I'm in search for a free package that do most matrix/vector operations. I can write some basic functions myself but for advanced ones like computing eigenvalues and eigenvectors I would prefer robust code and I would like to know if such packages are freely available. If I understand correctly Ada 2005 have more matrix operations facilities but it has a function to calculate the eigenvalues for a symmetric and hermitian matrices only. I'll need a more general packages which can handle any kind of matrix.
An Ada95 matrix package (54KB tar.gz file) from Drexel Fusion Laboratory had the link: http://dflwww.ece.drexel.edu/research/ada/ but the page for this ink is non-existent today.
Thanks a lot...
I think that the Ada95 package you mean is here -- but it's only 35k, and it seems to have less functionality than the Ada2005 standard library does.
Not sure how this Ada95 binding to BLAS came to be in my browser cache! I see that for general matrix solving you need LAPACK too, I wonder whether the bindings already in GNAT will help? Package System.Generic_Real_LAPACK in file s-gerela.ad[bs]. The comments say
-- LAPACK Computational Routines
-- gerfs Refines the solution of a system of linear equations with
-- a general matrix and estimates its error
-- getrf Computes LU factorization of a general m-by-n matrix
-- getri Computes inverse of an LU-factored general matrix
-- square matrix, with multiple right-hand sides
-- getrs Solves a system of linear equations with an LU-factored
-- square matrix, with multiple right-hand sides
-- orgtr Generates the Float orthogonal matrix Q determined by sytrd
-- steqr Computes all eigenvalues and eigenvectors of a symmetric or
-- Hermitian matrix reduced to tridiagonal form (QR algorithm)
-- sterf Computes all eigenvalues of a Float symmetric
-- tridiagonal matrix using QR algorithm
-- sytrd Reduces a Float symmetric matrix to tridiagonal form
which I suspect is a small subset of the full library. Still, could act as a useful springboard for more extensive bindings.
As suggested in John Barnes Rationale for Ada 2005, Ada's Annex G: Numerics is not intended "as a substitute for professional libraries such as the renowned BLAS," but nothing precludes an implementation from using BLAS internally. As a concrete example, the GNAT compiler implements both G.3.1 Real Vectors and Matrices and G.3.2 Complex Vectors and Matrices using BLAS and LAPACK. To see the details, you can examine the relevant package bodies:
$ export ADA_INC = /your/path/to/adinclude
$ view $ADA_INC/$(gnatkr Ada.Numerics.Generic_Real_Arrays.adb)
$ view $ADA_INC/$(gnatkr Ada.Numerics.Generic_Complex_Arrays.adb)
The site at which this package was previously available has been migrated and the old content is now available at:
http://dfl.ece.drexel.edu/content/ada95-matrix-package
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I am a student from Germany, currently doing the master thesis. In my master thesis, I am writing a Fortran code in code blocks. In my code, I am using some of the LAPACK functions.
I want help regarding adding LAPACK library in code block software. I searched a lot on the internet but I couldn't find anything. It'll be better if you provide me all the source links extension of the previous question.
In my code, I need to solve the following system of equation, {K}{p} = {m}
Where
{K} = Matrix
{p} = vector
{m} = vector
I have all the elements of vector {m} and matrix {K} computed and I have some known values of vector {p}. It's boundary value problem.
Now I want to find out only unknown values of elements of a vector {p}.
Which function should I use?
I went through the LAPACK manual available online but couldn't find.
Well you did not go through the documentation so thoroughly :) You are looking for solvers of a linear equation.
http://www.netlib.org/lapack/lug/node38.html
Please specify a little more about complex/real double/float. ill posed? Over or under determined or quadratic? If quadratic then symmetric or upper triangular? Banded?
There is a hord of different algorithms one would consider. Runtime / stability / convergence behaviour are very different dependent on K. The most stable would be [x]gelsd. It's a divide and conquer algorithm via SVD and gives you with proper conditioning the moore penrose generalised inverse. But it is by far the slowest algorithm too.
btw, http://www.netlib.org/lapack/lug/node27.html, outlines all general solvers.
If you already have some values of your p, you would like to go a different route than a straight forward inversion. You are a lot better off, if you use an iterative method like conjugate gradient least squares problem with regularization. This is discussed in length in Stoer, Bullirsch, Introduction to Numerical Analysis, Chapter 8.7 (The Conjugate-gradient Method of Heestens and Stiefel).
There are multiple implementations online. One you will find in a library I wrote during my PhD: https://github.com/kvahed/codeare/blob/master/src/optimisation/CGLS.hpp
I have a piece of code in Fortran 90 in which I have to solve both a non-linear (for which I have to invert the Jacobian matrix) and a linear system of equations. When I say small I mean n unknowns for both operations, with n<=4. Unfortunately, n is not known a priori. What do you think is the best option?
I thought of writing explicit formulas for cases with n=1,2 and using other methods for n=3,4 (e.g. some functions of the Intel MKL libraries), for the sake of performance. Is this sensible or should I write explicit formulas for the inverse matrix also for n=3,4?
I need to compute the determinant of complex matrix which is symmetric. Size of matrix ranges from 500*500 to 2000*2000. Is there any subroutine for me to call? By the way, I use ifort to compile.
The easiest way would be to do an LU-decomposition as described here. I would suggest using LAPACK for this task...
This article has some code in C doing that for a real-valued symmetric matrix, so you need to exchange dspsv by zspsv to handle double-precision complex matrices.
Is there a library with the inverse function included?
I am currently working on a direction finding algorithm as part of a project. I am using the Bartlett Correlation. In the Bartlett correlation I will need to divide the numerator, which is already 3 matrix multiplications(including Hermitian Transposes), by the denominator which is the product of a matrix and its Hermitian Transpose.
I realize that in order to divide I use the inverse. I am just trying to save time and hoping that there is a library where the inverse is included. I have only found links to source code for finding the inverse. This is only a small portion of the project and I am hoping to save time.
I do have the rest of my code written, but, have not started with the division/inverse yet. So, I will not include that code.
I suggest use an implementation of BLAS, they are generally very versatile language and platform wise and used for building LAPACK as well.
I am very new to programming and fortran in particular. I am using the LAPACK (Linear Algebra Package) software package for Fortran to find the eigenvalues and eigenvectors of a large symmetrical real matrix. Specifically, I calculate a scalar from each eigenvector, and I want to graph it against its associated eigenvalue.
I am using the subroutine DSYEV of LAPACK to do this. However, DSYEV outputs the eigenvalues in ascending order, and I'm not sure how it orders the eigenvectors. Is there a way to associate each eigenvector with its eigenvalue?
Edit: The official page for DSYEV is here: http://www.netlib.org/lapack/double/dsyev.f
Here is another page about it: http://www.nag.co.uk/numeric/fl/nagd...F08/f08faf.xml
They should be in the same order. You can actually check this by matrix multiplication. It is much easier and faster, than finding the eigenvectors.