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narayanamoorthy_k · Joined: 19 Jun 2014 Posts: 142 Location: Chennai, IN

Hi Paul,
Greetings. Is there any library tools and functions available with FTN95 to deal with Sparse Matrix Solutions like for efficient storing, retrieving and computing the matrix inverse calculations. This is applicable when we deal with large sized matrix say 1000x1000 matrix, but the 80% of the matrix will be zeros and when we find the inversion, the inverted matrix will be full.

Therefore, an efficient way of computer modelling in terms of storing, retrieving the matrix elements and computing the inverse will be needed. Do you have any suggestions ? Pls. let me know.
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Thanks and Regards
Moorthy

LitusSaxonicum · Posted: Thu Mar 17, 2016 6:49 pm Post subject:

I suggest that you look in a book on the Finite Element method. Zienkiewicz's book contains a lot of references you could follow, as what you describe is central to the method. Once, I found his book, presumably pirated, online as a PDF.

mecej4 · Joined: 31 Oct 2006 Posts: 1886

A compiler vendor is not often the source of libraries of routines of numerical methods. FTN95 does not even provide pre-built BLAS and Lapack routines.

The usual advice given for the question "how do I compute the inverse of a ... matrix" is "don't!". With few exceptions, the user only needs to solve simultaneous linear equations, and in this case only the inexperienced person insists on forming the inverse explicitly.

Search the Web for SuiteSparse, SuperLU, Mumps, Umfpack, Pardiso, DSS and WSMP.

The NA (Numerical Analysis) library packages from IMSL, NAG and HSL, among others, contain routines for working with sparse matrices.

narayanamoorthy_k · Joined: 19 Jun 2014 Posts: 142 Location: Chennai, IN

narayanamoorthy_k · Joined: 19 Jun 2014 Posts: 142 Location: Chennai, IN

PaulLaidler · Posted: Fri Mar 18, 2016 8:22 am Post subject:

Adding BLAS and Lapack routines to the FTN95 release is on my wish list with a fairly high priority.

JohnCampbell · Joined: 16 Feb 2006 Posts: 2554 Location: Sydney

Paul,

Please add SSE and hopefully AVX dot_product and Vector addition (daxpy) routines before adding BLAS and Lapack routines. They would work much better with that support.

John

LitusSaxonicum · Posted: Fri Mar 18, 2016 2:35 pm Post subject:

Hi Moorthy,

You'll have to search yourself for pirated material. As for me, I have several editions of the book, all paid for!

Regards

Eddie

DanRRight · Posted: Sat Mar 19, 2016 5:06 am Post subject:

Moorthy, Even dense matrix sizes 1000x1000 are not considered large nowadays. It may even fit into L2/L3 cache of your processor. What type of sparsity is your matrix?

As to inverting matrix the BLAS is probably the best but all depends on the type of sparse matrix. For dense matrices BLAS gives speedup versus Crout method for example by factor 1.3. I have fortran example with sources of Lapack and BLAS of using different methods of matrix inversion made by DaveGemini called testfpu, try to search this name and you may find it, if not let me know.

If matrix is larger than that then parallel methods are recommended, why not use extra cores, even cellphones are now multi-processors. You can see an example of parallel library speedup versus some other methods in my post today in another thread in "General"

narayanamoorthy_k · Joined: 19 Jun 2014 Posts: 142 Location: Chennai, IN

narayanamoorthy_k · Joined: 19 Jun 2014 Posts: 142 Location: Chennai, IN

LitusSaxonicum · Posted: Tue Mar 22, 2016 5:18 pm Post subject:

Hi Moorthy,

Your electrical networks are analogous to the finite elements dealt with by Zienkiewicz, with components equal to elements and connections equal to nodes. In the origins of FEM, computers were small, and systems were invented to not explicitly invert the matrix. Zienkiewicz gives simple Fortran codes to do this solution, but you would need to work out the analogies with your own problem.

I will look to see what I have in my library.

Eddie

DanRRight · Posted: Thu Mar 24, 2016 11:27 pm Post subject:

PM me your email address and I will send the source codes

LitusSaxonicum · Posted: Fri Mar 25, 2016 4:25 pm Post subject:

I see that in the last (3 volume) version of Zienkiewicz's book(s) he says that the computer codes have been moved to a website. I think that you could find solution schemes in an older version (e.g. 2nd edition - my personal favourite).

You might have success with the codes in Smith & Griffiths 'Programming the Finite Element Method, now in the 4th edition: get the codes from here: http://inside.mines.edu/~vgriffit/4th_ed/Software/

Eddie

John-Silver · Joined: 30 Jul 2013 Posts: 1520 Location: Aerospace Valley

1. I had a mooch around , as someone who doesn't have a clue what they're doing does, and dropped upon this resource which may prove interesting/irresistible to the experts in the field (just like strawberries to a donkey ? Wink

), as well as maybe helping answer the original post question ......

http://www.netlib.org/utk/people/JackDongarra/la-sw.html

(last updated Apr 2015 - see bottom of page)
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2. Apart from that, the great irishman ( Smile

) Zenk O'Vitch 's book codes relate to a free 'personal version of the FEAP package, with the code in the public domain) which can be found here:-

http://www.ce.berkeley.edu/projects/feap/feappv/

(the link given in 5th Ed of the book no longer being active - well it was in 2000 and things move on).
Beware though that it looks like you might have to spend some considerable time delving into it to make head or tail of it. (No support offered). Apparently it's geared to academic learning use so don't expect to have found an all singing all dancing solution (sic).