Fortran-Library

Mathematical & chemical routines e.g. nonlinear optimization etc. with c++ & python interface

Featured utilities

Geometry transformation:

• Standard geometry (also called standard orientaion)
• Assimilate a geometry to a reference
• Cartesian <-> internal coordinate
• Normal mode and vibrational frequency

Nonlinear optimization: (all parameters conveniently tunable)

• Unconstrained optimizer: Newton-Raphson, BFGS, limited memory BFGS, conjugate gradient (Dai-Yuan and Polak-Ribiere+), trust region
• Constrained optimizer: augmented Lagrangian

Integral transform:

• Fourier transform
• Fast Fourier transform

Clustering:

• K-means
• Gaussian mixture model

Statistics:

• Variance, R^2
• Distribution

Chemistry:

• Gradient of eigenstates
• Phase fixing
• Conical intersection adapted coordinate

StringUtility:

• Split string
• Converts multiple spaces and tabs to single spaces
• Removes spaces, tabs, and control characters in string str
• Forked from https://gbenthien.net/strings/index.html

General:

• Random number
• Sorting
• Some other basic routines

Mathematics:

• Selected special functions and combinatorics
• Quaternion operation
• Ordinary differential equation
• 1 dimensional integration

Linear algebra:

• All kinds of vector & matrix & tensor operation
• LAPACK wrapper for linear solver, eigensystem, matrix norm

Installation

libFL.a, libFL.so, *.mod, FortranLibrary.hpp, FortranLibrary (python package directory) will be installed to your prefix (default = Fortran-Library)

1. export LIBRARY_PATH=prefix/lib:$LIBRARY_PATH
2. export LD_LIBRARY_PATH=prefix/lib:$LD_LIBRARY_PATH
3. export CPATH=prefix/include:$CPATH
4. export PYTHONPATH=prefix:$PYTHONPATH
5. Copy mkl_rci.f90 & mkl_dfti.f90 from MKL installation path to source (for gnu compiler, additionally modify DJACOBI in mkl_rci.f90 to specify the dimension of x, fjac, f explicitly: x(n), fjac(m,n), f(m))
6. make, make install
7. (optional) make test, then check the logs

Optional flags to tune make:

• prefix=
• compiler= (can be intel or gnu)
• intelflag=
• gnuflag=

Usage

• fortran use FortranLibrary
• c++ #include <FortranLibrary.hpp>
• python import FortranLibrary as FL

Source

To see what this library is capable of in detail, you may open certain source file then fold all: routines are categorized and folded into different sections (VS code is recommended: press ctrl+k+0)

Source code level from bottom to top:

1. StringUtility.f90, General.f90, Mathematics.f90, LinearAlgebra.f90
2. NonlinearOptimization.f90, IntegralTransform.f90, Clustering.f90, Statistics.f90, Chemistry.f90
3. GeometryTransformation.f90
4. FortranLibrary.f90

Dependency

• MKL
• mkl_rci.f90 & mkl_dfti.f90 (can be found in MKL installation path)

Publications based on this work

1. Y. Shen and D. R. Yarkony, J. Phys. Chem. A 2020, 124, 22, 4539–4548 https://doi.org/10.1021/acs.jpca.0c02763
2. Y. Shen and D. R. Yarkony, J. Phys. Chem. Lett. 2020, 11, 17, 7245–7252 https://doi.org/10.1021/acs.jpclett.0c02199

Reference

1. J. Nocedal, S. J. Wright, Numerical Optimization 2nd edition (Springer, 2006)
2. E. B. Wilson, J. C. Decius, P. C. Cross, Molecular viobrations: the theory of infrared and Raman vibrational spectra (Dover, 1980)
3. D. R. Yarkony, J. Chem. Phys. 112, 2111 (2000)