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FLA_CAQR2_UT_blk_var1.c File Reference

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Functions

FLA_Error FLA_CAQR2_UT_blk_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T, fla_caqr2ut_t *cntl)
 

Function Documentation

◆ FLA_CAQR2_UT_blk_var1()

FLA_Error FLA_CAQR2_UT_blk_var1 ( FLA_Obj  U,
FLA_Obj  D,
FLA_Obj  T,
fla_caqr2ut_t cntl 
)

References FLA_Axpy_internal(), FLA_CAQR2_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_internal(), FLA_Gemm_internal(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), and FLA_Trsm_internal().

Referenced by FLA_CAQR2_UT_internal().

15 {
16  FLA_Obj UTL, UTR, U00, U01, U02,
17  UBL, UBR, U10, U11, U12,
18  U20, U21, U22;
19 
20  FLA_Obj DTL, DTR, D00, D01, D02,
21  DBL, DBR, D10, D11, D12,
22  D20, D21, D22;
23 
24  FLA_Obj TL, TR, T0, T1, W12;
25 
26  FLA_Obj D1;
27 
28  FLA_Obj W12T, W12B;
29 
30  FLA_Obj T1T, T2B;
31 
32  dim_t b_alg, b;
33  dim_t m_DT;
34 
35  // Query the algorithmic blocksize by inspecting the length of T.
36  b_alg = FLA_Obj_length( T );
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_1x2( T, &TL, &TR, 0, FLA_LEFT );
49 
50  while ( FLA_Obj_min_dim( UBR ) > 0 ){
51 
52  b = min( b_alg, FLA_Obj_min_dim( UBR ) );
53 
54  FLA_Repart_2x2_to_3x3( UTL, /**/ UTR, &U00, /**/ &U01, &U02,
55  /* ************* */ /* ******************** */
56  &U10, /**/ &U11, &U12,
57  UBL, /**/ UBR, &U20, /**/ &U21, &U22,
58  b, b, FLA_BR );
59 
60  FLA_Repart_2x2_to_3x3( DTL, /**/ DTR, &D00, /**/ &D01, &D02,
61  /* ************* */ /* ******************** */
62  &D10, /**/ &D11, &D12,
63  DBL, /**/ DBR, &D20, /**/ &D21, &D22,
64  b, b, FLA_BR );
65 
66  FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, /**/ &T1, &W12,
67  b, FLA_RIGHT );
68 
69  /*------------------------------------------------------------*/
70 
71  // T1T = FLA_Top_part( T1, b );
72 
73  FLA_Part_2x1( T1, &T1T,
74  &T2B, b, FLA_TOP );
75 
76  FLA_Merge_2x1( D01,
77  D11, &D1 );
78 
79  // [ U11, ...
80  // D1, T1 ] = FLA_CAQR2_UT( U11
81  // D1, T1T );
82 
84  D1, T1T,
85  FLA_Cntl_sub_caqr2ut( cntl ) );
86 
87 
88  if ( FLA_Obj_width( U12 ) > 0 )
89  {
90  // W12T = FLA_Top_part( W12, b );
91 
92  FLA_Part_2x1( W12, &W12T,
93  &W12B, b, FLA_TOP );
94 
95  // W12T = inv( triu( T1T ) )' * ( U12 + D1' * D2 );
96  // = inv( triu( T1T ) )' * ( U12 + D01' * D02 + D11' * D12 );
97 
98  FLA_Copy_internal( D12, W12T,
99  FLA_Cntl_sub_copy( cntl ) );
100 
101  FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
102  FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
103  FLA_ONE, D11, W12T,
104  FLA_Cntl_sub_trmm1( cntl ) );
105 
106  FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
107  FLA_ONE, D01, D02, FLA_ONE, W12T,
108  FLA_Cntl_sub_gemm1( cntl ) );
109 
110  FLA_Axpy_internal( FLA_ONE, U12, W12T,
111  FLA_Cntl_sub_axpy1( cntl ) );
112 
113  FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
114  FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
115  FLA_ONE, T1T, W12T,
116  FLA_Cntl_sub_trsm( cntl ) );
117 
118  // U12 = U12 - W12T;
119  // D2 = D2 - D1 * W12T;
120  // => D02 = D02 - D01 * W12T;
121  // D12 = D12 - D11 * W12T;
122 
123  FLA_Axpy_internal( FLA_MINUS_ONE, W12T, U12,
124  FLA_Cntl_sub_axpy2( cntl ) );
125 
126  FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
127  FLA_MINUS_ONE, D01, W12T, FLA_ONE, D02,
128  FLA_Cntl_sub_gemm2( cntl ) );
129 
130  FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
131  FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
132  FLA_ONE, D11, W12T,
133  FLA_Cntl_sub_trmm2( cntl ) );
134 
135  FLA_Axpy_internal( FLA_MINUS_ONE, W12T, D12,
136  FLA_Cntl_sub_axpy3( cntl ) );
137  }
138 
139  /*------------------------------------------------------------*/
140 
141  FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR, U00, U01, /**/ U02,
142  U10, U11, /**/ U12,
143  /* ************** */ /* ****************** */
144  &UBL, /**/ &UBR, U20, U21, /**/ U22,
145  FLA_TL );
146 
147  FLA_Cont_with_3x3_to_2x2( &DTL, /**/ &DTR, D00, D01, /**/ D02,
148  D10, D11, /**/ D12,
149  /* ************** */ /* ****************** */
150  &DBL, /**/ &DBR, D20, D21, /**/ D22,
151  FLA_TL );
152 
153  FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, T1, /**/ W12,
154  FLA_LEFT );
155 
156  }
157 
158  return FLA_SUCCESS;
159 }
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
FLA_Error FLA_Gemm_internal(FLA_Trans transa, FLA_Trans transb, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_gemm_t *cntl)
Definition: FLA_Gemm_internal.c:16
FLA_Error FLA_Copy_internal(FLA_Obj A, FLA_Obj B, fla_copy_t *cntl)
Definition: FLA_Copy_internal.c:16
unsigned long dim_t
Definition: FLA_type_defs.h:71
FLA_Error FLA_CAQR2_UT_internal(FLA_Obj U, FLA_Obj D, FLA_Obj T, fla_caqr2ut_t *cntl)
Definition: FLA_CAQR2_UT_internal.c:16
FLA_Obj FLA_MINUS_ONE
Definition: FLA_Init.c:22
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_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_Trmm_internal(FLA_Side side, FLA_Uplo uplo, FLA_Trans transa, FLA_Diag diag, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_trmm_t *cntl)
Definition: FLA_Trmm_internal.c:16
Definition: FLA_type_defs.h:158
dim_t FLA_Obj_width(FLA_Obj obj)
Definition: FLA_Query.c:123
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_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
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_Axpy_internal(FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_axpy_t *cntl)
Definition: FLA_Axpy_internal.c:16
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
FLA_Error FLA_Trsm_internal(FLA_Side side, FLA_Uplo uplo, FLA_Trans transa, FLA_Diag diag, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_trsm_t *cntl)
Definition: FLA_Trsm_internal.c:16