FLA_Apply_Q_UT_rnbc_blk_var1.c File Reference

(r)

Functions
FLA_Error	FLA_Apply_Q_UT_rnbc_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)

---

Function Documentation

FLA_Error FLA_Apply_Q_UT_rnbc_blk_var1	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	W,
		FLA_Obj	B,
		fla_apqut_t *	cntl
	)

References FLA_Axpyt_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_internal(), FLA_Gemm_internal(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), and FLA_Trsm_internal().

Referenced by FLA_Apply_Q_UT_rnbc().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj TL,    TR,       T0,  T1,  T2;

  FLA_Obj T1T,
          T2B;

  FLA_Obj WTL,  WTR,
          WBL,  WBR;

  FLA_Obj BL,    BR,       B0,  B1,  B2;

  dim_t   b_alg, b;
  dim_t   m_BR, n_BR;

  // Query the algorithmic blocksize by inspecting the length of T.
  b_alg = FLA_Obj_length( T );

  // If m > n, then we have to initialize our partitionings carefully so
  // that we begin in the proper location in A and B (since we traverse
  // matrix A from BR to TL).
  if ( FLA_Obj_length( A ) > FLA_Obj_width( A ) )
  {
    m_BR = FLA_Obj_length( A ) - FLA_Obj_width( A );
    n_BR = 0;
  }
  else
  {
    m_BR = 0;
    n_BR = 0;
  }

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     m_BR, n_BR, FLA_BR );

  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_RIGHT );

  FLA_Part_1x2( B,    &BL,  &BR,      m_BR, FLA_RIGHT );

  while ( FLA_Obj_min_dim( ATL ) > 0 ){

    b = min( b_alg, FLA_Obj_min_dim( ATL ) );

    // Since T was filled from left to right, and since we need to access them
    // in reverse order, we need to handle the case where the last block is
    // smaller than the other b x b blocks.
    if ( FLA_Obj_width( TR ) == 0 && FLA_Obj_width( T ) % b_alg > 0 )
      b = FLA_Obj_width( T ) % b_alg;

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, &A01, /**/ &A02,
                                                &A10, &A11, /**/ &A12,
                        /* ************* */   /* ******************** */
                           ABL, /**/ ABR,       &A20, &A21, /**/ &A22,
                           b, b, FLA_TL );

    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, &T1, /**/ &T2,
                           b, FLA_LEFT );

    FLA_Repart_1x2_to_1x3( BL,  /**/ BR,        &B0, &B1, /**/ &B2,
                           b, FLA_LEFT );

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

    FLA_Part_2x1( T1,    &T1T, 
                         &T2B,     b, FLA_TOP );

    FLA_Part_2x2( W,     &WTL, &WTR,
                         &WBL, &WBR,     b, FLA_Obj_length( B1 ), FLA_TL );

    // WTL = B1^T;

    FLA_Copyt_internal( FLA_TRANSPOSE, B1, WTL,
                        FLA_Cntl_sub_copyt( cntl ) );

    // U11 = trilu( A11 );
    // U21 = A21;
    // Let WTL^T be conformal to B1.
    //
    // WTL^T = ( B1 * U11 + B2 * U21 ) * inv( triu(T1T)' );
    // WTL   = inv( conj(triu(T1T)) ) * ( U11^T * B1^T + U21^T * B2^T );

    FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
                       FLA_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, A11, WTL,
                       FLA_Cntl_sub_trmm1( cntl ) );

    FLA_Gemm_internal( FLA_TRANSPOSE, FLA_TRANSPOSE,
                       FLA_ONE, A21, B2, FLA_ONE, WTL,
                       FLA_Cntl_sub_gemm1( cntl ) );

    FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
                       FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                       FLA_ONE, T1T, WTL,
                       FLA_Cntl_sub_trsm( cntl ) );

    // B2 = B2 - WTL^T * U21';
    // B1 = B1 - WTL^T * U11';
    //    = B1 - ( conj(U11) * WTL )^T;

    FLA_Gemm_internal( FLA_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, WTL, A21, FLA_ONE, B2,
                       FLA_Cntl_sub_gemm2( cntl ) );

    FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
                       FLA_CONJ_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_MINUS_ONE, A11, WTL,
                       FLA_Cntl_sub_trmm2( cntl ) );

    FLA_Axpyt_internal( FLA_TRANSPOSE, FLA_ONE, WTL, B1,
                        FLA_Cntl_sub_axpyt( cntl ) );

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, /**/ A01, A02,
                            /* ************** */  /* ****************** */
                                                     A10, /**/ A11, A12,
                              &ABL, /**/ &ABR,       A20, /**/ A21, A22,
                              FLA_BR );

    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, /**/ T1, T2,
                              FLA_RIGHT );

    FLA_Cont_with_1x3_to_1x2( &BL,  /**/ &BR,        B0, /**/ B1, B2,
                              FLA_RIGHT );
  }

  return FLA_SUCCESS;
}