## Glas :## Re: [glas] norms and inner products for vectors of matrices |

**From:** Karl Meerbergen (*Karl.Meerbergen_at_[hidden]*)

**Date:** 2006-01-09 11:22:27

**Next message:**Toon Knapen: "Re: [glas] norms and inner products for vectors of matrices"**Previous message:**Andrew Lumsdaine: "Re: [glas] norms and inner products for vectors of matrices"**In reply to:**Andrew Lumsdaine: "Re: [glas] norms and inner products for vectors of matrices"**Next in thread:**Toon Knapen: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Toon Knapen: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Peter Gottschling: "Re: [glas] norms and inner products for vectors of matrices"

I suggest we first agree what we mean by vector< matrix<T> > ? Why do we

need it? What do we want to use it for?

I do not interpret vector<matrix<T> > as a matrix, but a vector with

matrix<T> as value_type.

Strictly algebraically speaking, vector<matrix<T> > is an unusual

concept, so I would avoid its use if possible.

One possibility is to consider vector<matrix> as a matrix, but which is

its size? Suppose v[0] is a 2x3 matrix and v[1] a 4x1 matrix, which is

the number of columns of v?

An argument in favour of vector<matrix> is the possibility for blocking

in algorithms. But I think there is a better way than vector<matrix> for

doing this.

Perhaps we could introduce the notion of grid, where a matrix (or a

vector) can be mapped onto this grid for performing blocking operations.

For example, a matrix mapped onto a (1x10) grid still is a matrix and

not a vector<matrix>. The algorithms use the grid for computational

purposes or for accessing the data. To the outside world, the matrix

behaves like a matrix, while the algorithmic internals use the blocking

information.

The grid_type could be a template argument of vector and matrix.

Karl

Andrew Lumsdaine wrote:

>I think the definition of the norm for a vector of matrices depends

>on what is meant mathematically by a vector of matrices. If the

>vector of matrices is a block row (or block column) sliced out of a

>block matrix, then the definitions shown would not be the expected

>norms for that portion of the matrix without the blocking. And I

>think, at least in some cases, one would want those norms to be the

>same.

>

>

>

**Next message:**Toon Knapen: "Re: [glas] norms and inner products for vectors of matrices"**Previous message:**Andrew Lumsdaine: "Re: [glas] norms and inner products for vectors of matrices"**In reply to:**Andrew Lumsdaine: "Re: [glas] norms and inner products for vectors of matrices"**Next in thread:**Toon Knapen: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Toon Knapen: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Peter Gottschling: "Re: [glas] norms and inner products for vectors of matrices"