FLA_QR_UT_inc_blk_var2.c File Reference

(r)

Functions
FLA_Error	FLA_QR_UT_inc_blk_var2 (FLA_Obj A, FLA_Obj TW, FLA_Obj U, fla_qrutinc_t *cntl)

---

Function Documentation

FLA_Error FLA_QR_UT_inc_blk_var2	(	FLA_Obj	A,
		FLA_Obj	TW,
		FLA_Obj	U,
		fla_qrutinc_t *	cntl
	)

References FLA_Apply_Q2_UT_internal(), FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x2(), FLA_QR2_UT_internal(), FLA_QR_UT_copy_internal(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().

Referenced by FLASH_QR_UT_inc_opt1().

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

  FLA_Obj TTL,   WTR,      T00, W01, W02, 
          TBL,   TBR,      T10, T11, W12,
                           T20, T21, T22;

  FLA_Obj UL,    UR,       U0,  U11,  U2;

  dim_t b;

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

  FLA_Part_2x2( TW,   &TTL, &WTR,
                      &TBL, &TBR,     0, 0, FLA_TL );

  FLA_Part_1x2( U,    &UL,  &UR,      0, FLA_LEFT );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );

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

    FLA_Repart_2x2_to_3x3( TTL, /**/ WTR,       &T00, /**/ &W01, &W02,
                        /* ************* */   /* ******************** */
                                                &T10, /**/ &T11, &W12,
                           TBL, /**/ TBR,       &T20, /**/ &T21, &T22,
                           b, b, FLA_BR );

    FLA_Repart_1x2_to_1x3( UL,  /**/ UR,        &U0, /**/ &U11, &U2,
                           b, FLA_RIGHT );

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

    /*
       Use U11 to hold a copy of A11 to avoid a false
       write-after-read dependency so that FLA_QR2_UT() may proceed
       while FLA_Apply_Q_UT() executes.
    */


    /*
       Perform a QR factorization (via UT transform) on A11:
     
         [ A11, T11 ] = QR_UT( A11, T11 );

       where T11 refers to a single storage block that refers to an
       b_alg-by-b row-panel of upper triangular block Householder
       transforms. Here, b is the storage blocksize while b_alg is
       the algorithmic blocksize used by the QR factorization.
       Typically b_alg << b.
       
       After the factorization is complete, A11 is copied into U11.
     
    */

    FLA_QR_UT_copy_internal( A11, T11, U11,
                             FLA_Cntl_sub_qrut( cntl ) );


    /*
       Apply Q^H to A12 from the left:
     
         A12 = Q^H * A12
     
       where Q is formed from A11 and T11. Note that W12 refers
       to a row-panel of blocks where each block refers to an
       b_alg-by-b row-panel of workspace.
    */

    FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                             U11, T11, W12, A12,
                             FLA_Cntl_sub_apqut( cntl ) );


    /*
       Update QR factorization of A11 with each block of A21, storing
       block Householder transforms into corresponding blocks of T21.
     
         [ A11, ...
           A21, T21 ] = QR2_UT( A11, ...
                                A21, T21 );
    */

    FLA_QR2_UT_internal( A11,
                         A21, T21, 
                         FLA_Cntl_sub_qr2ut( cntl ) );


    /*
       Apply Q^H to A12 and A22 from the left:
     
           / A12 \ = Q^H * / A12 \
           \ A22 /         \ A22 / 
     
       where Q is formed from A21 and T21.
    */

    FLA_Apply_Q2_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                              A21, T21, W12, A12,
                                             A22,
                              FLA_Cntl_sub_apq2ut( 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_3x3_to_2x2( &TTL, /**/ &WTR,       T00, W01, /**/ W02,
                                                     T10, T11, /**/ W12,
                            /* ************** */  /* ****************** */
                              &TBL, /**/ &TBR,       T20, T21, /**/ T22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &UL,  /**/ &UR,        U0, U11, /**/ U2,
                              FLA_LEFT );

  }

  return FLA_SUCCESS;
}