1 /*
2
3 Copyright (C) 2014, The University of Texas at Austin
4
5 This file is part of libflame and is available under the 3-Clause
6 BSD license, which can be found in the LICENSE file at the top-level
7 directory, or at http://opensource.org/licenses/BSD-3-Clause
8
9 */
10
11 #include "FLAME.h"
12
FLA_Eig_gest_il_unb_var3(FLA_Obj A,FLA_Obj Y,FLA_Obj B)13 FLA_Error FLA_Eig_gest_il_unb_var3( FLA_Obj A, FLA_Obj Y, FLA_Obj B )
14 {
15 FLA_Obj ATL, ATR, A00, a01, A02,
16 ABL, ABR, a10t, alpha11, a12t,
17 A20, a21, A22;
18
19 FLA_Obj BTL, BTR, B00, b01, B02,
20 BBL, BBR, b10t, beta11, b12t,
21 B20, b21, B22;
22
23 FLA_Obj YTL, YTR, Y00, y01, Y02,
24 YBL, YBR, y10t, psi11, y12t,
25 Y20, y21, Y22;
26
27 FLA_Part_2x2( A, &ATL, &ATR,
28 &ABL, &ABR, 0, 0, FLA_TL );
29
30 FLA_Part_2x2( B, &BTL, &BTR,
31 &BBL, &BBR, 0, 0, FLA_TL );
32
33 FLA_Part_2x2( Y, &YTL, &YTR,
34 &YBL, &YBR, 0, 0, FLA_TL );
35
36 while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
37
38 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
39 /* ************* */ /* ************************** */
40 &a10t, /**/ &alpha11, &a12t,
41 ABL, /**/ ABR, &A20, /**/ &a21, &A22,
42 1, 1, FLA_BR );
43
44 FLA_Repart_2x2_to_3x3( BTL, /**/ BTR, &B00, /**/ &b01, &B02,
45 /* ************* */ /* ************************* */
46 &b10t, /**/ &beta11, &b12t,
47 BBL, /**/ BBR, &B20, /**/ &b21, &B22,
48 1, 1, FLA_BR );
49
50 FLA_Repart_2x2_to_3x3( YTL, /**/ YTR, &Y00, /**/ &y01, &Y02,
51 /* ************* */ /* ************************ */
52 &y10t, /**/ &psi11, &y12t,
53 YBL, /**/ YBR, &Y20, /**/ &y21, &Y22,
54 1, 1, FLA_BR );
55
56 /*------------------------------------------------------------*/
57
58 // a10t = a10t - 1/2 * y10t;
59 FLA_Axpy_external( FLA_MINUS_ONE_HALF, y10t, a10t );
60
61 // alpha11 = alpha11 - a10t * b10t' - b10t * a10t';
62 FLA_Dot2cs_external( FLA_CONJUGATE, FLA_MINUS_ONE, a10t, b10t, FLA_ONE, alpha11 );
63
64 // alpha11 = inv(beta11) * alpha11 * inv(conj(beta11));
65 // = inv(beta11) * alpha11 * inv(beta11);
66 FLA_Inv_scal_external( beta11, alpha11 );
67 FLA_Inv_scal_external( beta11, alpha11 );
68
69 // a21 = a21 - A20 * b10t';
70 FLA_Gemvc_external( FLA_NO_TRANSPOSE, FLA_CONJUGATE,
71 FLA_MINUS_ONE, A20, b10t, FLA_ONE, a21 );
72
73 // a21 = a21 * inv(conj(beta11));
74 // = a21 * inv(beta11);
75 FLA_Inv_scal_external( beta11, a21 );
76
77 // a10t = a10t - 1/2 * y10t;
78 FLA_Axpy_external( FLA_MINUS_ONE_HALF, y10t, a10t );
79
80 // a10t = inv(beta11) * a10t;
81 FLA_Inv_scal_external( beta11, a10t );
82
83 // Y20 = Y20 + b21 * a10t;
84 FLA_Ger_external( FLA_ONE, b21, a10t, Y20 );
85
86 // y21 = b21 * alpha11;
87 FLA_Copy_external( b21, y21 );
88 FLA_Scal_external( alpha11, y21 );
89
90 // y21 = y21 + B20 * a10t';
91 FLA_Gemvc_external( FLA_NO_TRANSPOSE, FLA_CONJUGATE,
92 FLA_ONE, B20, a10t, FLA_ONE, y21 );
93
94 /*------------------------------------------------------------*/
95
96 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
97 a10t, alpha11, /**/ a12t,
98 /* ************** */ /* ************************ */
99 &ABL, /**/ &ABR, A20, a21, /**/ A22,
100 FLA_TL );
101
102 FLA_Cont_with_3x3_to_2x2( &BTL, /**/ &BTR, B00, b01, /**/ B02,
103 b10t, beta11, /**/ b12t,
104 /* ************** */ /* *********************** */
105 &BBL, /**/ &BBR, B20, b21, /**/ B22,
106 FLA_TL );
107
108 FLA_Cont_with_3x3_to_2x2( &YTL, /**/ &YTR, Y00, y01, /**/ Y02,
109 y10t, psi11, /**/ y12t,
110 /* ************** */ /* ********************** */
111 &YBL, /**/ &YBR, Y20, y21, /**/ Y22,
112 FLA_TL );
113 }
114
115 return FLA_SUCCESS;
116 }
117
118