of the CADNA library for estimating round-off error propagation in Fortran programs

The CADNA library enables one to estimate, using a probabilistic approach, round-off error propagation in any simulation program. CADNA provides new numerical types, the so-called stochastic types, on which round-off errors can be estimated. Furthermore CADNA contains the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. On 64-bit processors, depending on the rounding mode chosen, the mathematical library associated with the GNU Fortran compiler may provide incorrect results or generate severe bugs. Therefore the CADNA library has been improved to enable the numerical validation of programs on 64-bit processors.

New version program summary

Program title: CADNACatalogue identifier: AEAT_v1_1Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_1.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 28 488No. of bytes in distributed program, including test data, etc.: 463 778Distribution format: tar.gzProgramming language: FortranNOTE: A C++ version of this program is available in the Library as AEGQ_v1_0Computer: PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBMOperating system: LINUX, UNIXClassification: 6.5Catalogue identifier of previous version: AEAT_v1_0Journal reference of previous version: Comput. Phys. Commun. 178 (2008) 933Does the new version supersede the previous version?: YesNature of problem: A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time.Solution method: The CADNA library [1-3] implements Discrete Stochastic Arithmetic [4,5] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic.Reasons for new version: On 64-bit processors, the mathematical library associated with the GNU Fortran compiler may provide incorrect results or generate severe bugs with rounding towards −∞ and +∞, which the random rounding mode is based on. Therefore a particular definition of mathematical functions for stochastic arguments has been included in the CADNA library to enable its use with the GNU Fortran compiler on 64-bit processors.Summary of revisions: If CADNA is used on a 64-bit processor with the GNU Fortran compiler, mathematical functions are computed with rounding to the nearest, otherwise they are computed with the random rounding mode. It must be pointed out that the knowledge of the accuracy of the stochastic argument of a mathematical function is never lost.Restrictions: CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as product or sum must not be used. Only the arithmetic operators and the abs, min, max and sqrt functions can be used for arrays.Additional comments: In the library archive, users are advised to read the INSTALL file first. The doc directory contains a user guide named ug.cadna.pdf which shows how to control the numerical accuracy of a program using CADNA, provides installation instructions and describes test runs. The source code, which is located in the src directory, consists of one assembly language file (cadna_rounding.s) and eighteen Fortran language files. cadna_rounding.s is a symbolic link to the assembly file corresponding to the processor and the Fortran compiler used. This assembly file contains routines which are frequently called in the CADNA Fortran files to change the rounding mode. The Fortran language files contain the definition of the stochastic types on which the control of accuracy can be performed, CADNA specific functions (for instance to enable or disable the detection of numerical instabilities), the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. The examples directory contains seven test runs which illustrate the use of the CADNA library and the benefits of Discrete Stochastic Arithmetic.Running time: The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected.References:

[1]

The CADNA library, URL address: http://www.lip6.fr/cadna.

[2]

F. Jézéquel, J.-M. Chesneaux, CADNA: a library for estimating round-off error propagation, Comput. Phys. Commun. 178 (12) (2008) 933-955.

[3]

N.S. Scott, F. Jézéquel, C. Denis, J.-M. Chesneaux, Numerical ‘health check’ for scientific codes: the CADNA approach, Comput. Phys. Commun. 176 (8) (2007) 507-521.

[4]

J. Vignes, A stochastic arithmetic for reliable scientific computation, Math. Comput. Simul. 35 (1993) 233-261.

[5]

J. Vignes, Discrete stochastic arithmetic for validating results of numerical software, Numer. Algorithms 37 (2004) 377-390.

     

A new version of Scilab software package for the study of dynamical systems

This work presents a new version of a software package for the study of chaotic flows, maps and fractals [1]. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well-known examples are implemented, with the capability of the users inserting their own ODE or iterative equations.

New version program summary

Program title: Chaos v2.0Catalogue identifier: AEAP_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1275No. of bytes in distributed program, including test data, etc.: 7135Distribution format: tar.gzProgramming language: Scilab 5.1.1. Scilab 5.1.1 should be installed before running the program. Information about the installation can be found at http://wiki.scilab.org/howto/install/windows.Computer: PC-compatible running Scilab on MS Windows or LinuxOperating system: Windows XP, LinuxRAM: below 150 MegabytesClassification: 6.2Catalogue identifier of previous version: AEAP_v1_0Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 788Does the new version supersede the previous version?: YesNature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE).Solution method:

1.

