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FLA_Apply_Q_UT_rnbc.h File Reference

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Functions

FLA_Error FLA_Apply_Q_UT_rnbc_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
 
FLA_Error FLA_Apply_Q_UT_rnbc_blk_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
 
FLA_Error FLA_Apply_Q_UT_rnbc_blk_var3 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
 

Function Documentation

◆ FLA_Apply_Q_UT_rnbc_blk_var1()

FLA_Error FLA_Apply_Q_UT_rnbc_blk_var1 ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  W,
FLA_Obj  B,
fla_apqut_t *  cntl 
)
90{
91 FLA_Obj ATL, ATR, A00, A01, A02,
92 ABL, ABR, A10, A11, A12,
93 A20, A21, A22;
94
95 FLA_Obj TL, TR, T0, T1, T2;
96
97 FLA_Obj T1T,
98 T2B;
99
100 FLA_Obj WTL, WTR,
101 WBL, WBR;
102
103 FLA_Obj BL, BR, B0, B1, B2;
104
105 dim_t b_alg, b;
106 dim_t m_BR, n_BR;
107
108 // Query the algorithmic blocksize by inspecting the length of T.
109 b_alg = FLA_Obj_length( T );
110
111 // If m > n, then we have to initialize our partitionings carefully so
112 // that we begin in the proper location in A and B (since we traverse
113 // matrix A from BR to TL).
114 if ( FLA_Obj_length( A ) > FLA_Obj_width( A ) )
115 {
116 m_BR = FLA_Obj_length( A ) - FLA_Obj_width( A );
117 n_BR = 0;
118 }
119 else if ( FLA_Obj_length( A ) < FLA_Obj_width( A ) )
120 {
121 m_BR = 0;
122 n_BR = FLA_Obj_width( A ) - FLA_Obj_length( A );
123 }
124 else
125 {
126 m_BR = 0;
127 n_BR = 0;
128 }
129
130 FLA_Part_2x2( A, &ATL, &ATR,
131 &ABL, &ABR, m_BR, n_BR, FLA_BR );
132
133 // A and T are dependent; we determine T matrix w.r.t. A
134 FLA_Part_1x2( T, &TL, &TR, FLA_Obj_min_dim( A ), FLA_LEFT );
135
136 FLA_Part_1x2( B, &BL, &BR, m_BR, FLA_RIGHT );
137
138 while ( FLA_Obj_min_dim( ATL ) > 0 ){
139
140 b = min( b_alg, FLA_Obj_min_dim( ATL ) );
141
142 // Since T was filled from left to right, and since we need to access them
143 // in reverse order, we need to handle the case where the last block is
144 // smaller than the other b x b blocks.
145 if ( FLA_Obj_width( TR ) == 0 && FLA_Obj_width( T ) % b_alg > 0 )
146 b = FLA_Obj_width( T ) % b_alg;
147
148 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02,
149 &A10, &A11, /**/ &A12,
150 /* ************* */ /* ******************** */
151 ABL, /**/ ABR, &A20, &A21, /**/ &A22,
152 b, b, FLA_TL );
153
154 FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, &T1, /**/ &T2,
155 b, FLA_LEFT );
156
157 FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &B1, /**/ &B2,
158 b, FLA_LEFT );
159
160 /*------------------------------------------------------------*/
161
162 FLA_Part_2x1( T1, &T1T,
163 &T2B, b, FLA_TOP );
164
165 FLA_Part_2x2( W, &WTL, &WTR,
166 &WBL, &WBR, b, FLA_Obj_length( B1 ), FLA_TL );
167
168 // WTL = B1^T;
169
170 FLA_Copyt_internal( FLA_TRANSPOSE, B1, WTL,
171 FLA_Cntl_sub_copyt( cntl ) );
172
173 // U11 = trilu( A11 );
174 // U21 = A21;
175 // Let WTL^T be conformal to B1.
176 //
177 // WTL^T = ( B1 * U11 + B2 * U21 ) * inv( triu(T1T)' );
