FLA_LQ_UT_blk_var1.c File Reference

(r)

Functions
FLA_Error	FLA_LQ_UT_blk_var1 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)

Function Documentation

FLA_LQ_UT_blk_var1()

FLA_Error FLA_LQ_UT_blk_var1	(	FLA_Obj	A,
		FLA_Obj	T,
		fla_lqut_t *	cntl
	)

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;
 
  FLA_Obj TL,    TR,       T0,  T1,  W12;
 
  FLA_Obj T1T,   T2B;
 
  FLA_Obj AR1,   AR2;
 
  dim_t   b_alg, b;
 
  // Query the algorithmic blocksize by inspecting the length of T.
  b_alg = FLA_Obj_length( T );
 
  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
 
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT );
 
  while ( FLA_Obj_min_dim( ABR ) > 0 ){
 
    b = min( b_alg, FLA_Obj_min_dim( ABR ) );
 
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
 
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &W12,
                           b, FLA_RIGHT );
 
    /*------------------------------------------------------------*/
 
    FLA_Part_2x1( T1,   &T1T,
                        &T2B,    b, FLA_TOP );
 
    FLA_Merge_1x2( A11, A12,   &AR1 );
 
    // Perform an LQ factorization via the UT transform on AR1:
    //
    //   ( A11 A12 ) -> L11 QR1
    //
    // where:
    //  - QR1 is formed from UR1 (which is stored row-wise above the
    //    diagonal of AR1) and T11 (which is stored to the upper triangle
    //    of T11).
    //  - L11 is stored to the lower triangle of AR1.
  
    FLA_LQ_UT_internal( AR1, T1T, 
                        FLA_Cntl_sub_lqut( cntl ));
 
 
    if ( FLA_Obj_length( A21 ) > 0 )
    {
      FLA_Merge_1x2( A21, A22,   &AR2 );
 
      // Apply the Householder transforms associated with UR1 and T11 to 
      // AR2:
      //
      //   ( A21 A22 ) := ( A21 A22 ) Q1
      //
      // where QR1 is formed from UR1 and T11.
 
      FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE,
                               AR1, T1T, W12, AR2,
                               FLA_Cntl_sub_apqut( cntl ) );
    }
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
 
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ W12,
                              FLA_LEFT );
  }
 
  return FLA_SUCCESS;
}

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), and i.

Referenced by FLA_LQ_UT_internal().