FLA_Eig_gest_il_unb_var1.c File Reference

(r)

Functions
FLA_Error	FLA_Eig_gest_il_unb_var1 (FLA_Obj A, FLA_Obj Y, FLA_Obj B)

---

Function Documentation

FLA_Error FLA_Eig_gest_il_unb_var1	(	FLA_Obj	A,
		FLA_Obj	Y,
		FLA_Obj	B
	)

References FLA_Axpy_external(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Dot2cs_external(), FLA_Hemvc_external(), FLA_Inv_scal_external(), FLA_MINUS_ONE, FLA_MINUS_ONE_HALF, FLA_Obj_length(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), FLA_Trsv_external(), and FLA_ZERO.

Referenced by FLA_Eig_gest_il().

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

  FLA_Obj BTL,   BTR,      B00,  b01,    B02, 
          BBL,   BBR,      b10t, beta11, b12t,
                           B20,  b21,    B22;

  FLA_Obj yL,    yR,       y10t, psi11,  y12t;

  FLA_Obj y10t_t,
          y10t_b;

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

  FLA_Part_2x2( B,    &BTL, &BTR,
                      &BBL, &BBR,     0, 0, FLA_TL );

  FLA_Part_1x2( Y,    &yL,  &yR,      0, FLA_LEFT );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){

    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( BTL, /**/ BTR,       &B00,  /**/ &b01,    &B02,
                        /* ************* */   /* ************************* */
                                                &b10t, /**/ &beta11, &b12t,
                           BBL, /**/ BBR,       &B20,  /**/ &b21,    &B22,
                           1, 1, FLA_BR );

    FLA_Repart_1x2_to_1x3( yL,  /**/ yR,        &y10t, /**/ &psi11,  &y12t,
                           1, FLA_RIGHT );

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

    FLA_Part_2x1( y10t,   &y10t_t,
                          &y10t_b,    1, FLA_TOP );

    // y10t   = b10t * A00;
    // y10t^T = A00^T * b10t^T;
    //        = conj(A00) * b10t^T;
    FLA_Hemvc_external( FLA_LOWER_TRIANGULAR, FLA_CONJUGATE,
                        FLA_ONE, A00, b10t, FLA_ZERO, y10t_t );

    // a10t   = a10t * inv( tril( B00 )' );
    // a10t^T = inv( conj(tril( B00 )) ) * a10t^T;
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                       B00, a10t );

    // a10t = a10t - 1/2 * y10t;
    FLA_Axpy_external( FLA_MINUS_ONE_HALF, y10t_t, a10t );

    // alpha11 = alpha11 - a10t * b10t' - b10t * a10t';
    FLA_Dot2cs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a10t, b10t, FLA_ONE, alpha11 );

    // alpha11 = inv(beta11) * alpha11 * inv(conj(beta11));
    //         = inv(beta11) * alpha11 * inv(beta11);
    FLA_Inv_scal_external( beta11, alpha11 );
    FLA_Inv_scal_external( beta11, alpha11 );

    // a10t = a10t - 1/2 * y10t;
    FLA_Axpy_external( FLA_MINUS_ONE_HALF, y10t_t, a10t );

    // a10t = inv(beta11) * a10t;
    FLA_Inv_scal_external( beta11, a10t );

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

    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( &BTL, /**/ &BTR,       B00,  b01,    /**/ B02,
                                                     b10t, beta11, /**/ b12t,
                            /* ************** */  /* *********************** */
                              &BBL, /**/ &BBR,       B20,  b21,    /**/ B22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &yL,  /**/ &yR,        y10t, psi11, /**/  y12t,
                              FLA_LEFT );
  }

  return FLA_SUCCESS;
}