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FLA_QR_UT_blk_var2.c File Reference

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Functions

FLA_Error FLA_QR_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl)
 

Function Documentation

◆ FLA_QR_UT_blk_var2()

FLA_Error FLA_QR_UT_blk_var2 ( FLA_Obj  A,
FLA_Obj  T,
fla_qrut_t cntl 
)

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_Merge_2x1(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x2(), FLA_QR_UT_internal(), FLA_Repart_2x2_to_3x3(), and FLA_Trmm_external().

Referenced by FLA_QR_UT_internal().

14 {
15  FLA_Obj ATL, ATR, A00, A01, A02,
16  ABL, ABR, A10, A11, A12,
17  A20, A21, A22;
18 
19  FLA_Obj TTL, TTR, T00, T01, T02,
20  TBL, TBR, T10, T11, W12,
21  T20, T21, T22;
22 
23  FLA_Obj AB1, AB2;
24 
25  dim_t b;
26 
27  FLA_Part_2x2( A, &ATL, &ATR,
28  &ABL, &ABR, 0, 0, FLA_TL );
29 
30  FLA_Part_2x2( T, &TTL, &TTR,
31  &TBL, &TBR, 0, 0, FLA_TL );
32 
33  while ( FLA_Obj_min_dim( ABR ) > 0 ){
34 
35  b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
36 
37  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
38  /* ************* */ /* ******************** */
39  &A10, /**/ &A11, &A12,
40  ABL, /**/ ABR, &A20, /**/ &A21, &A22,
41  b, b, FLA_BR );
42 
43  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &T01, &T02,
44  /* ************* */ /* ******************** */
45  &T10, /**/ &T11, &W12,
46  TBL, /**/ TBR, &T20, /**/ &T21, &T22,
47  b, b, FLA_BR );
48 
49  /*------------------------------------------------------------*/
50 
51  FLA_Merge_2x1( A11,
52  A21, &AB1 );
53 
54  // Perform a QR factorization via the UT transform on AB1:
55  //
56  // / A11 \ -> QB1 R11
57  // \ A21 /
58  //
59  // where:
60  // - QB1 is formed from UB1 (which is stored column-wise below the
61  // diagonal of AB1) and T11 (which is stored to the upper triangle
62  // of T11).
63  // - R11 is stored to the upper triangle of AB1.
64 
65  FLA_QR_UT_internal( AB1, T11,
66  FLA_Cntl_sub_qrut( cntl ) );
67 
68 
69  if ( FLA_Obj_width( A12 ) > 0 )
70  {
71  FLA_Merge_2x1( A12,
72  A22, &AB2 );
73 
74  // Apply the Householder transforms associated with UB1 and T11 to
75  // AB2:
76  //
77  // / A12 \ := QB1' / A12 \
78  // \ A22 / \ A22 /
79  //
80  // where QB1 is formed from UB1 and T11.
81 
82  FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
83  AB1, T11, W12, AB2,
84  FLA_Cntl_sub_apqut( cntl ) );
85  }
86 
87 
88  // Update T
89  //
90  // T01 = A10' * U11 + A20' * U21;
91  //
92  // Recall: U11 = trilu( A11 );
93  // U21 = A21;
94 
95  FLA_Copyt_external( FLA_CONJ_TRANSPOSE, A10, T01 );
96  FLA_Trmm_external( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
97  FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
98  FLA_ONE, A11, T01 );
99  FLA_Gemm_external( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
100  FLA_ONE, A20, A21, FLA_ONE, T01 );
101 
102  /*------------------------------------------------------------*/
103 
104  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
105  A10, A11, /**/ A12,
106  /* ************** */ /* ****************** */
107  &ABL, /**/ &ABR, A20, A21, /**/ A22,
108  FLA_TL );
109 
110  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, T01, /**/ T02,
111  T10, T11, /**/ W12,
112  /* ************** */ /* ****************** */
113  &TBL, /**/ &TBR, T20, T21, /**/ T22,
114  FLA_TL );
115  }
116 
117  return FLA_SUCCESS;
118 }
FLA_Error FLA_Trmm_external(FLA_Side side, FLA_Uplo uplo, FLA_Trans trans, FLA_Diag diag, FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition: FLA_Trmm_external.c:13
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_Copyt_external(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition: FLA_Copyt_external.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_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_Gemm_external(FLA_Trans transa, FLA_Trans transb, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C)
Definition: FLA_Gemm_external.c:13
FLA_Error FLA_QR_UT_internal(FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl)
Definition: FLA_QR_UT_internal.c:17
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