From help-octave-request at bevo dot che dot wisc dot edu  Thu Apr  6 19:06:10 2000
Subject: Re: matrix-vector-op class ? 
From: Jamie Morris <jemorris at MIT dot EDU>
To: "John W. Eaton" <jwe at bevo dot che dot wisc dot edu>
cc: pkienzle at kienzle dot powernet dot co dot uk, fabian@tu-cottbus.de
Date: Thu, 06 Apr 2000 20:06:04 -0400



> How should we decide whether the rows or columns are to be scaled?

> A simple definition would be that
>
>  v .* M  ==  diag (v) * M  (row scaling)
>  M .* v  ==  M * diag (v)  (column scaling)

> I have also thought about allowing row or column scaling based on the
> orientation of the vector.  Then v .* M or M .* v could do either
> operation, depending on the orientation of v.  My idea is that if v
> is a column vector, it scales the rows and if it is a row vector it
> scales the columns.


Arrays with dimension larger than two are on the to-do list, right?

The first scale-orientation method presupposes there are only two choices;
the second one extends smoothly to arbitrary dimensionality.

If size(M) = [A B C D E F G H] and size(v) = [1 1 P 1 1 Q 1 1],
then v .* M and M .* v both have the effect
  M(xa, xb, xc, xd, xe, xf, xg, xh) *= v(xc, xf)  [ aka v(1,1,xc,1,1,xf,1,1) ]

(There are issues with how to deal nicely when you have a single low-dim v 
that you want to use to scale m's of different high dims, or to scale
different indices of some high-dim m's, but I think they're issues that
arise in having high-dim arrays anyway.)



Jamie



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