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Add test to krylov function and funded small bags in it


From: Vladimir Polishchuk
Subject: Add test to krylov function and funded small bags in it
Date: Thu, 22 Aug 2013 22:19:02 +0300
User-agent: Mozilla/5.0 (X11; Linux i686; rv:17.0) Gecko/20130803 Thunderbird/17.0.8

I write test of function krylov and funded bags - part of them in help.
In help write:

Construct an orthogonal basis U of block Krylov subspace
[v a*v a^2*v ... a^(k+1)*v]
Bat mast be (with not rectification confusion in size of letter):
[v a*v a^2*v ... a^(k-1)*v] At that if k=1 then get [v] it mast be and function that return that.
Paragraph
If V is a vector, then H contains the Hessenberg matrix such that
a*u == u*h+rk*ek', in which `rk = a*u(:,k)-u*h(:,k)', and ek' is
the vector `[0, 0, ..., 1]' of length `k'. Otherwise, H is
meaningless.
if h<k mistaken - in u there is only h column.
And there is mistaken in quotation marks.

And there is bags:
>> krylov
error: 'A' undefined near line 61 column 12
error: evaluating argument list element number 1
error: called from:
error:   /usr/local/share/octave/3.7.5/m/linear-algebra/krylov.m at line -1, column -1
for correct this need trade places:
  if (isa (A, "single") || isa (V, "single"))
    defeps = 1e-6;
  else
    defeps = 1e-12;
  endif

with
  if (nargin < 3 || nargin > 5)
    print_usage ();
  elseif (nargin < 5)
    ## Default permutation flag.
    pflg = 0;
  endif

And there is not test if k>0 in help this may think k mast be bigger -2:
>> krylov([0,1;1,0],[1;0],0);
error: 'U' undefined near line 221 column 17
error: evaluating argument list element number 1
error: called from:
error:   /usr/local/share/octave/3.7.5/m/linear-algebra/krylov.m at line 221, column 6


-- Vladimir Polishchuk

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