U
Une Bévue
is there algo allready implemented to find eigenvalues, eigenvectors in
Ruby ???
for symetrical matrices ?
Ruby ???
for symetrical matrices ?
E
Edwin Van leeuwen
Une Bév
It is a binding to the gsl library (written in c).
Edwin
You can use rb-gsl to do that. http://rb-gsl.rubyforge.org/eigen.htmlue said:
It is a binding to the gsl library (written in c).
Edwin
A
Alex Shulgin
Take a look at RNum: http://rnum.rubyforge.org/
Ruby Numerical Library is a linear algebra package using Blas and
Lapack (the highly regarded scientific libraries originally written in
FORTRAN.)
A
Axel Etzold
-------- Original-Nachricht --------
As far as I know, there is nothing like that in the "matrix.rb" Matrix
class, but you can find this information by using Ruby bindings to GSL
http://rb-gsl.rubyforge.org/
or, alternatively, via the bindings to the R statistical language,
http://raa.ruby-lang.org/project/rsruby/
Best regards,
Axel
As far as I know, there is nothing like that in the "matrix.rb" Matrix
class, but you can find this information by using Ruby bindings to GSL
http://rb-gsl.rubyforge.org/
or, alternatively, via the bindings to the R statistical language,
http://raa.ruby-lang.org/project/rsruby/
Best regards,
Axel
M
M. Edward (Ed) Borasky
Axel said:
One of the Summer of Code projects extends Matrix to do most of the
common matrix operations. Try
http://rubyforge.org/projects/matrix
C
Cameron McBride
Like several have already said, if you're doing numerical work - you
should use something besides the matrix lib in the stdlib.
For yet another working suggestion, NArray has an extension to do
eigenvalues and eigenvectors based on lapack.
http://narray.rubyforge.org/
(ext is called na_geev, it's also available on that page)
It's worked for me.
Cameron
C
Cameron McBride
That's kind of neat, I missed it. Thanks.
Do you know right off how its accuracy compares to GSL/LAPACK routines?
Cameron
A
Axel Etzold
-------- Original-Nachricht --------
Dear Ed and Cameron,
Me too. Very nice.
Am I wrong in thinking that you can use that library without being
forced to calculate in Floats, i.e. can one use Rationals, Sqrts,
continued fractions, whatever as matrix entries ?
Then, its accuracy should only be limited by the space available on
the machine.
Best regards,
Axel
Dear Ed and Cameron,
Me too. Very nice.
Am I wrong in thinking that you can use that library without being
forced to calculate in Floats, i.e. can one use Rationals, Sqrts,
continued fractions, whatever as matrix entries ?
Then, its accuracy should only be limited by the space available on
the machine.
Best regards,
Axel
U
Une Bévue
Alex Shulgin said:
ok, fine thanks, to both !
U
Une Bévue
Axel Etzold said:
yes i had this prob with gsl, my matrices (coming from chemistry then
having only integer numbers...) print out with -0.000e+00 for 0 and
1.000e+00 for 1 ...)
I'll try it asap ( http://rubyforge.org/projects/matrix ) because the
readme says :
The project consists of some enhancements to the Ruby "Matrix" module
and includes: LU and QR (Householder, Givens, Gram Schmidt, Hessenberg)
decompositions, bidiagonalization, eigenvalue and eigenvector
-----------------------------------^^^^^^^^^^^----^^^^^^^^^^^
calculations.
i need also permutation matrices, whose i didn't understood in gsl...
anyway, thanks a lot !!!
U
Une Bévue
Cameron McBride said:
OK, fine thanks, i've a lot a orking solution right now...
C
Cameron McBride
To be clear, the printing accuracy isn't the machine accuracy. The
-0.000e+00 is just the specific
format that the GSL::Matrix object uses for printing.
Also, the default matrix in GSL is a double (float) based one. You
can create integer matricies. Look at the manual.
Cameron
A
Axel Etzold
-------- Original-Nachricht --------
That's because GSL internally calculates with double precision numbers,
which cannot represent every number correctly, as not every number
is a sum of positive and negative powers of 2. But you can always
round to whole numbers ...
Have a look at the example on the Wikipedia article.
http://en.wikipedia.org/wiki/Permutation_matrix#Examples
A permutation matrix has exactly one 1 entry in every row, at the
place that the permutation vector indicates (note that Ruby starts
counting at 0, so the permutation vector given in the Wikipedia article
should actually be (0 3 1 4 2)), the remaining entries are 0.
The reason to associate a vector and a matrix like this is that
due to the way multiplication of matrices is defined, multiplying
permutation_matrix*matrix
gives you the column vectors of 'matrix' shuffled as the permutation
vector indicates, i.e.
the matrix (inner arrays=rows)
[[1,1,1,1,1],[2,2,2,2,2],[3,3,3,3,3],[4,4,4,4,4],[5,5,5,5,5]]
would be mapped to
[[1,1,1,1,1],[4,4,4,4,4],[2,2,2,2,2],[5,5,5,5,5],[3,3,3,3,3]]
Best regards,
Axel
That's because GSL internally calculates with double precision numbers,
which cannot represent every number correctly, as not every number
is a sum of positive and negative powers of 2. But you can always
round to whole numbers ...
Have a look at the example on the Wikipedia article.
http://en.wikipedia.org/wiki/Permutation_matrix#Examples
A permutation matrix has exactly one 1 entry in every row, at the
place that the permutation vector indicates (note that Ruby starts
counting at 0, so the permutation vector given in the Wikipedia article
should actually be (0 3 1 4 2)), the remaining entries are 0.
