Re: [Lapackpp-devel] SVD that ignores U, Sigma or VT

[Christian S. <sti...@tu...>]

Jacob (Jack) Gryn schrieb:
> I=92m writing some code that only uses data from VT of an SVD, and don=92=
t=20
> need the data in U and Sigma.  Although I can ignore it; the resulting =
U=20
> is significantly large (512^2x512^2), which is too large a matrix for=20
> the system to handle; and is clearly a waste.

Absolutely agreed. I guess you mean the JOBZ argument of the LAPACK=20
function dgesdd http://docs.sun.com/source/817-6700/dgesdd.html, where=20
currently only the settings 'A' and 'N' are used, and instead you would=20
like to use either the 'O' or the 'S' setting.

> I=92ve noticed that there is a function that ignores both U and VT, by=20
> essentially setting ldv and ldu to 0, that seemingly tells LAPACK to=20
> ignore the data. =20

The point here is that the argument JOBZ was set to 'N'. Only this is=20
the reason for LAPACK not to use the U and VT arguments. Look into the=20
man page mentioned above.

> Maybe it would be better just to use a single LaSVD_IP=20
> function, and allow uninitialized LaGenMat[Double/Complex] as input.=20
>  If, for example U is declared with the default constructor, since=20
> U.gdim(0) =3D=3D 0, I would guess that LAPACK will ignore writing outpu=
t to U.

For people who only want the singular values but not the vectors, I=20
would rather want to leave that extra function in there, since it is=20
totally unambiguous what this function will do. But for your case where=20
you want only some of the singular vectors, there are several=20
possibilities. As you say, one possibility would be to do different=20
things according to what the input arguments U and VT have been set to.=20
Let's assume A to be M-by-N and M !=3D N. Right now we do the following:

If (U.size =3D=3D M-by-M) && (VT.size =3D=3D N-by-N)
   calculate all singular vectors (JOBZ=3D'A')
else
   error.

Instead, we could also do the following:

MNmin =3D min(M,N);
If (U.size =3D=3D M-by-M) && (VT.size =3D=3D N-by-N)
   calculate all singular vectors (JOBZ=3D'A')
else if (U.size =3D=3D M-by-MNmin) && (VT.size =3D=3D MNmin-by-N)
   calculate the MNmin first singular vectors (JOBZ=3D'S')
else if (M >=3D N) && (U.size =3D 0) && (VT.size =3D=3D N-by-N)
   calculate full VT and first N vectors of U (JOBZ=3D'O')
else if (M < N) && (U.size =3D M-by-M) && (VT.size =3D 0)
   calculate full U and first M vectors of VT (JOBZ=3D'O')
else
   error

Does this meet your requirements? On the other hand, this increases the=20
risk of the programmer to be totally confused about what the arguments=20
are supposed to be. But nevertheless I think it would be possible. Do=20
you want me to implement this? Or do you want to give it a try for yourse=
lf?

Christian