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Functions
FLA_Lyap_h_unb_var2.c File Reference

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Functions

FLA_Error FLA_Lyap_h_unb_var2 (FLA_Obj isgn, FLA_Obj A, FLA_Obj C)
 

Function Documentation

◆ FLA_Lyap_h_unb_var2()

FLA_Error FLA_Lyap_h_unb_var2 ( FLA_Obj  isgn,
FLA_Obj  A,
FLA_Obj  C 
)

References FLA_Axpys(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyrt(), FLA_Copyt(), FLA_Dot2cs(), FLA_Gemvc(), FLA_Ger(), 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().

14 {
15  FLA_Obj ATL, ATR, A00, a01, A02,
16  ABL, ABR, a10t, alpha11, a12t,
17  A20, a21, A22;
18 
19  FLA_Obj CTL, CTR, C00, c01, C02,
20  CBL, CBR, c10t, gamma11, c12t,
21  C20, c21, C22;
22 
23  FLA_Obj WTL, WTR, W00, w01, W02,
24  WBL, WBR, w10t, omega11, w12t,
25  W20, w21, W22;
26 
27  FLA_Obj W, omega;
28 
29  FLA_Scal( isgn, C );
30 
31  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &W );
32  FLA_Obj_create( FLA_Obj_datatype( A ), 1, 1, 0, 0, &omega );
33 
34  FLA_Part_2x2( A, &ATL, &ATR,
35  &ABL, &ABR, 0, 0, FLA_TL );
36 
37  FLA_Part_2x2( C, &CTL, &CTR,
38  &CBL, &CBR, 0, 0, FLA_TL );
39 
40  FLA_Part_2x2( W, &WTL, &WTR,
41  &WBL, &WBR, 0, 0, FLA_TL );
42 
43  while ( FLA_Obj_length( CBR ) > 0 ){
44 
45  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
46  /* ************* */ /* ************************** */
47  &a10t, /**/ &alpha11, &a12t,
48  ABL, /**/ ABR, &A20, /**/ &a21, &A22,
49  1, 1, FLA_BR );
50 
51  FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, /**/ &c01, &C02,
52  /* ************* */ /* ************************** */
53  &c10t, /**/ &gamma11, &c12t,
54  CBL, /**/ CBR, &C20, /**/ &c21, &C22,
55  1, 1, FLA_BR );
56 
57  FLA_Repart_2x2_to_3x3( WTL, /**/ WTR, &W00, /**/ &w01, &W02,
58  /* ************* */ /* ************************** */
59  &w10t, /**/ &omega11, &w12t,
60  WBL, /**/ WBR, &W20, /**/ &w21, &W22,
61  1, 1, FLA_BR );
62 
63  /*------------------------------------------------------------*/
64 
65  // c01 = inv( triu(A00) + conj(alpha11) * I )' * c01;
66  FLA_Copyrt( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, A00, W00 );
67  FLA_Shift_diag( FLA_CONJUGATE, alpha11, W00 );
68  FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, W00, c01 );
69 
70  // gamma11 = gamma11 - a01' * c01 - c01' * a01;
71  FLA_Dot2cs( FLA_CONJUGATE, FLA_MINUS_ONE, a01, c01, FLA_ONE, gamma11 );
72 
73  // gamma11 = gamma11 / ( alpha11 + alpha11' );
74  FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, alpha11, omega );
75  FLA_Mult_add( FLA_ONE, alpha11, omega );
76  FLA_Inv_scal( omega, gamma11 );
77 
78  // C02 = C02 - c01 * a12t;
79  FLA_Ger( FLA_MINUS_ONE, c01, a12t, C02 );
80 
81  // c12t = c12t - gamma11 * a12t;
82  // c12t = c12t - c01' * A02;
83  // = c12t - A02^T conj(c01);
84  FLA_Axpys( FLA_MINUS_ONE, gamma11, a12t, FLA_ONE, c12t );
85  FLA_Gemvc( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A02, c01, FLA_ONE, c12t );
86 
87  /*------------------------------------------------------------*/
88 
89  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
