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A collection of general Fortran modules in the categories Computational, Date and Time, Input / Output, Math / Numerics, Screening, Sensitivity Analysis and Optimising / Fitting, and Miscellaneous.

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This is the JAMS Fortran library.

The JAMS Fortran library is a collection of general Fortran modules offering miscellaneous functions in the categories Computational, Date and Time, Input / Output, Math / Numerics, Screening, Sensitivity Analysis and Optimising / Fitting, and Miscellaneous.

Created November 2011 by Matthias Cuntz and Juliane Mai
while at the Department Computational Hydrosystems, Helmholtz Centre for Environmental Research - UFZ, Permoserstr. 15, 04318 Leipzig, Germany, and continued while M Cuntz is at the Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Nancy, France, and J Mai is at the Department of Civil and Environmental Engineering of the University of Waterloo, ON, Canada.

It is distributed under the MIT License (see LICENSE file and below).

Copyright (c) 2011-2020 Matthias Cuntz and Juliane Mai

Contact Matthias Cuntz - mc (at) macu (dot) de


Installation

The library is maintained on a git repository at:

https://github.com/mcuntz/jams_fortran/

To use it, checkout the git repository

git clone https://github.com/mcuntz/jams_fortran.git

Copy the mo_*.f90 file of the chosen utility to your Fortran project. grep -i 'use' mo_*.f90 to check for dependencies. All Fortran modules use at least the kind definitions of mo_kind.f90; quite a few use also the general utilities in mo_utils.f90.


Documentation

Documentation of the functions is above each function code or above the module procedure interface at the top of the file. There is a very brief introduction to the modules at the beginning of each file.

Some but not all documentation is in doxygen format and can be formatted with the appropriate tools, e.g. using the JAMS Makefile project.

Each module has a test program in the directory test/test_mo_*/. These test programs try to test all functionalities of the modules and provide hence examples of code usage of (almost) all subroutines.


Dependencies

The library is compatible with the Fortran 2003 standard. It was tested with the GNU gfortran, Intel ifort, NAG nagfor, and PGI pgfortran compilers in various revisions.

Interoperability with C is assured by the use of the intrinsic module iso_c_binding in mo_kind.f90. The use of C functions were tested using the C-header file cfortran.h, for example with the qhull library. See the use of cfortran.h in qhull/qhull_c.c and the corresponding Fortran call in mo_qhull.f90.

The library uses C preprocessor flags to deal with special compiler behaviours, i.e. one has to compile with the -cpp or -fpp compiler flag. For example, gfortran (revisions < 5) did not include an intrinsic ieee_arithmetic module so that mo_utils has convenience funtions such as is_nan(x), which uses either the gfortran extension isnan(x) or the Fortran standard ieee_is_nan(x). The decision is made during compile time, checking if the variable __GFORTRAN__ is defined. The following preprocessor variables are currently checked:
__ABSOFT__, __GFORTRAN__, __GFORTRAN41__, __NETCDF3__, __pgiFortran__, __NAG__, __NAGf90Fortran__.

Some modules use third-party packages such as LAPack or netCDF.
The libraries MinPack, QHull, and netCDF3 are given for convenience with the JAMS library. It is always recommended to use specific installations for the computer system, for example for blas and lapack, which are highly optimised. The netcdf3 directory includes only the parts of the netCDF 3.6.3 version that are necessary for Fortran projects. Read the README in the netcdf3 directory for two system-specific configuration files. The JAMS Makefile project handles these kind of special configuration files.

The only other third-party softwares are LAPack and netCDF 4, which have to be installed independently. The latter can be installed by using, for example the installation script install_netcdf of https://github.com/mcuntz/install_netcdf.