Numerical solving of ordinary differential equations for the study of chaotic flows. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincare sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies.

2.

Numerical solving of iterative equations for the study of maps and fractals.

Reasons for new version: The program has been updated to use the new version 5.1.1 of Scilab with new graphical capabilities [2]. Moreover, new use cases have been added which make the handling of the program easier and more efficient.Summary of revisions:

1.

A new use case concerning coupled predator-prey models has been added [3].

2.

Three new use cases concerning fractals (Sierpinsky gasket, Barnsley's Fern and Tree) have been added [3].

3.

The graphical user interface (GUI) of the program has been reconstructed to include the new use cases.

4.

The program has been updated to use Scilab 5.1.1 with the new graphical capabilities.

Additional comments: The program package contains 12 subprograms.

•

interface.sce - the graphical user interface (GUI) that permits the choice of a routine as follows

•

1.sci - Lorenz dynamical system

•

2.sci - Chua dynamical system

•

3.sci - Rosler dynamical system

•

4.sci - Henon map

•

5.sci - Lyapunov exponents for Lorenz dynamical system

•

6.sci - Lyapunov exponent for the logistic map

•

7.sci - Shannon entropy for the logistic map

•

8.sci - Coupled predator-prey model

•

1f.sci - Sierpinsky gasket

•

2f.sci - Barnsley's Fern

•

3f.sci - Barnsley's Tree

Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE, Lyapunov exponents calculation and fractals.References:

[1]

C.C. Bordeianu, C. Besliu, Al. Jipa, D. Felea, I. V. Grossu, Comput. Phys. Comm. 178 (2008) 788.

[2]

S. Campbell, J.P. Chancelier, R. Nikoukhah, Modeling and Simulation in Scilab/Scicos, Springer, 2006.

[3]

R.H. Landau, M.J. Paez, C.C. Bordeianu, A Survey of Computational Physics, Introductory Computational Science, Princeton University Press, 2008.

     

An enhanced version of SMMP—open-source software package for simulation of proteins

We describe a revised and updated version of the program package SMMP (Simple Molecular Mechanics for Proteins) [F. Eisenmenger, U.H.E. Hansmann, Sh. Hayryan, C.-K. Hu, Comput. Phys. Comm. 138 (2001) 192-212]. SMMP is an open-source FORTRAN package for molecular simulation of proteins within the standard geometry model. It is designed as a simple and inexpensive tool for researchers and students to become familiar with protein simulation techniques. This announcement describes the first major revision of this software package and its newly added features.

Program summary

Title of program:SMMPCatalogue identifier:ADOJ₋v2₋0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADOJ_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating system under which the program has been tested:LINUX systemProgramming language used:FORTRANComputer:PC PentiumNumber of lines in distributed program, including test data, etc.:18 492Number of bytes in distributed program, including test data, etc.:278 995Distribution format:ASCIICard punching code:ASCIICatalogue Identifier of previous version:ADOJJournal Reference of previous version:F. Eisenmenger, U.H.E. Hansmann, Sh. Hayryan, C.-K. Hu, Comput. Phys. Comm. 138 (2001) 192-212Does the new version supersede the previous version?:YesNature of physical problem:Molecular mechanics computations and Monte Carlo simulation of proteinsReasons for the new version:Increased functionalitySummary of revisions:Changes in energy function and protein representation; differences in program structure and organization; new functionalities added; miscellaneous changes and additionsMethod of solution:Utilizes ECEPP2/3 and FLEX potentials. Includes Monte Carlo simulation algorithms for canonical, as well as for generalized ensemblesRestrictions on the complexity of the problem:The consumed CPU time increases with the size of protein moleculeTypical running time:Depends on the size of the molecule under simulationUnusual features of the program:No     

