Setting precision in Ruby-GSL calculations?

ruby-talk
1

Hi Axel, sorry for late reply.

Ruby-Gsl defines these as M= U S V^tr,
where U can have uneven dimensions, but many
authors require U to
be square (and softwares, eg. Mathematica)

   This is because GSL can do so.

I still don't know why I don't get singular
values to higher precision ...
does one have to convert to Float or something ?

   All the values in Ruby/GSL including elements
in a GSL::Vector object are calculated in double
precision. But when you use e.g.
  > p v or
  > v.print
only 4 digits of each element are displayed using
printf() with the format "%4.3e". This does not
mean the precision of 4 significant digits. If you
need to "see" vector elements, you can obtain
them as Ruby Float by accessing with indices as
v[0], v[1].

   If you really need more higher precision better
than double, I have no idea.

   Yoshiki

2

yoshiki9@mac.com wrote:

  Hi Axel, sorry for late reply.

Ruby-Gsl defines these as M= U S V^tr,
where U can have uneven dimensions, but many
authors require U to
be square (and softwares, eg. Mathematica)

  This is because GSL can do so.

I still don't know why I don't get singular
values to higher precision ...
does one have to convert to Float or something ?

  All the values in Ruby/GSL including elements
in a GSL::Vector object are calculated in double
precision. But when you use e.g.
> p v or
> v.print
only 4 digits of each element are displayed using
printf() with the format "%4.3e". This does not
mean the precision of 4 significant digits. If you
need to "see" vector elements, you can obtain
them as Ruby Float by accessing with indices as
v[0], v[1].

  If you really need more higher precision better
than double, I have no idea.

  Yoshiki

You shouldn't need more than 64-bit (double) arithmetic for a singular value decomposition. It's a very stable process ... in fact, it's so stable it's the method of choice for solving least squares problems, rather than the cross-multiply / Cholesky decomposition that was commonly used in the "old days". Cross-multiply / Cholesky is faster, but much less stable.