FLA_Lyap_n_unb_var1.c File Reference

(r)

Functions
FLA_Error	FLA_Lyap_n_unb_var1 (FLA_Obj isgn, FLA_Obj A, FLA_Obj C)

Function Documentation

FLA_Lyap_n_unb_var1()

FLA_Error FLA_Lyap_n_unb_var1	(	FLA_Obj	isgn,
		FLA_Obj	A,
		FLA_Obj	C
	)

{
  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_BR );
 
  FLA_Part_2x2( C,    &CTL, &CTR,
                      &CBL, &CBR,     0, 0, FLA_BR );
 
  FLA_Part_2x2( W,    &WTL, &WTR,
                      &WBL, &WBR,     0, 0, FLA_BR );
 
  while ( FLA_Obj_length( CTL ) > 0 ){
 
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  &a01,     /**/ &A02,
                                                &a10t, &alpha11, /**/ &a12t,
                        /* ************* */   /* ************************** */
                           ABL, /**/ ABR,       &A20,  &a21,     /**/ &A22,
                           1, 1, FLA_TL );
 
    FLA_Repart_2x2_to_3x3( CTL, /**/ CTR,       &C00,  &c01,     /**/ &C02,
                                                &c10t, &gamma11, /**/ &c12t,
                        /* ************* */   /* ************************** */
                           CBL, /**/ CBR,       &C20,  &c21,     /**/ &C22,
                           1, 1, FLA_TL );
 
    FLA_Repart_2x2_to_3x3( WTL, /**/ WTR,       &W00,  &w01,     /**/ &W02,
                                                &w10t, &omega11, /**/ &w12t,
                        /* ************* */   /* ************************** */
                           WBL, /**/ WBR,       &W20,  &w21,     /**/ &W22,
                           1, 1, FLA_TL );
 
    /*------------------------------------------------------------*/
 
    // c12t   = c12t   - a12t * C22;
    // c12t^T = c12t^T - C22^T a12t^T;
    FLA_Hemvc( FLA_UPPER_TRIANGULAR, FLA_CONJUGATE, FLA_MINUS_ONE, C22, a12t, FLA_ONE, c12t );
 
    // c12t   = c12t * inv( triu(A22') + alpha11 * I );
    // c12t^T = inv( triu(conj(A22)) + alpha11 * I ) * c12t^T;
    FLA_Copyrt( FLA_UPPER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, A22, W22 );
    FLA_Shift_diag( FLA_NO_CONJUGATE, alpha11, W22 );
    FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, W22, c12t );
 
    // gamma11 = gamma11 - a12t * c12t' - c12t * a12t';
    FLA_Dot2cs( FLA_CONJUGATE, FLA_MINUS_ONE, a12t, c12t, FLA_ONE, gamma11 );
 
    // gamma11 = gamma11 / ( alpha11 + alpha11' );
    FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, alpha11, omega );
    FLA_Mult_add( FLA_ONE, alpha11, omega );
    FLA_Inv_scal( omega, gamma11 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  /**/ a01,     A02,
                            /* ************** */  /* ************************ */
                                                     a10t, /**/ alpha11, a12t,
                              &ABL, /**/ &ABR,       A20,  /**/ a21,     A22,
                              FLA_BR );
 
    FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR,       C00,  /**/ c01,     C02,
                            /* ************** */  /* ************************ */
                                                     c10t, /**/ gamma11, c12t,
                              &CBL, /**/ &CBR,       C20,  /**/ c21,     C22,
                              FLA_BR );
 
    FLA_Cont_with_3x3_to_2x2( &WTL, /**/ &WTR,       W00,  /**/ w01,     W02,
                            /* ************** */  /* ************************ */
                                                     w10t, /**/ omega11, w12t,
                              &WBL, /**/ &WBR,       W20,  /**/ w21,     W22,
                              FLA_BR );
  }
 
  FLA_Obj_free( &W );
  FLA_Obj_free( &omega );
 
  return FLA_SUCCESS;
}

References FLA_Cont_with_3x3_to_2x2(), FLA_Copyrt(), FLA_Copyt(), FLA_Dot2cs(), FLA_Hemvc(), 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(), FLA_Trsv(), and i.

Referenced by FLA_Lyap_n().