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Creating a numerical algorithm can take years.
Finding and adapting a numerical algorithm is practical.
In 2014, 10 top programming languages:
actually top 30
Some history and dates of programming languages:
http://en.wikipedia.org/wiki/History_of_programming_languages
LAPACK is a good starting place to find high quality numerical code.
Yes, much is in Fortran 77, some in Fortran 95, and yes much of the code
is a very mature 30 years old. The good news is that the code produces
correct numeric results with known accuracy. A download typically
includes test drivers and timing programs.
LAPACK is used in Maple, Matlab, and libraries are available for
C, Python, Ruby, Java, Ada, and many other languages.
see www.netlib.org/lapack
ACM Transactions on Mathematical Software, TOMS is another
source. see www.netlib.org/toms
LAPACK includes prior LINPACK and EISPACK and uses the BLAS,
Basic Linear Algebra Subroutines, for low level operations.
Almost every LAPACK routine is available in four types:
Single precision floating point prefix "s"
Double precision floating point prefix "d"
Complex single precision prefix "c"
Complex double precision prefix "z"
LAPACK is available locally, may be out of date, and on Internet:
LAPACK FAQ
naming conventions
single
double
complex
complex16
LAPACK Users Guide
The Fortran source code for the Linear Algebra Package, LAPACK
are under the LAPACK directory with subdirectories
SRC BLAS TESTING TIMING INSTALL
And, for g95 users, the Fortran95 interface lapack95.tgz
Or, on Debian or Ubuntu sudo apt-get install gfortran
and compile and link LAPACK and all my examples.
On CSEE Help WEB pages: www.csee.umbc.edu/help/fortran
lapack.tar big, about 35MB
LAPACK installation guide (postscript)
LAPACK quick reference (PostScript)
Raw LAPACK directory use lapack.a and blas.a on Linux on Intel
Raw LAPACK/SRC directory
Raw LAPACK/BLAS directory
Raw LAPACK/TESTING directory
Raw LAPACK/TIMING directory
Raw LAPACK/INSTALL directory
lapcak95.tgz
g95 for Linux, tar -xvzf g95-x86-linux.tgz
Self installing executable,g95 for MS Windows
Much more information on Fortran, including a full manual, is at
www.csee.umbc.edu/help/fortran
For Java users:
Java Numerics WEB Site
includes an early version of LAPACK translated to Java plus many other
numeric routines.
For Python users: Python has numpy and scipy and can call Fortran code
Python bindings
For Ada users there is an interface binding
Ada bindings
For Scala users: No LAPACK I could find, alternative
Scalala math library
There is a learning curve to using LAPACK.
I suggest finding a routine you need.
Copy the comments from the front of that routine into your program.
Create the necessary declarations needed for calling the routine.
Create a Makefile with the compilation and library commands.
You will need lapack.a and blas.a or equivalent.
An example use on our CSEE system is
Makefile_LAPACK
test_eigen2.f90
test_eigen2_f90.out
This is really old code that still works and uses
invrse.for
eigdet.for
matmul.for
evalvec.for
a02ftext.for
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