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A Fortran 90 Numerical Library (AFNL) - http://sourceforge.net/projects/afnl/
Set of MODULES by Alberto Ramos containing definitions of Fourier series and polynomials and able to perform linear (multi-)dimensional fittings, compute integrals, sort data, compute roots of functions, and perform other numerical tasks.

AMD Core Math Library (ACML) - http://www.amd.com/us-en/Processors/DevelopWithAMD/0,,30_2252_2282,00.html
Download the library which incorporates BLAS, LAPACK and FFT routines.

BLAS (Basic Linear Algebra Subprograms) - http://www.netlib.org/blas/
A high quality "building block" routines for performing basic vector and matrix operations. Level 1 BLAS do vector-vector operations, Level 2 BLAS do matrix-vector operations, and Level 3 BLAS do matrix-matrix operations.

Boeing Mathematics and Information Software - http://www.boeing.com/phantom/math_infosw/
Algorithms for solving large linear systems, optimal control problems, and other topics.

DSP Library - http://www-ocean.tamu.edu/~baum/dsp.tar.gz
Digital signal processing programs written in Fortran. It includes subroutines for FIR and IIR filter design, FFT routines, and various other programs for signal processing.

Ezconsole - http://www.fortranlib.com/ezann.html
Set of simple procedures by Gary Scott for interfacing with the console window on Windows from Fortran.

FGSL: A Fortran interface to the GNU Scientific Library - http://www.lrz-muenchen.de/services/software/mathematik/gsl/fortran/index.html
Portable, object-based Fortran interface to the GNU scientific library, a collection of numerical routines for scientific computing. The package is licensed under the GPL.

FLIBS - A collection of Fortran modules - http://flibs.sourceforge.net/
Fortran modules by Arjen Markus to interface with C libraries, manipulate strings, write CSV files, manipulate file and directory names, implement abstract data types and structures, do automatic differentiation, and perform other tasks.

GinoMenu - http://www.gino-graphics.com/products/menu.htm
Interactive GUI builder and Fortran subroutine toolkit for developing GUI applications under Windows.

http://lib.stat.cmu.edu/cmlib/index/index - http://lib.stat.cmu.edu/cmlib/index/index
A Fortran 77 library.

http://sepwww.stanford.edu/doku.php?id=sep:software:seplib - http://sepwww.stanford.edu/doku.php?id=sep:software:seplib
Stanford Exploration Project library, containing basic seismic data processing routines such as phase shift migration and velocity stacking. Includes documentation, source code, and binary packages for Mac OS X and Cygwin.

http://sourceforge.net/projects/pilib - http://sourceforge.net/projects/pilib
Platform-independent library under development for Fortran 90/95 to create GUIs, do file I/O.

http://uszla.me.uk/space/software/FoX/ - http://uszla.me.uk/space/software/FoX/
Fortran library to facilitate XML input and output.

http://www.canaimasoft.com/f90sql/ - http://www.canaimasoft.com/f90sql/
Enables Fortran programs to read or write data directly from or into any format that has a Windows Open Database Connectivity (ODBC) driver.

http://www.canaimasoft.com/f90vb/Features.htm - http://www.canaimasoft.com/f90vb/Features.htm
Enables Fortran programs to access COM/ActiveX objects and call Visual Basic DLLs. Enables creation of Fortran DLLs that handle intrinsic Visual Basic data types. Includes TLView, a Type Library browser.

http://www.cisl.ucar.edu/softlib/FISHPAK.html - http://www.cisl.ucar.edu/softlib/FISHPAK.html
A library for the direct solution of finite difference approximations to two-dimensional Helmholz equations. Includes documentation and source code.

http://www.cisl.ucar.edu/softlib/MINPACK.html - http://www.cisl.ucar.edu/softlib/MINPACK.html
A free, portable library for solving nonlinear systems of equations and nonlinear least squares problems.

http://www.cse.clrc.ac.uk/nag/hsl/contents.shtml - http://www.cse.clrc.ac.uk/nag/hsl/contents.shtml
Codes for large-scale scientific computation.

http://www.icm.tu-bs.de/NICONET/ - http://www.icm.tu-bs.de/NICONET/
Subroutine library providing Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Based on numerical linear algebra routines from BLAS and LAPACK libraries, it provides methods for the design and analysis of control systems. [Freeware for scientific (non-commercial) use]

http://www.indowsway.com/ - http://www.indowsway.com/
Library for writing Windows applications in Fortran.