Content

Modules are provided in the following categories:


Modules ordered alphabetically

mo_anneal Simulated Annealing with estimation of initial temperature
mo_ansi_colors Provide colouriser to output coloured text on terminal
mo_append Appends vectors and/or matrixes like *nix cat and paste
mo_bootstrapping_sensitivity_analysis.f90 Bootstrapping for sensitivity analysis
mo_boxcox Box-Cox transformation, inverse transformation & estimating best exponent for transformation
mo_combinatorics Combinatorial algorithms, e.g. binomial coefficient and k-subsets
mo_constants Mathematical and physical constants
mo_corr Correlation function with Fast Fourier Transform, or auto- & cross-correlations via direct calculation
mo_dds Dynamically Dimensioned Search (DDS) and Modified DDS (MDDS)
mo_delsa Distributed Evaluation of Local Sensitivity Analysis (DELSA)
mo_distributions.f90 Continuous distributions density functions such as for the normal distribution
mo_elemeffects Calculation of parameter's Elementary Effect on model/function output
mo_errormeasures Distance or error measures between two datasets, e.g. bias, RMSE, ...
mo_file_utils Utilities for file handling, e.g. search free unit
mo_finish Routine to end program gracefully
mo_fit Linear & polynomial fitting, and general fit with singular value decomposition
mo_functional.f90 Functional programming for modern Fortran
mo_functions Special functions such as the Gamma function
mo_histo Histogram of data (useable also for variogram)
mo_integrate Integration routines
mo_interpol Linear interpolation for irregular grids
mo_julian Converts dates between calendars, e.g. Julian Day into Day, Month and Year, and vice versa; Standard and IMSL convention
mo_kernel Kernel regression and kernel density estimation for PDF and CDF
mo_kind Definition of numerical precisions
mo_laplace_inversion.f90 Numerical Laplace inversion
mo_linear_algebra Wrapper functions for LAPACK's F77 linear algebra routines + some convenience functions such as the diagonal of a matrix
mo_linfit Fit a straight line with model I or model II (geometric mean) regression without error bars on input
mo_mad Median absolute deviation test
mo_mcmc Monte Carlo Markov Chain sampling of parameter distribution around optimum
mo_message Write out message; works with num2str from mo_string_utils
mo_minpack Optimization package minpack (F90 interfaces)
mo_moment 1st to 4th moments, central and mixed central moments
mo_mpi_stubs.f90 Dummy functions for common MPI routines
mo_mtclim.f90 Peter E Thornton's climate generator
mo_ncdump.f90 Quick dumping of variables into netcdf files
mo_ncread Reading nc files using the netcdf4 library
mo_ncwrite Writing nc files using the netcdf4 library
mo_nelmin Minimizes a function using the Nelder-Mead algorithm with the Applied Statistics algorithms No. 047
mo_netcdf David Schaefer's NetCDF Fortran 90 interface wrapper, with NETCDF3 support
mo_nml Routines to handle namelist files
mo_nr Main numerical recipes module containing the interfaces
mo_nrutil Numerical recipes utilities module
mo_ode_generator Given N reactants, generates and solves all corresponding ODE systems
mo_ode_solver Iterative methods for the approximation of solutions of Ordinary Differential Equations (ODE)
mo_opt_functions Test functions for optimization routines
mo_orderpack Orderpack 2.0 from Michel Olagnon provides order and unconditional, unique, and partial ranking, sorting, and permutation. Provides also convenience routines sort and sort_index
mo_percentile Median, Percentiles
mo_pi_index Parameter importance index PI or alternatively B index calculation
mo_poly Tests if a given 2D point lies inside, outside, or on edge/vertex of a 2D polygon, compute area and center of mass
mo_pumpingtests.f90 Thiem and Theis solutions for groundwater-flow equation, and effektive well-flow solution for the effective coarse-graining conductivity
mo_qhull.f90 Wrapper of C program for convex hull calculation from number of points
mo_quicksort Several different implementations of Quicksort including an OpenMP version
mo_random_field.f90 Generation of random fields with certain statistical properties, e.g. a given correlation length
mo_remap Remaps a grid to another grid
mo_sampling Random and Latin Hypercube Sampling for a set of parameters with Uniform(0,1) or Gaussian(0,1) Distribution
mo_sce Shuffled Complex Evolution optimisation
mo_select_distant_entries.f90 Select elements of matrix with largest distance to each other
mo_sobol Sampling of parameters using Sobol sequences
mo_sobol_index Sobol indexes (main and total effects)
mo_sort Quicksort arrays or indices
mo_spatialsimilarity.f90 Routines for bias insensitive comparison of spatial patterns
mo_specan Spectral analysis using FFT
mo_spline Spline functions to approximate or interpolate data
mo_standard_score.f90 Normalized (anomaly)/standard score/z score and deseasonalized (standard score on monthly basis) values of a time series
mo_string_utils Utilities for strings
mo_tee.f90 Write out concatenated strings on standard out and to a given file or unit
mo_template Module template demonstrating the coding standard of the library
mo_timer CPU time routines, allows setting of multiple CPU timers
mo_utils Provides general utilities such as comparisons of two reals, swapping of two elements in an array, is_nan, etc.
mo_var2nc.f90 Writing variables to netcdf files
mo_xor4096 Generating Uniform or Gaussian Random Numbers using the xor4096 algorithm
mo_xor4096_apps Wrapper functions for random number generator xor4096 (Arrays of RNs, ranged RNs, Multivariate Normal Distribution)

