changeset: improve norm computation capabilities

[Jaroslav Hajek]

hello,
please comment the attached changeset, improving capabilities of the
"norm" built-in.

Summary of changes:

1. All algorithms are available from within liboctave. __norm__ is removed.

2. Scaled summation for vector p-norms to avoid overflows. Expressions
such as `norm (1e20*ones (5,1), 20)' no longer produce an infinity.

3. norm (a, [p,] 'columns') or norm(a, [p,] 'rows') can compute column
or row norms of a matrix. Currently, there seems to be no way in
Octave (nor Matlab) to compute norms for a set of vectors both
efficiently and robustly. Also, this operation is sometimes useful in
linear algebra (used in the upcoming fsolve patch). Works efficiently
on sparse matrices, too.

4. Support for general matrix p-norms using Higham's hybrid algorithm.
There may still be problems with this part, but it seems to work even
for complex matrices (which the Higham's paper doesn't deal with). Of
course, the 1-, Inf- and 0- norms are calculated using their
closed-form expressions, and 2-norm of a dense matrix is still done
via SVD.

regards

-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz

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