The reason to associate a vector and a matrix like this is that
due to the way multiplication of matrices is defined, multiplying
permutation_matrix*matrix
gives you the column vectors of 'matrix' shuffled as the permutation
vector indicates, i.e.
the matrix (inner arrays=rows)
[[1,1,1,1,1],[2,2,2,2,2],[3,3,3,3,3],[4,4,4,4,4],[5,5,5,5,5]]
would be mapped to
[[1,1,1,1,1],[4,4,4,4,4],[2,2,2,2,2],[5,5,5,5,5],[3,3,3,3,3]]
Best regards,
Axel
M
M. Edward (Ed) Borasky
Axel said:
Yes, one of the design goals was to support Rational arithmetic. But
unless the matrix is poorly-conditioned, you shouldn't have to do so,
and for real symmetric eigensolutions, the only problem with using
floating arithmetic would be if you have some pathologically close
eigenvalues you need to separate.
I don't know about continued fractions ... I don't think that's in
there. If you want to do that, you'll need something like Maxima, Axiom
or Yacas. Or a special-purpose exact linear algebra library.
Anybody up to do a Ruby binding to Yacas? There's an R binding to it, so
it can't be too difficult. There are also Java hooks, so this may be yet
another JRuby killer app.
U
Une Bévue
M. Edward (Ed) Borasky said:
I've downloadd it, how do I install it ?
I've found this only file (except docs) :
/opt/local/lib/ruby/1.8/matrix.rb
U
Une Bévue
Axel Etzold said:
YES, that's the one i've followed...
i see, now why permutation isn't a matrix like that :
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0
but rather a vector indicating the permutations to be done...
thanks a lot !
A
Axel Etzold
-------- Original-Nachricht --------
You should just require it : require "matrix".
Since there is already a matrix.rb in the standard library,
make sure you require the right one - an alternative would
be to rename the matrix.rb file with the extended functionality and keep the old.
Best regards,
Axel
You should just require it : require "matrix".
Since there is already a matrix.rb in the standard library,
make sure you require the right one - an alternative would
be to rename the matrix.rb file with the extended functionality and keep the old.
Best regards,
Axel
A
Axel Etzold
-------- Original-Nachricht --------
Dear Ed,
it's very good that one doesn't have to do every calculation in
Float or Double .. of course, Rationals and Symbolic computations can
become very complex, but if one needs to do it,
it's nice to know that Ruby has an option that can help.
Best regards,
Axel
Axel said:
Yes, one of the design goals was to support Rational arithmetic. But
unless the matrix is poorly-conditioned, you shouldn't have to do so,
and for real symmetric eigensolutions, the only problem with using
floating arithmetic would be if you have some pathologically close
eigenvalues you need to separate.
I don't know about continued fractions ... I don't think that's in
there. If you want to do that, you'll need something like Maxima, Axiom
or Yacas. Or a special-purpose exact linear algebra library.
Anybody up to do a Ruby binding to Yacas? There's an R binding to it, so
it can't be too difficult. There are also Java hooks, so this may be yet
another JRuby killer app.
Dear Ed,
it's very good that one doesn't have to do every calculation in
Float or Double .. of course, Rationals and Symbolic computations can
become very complex, but if one needs to do it,
it's nice to know that Ruby has an option that can help.
Best regards,
Axel
E
Edwin Van leeuwen
M. Edward (Ed) Borasky said:I don't know about continued fractions ... I don't think that's in
there. If you want to do that, you'll need something like Maxima, Axiom
or Yacas. Or a special-purpose exact linear algebra library.
Anybody up to do a Ruby binding to Yacas? There's an R binding to it, so
it can't be too difficult. There are also Java hooks, so this may be yet
another JRuby killer app.
You can talk to maxima quite easily, because maxima can start as a
server/daemon, allowing you to just send commands to it via a socket
(and read the results).
Edwin
U
Une Bévue
Cameron McBride said:
I don't know, however i found a discreapency between GSL and
extendedMatrix for eigenvectors :
require 'extendmatrix.rb'
a = Matrix[ [ 0, 1, 1, 0 ],
[ 1, 0, 1, 0 ],
[ 1, 1, 0, 1 ],
[ 0, 0, 1, 0 ] ]
p a.det
# => 2
p a.trace
# => 0
p a.eigenvaluesJacobi
# Vector[-1.0, 2.17008648662603, -1.48119430409202, 0.311107817465982]
# GSL : a.eigval = [ 2.170e+00 3.111e-01 -1.000e+00 -1.481e+00 ]
p a.cJacobiV
=begin
Matrix[[0.707106781186547, 0.522720725656538, -0.302028136647909,
-0.368160355880552],
[-0.707106781186547, 0.522720725656538, -0.302028136647909,
-0.368160355880552],
[0.0, 0.611628457346727, 0.749390492326316, 0.253622791118195],
[0.0, 0.281845198827065, -0.505936655478633, 0.815224744804294]]
GSL : a.eigvec =
[ 5.227e-01 3.682e-01 -7.071e-01 3.020e-01
5.227e-01 3.682e-01 7.071e-01 3.020e-01
6.116e-01 -2.536e-01 -9.158e-16 -7.494e-01
2.818e-01 -8.152e-01 4.852e-16 5.059e-01 ]
=end
the eigenvalues are "the same" however eigenvectors doesn't have even
the same sign to within a multiplicative constant ???
what did i miss this morning ?
a cofee cup ??