178 // WTL = inv( conj(triu(T1T)) ) * ( U11^T * B1^T + U21^T * B2^T );
179
180 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
181 FLA_TRANSPOSE, FLA_UNIT_DIAG,
182 FLA_ONE, A11, WTL,
183 FLA_Cntl_sub_trmm1( cntl ) );
184
185 FLA_Gemm_internal( FLA_TRANSPOSE, FLA_TRANSPOSE,
186 FLA_ONE, A21, B2, FLA_ONE, WTL,
187 FLA_Cntl_sub_gemm1( cntl ) );
188
189 FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
190 FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
191 FLA_ONE, T1T, WTL,
192 FLA_Cntl_sub_trsm( cntl ) );
193
194 // B2 = B2 - WTL^T * U21';
195 // B1 = B1 - WTL^T * U11';
196 // = B1 - ( conj(U11) * WTL )^T;
197
198 FLA_Gemm_internal( FLA_TRANSPOSE, FLA_CONJ_TRANSPOSE,
199 FLA_MINUS_ONE, WTL, A21, FLA_ONE, B2,
200 FLA_Cntl_sub_gemm2( cntl ) );
201
202 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
203 FLA_CONJ_NO_TRANSPOSE, FLA_UNIT_DIAG,
204 FLA_MINUS_ONE, A11, WTL,
205 FLA_Cntl_sub_trmm2( cntl ) );
206
207 FLA_Axpyt_internal( FLA_TRANSPOSE, FLA_ONE, WTL, B1,
208 FLA_Cntl_sub_axpyt( cntl ) );
209
210 /*------------------------------------------------------------*/
211
212 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02,
213 /* ************** */ /* ****************** */
214 A10, /**/ A11, A12,
215 &ABL, /**/ &ABR, A20, /**/ A21, A22,
216 FLA_BR );
217
218 FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, /**/ T1, T2,
219 FLA_RIGHT );
220
221 FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ B1, B2,
222 FLA_RIGHT );
223 }
224
225 return FLA_SUCCESS;
226}
FLA_Axpyt_internal
FLA_Error FLA_Axpyt_internal(FLA_Trans trans, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_axpyt_t *cntl)
Definition FLA_Axpyt_internal.c:16
FLA_Copyt_internal
FLA_Error FLA_Copyt_internal(FLA_Trans trans, FLA_Obj A, FLA_Obj B, fla_copyt_t *cntl)
Definition FLA_Copyt_internal.c:16
FLA_Gemm_internal
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_Trmm_internal
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
FLA_Trsm_internal
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
FLA_MINUS_ONE
FLA_Obj FLA_MINUS_ONE
Definition FLA_Init.c:22
FLA_ONE
FLA_Obj FLA_ONE
Definition FLA_Init.c:18
FLA_Cont_with_3x3_to_2x2
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_Part_2x2
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_Cont_with_1x3_to_1x2
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_Obj_width
dim_t FLA_Obj_width(FLA_Obj obj)
Definition FLA_Query.c:123
FLA_Part_1x2
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_Part_2x1
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_Obj_length
dim_t FLA_Obj_length(FLA_Obj obj)
Definition FLA_Query.c:116
FLA_Repart_2x2_to_3x3
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_Repart_1x2_to_1x3
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_Obj_min_dim
dim_t FLA_Obj_min_dim(FLA_Obj obj)
Definition FLA_Query.c:153
dim_t
unsigned long dim_t
Definition FLA_type_defs.h:71
i
int i
Definition bl1_axmyv2.c:145
FLA_Obj_view
Definition FLA_type_defs.h:159