http://www.ncarg.ucar.edu/ngmath/ - http://www.ncarg.ucar.edu/ngmath/
Collection of interpolators and approximators for one-dimensional, two-dimensional, and three-dimensional data, callable from Fortran and C.

http://www.netlib.org/contin/manpak/ - http://www.netlib.org/contin/manpak/
A subroutines for solving some types of algebraically explicit differential algebraic equations.

http://www.netlib.org/itpack/ - http://www.netlib.org/itpack/
A packages for solving large sparse linear systems by iterative methods.

http://www.netlib.org/odepack/ - http://www.netlib.org/odepack/
A collection of Fortran solvers for the initial value problem for ordinary differential equation systems.

http://www.netlib.org/scilib/ - http://www.netlib.org/scilib/
A portable FORTRAN emulation of CRAY SCILIB.

http://www.netlib.org/slatec/ - http://www.netlib.org/slatec/
A software library containing over 1400 general purpose mathematical and statistical routines written in Fortran 77.

http://www.quandt.com/req.html - http://www.quandt.com/req.html
Fortran package by Richard Quandt for numerical optimization and numerous other statistical and utility routines. It is available for a number of platforms, such as IBM mainframes, Vax computers, CRAY supercomputers, IBM-compatible PCs, and Sun, DEC, and RS/6000 workstations.

http://www.shocksolution.com/math_tools/odepack/ - http://www.shocksolution.com/math_tools/odepack/
A repackaged version of ODEPACK with usability improvements such as GNU makefiles, examples, and HTML documentation. Numerical code is unchanged.

http://www.vni.com/products/imsl/fortran/overview.html - http://www.vni.com/products/imsl/fortran/overview.html
A mathematical and statistical library produced by Visual Numerics.

http://www.xeffort.com/ - http://www.xeffort.com/
Free, open-source library for building GUI applications in all flavors of Visual Fortran. Site has other Fortran resources and samples.

http://www.zib.de/Numerik/numsoft/CodeLib/index.en.html - http://www.zib.de/Numerik/numsoft/CodeLib/index.en.html
Fortran 77 codes for large systems of linear equations, systems of nonlinear equations, nonlinear least squares, ordinary differential equations, and quadrature.

http://yoric.mit.edu/daepack/daepack.html - http://yoric.mit.edu/daepack/daepack.html
Library for combined symbolic/numeric analysis of Fortran models, including sparsity pattern generation, discontinuity locking, and automatic differentiation.

Intel Math Kernel Library - http://www.intel.com/software/products/mkl/
Set of optimized, thread-safe mathematical functions for engineering, scientific and financial applications requiring high performance. The functional areas of the library include the BLAS and LAPACK Libraries, Discrete Fourier Transforms, Vector Math Library, Vector Statistical Library, random number generators and the PARDISO Direct Sparse Solver.

LAPACK95: Fortran 95 Interface to LAPACK - http://www.netlib.org/lapack95/
A collection of linear algebra routines with an improved interface which exploits Fortran 95 features such as assumed-shape arrays, optional arguments, and generic interfaces. Includes source code, documentation, and related papers.

Math a la Carte - http://mathalacarte.com
Collections of mathematical software in Fortan and C. Software is free for some uses and can be purchased for others. Much of the software was developed at the Jet Propulsion Laboratory.

Microglyph Systems - http://www.microglyph.com/
SciComm serial communications library, SciPlot scientific plotting graphics library, SciSnet sockets network communication library. Compatible with Fortran and C compilers.

NCAR's Mathematical and Statistical Libraries - http://www.cisl.ucar.edu/softlib/mathlib.html
Source code and documentation for libraries in the areas of geophysical science, Fast Fourier Transforms, separable elliptic PDEs, interpolation, Legendre polynomials, spherical harmonics, general mathematics, eigensystem solvers, linear equation solvers, nonlinear equation solvers, ordinary differential equations, special functions, and statistics.

Numerical Algorithms Group (NAG) - http://www.nag.co.uk/
Libraries, compilers, tools, information, software for statistics, visualization, symbolic calculation, simulation.

PNNL Fortran Library (FLIB) - http://rh.healthsciences.purdue.edu/flib/
General-purpose Fortran 90 routines primarily for text processing such as parsing, accessing the command line, and manipulating dates and times. Also includes some numerical routines for tasks such as random number generation. Includes downloads, documentation, and utility programs.

Transient Energy System Simulation Tool - http://www.trnsys.com
Fortran program to simulate the transient performance of thermal energy systems.

Winteracter - http://www.winteracter.com/iss.htm
Multi-platform user interface and graphics subroutine library for Fortran 77/9x developers.

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