Re: [Help-gsl] Please, run the two programms.

[Patrick Alken]

The reason your program is not changing the vector is because of this
line:

gsl_vector_set_zero ( tau ) ;

If you set all the tau coefficients to 0, then the QR_Qvec function
will leave the input vector unchanged. As Brian mentioned, you need
to first call gsl_linalg_QR_decomp() to setup the Q matrix as well
as the tau vector.

On Wed, Oct 24, 2007 at 05:07:00PM +0200, Jo_Jo wrote:
> Brian Gough wrote:
> > At Thu, 18 Oct 2007 12:07:13 +0200,
> > andrzej buczynski wrote:
> >   
> >> Please, run the two programms.
> >> In both programms vector v is not equal to vector Q*v, or Qtraqnsp * v.
> >>     
> >
> > The function requires the input matrix to be decomposed with
> > gsl_linalg_QR_decomp first.
> >
> >   
> Dear Brian,
> 
> In  the Chapter 13 of the User Manual in pdf -format, about  Linear
> Algebra,  page 130
> on reads:
> " .....                                                                
>                      It may be useful if the
> product b??? = QT b has already been computed using gsl_linalg_QR_QTvec."
> 
> And about gsl_linalg_QR_QTvec one reads:
> 
> "int gsl_linalg_QR_QTvec (const gsl matrix * QR, const gsl vector
> *                 [Function]
>           tau, gsl vector * v )
>      This function applies the matrix QT encoded in the decomposition
> (QR,tau) to the
>      vector v, storing the result QT v in v. The matrix multiplication
> is carried out directly
>      using the encoding of the Householder vectors without needing to
> form the full matrix
>      QT ."
> 
> That means, that these vector v = QT * b  ?
> 
> And about function int gsl_linalg_QR_Qvec one read :
> " Function  int gsl_linalg_QR_Qvec (const gsl matrix * QR, const gsl
> vector *                [Function]
>          tau, gsl vector * v )
>      This function applies the matrix Q encoded in the decomposition
> (QR,tau) to the
>      vector v, storing the result Qv in v. The matrix multiplication is
> carried out directly
>      using the encoding of the Householder vectors without needing to
> form the full matrix
>      Q."
> 
> That means that these vector v = Q * b ?
> 
> These two descriptions of both functions should be :
> 
> 1.)  in the first  description:
> 
> "Function  int gsl_linalg_QR_QTvec (const gsl matrix * QR, const gsl
> vector *                 [Function]
>           tau, gsl vector * b )
>      This function applies the matrix QT encoded in the decomposition
> (QR,tau) to the
>      vector b, storing the result QT* b in b. The matrix multiplication
> is carried out directly
>      using the encoding of the Householder vectors without needing to
> form the full matrix
>      QT ."
> 
> 2.) in the  second description:
> 
> " Function  int gsl_linalg_QR_Qvec (const gsl matrix * QR, const gsl
> vector *                [Function]
>          tau, gsl vector * b )
>      This function applies the matrix Q encoded in the decomposition
> (QR,tau) to the
>      vector b, storing the result Q*b in b. The matrix multiplication is
> carried out directly
>      using the encoding of the Householder vectors without needing to
> form the full matrix
>      Q."
> 
> 
> In my two programs :
> 
> - program  QRQvec.c :
> 
> 
> //------program QRQvec.c
> /*
> 
>   int gsl_linalg_QR_Qvec (const gsl matrix * QR,
>                           const gsl vector * tau,
>                           gsl vector * v )
> 
> * This function applies the matrix Q encoded in the decomposition
> *  (QR,tau) to the vector v, storing the result Qv in v.
> *
> *  Should be :   v = Qv
> * 
> */
> 
> #include <stdio.h>
> #include <gsl/gsl_linalg.h>
> 
> int main (void)
> {
>   double a_data[] =       {-0.18, 0.60,  0.57, 0.96,
>                                            0.41, 0.24, -0.99, 0.58,