References FLA_Axpyt_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_internal(), FLA_Gemm_internal(), 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(), FLA_Trsm_internal(), and i.

Referenced by FLA_Apply_Q_UT_rnbc().

◆ FLA_Apply_Q_UT_rnbc_blk_var2()

FLA_Error FLA_Apply_Q_UT_rnbc_blk_var2 ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  W,
FLA_Obj  B,
fla_apqut_t *  cntl 
)
14{
15 FLA_Obj BT, B0,
16 BB, B1,
17 B2;
18
19 FLA_Obj WL, WR, W0, W1, W2;
20
21 dim_t b;
22
23 FLA_Part_2x1( B, &BT,
24 &BB, 0, FLA_TOP );
25
26 FLA_Part_1x2( W, &WL, &WR, 0, FLA_LEFT );
27
28 while ( FLA_Obj_length( BT ) < FLA_Obj_length( B ) ){
29
30 b = FLA_Determine_blocksize( BT, FLA_TOP, FLA_Cntl_blocksize( cntl ) );
31
32 FLA_Repart_2x1_to_3x1( BT, &B0,
33 /* ** */ /* ** */
34 &B1,
35 BB, &B2, b, FLA_BOTTOM );
36
37 FLA_Repart_1x2_to_1x3( WL, /**/ WR, &W0, /**/ &W1, &W2,
38 b, FLA_RIGHT );
39
40 /*------------------------------------------------------------*/
41
42 // B1 = B1 * Q;
43 FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_BACKWARD, FLA_COLUMNWISE,
44 A, T, W1, B1,
45 FLA_Cntl_sub_apqut( cntl ) );
46
47 /*------------------------------------------------------------*/
48
49 FLA_Cont_with_3x1_to_2x1( &BT, B0,
50 B1,
51 /* ** */ /* ** */
52 &BB, B2, FLA_TOP );
53
54 FLA_Cont_with_1x3_to_1x2( &WL, /**/ &WR, W0, W1, /**/ W2,
55 FLA_LEFT );
56 }
57
58 return FLA_SUCCESS;
59}
FLA_Apply_Q_UT_internal
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_Cont_with_3x1_to_2x1
FLA_Error FLA_Cont_with_3x1_to_2x1(FLA_Obj *AT, FLA_Obj A0, FLA_Obj A1, FLA_Obj *AB, FLA_Obj A2, FLA_Side side)
Definition FLA_View.c:428
FLA_Repart_2x1_to_3x1
FLA_Error FLA_Repart_2x1_to_3x1(FLA_Obj AT, FLA_Obj *A0, FLA_Obj *A1, FLA_Obj AB, FLA_Obj *A2, dim_t mb, FLA_Side side)
Definition FLA_View.c:226
FLA_Determine_blocksize
dim_t FLA_Determine_blocksize(FLA_Obj A_unproc, FLA_Quadrant to_dir, fla_blocksize_t *cntl_blocksizes)
Definition FLA_Blocksize.c:234

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Determine_blocksize(), FLA_Obj_length(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), and i.

Referenced by FLA_Apply_Q_UT_rnbc().

◆ FLA_Apply_Q_UT_rnbc_blk_var3()

