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FLA_LQ_UT_blk_var2.c File Reference

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Functions

FLA_Error FLA_LQ_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)
 

Function Documentation

◆ FLA_LQ_UT_blk_var2()

FLA_Error FLA_LQ_UT_blk_var2 ( FLA_Obj  A,
FLA_Obj  T,
fla_lqut_t cntl 
)
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 AR1,
24  AR2;
25 
26  dim_t b;
27 
28  FLA_Part_2x2( A, &ATL, &ATR,
29  &ABL, &ABR, 0, 0, FLA_TL );
30 
31  FLA_Part_2x2( T, &TTL, &TTR,
32  &TBL, &TBR, 0, 0, FLA_TL );
33 
34  while ( FLA_Obj_min_dim( ABR ) > 0 ){
35 
36  b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
37 
38  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
39  /* ************* */ /* ******************** */
40  &A10, /**/ &A11, &A12,
41  ABL, /**/ ABR, &A20, /**/ &A21, &A22,
42  b, b, FLA_BR );
43 
44  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &T01, &T02,
45  /* ************* */ /* ******************** */
46  &T10, /**/ &T11, &W12,
47  TBL, /**/ TBR, &T20, /**/ &T21, &T22,
48  b, b, FLA_BR );
49 
50  /*------------------------------------------------------------*/
51 
52  FLA_Merge_1x2( A11, A12, &AR1 );
53 
54  // Perform an LQ factorization via the UT transform on AR1:
55  //
56  // ( A11 A12 ) -> L11 QR1
57  //
58  // where:
59  // - QR1 is formed from UR1 (which is stored row-wise above the
60  // diagonal of AR1) and T11 (which is stored to the upper triangle
61  // of T11).
62  // - L11 is stored to the lower triangle of AR1.
63 
64  FLA_LQ_UT_internal( AR1, T11,
65  FLA_Cntl_sub_lqut( cntl ) );
66 
67 
68  if ( FLA_Obj_length( A21 ) > 0 )
69  {
70  FLA_Merge_1x2( A21, A22, &AR2 );
71 
72  // Apply the Householder transforms associated with UR1 and T11 to
73  // AR2:
74  //
75  // ( A21 A22 ) := ( A21 A22 ) Q1
76  //
77  // where QR1 is formed from UR1 and T11.
78 
79  FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE,
80  AR1, T11, W12, AR2,
81  FLA_Cntl_sub_apqut( cntl ) );
82  }
83 
84 
85  // Update T
86  //
87  // T01 = conj(A01) * U11^T + conj(A02) * U12^T;
88  //
89  // Recall: U11 = triuu( A11 );
90  // U12 = A12;
91 
92  FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, A01, T01 );
93  FLA_Trmm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
94  FLA_TRANSPOSE, FLA_UNIT_DIAG,
95  FLA_ONE, A11, T01 );
96  FLA_Gemm_external( FLA_CONJ_NO_TRANSPOSE, FLA_TRANSPOSE,
97  FLA_ONE, A02, A12, FLA_ONE, T01 );
98 
99  /*------------------------------------------------------------*/
100 
101  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
102  A10, A11, /**/ A12,
103  /* ************** */ /* ****************** */
104  &ABL, /**/ &ABR, A20, A21, /**/ A22,
105  FLA_TL );
106 
107  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, T01, /**/ T02,
108  T10, T11, /**/ W12,
109  /* ************** */ /* ****************** */
110  &TBL, /**/ &TBR, T20, T21, /**/ T22,
111  FLA_TL );
112  }
113 
114  return FLA_SUCCESS;
115 }
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
FLA_Error FLA_LQ_UT_internal(FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)
Definition: FLA_LQ_UT_internal.c:17
FLA_Error FLA_Copyt_external(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition: FLA_Copyt_external.c:13
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_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
FLA_Obj FLA_ONE
Definition: FLA_Init.c:18
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
dim_t FLA_Obj_length(FLA_Obj obj)
Definition: FLA_Query.c:116
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_Merge_1x2(FLA_Obj AL, FLA_Obj AR, FLA_Obj *A)
Definition: FLA_View.c:562
dim_t FLA_Determine_blocksize(FLA_Obj A_unproc, FLA_Quadrant to_dir, fla_blocksize_t *cntl_blocksizes)
Definition: FLA_Blocksize.c:234
dim_t FLA_Obj_min_dim(FLA_Obj obj)
Definition: FLA_Query.c:153
unsigned long dim_t
Definition: FLA_type_defs.h:71
Definition: FLA_type_defs.h:159

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trmm_external().

Referenced by FLA_LQ_UT_internal().