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FLA_CAQR2_UT_unb_var1.c File Reference

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Functions

FLA_Error FLA_CAQR2_UT_unb_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T)
 

Function Documentation

◆ FLA_CAQR2_UT_unb_var1()

FLA_Error FLA_CAQR2_UT_unb_var1 ( FLA_Obj  U,
FLA_Obj  D,
FLA_Obj  T 
)

References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_2x1(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trmv_external().

Referenced by FLA_CAQR2_UT_internal().

15 {
16  FLA_Obj UTL, UTR, U00, u01, U02,
17  UBL, UBR, u10t, upsilon11, u12t,
18  U20, u21, U22;
19 
20  FLA_Obj DTL, DTR, D00, d01, D02,
21  DBL, DBR, d10t, delta11, d12t,
22  D20, d21, D22;
23 
24  FLA_Obj TTL, TTR, T00, t01, T02,
25  TBL, TBR, t10t, tau11, t12t,
26  T20, t21, T22;
27 
28  FLA_Obj d1, D2;
29 
30  FLA_Obj d01T,
31  d01B;
32 
33  FLA_Obj D00T,
34  D00B;
35 
36  dim_t m_DT;
37 
38  // Begin partitioning diagonally through D with m - n rows above
39  // the diagonal.
40  m_DT = FLA_Obj_length( D ) - FLA_Obj_width( D );
41 
42  FLA_Part_2x2( U, &UTL, &UTR,
43  &UBL, &UBR, 0, 0, FLA_TL );
44 
45  FLA_Part_2x2( D, &DTL, &DTR,
46  &DBL, &DBR, m_DT, 0, FLA_TL );
47 
48  FLA_Part_2x2( T, &TTL, &TTR,
49  &TBL, &TBR, 0, 0, FLA_TL );
50 
51  while ( FLA_Obj_min_dim( UBR ) > 0 ){
52 
53  FLA_Repart_2x2_to_3x3( UTL, /**/ UTR, &U00, /**/ &u01, &U02,
54  /* ************* */ /* ************************** */
55  &u10t, /**/ &upsilon11, &u12t,
56  UBL, /**/ UBR, &U20, /**/ &u21, &U22,
57  1, 1, FLA_BR );
58 
59  FLA_Repart_2x2_to_3x3( DTL, /**/ DTR, &D00, /**/ &d01, &D02,
60  /* ************* */ /* ************************** */
61  &d10t, /**/ &delta11, &d12t,
62  DBL, /**/ DBR, &D20, /**/ &d21, &D22,
63  1, 1, FLA_BR );
64 
65  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
66  /* ************* */ /* ************************ */
67  &t10t, /**/ &tau11, &t12t,
68  TBL, /**/ TBR, &T20, /**/ &t21, &T22,
69  1, 1, FLA_BR );
70 
71  /*------------------------------------------------------------*/
72 
73  FLA_Merge_2x1( d01,
74  delta11, &d1 );
75 
76  FLA_Merge_2x1( D02,
77  d12t, &D2 );
78 
79  // Compute tau11 and u2 from upsilon11 and d1 such that tau11 and u2
80  // determine a Householder transform H such that applying H from the
81  // left to the column vector consisting of upsilon11 and d1 annihilates
82  // the entries in d1 (and updates upsilon11).
83  FLA_Househ2_UT( FLA_LEFT,
84  upsilon11,
85  d1, tau11 );
86 
87  // / u12t \ = H / u12t \
88  // \ D2 / \ D2 /
89  //
90  // where H is formed from tau11 and d1.
91  FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
92  D2 );
93 
94  FLA_Part_2x1( d01, &d01T,
95  &d01B, m_DT, FLA_TOP );
96 
97  FLA_Part_2x1( D00, &D00T,
98  &D00B, m_DT, FLA_TOP );
99 
100  // t01 = D00' * d01;
101  // = D00T' * d01T + triu( D00B )' * d01B;
102  FLA_Copy_external( d01B, t01 );
103  FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
104  D00B, t01 );
105  FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 );
106 
107  /*------------------------------------------------------------*/
108 
109  FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR, U00, u01, /**/ U02,
110  u10t, upsilon11, /**/ u12t,
111  /* ************** */ /* ************************ */
112  &UBL, /**/ &UBR, U20, u21, /**/ U22,
113  FLA_TL );
114 
115  FLA_Cont_with_3x3_to_2x2( &DTL, /**/ &DTR, D00, d01, /**/ D02,
116  d10t, delta11, /**/ d12t,
117  /* ************** */ /* ************************ */
118  &DBL, /**/ &DBR, D20, d21, /**/ D22,
119  FLA_TL );
120 
121  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
122  t10t, tau11, /**/ t12t,
123  /* ************** */ /* ********************** */
124  &TBL, /**/ &TBR, T20, t21, /**/ T22,
125  FLA_TL );
126  }
127 
128  return FLA_SUCCESS;
129 }
FLA_Error FLA_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition: FLA_Househ2_UT.c:16
unsigned long dim_t
Definition: FLA_type_defs.h:71
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_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_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_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_Error FLA_Copy_external(FLA_Obj A, FLA_Obj B)
Definition: FLA_Copy_external.c:13
Definition: FLA_type_defs.h:158
dim_t FLA_Obj_width(FLA_Obj obj)
Definition: FLA_Query.c:123
FLA_Error FLA_Trmv_external(FLA_Uplo uplo, FLA_Trans transa, FLA_Diag diag, FLA_Obj A, FLA_Obj x)
Definition: FLA_Trmv_external.c:13
FLA_Error FLA_Part_2x1(FLA_Obj A, FLA_Obj *A1, FLA_Obj *A2, dim_t mb, FLA_Side side)
Definition: FLA_View.c:76
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_Merge_2x1(FLA_Obj AT, FLA_Obj AB, FLA_Obj *A)
Definition: FLA_View.c:541
dim_t FLA_Obj_min_dim(FLA_Obj obj)
Definition: FLA_Query.c:153