Dear all,

I’d like to use ruby-gsl for some singular value decompositions, i.e.

a matrix m should be decomposed into a product of three matrices,

m=u*s*v.transposed,

now,as the documentation says that this algorithm is not implemented

if the dimensions of m (m1 x m2) are such that m1<m2, I’ve implemented

my own version, re-reading some long-forgotten linear algebra book.

In the process, I need to find the eigenvectors and the eigenvalues of

m*m.transposed,

but these are printed out and apparently also calculated only to three

decimal digits

by the command

```
eigval, eigvec = Eigen::symmv(m*m.transposed).
```

This causes the matrix u, which is constructed from the values eigval,

to have quite strange values for its determinant (I get values of

1.06,

0.96 for u*u.transpose.det, but u is unitary by definition, i.e.,*

uu.transpose.det=1).

Then, of course, m isn’t remotely equal to u*s*v.transposed …

Is there a way of setting the precision of the eigenvalue and

eigenvector

calculations

any higher ?

Thank you very much,

Best regards,

Axel

[email protected] wrote:

In the process, I need to find the eigenvectors and the eigenvalues of

u*u.transpose.det=1).

Best regards,

Axel

If m = u*s*v.transposed, what does m.transposed equal? Isn’t it

m.transposed = v*s.transposed*u.transposed?

In other words, can you transpose m … m.transposed has dimensions m2 x

m1 … and take the SVD of m.transposed, and then recover the SVD of m

from that?

I’ve forgotten most of my computational linear algebra too.

By the way, how large are m1 and m2?

Hi,

I’d like to use ruby-gsl for some singular value decompositions, i.e.

Which library do you use? There are two extensions,

ruby-gsl and rb-gsl(Ruby/GSL).

```
ruby-gsl http://ruby-gsl.sourceforge.net/
rb-gsl (Ruby/GSL) http://rubyforge.org/projects/rb-gsl/
```

but these are printed out and apparently also calculated only to three

decimal digits

If you use Ruby/GSL, this is just because

matrices are displayed with the printf format

%4.3e, not because of precision. You can get

more significant figures by displaying elements

as m[0][1].

by the command

```
eigval, eigvec = Eigen::symmv(m*m.transposed).
```

This causes the matrix u, which is constructed from the values

eigval,

to have quite strange values for its determinant (I get values of

1.06,

0.96 for u*u.transpose.det, but u is unitary by definition, i.e.,*

uu.transpose.det=1).

Is it unitary? Isn’t it an orthogonal matrix?

Then, of course, m isn’t remotely equal to u*s*v.transposed …

The following is rb-gsl(Ruby/GSL) outputs.

irb(main):001:0> require(“gsl”)

=> true

irb(main):002:0> m = GSL::Matrix[[10, 5, -10], [2, -11, 10]].trans

=> GSL::Matrix

[ 1.000e+01 2.000e+00

5.000e+00 -1.100e+01

-1.000e+01 1.000e+01 ]

irb(main):003:0> u, v, s = m.SV_decomp

=> [GSL::Linalg::SV::UMatrix

[ -2.981e-01 8.944e-01

-5.963e-01 -4.472e-01

7.454e-01 5.356e-17 ], GSL::Linalg::SV::VMatrix

[ -7.071e-01 7.071e-01

7.071e-01 7.071e-01 ], GSL::Linalg::SV::SingularValues

[ 1.897e+01 9.487e+00 ]]

irb(main):004:0> u.trans*u (U is orthogonal)*

=> GSL::Matrix

[ 1.000e+00 1.408e-16

1.408e-16 1.000e+00 ]

irb(main):005:0> vv.trans (V is also orthogonal)

=> GSL::Matrix

[ 1.000e+00 -1.015e-17

-1.015e-17 1.000e+00 ]

irb(main):006:0> u*Matrix.diagonal(s)*v.trans

=> GSL::Matrix (Reconstruct m)

[ 1.000e+01 2.000e+00

5.000e+00 -1.100e+01

-1.000e+01 1.000e+01 ]

Is this what you expect?

Yoshiki