Re: [Vxl-users] complex matrices, multiprecision data types

[Ian S. <ian...@st...>]

Riccardo Lattanzi wrote:
> Hi,
> 
> A friend of mine has just introduced me to VNL, but I'm not sure
> if I'll be able to use it as-is for my purposes.
> 
> I need to invert a matrix of complex numbers whose rows are  almost
> linearly dependent. I hope somebody can help me with the following
> questions:

I take it using an SVD based inverse with double precision is not 
sufficient?

> 
> 1- Can I create a matrix of complex elements?
> 
Yes

vnl_matrix<vcl_complex<double> > M(m,n);

> 2- Is there a way to use arbitrary precision for the complex
> data type (kind of what can be done with mathematica)?

Unfortunately we don't have an infinite precision real number class.
That said it would not be difficult to create one. Create a new class 
vnl_arbitrary_precision, that looks the same as vnl_rational, and change 
the type of the numerator and denominator to vnl_bignum. There would no 
doubt be a several other changes to the class's API to get this to work 
smoothly.

vnl should then allow you to create a matrix with a complex version of 
this new type:

vnl_matrix<vcl_complex<vnl_arbitrary_precision> >

The biggest problem however is that most (and probably all) of the 
matrix decomposition and inversion classes in vnl_algo are actually just 
thin wrappers around the netlib library. This Fortran library can only 
cope with matrices of float, double, complex<float> and complex<double> 
types. Writing a basic LU decomposition based class would be possible.

Ian.