FLA_Error FLA_Apply_Q_UT_rnbc_blk_var3 ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  W,
FLA_Obj  B,
fla_apqut_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 TWTL, TWTR, TW00, TW01, TW02,
20 TWBL, TWBR, TW10, T11, W12,
21 TW20, TW21, TW22;
22
23 FLA_Obj WTL, WTR,
24 WBL, WBR;
25
26 FLA_Obj BL, BR, B0, B1, B2;
27
28 dim_t b, m_BR, n_BR;
29
30 // If m > n, then we have to initialize our partitionings carefully so
31 // that we begin in the proper location in A and B (since we traverse
32 // matrix A from BR to TL).
33 if ( FLA_Obj_length( A ) > FLA_Obj_width( A ) )
34 {
35 m_BR = FLA_Obj_length( A ) - FLA_Obj_width( A );
36 n_BR = 0;
37 }
38 else
39 {
40 m_BR = 0;
41 n_BR = 0;
42 }
43
44 FLA_Part_2x2( A, &ATL, &ATR,
45 &ABL, &ABR, m_BR, n_BR, FLA_BR );
46
47 FLA_Part_2x2( TW, &TWTL, &TWTR,
48 &TWBL, &TWBR, 0, 0, FLA_BR );
49
50 FLA_Part_1x2( B, &BL, &BR, m_BR, FLA_RIGHT );
51
52 while ( FLA_Obj_min_dim( ATL ) > 0 ){
53
54 b = FLA_Determine_blocksize( ATL, FLA_TL, FLA_Cntl_blocksize( cntl ) );
55
56 // Since T was filled from TL to BR, and since we need to access them in
57 // reverse order, we need to handle the case where the bottom-right-most
58 // block is smaller than the other b x b blocks.
59 if ( FLA_Obj_width( TWBR ) == 0 &&
60 FLA_Obj_width( TW ) % b > 0 )
61 b = FLA_Obj_width( TW ) % b;
62
63 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02,
64 &A10, &A11, /**/ &A12,
65 /* ************* */ /* ******************** */
66 ABL, /**/ ABR, &A20, &A21, /**/ &A22,
67 b, b, FLA_TL );
68
69 FLA_Repart_2x2_to_3x3( TWTL, /**/ TWTR, &TW00, &TW01, /**/ &TW02,
70 &TW10, &T11, /**/ &W12,
71 /* *************** */ /* *********************** */
72 TWBL, /**/ TWBR, &TW20, &TW21, /**/ &TW22,
73 b, b, FLA_TL );
74
75 FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &B1, /**/ &B2,
76 b, FLA_LEFT );
77
78 /*------------------------------------------------------------*/
79
80 FLA_Part_2x2( W, &WTL, &WTR,
81 &WBL, &WBR, b, FLA_Obj_length( B1 ), FLA_TL );
82
83 // WTL = B1^T;
84
85 FLA_Copyt_internal( FLA_TRANSPOSE, B1, WTL,
86 FLA_Cntl_sub_copyt( cntl ) );
87
88 // U11 = trilu( A11 );
89 // U21 = A21;
90 // Let WTL^T be conformal to B1.
91 //
92 // WTL^T = ( B1 * U11 + B2 * U21 ) * inv( triu(T11)' );
93 // WTL = inv( conj(triu(T11)) ) * ( U11^T * B1^T + U21^T * B2^T );
94
95 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
96 FLA_TRANSPOSE, FLA_UNIT_DIAG,
97 FLA_ONE, A11, WTL,
98 FLA_Cntl_sub_trmm1( cntl ) );
99
100 FLA_Gemm_internal( FLA_TRANSPOSE, FLA_TRANSPOSE,
101 FLA_ONE, A21, B2, FLA_ONE, WTL,
102 FLA_Cntl_sub_gemm1( cntl ) );
103
104 FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
105 FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
106 FLA_ONE, T11, WTL,
107 FLA_Cntl_sub_trsm( cntl ) );
108
109 // B2 = B2 - WTL^T * U21';
110 // B1 = B1 - WTL^T * U11';
111 // = B1 - ( conj(U11) * WTL )^T;
112
113 FLA_Gemm_internal( FLA_TRANSPOSE, FLA_CONJ_TRANSPOSE,
114 FLA_MINUS_ONE, WTL, A21, FLA_ONE, B2,
115 FLA_Cntl_sub_gemm2( cntl ) );
116
117 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
118 FLA_CONJ_NO_TRANSPOSE, FLA_UNIT_DIAG,
119 FLA_MINUS_ONE, A11, WTL,
120 FLA_Cntl_sub_trmm2( cntl ) );
121
122 FLA_Axpyt_internal( FLA_TRANSPOSE, FLA_ONE, WTL, B1,
123 FLA_Cntl_sub_axpyt( cntl ) );
124
125 /*------------------------------------------------------------*/
126
127 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02,
128 /* ************** */ /* ****************** */
129 A10, /**/ A11, A12,
130 &ABL, /**/ &ABR, A20, /**/ A21, A22,
131 FLA_BR );
132
133 FLA_Cont_with_3x3_to_2x2( &TWTL, /**/ &TWTR, TW00, /**/ TW01, TW02,
134 /* **************** */ /* ********************* */
135 TW10, /**/ T11, W12,
136 &TWBL, /**/ &TWBR, TW20, /**/ TW21, TW22,
137 FLA_BR );
138
139 FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ B1, B2,
140 FLA_RIGHT );
141 }
142
143 return FLA_SUCCESS;
144}

References FLA_Axpyt_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_internal(), FLA_Determine_blocksize(), FLA_Gemm_internal(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), FLA_Trsm_internal(), and i.

Referenced by FLA_Apply_Q_UT_rnbc().

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