FLA_Lyap_h_unb_var4.c File Reference

(r)

Functions
FLA_Error	FLA_Lyap_h_unb_var4 (FLA_Obj isgn, FLA_Obj A, FLA_Obj C)

---

Function Documentation

FLA_Error FLA_Lyap_h_unb_var4	(	FLA_Obj	isgn,
		FLA_Obj	A,
		FLA_Obj	C
	)

References FLA_Axpys(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyrt(), FLA_Copyt(), FLA_Her2c(), FLA_Inv_scal(), FLA_MINUS_ONE, FLA_Mult_add(), FLA_Obj_create(), FLA_Obj_create_conf_to(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Shift_diag(), and FLA_Trsv().

Referenced by FLA_Lyap_h().

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

  FLA_Obj CTL,   CTR,      C00,  c01,     C02, 
          CBL,   CBR,      c10t, gamma11, c12t,
                           C20,  c21,     C22;

  FLA_Obj WTL,   WTR,      W00,  w01,     W02, 
          WBL,   WBR,      w10t, omega11, w12t,
                           W20,  w21,     W22;

  FLA_Obj W, omega;

  FLA_Scal( isgn, C );

  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &W );
  FLA_Obj_create( FLA_Obj_datatype( A ), 1, 1, 0, 0, &omega );

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

  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_TL );

  FLA_Part_2x2( W,    &WTL, &WTR,
                      &WBL, &WBR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( CBR ) > 0 ){

    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( CTL, /**/ CTR,       &C00,  /**/ &c01,     &C02,
                        /* ************* */   /* ************************** */
                                                &c10t, /**/ &gamma11, &c12t,
                           CBL, /**/ CBR,       &C20,  /**/ &c21,     &C22,
                           1, 1, FLA_BR );

    FLA_Repart_2x2_to_3x3( WTL, /**/ WTR,       &W00,  /**/ &w01,     &W02,
                        /* ************* */   /* ************************** */
                                                &w10t, /**/ &omega11, &w12t,
                           WBL, /**/ WBR,       &W20,  /**/ &w21,     &W22,
                           1, 1, FLA_BR );

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

    // gamma11 = gamma11 / ( alpha11 + alpha11' );
    FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, alpha11, omega );
    FLA_Mult_add( FLA_ONE, alpha11, omega );
    FLA_Inv_scal( omega, gamma11 );

    // c12t = c12t - gamma11 * a12t;
    FLA_Axpys( FLA_MINUS_ONE, gamma11, a12t, FLA_ONE, c12t );

    // c12t = inv( triu(A22) + conj(alpha11) * I )^T * c12t;
    FLA_Copyrt( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, A22, W22 );
    FLA_Shift_diag( FLA_CONJUGATE, alpha11, W22 );
    FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_TRANSPOSE, FLA_NONUNIT_DIAG, W22, c12t );

    // C22 = C22 - conj(a12t) * c12t^T - conj(c12t) * a12t^T;
    FLA_Her2c( FLA_UPPER_TRIANGULAR, FLA_CONJUGATE, FLA_MINUS_ONE, a12t, c12t, C22 );

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

    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( &CTL, /**/ &CTR,       C00,  c01,     /**/ C02,
                                                     c10t, gamma11, /**/ c12t,
                            /* ************** */  /* ************************ */
                              &CBL, /**/ &CBR,       C20,  c21,     /**/ C22,
                              FLA_TL );

    FLA_Cont_with_3x3_to_2x2( &WTL, /**/ &WTR,       W00,  w01,     /**/ W02,
                                                     w10t, omega11, /**/ w12t,
                            /* ************** */  /* ************************ */
                              &WBL, /**/ &WBR,       W20,  w21,     /**/ W22,
                              FLA_TL );
  }

  FLA_Obj_free( &W );
  FLA_Obj_free( &omega );

  return FLA_SUCCESS;
}