>                                           -0.14, 0.30,  0.97, 0.66,
>                                           -0.51, 0.13,  0.19, 0.85,
>                                           0.33, 0.44, -0.66, 0.12 };
>        
>        double b_data[] = { 1.0, 1.0, 1.0, 1.0 };
> 
>        int M = 4, N = 4 , i ;
> 
>        gsl_vector * tau = gsl_vector_alloc( GSL_MIN_INT ( M, N ) );
>        gsl_matrix_view m = gsl_matrix_view_array (a_data, M, N);
>        gsl_vector_set_zero ( tau ) ;
>        gsl_vector_view v = gsl_vector_view_array (b_data, N);
>  
>  printf("-----vector v   ---------\n");
> for (i = 0; i < M; i++) {
>     printf ("%f ",gsl_vector_get (&v.vector, i ) );
>     printf("\n"); };
> 
> printf("now, we are calling the function gsl_linalg_QR_Qvec()--\n");
> 
>        (void) gsl_linalg_QR_Qvec (&m.matrix, tau, &v.vector ) ;
> 
> printf(" and the-vector v should be Q *v , but is't ---------\n");
> 
> for (i = 0; i < M; i++) {
>     printf ("%f ",gsl_vector_get (&v.vector, i ) );
>    
>     printf("\n"); };
> 
> 
> 
>  printf(" the-vector tau is not chenged too---------\n");
>  for (i = 0; i < M; i++) {
>     printf ("%f ",gsl_vector_get (tau, i ) );
>     printf("\n"); };
>  
>  
>      gsl_vector_free(tau);
> 
>        return 0;
>   } ;
> //---------- end of program QRQvec.c
> 
> 
> 
> - and in program QRQTvec.c  :
> 
> 
> //-----program QRQTvec.c
> 
> /*
>   int gsl_linalg_QR_QTvec (const gsl_matrix * QR,
>                            const gsl_vector * tau,
>                                   gsl_vector * v )
>  
> This function applies the matrix QT encoded in the decomposition
> (QR,tau) to the vector v, storing the result QT*v in v.
> The matrix multiplication is carried out directly
> using the encoding of the Householder vectors without
> needing to form the full matrix  QT .
>    
> */
> 
> #include <stdio.h>
> #include <gsl/gsl_linalg.h>
> 
> int main (void)
> {
>   double a_data[] =       {-0.18, 0.60,  0.57, 0.96,
>                                           0.41, 0.24, -0.99, 0.58,
>                                          -0.14, 0.30,  0.97, 0.66,
>                                          -0.51, 0.13,  0.19, 0.85,
>                                          0.33, 0.44, -0.66, 0.12 };
>        
>        double b_data[] = { 1.0, 1.0, 1.0, 1.0 };
> 
>        int M = 4, N = 4 , i ;
> 
>        gsl_vector * tau = gsl_vector_alloc( GSL_MIN_INT ( M, N ) );
>        gsl_matrix_view m = gsl_matrix_view_array (a_data, M, N);
> //       gsl_vector_set_zero ( tau ) ;
>        gsl_vector_view v = gsl_vector_view_array (b_data, N);
> 
>        (void) gsl_linalg_QR_QTvec (&m.matrix, tau, &v.vector ) ;
> 
>    printf("-----vector v = QTrans*v---------\n");
> 
> for (i = 0; i < M; i++) {
>     printf ("%f ",gsl_vector_get (&v.vector, i ) );
>    
>     printf("\n"); };
> 
>  printf("-----vector tau---------\n");
>  for (i = 0; i < M; i++) {
>     printf ("%f ",gsl_vector_get (tau, i ) );
>     printf("\n"); };
> 
>  
>  
>      gsl_vector_free(tau);
>        return 0;
>      }
> //---end of programm QRQTvec-c-------------------------
> 
> first, I  have initialize the vector v=b  with the values: 1.0, 1.0,
> 1.0, 1.0   , and
> then I've tried to obtain only the vectors  Q*b  or QT*b respectively.
> 
> But in both cases the vector v = b is unchanged and  v = b = {  1.0,
> 1.0, 1.0, 1.0  } in output.
> 
> Please, run these two  programs.  For some reason I need  from the
> linear system Ax = b
> only the right hand  sites  of the systems:
>           Rx = QT* b , or
>           Rx = Q * b. 
> 
>  These two functions
> 
>     gsl_linalg_QR_QTvec() and gsl_linalg_QR_Qvec() don't provides the
> result.
> 
> Best regards
> 
> 
> Andrzej Buczynski
> Moosburg, Germany
> 
> 
> 
> 
> 
> 
> 
>   
> 
> 
> 
> 
> 
> 
> 
> 
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