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Functions
FLA_QR_UT_inc_blk_var1.c File Reference

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Functions

FLA_Error FLA_QR_UT_inc_blk_var1 (FLA_Obj A, FLA_Obj TW, fla_qrutinc_t *cntl)
 

Function Documentation

◆ FLA_QR_UT_inc_blk_var1()

FLA_Error FLA_QR_UT_inc_blk_var1 ( FLA_Obj  A,
FLA_Obj  TW,
fla_qrutinc_t cntl 
)

References FLA_Apply_Q2_UT_internal(), FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_2x2(), FLA_QR2_UT_internal(), FLA_QR_UT_internal(), and FLA_Repart_2x2_to_3x3().

Referenced by FLASH_QR_UT_inc_noopt().

14 {
15  FLA_Obj ATL, ATR, A00, A01, A02,
16  ABL, ABR, A10, A11, A12,
17  A20, A21, A22;
18 
19  FLA_Obj TTL, WTR, T00, W01, W02,
20  TBL, TBR, T10, T11, W12,
21  T20, T21, T22;
22 
23  dim_t b;
24 
25  FLA_Part_2x2( A, &ATL, &ATR,
26  &ABL, &ABR, 0, 0, FLA_TL );
27 
28  FLA_Part_2x2( TW, &TTL, &WTR,
29  &TBL, &TBR, 0, 0, FLA_TL );
30 
31  while ( FLA_Obj_min_dim( ABR ) > 0 ){
32 
33  b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
34 
35  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
36  /* ************* */ /* ******************** */
37  &A10, /**/ &A11, &A12,
38  ABL, /**/ ABR, &A20, /**/ &A21, &A22,
39  b, b, FLA_BR );
40 
41  FLA_Repart_2x2_to_3x3( TTL, /**/ WTR, &T00, /**/ &W01, &W02,
42  /* ************* */ /* ******************** */
43  &T10, /**/ &T11, &W12,
44  TBL, /**/ TBR, &T20, /**/ &T21, &T22,
45  b, b, FLA_BR );
46 
47  /*------------------------------------------------------------*/
48 
49  /*
50  Perform a QR factorization (via UT transform) on A11:
51 
52  [ A11, T11 ] = QR_UT( A11, T11 );
53 
54  where T11 refers to a single storage block that refers to an
55  b_alg-by-b row-panel of upper triangular block Householder
56  transforms. Here, b is the storage blocksize while b_alg is
57  the algorithmic blocksize used by the QR factorization.
58  Typically b_alg << b.
59 
60  */
61 
62  FLA_QR_UT_internal( A11, T11,
63  FLA_Cntl_sub_qrut( cntl ) );
64 
65 
66  if ( FLA_Obj_width( A12 ) > 0 )
67  {
68  /*
69  Apply Q^H to A12 from the left:
70 
71  A12 = Q^H * A12
72 
73  where Q is formed from A11 and T11. Note that W12 refers
74  to a row-panel of blocks where each block refers to an
75  b_alg-by-b row-panel of workspace.
76  */
77 
78  FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
79  A11, T11, W12, A12,
80  FLA_Cntl_sub_apqut( cntl ) );
81  }
82 
83 
84  /*
85  Update QR factorization of A11 with each block of A21, storing
86  block Householder transforms into corresponding blocks of T21.
87 
88  [ A11, ...
89  A21, T21 ] = QR2_UT( A11, ...
90  A21, T21 );
91  */
92 
94  A21, T21,
95  FLA_Cntl_sub_qr2ut( cntl ) );
96 
97 
98  if ( FLA_Obj_width( A12 ) > 0 )
99  {
100  /*
101  Apply Q^H to A12 and A22 from the left:
102 
103  / A12 \ = Q^H * / A12 \
104  \ A22 / \ A22 /
105 
106  where Q is formed from A21 and T21.
107  */
108 
109  FLA_Apply_Q2_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
110  A21, T21, W12, A12,
111  A22,
112  FLA_Cntl_sub_apq2ut( cntl ) );
113  }
114 
115  /*------------------------------------------------------------*/
116 
117  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
118  A10, A11, /**/ A12,
119  /* ************** */ /* ****************** */
120  &ABL, /**/ &ABR, A20, A21, /**/ A22,
121  FLA_TL );
122 
123  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &WTR, T00, W01, /**/ W02,
124  T10, T11, /**/ W12,
125  /* ************** */ /* ****************** */
126  &TBL, /**/ &TBR, T20, T21, /**/ T22,
127  FLA_TL );
128 
129  }
130 
131  return FLA_SUCCESS;
132 }
unsigned long dim_t
Definition: FLA_type_defs.h:71
dim_t FLA_Determine_blocksize(FLA_Obj A_unproc, FLA_Quadrant to_dir, fla_blocksize_t *cntl_blocksizes)
Definition: FLA_Blocksize.c:234
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_QR2_UT_internal(FLA_Obj U, FLA_Obj D, FLA_Obj T, fla_qr2ut_t *cntl)
Definition: FLA_QR2_UT_internal.c:16
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_Apply_Q_UT_internal(FLA_Side side, FLA_Trans trans, FLA_Direct direct, FLA_Store storev, FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
Definition: FLA_Apply_Q_UT_internal.c:17
Definition: FLA_type_defs.h:158
dim_t FLA_Obj_width(FLA_Obj obj)
Definition: FLA_Query.c:123
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_Apply_Q2_UT_internal(FLA_Side side, FLA_Trans trans, FLA_Direct direct, FLA_Store storev, FLA_Obj D, FLA_Obj T, FLA_Obj W, FLA_Obj C, FLA_Obj E, fla_apq2ut_t *cntl)
Definition: FLA_Apply_Q2_UT_internal.c:17
FLA_Error FLA_QR_UT_internal(FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl)
Definition: FLA_QR_UT_internal.c:17
dim_t FLA_Obj_min_dim(FLA_Obj obj)
Definition: FLA_Query.c:153