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Functions
FLA_Hess_UT_unb_var3.c File Reference

(r)

Functions

FLA_Error FLA_Hess_UT_unb_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_unb_var3 (FLA_Obj A, FLA_Obj T)

Function Documentation

References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dotc(), FLA_Gemv(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Set(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var3().

{
  FLA_Obj  ATL,   ATR,      A00,  a01,     A02, 
           ABL,   ABR,      a10t, alpha11, a12t,
                            A20,  a21,     A22;
  FLA_Obj  TTL,   TTR,      T00,  t01,   T02, 
           TBL,   TBR,      t10t, tau11, t12t,
                            T20,  t21,   T22;
  FLA_Obj  uT,              u0,
           uB,              upsilon1,
                            u2;
  FLA_Obj  yT,              y0,
           yB,              psi1,
                            y2;
  FLA_Obj  zT,              z0,
           zB,              zeta1,
                            z2;
  FLA_Obj  vT,              v0,
           vB,              nu1,
                            v2;
  FLA_Obj  wT,              w0,
           wB,              omega1,
                            w2;
  FLA_Obj  u, y, z, v, w;

  FLA_Obj  inv_tau11;
  FLA_Obj  minus_inv_tau11;
  FLA_Obj  first_elem;
  FLA_Obj  beta;
  FLA_Obj  conj_beta;
  FLA_Obj  dot_product;
  FLA_Obj  minus_upsilon1;
  FLA_Obj  minus_conj_upsilon1;
  FLA_Obj  minus_psi1;
  FLA_Obj  minus_conj_psi1;
  FLA_Obj  minus_zeta1;

  FLA_Obj  a21_t,
           a21_b;

  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg;


  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &first_elem );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &conj_beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &dot_product );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_upsilon1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_conj_upsilon1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_psi1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_conj_psi1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_zeta1 );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
  FLA_Part_2x1( u,    &uT, 
                      &uB,            0, FLA_TOP );
  FLA_Part_2x1( y,    &yT, 
                      &yB,            0, FLA_TOP );
  FLA_Part_2x1( z,    &zT, 
                      &zB,            0, FLA_TOP );
  FLA_Part_2x1( v,    &vT, 
                      &vB,            0, FLA_TOP );
  FLA_Part_2x1( w,    &wT, 
                      &wB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < b_alg )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************** */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
    FLA_Repart_2x1_to_3x1( uT,                &u0, 
                        /* ** */            /* ******** */
                                              &upsilon1, 
                           uB,                &u2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( yT,                &y0, 
                        /* ** */            /* **** */
                                              &psi1, 
                           yB,                &y2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( zT,                &z0, 
                        /* ** */            /* ***** */
                                              &zeta1, 
                           zB,                &z2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( vT,                &v0, 
                        /* ** */            /* *** */
                                              &nu1, 
                           vB,                &v2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( wT,                &w0, 
                        /* ** */            /* ****** */
                                              &omega1, 
                           wB,                &w2,        1, FLA_BOTTOM );

    /*------------------------------------------------------------*/
    
    if ( FLA_Obj_length( ATL ) > 0 )
    {
      FLA_Copy( upsilon1, minus_upsilon1 );
      FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );

      FLA_Copy( psi1, minus_psi1 );
      FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );

      FLA_Copy( zeta1, minus_zeta1 );
      FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );

      // alpha11 = alpha11 - upsilon11 * conj(psi11) - zeta11 * conj(upsilon11);
      FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );

      // a12t = a12t - upsilon11 * y21' - zeta11 * u21';
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );

      // a21 = a21 - conj(psi11) * u21 - conj(upsilon11) * z21;
      FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
    }

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      FLA_Part_2x1( a21,    &a21_t,
                            &a21_b,            1, FLA_TOP );

      // [ x21, tau11, a21 ] = House( a21 );
      FLA_Househ2_UT( FLA_LEFT,
                      a21_t,
                      a21_b, tau11 );

