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_QR2_UT_unb_var1(FLA_Obj U,FLA_Obj D,FLA_Obj T)13 FLA_Error FLA_QR2_UT_unb_var1( FLA_Obj U,
14 FLA_Obj D, FLA_Obj T )
15 {
16 FLA_Obj UTL, UTR, U00, u01, U02,
17 UBL, UBR, u10t, upsilon11, u12t,
18 U20, u21, U22;
19
20 FLA_Obj DL, DR, D0, d1, D2;
21
22 FLA_Obj TTL, TTR, T00, t01, T02,
23 TBL, TBR, t10t, tau11, t12t,
24 T20, t21, T22;
25
26
27 FLA_Part_2x2( U, &UTL, &UTR,
28 &UBL, &UBR, 0, 0, FLA_TL );
29
30 FLA_Part_1x2( D, &DL, &DR, 0, FLA_LEFT );
31
32 FLA_Part_2x2( T, &TTL, &TTR,
33 &TBL, &TBR, 0, 0, FLA_TL );
34
35 while ( FLA_Obj_min_dim( UBR ) > 0 ){
36
37 FLA_Repart_2x2_to_3x3( UTL, /**/ UTR, &U00, /**/ &u01, &U02,
38 /* ************* */ /* ************************** */
39 &u10t, /**/ &upsilon11, &u12t,
40 UBL, /**/ UBR, &U20, /**/ &u21, &U22,
41 1, 1, FLA_BR );
42
43 FLA_Repart_1x2_to_1x3( DL, /**/ DR, &D0, /**/ &d1, &D2,
44 1, FLA_RIGHT );
45
46 FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
47 /* ************* */ /* ************************ */
48 &t10t, /**/ &tau11, &t12t,
49 TBL, /**/ TBR, &T20, /**/ &t21, &T22,
50 1, 1, FLA_BR );
51
52 /*------------------------------------------------------------*/
53
54 // Compute tau11 and u2 from upsilon11 and d1 such that tau11 and u2
55 // determine a Householder transform H such that applying H from the
56 // left to the column vector consisting of upsilon11 and d1 annihilates
57 // the entries in d1 (and updates upsilon11).
58 FLA_Househ2_UT( FLA_LEFT,
59 upsilon11,
60 d1, tau11 );
61
62 // / u12t \ = H / u12t \
63 // \ D2 / \ D2 /
64 //
65 // where H is formed from tau11 and d1.
66 FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
67 D2 );
68
69 // t01 = D0' * d1;
70 FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D0, d1, FLA_ZERO, t01 );
71
72 /*------------------------------------------------------------*/
73
74 FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR, U00, u01, /**/ U02,
75 u10t, upsilon11, /**/ u12t,
76 /* ************** */ /* ************************ */
77 &UBL, /**/ &UBR, U20, u21, /**/ U22,
78 FLA_TL );
79
80 FLA_Cont_with_1x3_to_1x2( &DL, /**/ &DR, D0, d1, /**/ D2,
81 FLA_LEFT );
82
83 FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
84 t10t, tau11, /**/ t12t,
85 /* ************** */ /* ********************** */
86 &TBL, /**/ &TBR, T20, t21, /**/ T22,
87 FLA_TL );
88 }
89
90 return FLA_SUCCESS;
91 }
92
93