Householder solver

[Henri Lindén <hlinden at cc dot helsinki dot fi>]

Hi!

I am having problems with the Householder alogithm. Usually this is used
for overdetermined linear systems, i.e. systems in which 
m > n, where A \in R^{m \times n}. Then how come i.e. the following code:

//=========================================================
  gsl_matrix *a=gsl_matrix_alloc(5,3);
  gsl_vector *b=gsl_vector_alloc(5);
  gsl_vector *x=gsl_vector_calloc(3);
  
  gsl_vector_set(b,0,2.0); gsl_vector_set(b,1,2.0);
  gsl_vector_set(b,2,3.0); gsl_vector_set(b,3,5.0);
  gsl_vector_set(b,4,6.0);

  gsl_matrix_set(a,0,0,1.0); gsl_matrix_set(a,0,1,1.0);
  gsl_matrix_set(a,0,2,1.0); gsl_matrix_set(a,1,0,1.0);
  gsl_matrix_set(a,1,1,2.0); gsl_matrix_set(a,1,2,4.0);
  gsl_matrix_set(a,2,0,1.0); gsl_matrix_set(a,2,1,3.0);
  gsl_matrix_set(a,2,2,9.0); gsl_matrix_set(a,3,0,1.0);
  gsl_matrix_set(a,3,1,3.0); gsl_matrix_set(a,3,2,9.0);
  gsl_matrix_set(a,4,0,1.0); gsl_matrix_set(a,4,1,4.0);
  gsl_matrix_set(a,4,2,16.0);

  gsl_linalg_HH_solve(a,b,x); 

//=============================================================

yields the following error message:

gsl: hh.c:41: ERROR: System is underdetermined
Aborted

??? 

Usually the first dimension refers to row dimension and the second to
columns, which is exactly as things generally are done in GSL. Thus my
example system should by all means be overdetermined with 5 equalities and
3 variables. However the Householder solver seems to disagree!  


O========================================================================O
O       Henri Lindén                   address: Korkeavuorenkatu 4 A 5   O
O       Department of Mathematics               00150 Helsinki           O
O       University of Helsinki           email: hlinden@cc.helsinki.fi   O
O                                      to work: +358 (0)9-191 23207      O
O                                    cellphone: +358 (0)50-5884288       O
O========================================================================O