L1PMA: A Fortran 77 package for best L1 piecewise monotonic data smoothing

Fortran 77 software is presented for the calculation of a best L₁ approximation to n measurements that include random errors by requiring k−1 sign changes in the first divided differences of the approximation or equivalently k monotonic sections, alternately increasing and decreasing. A dynamic programming algorithm separates the measurements into optimal disjoint sections of adjacent data and applies to each section a single L₁ monotonic calculation. The most distinctive feature of the algorithm is that it terminates at a global minimum in at most n³+O(kn²) computer operations, although this calculation can exhibit O(n^k) local minima, because the optimal positions of the turning points are also unknowns of the optimization process. The arithmetic operations involved in this calculation are comparisons mainly spent in finding the medians of subranges of data during the monotonic calculations. The package employs techniques for median and for best L₁ monotonic approximation, while full details of these techniques are specified. The package has been applied and tested on a variety of data that have substantial differences and showed quadratic behaviour in n. Some numerical results demonstrate the performance of the method. Further, there is a commentary on the division of the code into subroutines. Driver programs and numerical examples with output are provided to help new users of the method. Besides that piecewise monotonicity is a property of a wide range of functions, an important application of the method is in estimating turning points of a function from some noisy measurements of its values.     

ARVO: A Fortran package for computing the solvent accessible surface area and the excluded volume of overlapping spheres via analytic equations

In calculating the solvation energy of proteins, the hydration effects, drug binding, molecular docking, etc., it is important to have an efficient and exact algorithms for computing the solvent accessible surface area and the excluded volume of macromolecules. Here we present a Fortran package based on the new exact analytical methods for computing volume and surface area of overlapping spheres. In the considered procedure the surface area and volume are expressed as surface integrals of the second kind over the closed region. Using the stereographic projection the surface integrals are transformed to a sum of double integrals which are reduced to the curve integrals. MPI Fortran version is described as well. The package is also useful for computing the percolation probability of continuum percolation models.

Program summary

Title of program: ARVOCatalogue identifier: ADULProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADULProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating system under which the program has been tested: LINUX system and Windows systemProgramming language used: FORTRANComputer: PC Pentium; SPP'2000;Number of bytes in distributed program, including test data, etc.: 322 633Number of lines in distributed program, including test data, etc.: 5051Distribution format: tar.gzCard punching code: ASCIINature of physical problem: Molecular mechanics computations, continuum percolations.Method of solution: Numerical algorithm based on the analytical formulas, after using the stereographic transformation.Restriction on the complexity of the problem: The program does not account explicitly for cavities inside the molecule.Typical running time: Depends on the size of the molecule under consideration.Unusual features of the program: No     

The collisions of high-velocity clouds with the galactic halo

Spiral galaxies are surrounded by a widely distributed hot coronal gas and seem to be fed by infalling clouds of neutral hydrogen gas with low metallicity and high velocities. We numerically study plasma waves produced by the collisions of these high-velocity clouds (HVCs) with the hot halo gas and with the gaseous disk. In particular, we tackle two problems numerically: 1) collisions of HVCs with the galactic halo gas and 2) the dispersion relations to obtain the phase and group velocities of plasma waves from the equations of plasma motion as well as further important physical characteristics such as magnetic tension force, gas pressure, etc. The obtained results allow us to understand the nature of MHD waves produced during the collisions in galactic media and lead to the suggestion that these waves can heat the ambient halo gas. These calculations are aiming at leading to a better understanding of dynamics and interaction of HVCs with the galactic halo and of the importance of MHD waves as a heating process of the halo gas.     

A Comparison of Co-Array Fortran and OpenMP Fortran for SPMD Programming

Co-Array Fortran, formally called F^––, is a small set of extensions to Fortran 90/95 for Single-Program-Multiple-Data (SPMD) parallel processing. OpenMP Fortran is a set of compiler directives that provide a high level interface to threads in Fortran, with both thread-local and thread-shared memory. OpenMP is primarily designed for loop-level directive-based parallelization, but it can also be used for SPMD programs by spawning multiple threads as soon as the program starts and having each thread then execute the same code independently for the duration of the run. The similarities and differences between these two SPMD programming models are described.Co-Array Fortran can be implemented using either threads or processes, and is therefore applicable to a wider range of machine types than OpenMP Fortran. It has also been designed from the ground up to support the SPMD programming style. To simplify the implementation of Co-Array Fortran, a formal Subset is introduced that allows the mapping of co-arrays onto standard Fortran arrays of higher rank. An OpenMP Fortran compiler can be extended to support Subset Co-Array Fortran with relatively little effort.