From: "M. Edward (Ed) Borasky" <znmeb@...>
Date: 2006-08-04T12:53:41+09:00
Subject: Re: Setting precision in Ruby-GSL calculations ?

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.
>  irb> p v      or
>  irb> 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.