Modules per category

Computational

mo_append Appends vectors and/or matrixes like *nix cat and paste
mo_constants Mathematical and physical constants
mo_functional.f90 Functional programming for modern Fortran
mo_kind Definition of numerical precisions
mo_message Write out message; works with num2str from mo_string_utils
mo_mpi_stubs.f90 Dummy functions for common MPI routines
mo_nml Routines to handle namelist files
mo_nr Main numerical recipes module containing the interfaces
mo_nrutil Numerical recipes utilities module
mo_orderpack Orderpack 2.0 from Michel Olagnon provides order and unconditional, unique, and partial ranking, sorting, and permutation. Provides also convenience routines sort and sort_index
mo_quicksort Several different implementations of Quicksort including an OpenMP version
mo_remap Remaps a grid to another grid
mo_sort Quicksort arrays or indices
mo_string_utils Utilities for strings
mo_template Module template demonstrating the coding standard of the library
mo_timer CPU time routines, allows setting of multiple CPU timers
mo_utils Provides general utilities such as comparisons of two reals, swapping of two elements in an array, is_nan, etc.
mo_finish Routine to end program gracefully

Date and Time

mo_julian Converts dates between calendars, e.g. Julian Day into Day, Month and Year, and vice versa; Standard and IMSL convention

Input / Output

mo_ansi_colors Provide colouriser to output coloured text on terminal
mo_file_utils Utilities for file handling, e.g. search free unit
mo_ncdump.f90 Quick dumping of variables into netcdf files
mo_ncread Reading nc files using the netcdf4 library
mo_ncwrite Writing nc files using the netcdf4 library
mo_netcdf David Schaefer's NetCDF Fortran 90 interface wrapper, with NETCDF3 support
mo_tee.f90 Write out concatenated strings on standard out and to a given file or unit
mo_var2nc.f90 Writing variables to netcdf files

Math / Numerics

mo_boxcox Box-Cox transformation, inverse transformation & estimating best exponent for transformation
mo_combinatorics Combinatorial algorithms, e.g. binomial coefficient and k-subsets
mo_corr Correlation function with Fast Fourier Transform, or auto- & cross-correlations via direct calculation
mo_distributions.f90 Continuous distributions density functions such as for the normal distribution
mo_errormeasures Distance or error measures between two datasets, e.g. bias, RMSE, ...
mo_functions Special functions such as the Gamma function
mo_histo Histogram of data (useable also for variogram)
mo_integrate Integration routines
mo_interpol Linear interpolation for irregular grids
mo_kernel Kernel regression and kernel density estimation for PDF and CDF
mo_laplace_inversion.f90 Numerical Laplace inversion
mo_linear_algebra Wrapper functions for LAPACK's F77 linear algebra routines + some convenience functions such as the diagonal of a matrix
mo_linfit Fit a straight line with model I or model II (geometric mean) regression without error bars on input
mo_mad Median absolute deviation test
mo_moment 1st to 4th moments, central and mixed central moments
mo_ode_solver Iterative methods for the approximation of solutions of Ordinary Differential Equations (ODE)
mo_percentile Median, Percentiles
mo_poly Tests if a given 2D point lies inside, outside, or on edge/vertex of a 2D polygon, compute area and center of mass
mo_qhull.f90 Wrapper of C program for convex hull calculation from number of points
mo_sampling Random and Latin Hypercube Sampling for a set of parameters with Uniform(0,1) or Gaussian(0,1) Distribution
mo_select_distant_entries.f90 Select elements of matrix with largest distance to each other
mo_sobol Sampling of parameters using Sobol sequences
mo_spatialsimilarity.f90 Routines for bias insensitive comparison of spatial patterns
mo_spline Spline functions to approximate or interpolate data
mo_standard_score.f90 Normalized (anomaly)/standard score/z score and deseasonalized (standard score on monthly basis) values of a time series
mo_xor4096 Generating Uniform or Gaussian Random Numbers using the xor4096 algorithm
mo_xor4096_apps Wrapper functions for random number generator xor4096 (Arrays of RNs, ranged RNs, Multivariate Normal Distribution)

