[Lazarus] fast mathematical matrix operations

[Mehmet Erol Sanliturk]

On Mon, Jun 8, 2015 at 1:57 AM, Andrea Mauri <andrea.mauri.75 at gmail.com>
wrote:

> Dear all,
>
> I am looking for units/packages to deal with numerical matrix manipulation
> (typical double type numerical matrices).
> I need code able to perform typical matrix operations (e.g. matrix
> multiplication, inversion, determinant and so on) as fast as possible since
> I deal with big matrices (thousands of rows and columns). I need it for
> both windows and linux (32/64).
>
> I found some libraries doing it (e.g. dmath and mrmath).
>
> dmath units (http://sourceforge.net/projects/dmath/) can be used both on
> windows and linux but operations are slow on big matrices. calculation of
> correlation matrix on a matrix with 3500 rows and 2000 columns get minutes.
>
> mrmath units (https://github.com/mikerabat/mrmath) is the fastest I found
> (just few seconds to calculate correlation matrix on the same data matrix
> as before) but is available only for windows and mac os.
>
> any other suggestions? anyone interested in evaluating the possibility to
> make mrmath usable under linux too?
>
> thanks,
> Andrea
>
> --
> _______________________________________________
>



Here most important problem is not Pascal or any other programming language
but numerical accuracy of the computations .

For large matrices without using multiple precision arithmetic , if
matrices are not special types as suitable for good numerical accuracy
during computations , i.e. , they are ill-conditioned , the results will be
meaningless even if they can be obtained .


Matrix inversion is an n-cube order of operations means , for 1000 rows ,
computations will be more than ( 1 000 000 000 ) operations . Accumulation
of round off errors will be enormous .

Please see

http://www.wolfgang-ehrhardt.de/
( Pascal )

http://code.google.com/p/mpmath/
( Python )

or search in Internet

arbitrary precision arithmetic
multiple precision arithmetic


Julia language has multiple precision arithmetic capability .



Thank you very much .


Mehmet Erol Sanliturk
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