90  a10t, alpha11, /**/ a12t,
91  /* ************** */ /* ************************ */
92  &ABL, /**/ &ABR, A20, a21, /**/ A22,
93  FLA_TL );
94 
95  FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, c01, /**/ C02,
96  c10t, gamma11, /**/ c12t,
97  /* ************** */ /* ************************ */
98  &CBL, /**/ &CBR, C20, c21, /**/ C22,
99  FLA_TL );
100 
101  FLA_Cont_with_3x3_to_2x2( &WTL, /**/ &WTR, W00, w01, /**/ W02,
102  w10t, omega11, /**/ w12t,
103  /* ************** */ /* ************************ */
104  &WBL, /**/ &WBR, W20, w21, /**/ W22,
105  FLA_TL );
106  }
107 
108  FLA_Obj_free( &W );
109  FLA_Obj_free( &omega );
110 
111  return FLA_SUCCESS;
112 }
FLA_Error FLA_Obj_create(FLA_Datatype datatype, dim_t m, dim_t n, dim_t rs, dim_t cs, FLA_Obj *obj)
Definition: FLA_Obj.c:55
FLA_Error FLA_Gemvc(FLA_Trans transa, FLA_Conj conjx, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Gemvc.c:13
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition: FLA_Obj.c:588
FLA_Obj FLA_MINUS_ONE
Definition: FLA_Init.c:22
FLA_Error FLA_Trsv(FLA_Uplo uplo, FLA_Trans transa, FLA_Diag diag, FLA_Obj A, FLA_Obj x)
Definition: FLA_Trsv.c:15
FLA_Error FLA_Repart_2x2_to_3x3(FLA_Obj ATL, FLA_Obj ATR, FLA_Obj *A00, FLA_Obj *A01, FLA_Obj *A02, FLA_Obj *A10, FLA_Obj *A11, FLA_Obj *A12, FLA_Obj ABL, FLA_Obj ABR, FLA_Obj *A20, FLA_Obj *A21, FLA_Obj *A22, dim_t mb, dim_t nb, FLA_Quadrant quadrant)
Definition: FLA_View.c:142
FLA_Error FLA_Axpys(FLA_Obj alpha0, FLA_Obj alpha1, FLA_Obj A, FLA_Obj beta, FLA_Obj B)
Definition: FLA_Axpys.c:13
FLA_Error FLA_Ger(FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj A)
Definition: FLA_Ger.c:13
FLA_Error FLA_Copyt(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition: FLA_Copyt.c:15
FLA_Error FLA_Part_2x2(FLA_Obj A, FLA_Obj *A11, FLA_Obj *A12, FLA_Obj *A21, FLA_Obj *A22, dim_t mb, dim_t nb, FLA_Quadrant quadrant)
Definition: FLA_View.c:17
FLA_Obj FLA_ONE
Definition: FLA_Init.c:18
FLA_Datatype FLA_Obj_datatype(FLA_Obj obj)
Definition: FLA_Query.c:13
Definition: FLA_type_defs.h:158
FLA_Error FLA_Dot2cs(FLA_Conj conj, FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj beta, FLA_Obj rho)
Definition: FLA_Dot2cs.c:13
FLA_Error FLA_Scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Scal.c:15
FLA_Error FLA_Obj_create_conf_to(FLA_Trans trans, FLA_Obj old, FLA_Obj *obj)
Definition: FLA_Obj.c:286
FLA_Error FLA_Shift_diag(FLA_Conj conj, FLA_Obj sigma, FLA_Obj A)
Definition: FLA_Shift_diag.c:13
FLA_Error FLA_Inv_scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scal.c:13
FLA_Error FLA_Mult_add(FLA_Obj alpha, FLA_Obj beta, FLA_Obj gamma)
Definition: FLA_Mult_add.c:13
FLA_Error FLA_Cont_with_3x3_to_2x2(FLA_Obj *ATL, FLA_Obj *ATR, FLA_Obj A00, FLA_Obj A01, FLA_Obj A02, FLA_Obj A10, FLA_Obj A11, FLA_Obj A12, FLA_Obj *ABL, FLA_Obj *ABR, FLA_Obj A20, FLA_Obj A21, FLA_Obj A22, FLA_Quadrant quadrant)
Definition: FLA_View.c:304
dim_t FLA_Obj_length(FLA_Obj obj)
Definition: FLA_Query.c:116
FLA_Error FLA_Copyrt(FLA_Uplo uplo, FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition: FLA_Copyrt.c:13