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Functions
FLA_QR2_UT_unb_var1.c File Reference

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Functions

FLA_Error FLA_QR2_UT_unb_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T)
 

Function Documentation

◆ FLA_QR2_UT_unb_var1()

FLA_Error FLA_QR2_UT_unb_var1 ( FLA_Obj  U,
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 }
FLA_Error FLA_Gemv_external(FLA_Trans transa, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Gemv_external.c:13
FLA_Obj FLA_ZERO
Definition: FLA_Init.c:20
FLA_Obj FLA_ONE
Definition: FLA_Init.c:18
FLA_Error FLA_Apply_H2_UT(FLA_Side side, FLA_Obj tau, FLA_Obj u2, FLA_Obj a1, FLA_Obj A2)
Definition: FLA_Apply_H2_UT.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
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_Error FLA_Cont_with_1x3_to_1x2(FLA_Obj *AL, FLA_Obj *AR, FLA_Obj A0, FLA_Obj A1, FLA_Obj A2, FLA_Side side)
Definition: FLA_View.c:475
FLA_Error FLA_Part_1x2(FLA_Obj A, FLA_Obj *A1, FLA_Obj *A2, dim_t nb, FLA_Side side)
Definition: FLA_View.c:110
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_Repart_1x2_to_1x3(FLA_Obj AL, FLA_Obj AR, FLA_Obj *A0, FLA_Obj *A1, FLA_Obj *A2, dim_t nb, FLA_Side side)
Definition: FLA_View.c:267
dim_t FLA_Obj_min_dim(FLA_Obj obj)
Definition: FLA_Query.c:153
FLA_Error FLA_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition: FLA_Househ2_UT.c:16
Definition: FLA_type_defs.h:159

References FLA_Apply_H2_UT(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), and FLA_ZERO.

Referenced by FLA_QR2_UT_internal().