FLA_LU_piv_unb_var3.c File Reference

(r)

Functions
FLA_Error	FLA_LU_piv_unb_var3 (FLA_Obj A, FLA_Obj p)

---

Function Documentation

FLA_Error FLA_LU_piv_unb_var3	(	FLA_Obj	A,
		FLA_Obj	p
	)

References FLA_Amax_external(), FLA_Apply_pivots(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Dots_external(), FLA_Gemv_external(), FLA_Inv_scal_external(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trsm_external(), and FLA_Trsv_external().

Referenced by FLA_LU_piv_internal().

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj AL,    AR,       A0,  a1,  A2;

  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;

  FLA_Obj AB0, aB1;


  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_1x2( A,    &AL,  &AR,      0, FLA_LEFT );

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    FLA_Repart_1x2_to_1x3( AL,  /**/ AR,        &A0, /**/ &a1, &A2,
                           1, FLA_RIGHT );

    FLA_Repart_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* *** */
                                              &pi1, 
                           pB,                &p2,        1, FLA_BOTTOM );

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

    // Apply previously computed pivots
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );

    // a01 = trilu( A00 ) \ a01 
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );

    // alpha11 = alpha11 - a10t * a01
    FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );

    // a21 = a21 - A20 * a01
    FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );

    // aB1 = / alpha11 \
    //       \  a21    /
    FLA_Merge_2x1( alpha11,
                       a21,      &aB1 );

    // Determine pivot index
    FLA_Amax_external( aB1, pi1 );

    // Apply pivots to current column
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );

    // a21 = a21 / alpha11 
    FLA_Inv_scal_external( alpha11, a21 );

    // AB0 = / a10t \
    //       \ A20  /
    FLA_Merge_2x1( a10t,
                   A20,      &AB0 );

    // Apply pivots to previous columns
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &AL,  /**/ &AR,        A0, a1, /**/ A2,
                              FLA_LEFT );

    FLA_Cont_with_3x1_to_2x1( &pT,                p0, 
                                                  pi1, 
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );

  }

  if ( FLA_Obj_width( ATR ) > 0 )
  {
    /* Apply pivots to untouched columns */
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );

    /* ATR = trilu( ATL ) \ ATR */ 
    FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, ATL, ATR );
  }

  return FLA_SUCCESS;
}