Screening, Sensitivity Analysis and Optimising / Fitting

mo_anneal Simulated Annealing with estimation of initial temperature
mo_bootstrapping_sensitivity_analysis.f90 Bootstrapping for sensitivity analysis
mo_dds Dynamically Dimensioned Search (DDS) and Modified DDS (MDDS)
mo_delsa Distributed Evaluation of Local Sensitivity Analysis (DELSA)
mo_elemeffects Calculation of parameter's Elementary Effect on model/function output
mo_fit Linear & polynomial fitting, and general fit with singular value decomposition
mo_mcmc Monte Carlo Markov Chain sampling of parameter distribution around optimum
mo_minpack Optimization package minpack (F90 interfaces)
mo_nelmin Minimizes a function using the Nelder-Mead algorithm with the Applied Statistics algorithms No. 047
mo_opt_functions Test functions for optimization routines
mo_pi_index Parameter importance index PI or alternatively B index calculation
mo_sce Shuffled Complex Evolution optimisation
mo_sobol_index Sobol indexes (main and total effects)

Miscellaneous

mo_mtclim.f90 Peter E Thornton's climate generator
mo_ode_generator Given N reactants, generates and solves all corresponding ODE systems
mo_pumpingtests.f90 Thiem and Theis solutions for groundwater-flow equation, and effektive well-flow solution for the effective coarse-graining conductivity
mo_random_field.f90 Generation of random fields with certain statistical properties, e.g. a given correlation length
mo_specan Spectral analysis using FFT

License

This file is part of the JAMS Fortran library, distributed under the MIT License.

Copyright (c) 2011-2020 Matthias Cuntz, Juliane Mai, Stephan Thober - mc (at) macu (dot) de

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.


Note on Numerical Recipes License

Be aware that some code is under the Numerical Recipes License 3rd edition http://www.nr.com/aboutNR3license.html. You can identity it by the use of mo_nr or mo_nrutil.

The Numerical Recipes Personal Single-User License lets you personally use Numerical Recipes code ("the code") on any number of computers, but only one computer at a time. You are not permitted to allow anyone else to access or use the code. You may, under this license, transfer precompiled, executable applications incorporating the code to other, unlicensed, persons, providing that (i) the application is noncommercial (i.e., does not involve the selling or licensing of the application for a fee), and (ii) the application was first developed, compiled, and successfully run by you, and (iii) the code is bound into the application in such a manner that it cannot be accessed as individual routines and cannot practicably be unbound and used in other programs. That is, under this license, your application user must not be able to use Numerical Recipes code as part of a program library or "mix and match" workbench.

Businesses and organizations that purchase the disk or code download, and that thus acquire one or more Numerical Recipes Personal Single-User Licenses, may permanently assign those licenses, in the number acquired, to individual employees. Such an assignment must be made before the code is first used and, once made, it is irrevocable and can not be transferred.

If you do not hold a Numerical Recipes License, this code is only for informational and educational purposes but cannot be used.

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A collection of general Fortran modules in the categories Computational, Date and Time, Input / Output, Math / Numerics, Screening, Sensitivity Analysis and Optimising / Fitting, and Miscellaneous.

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