      // inv_tau11            =  1 / tau11;
      // minus_inv_tau11      = -1 / tau11;
      FLA_Set( FLA_ONE, inv_tau11 );
      FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      FLA_Copy( inv_tau11, minus_inv_tau11 );
      FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );

      // Save first element of a21_t and set it to one so we can use a21 as
      // u21 in subsequent computations. We will restore a21_t later on.
      FLA_Copy( a21_t, first_elem );
      FLA_Set( FLA_ONE, a21_t );
    }

    if ( FLA_Obj_length( ATL ) > 0 )
    {
      // A22 = A22 - u21 * y21' - z21 * u21';
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
    }

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      // v2 = A22' * x21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );

      // w2 = A22 * x21;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );

      // u21 = x21; 
      // y21 = v2;
      // z21 = w2;
      FLA_Copy( a21, u2 );
      FLA_Copy( v2, y2 );
      FLA_Copy( w2, z2 );

      // beta      = u21' * z21 / 2;
      // conj_beta = conj(beta);
      FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      FLA_Inv_scal( FLA_TWO, beta );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );

      // y21' = ( y21' - beta / tau * u21' ) / tau;
      // y21  = ( y21 - conj(beta) / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, conj_beta );
      FLA_Axpy( conj_beta, a21, y2 );
      FLA_Scal( inv_tau11, y2 );

      // z21 = ( z21 - beta / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, beta );
      FLA_Axpy( beta, a21, z2 );
      FLA_Scal( inv_tau11, z2 );

      // a12t = a12t * ( I - u21 * u21' / tau );
      //      = a12t - ( a12t * u21 ) * u21' / tau;
      FLA_Dot( a12t, a21, dot_product );
      FLA_Scal( minus_inv_tau11, dot_product );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );

      // A02 = A02 * ( I - u21 * u21' / tau );
      //     = A02 - ( A02 * u21 ) * u21' / tau;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );

      // t01 = U20' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );

      // Restore first element of a21.
      FLA_Copy( first_elem, a21_t );
    }

    // Update A22 if this is the last iteration; this is needed when we're
    // being called from the blocked routine so A22 is left in a valid state.
    if ( FLA_Obj_length( ATL ) + 1 == b_alg &&
         FLA_Obj_length( A22 ) > 0 )
    {
      // A22 = A22 - u21 * y21' - z21 * u21';
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ************************ */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &uT,                u0, 
                                                  upsilon1, 
                            /* ** */           /* ******** */
                              &uB,                u2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &yT,                y0, 
                                                  psi1, 
                            /* ** */           /* **** */
                              &yB,                y2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &zT,                z0, 
                                                  zeta1, 
                            /* ** */           /* ***** */
                              &zB,                z2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &vT,                v0, 
                                                  nu1, 
                            /* ** */           /* *** */
                              &vB,                v2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &wT,                w0, 
                                                  omega1, 
                            /* ** */           /* ****** */
                              &wB,                w2,     FLA_TOP );
  }

  FLA_Obj_free( &inv_tau11 );
  FLA_Obj_free( &minus_inv_tau11 );
  FLA_Obj_free( &first_elem );
  FLA_Obj_free( &beta );
  FLA_Obj_free( &conj_beta );
  FLA_Obj_free( &dot_product );
  FLA_Obj_free( &minus_upsilon1 );
  FLA_Obj_free( &minus_conj_upsilon1 );
  FLA_Obj_free( &minus_psi1 );
  FLA_Obj_free( &minus_conj_psi1 );
  FLA_Obj_free( &minus_zeta1 );
  FLA_Obj_free( &u );
  FLA_Obj_free( &y );
  FLA_Obj_free( &z );
  FLA_Obj_free( &v );
  FLA_Obj_free( &w );

  return FLA_SUCCESS;
}

References FLA_Hess_UT_step_unb_var3().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_unb_var3( A, T );
}