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FLA_Apply_Q_UT_lnfc.h File Reference

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Functions

FLA_Error FLA_Apply_Q_UT_lnfc_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
 
FLA_Error FLA_Apply_Q_UT_lnfc_blk_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
 
FLA_Error FLA_Apply_Q_UT_lnfc_blk_var3 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl)
 

Function Documentation

◆ FLA_Apply_Q_UT_lnfc_blk_var1()

FLA_Error FLA_Apply_Q_UT_lnfc_blk_var1 ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  W,
FLA_Obj  B,
fla_apqut_t *  cntl 
)
87{
88 FLA_Obj ATL, ATR, A00, A01, A02,
89 ABL, ABR, A10, A11, A12,
90 A20, A21, A22;
91
92 FLA_Obj TL, TR, T0, T1, T2;
93
94 FLA_Obj T1T,
95 T2B;
96
97 FLA_Obj WTL, WTR,
98 WBL, WBR;
99
100 FLA_Obj BT, B0,
101 BB, B1,
102 B2;
103
104 dim_t b_alg, b;
105 dim_t m_BR, n_BR;
106
107 // Query the algorithmic blocksize by inspecting the length of T.
108 b_alg = FLA_Obj_length( T );
109
110 // If m > n, then we have to initialize our partitionings carefully so
111 // that we begin in the proper location in A and B (since we traverse
112 // matrix A from BR to TL).
113 if ( FLA_Obj_length( A ) > FLA_Obj_width( A ) )
114 {
115 m_BR = FLA_Obj_length( A ) - FLA_Obj_width( A );
116 n_BR = 0;
117 }
118 else if ( FLA_Obj_length( A ) < FLA_Obj_width( A ) )
119 {
120 m_BR = 0;
121 n_BR = FLA_Obj_width( A ) - FLA_Obj_length( A );
122 }
123 else
124 {
125 m_BR = 0;
126 n_BR = 0;
127 }
128
129 FLA_Part_2x2( A, &ATL, &ATR,
130 &ABL, &ABR, m_BR, n_BR, FLA_BR );
131
132 // A and T are dependent; we determine T matrix w.r.t. A
133 FLA_Part_1x2( T, &TL, &TR, FLA_Obj_min_dim( A ), FLA_LEFT );
134
135 FLA_Part_2x1( B, &BT,
136 &BB, m_BR, FLA_BOTTOM );
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_2x1_to_3x1( BT, &B0,
158 &B1,
159 /* ** */ /* ** */
160 BB, &B2, b, FLA_TOP );
161
162 /*------------------------------------------------------------*/
163
164 FLA_Part_2x1( T1, &T1T,
165 &T2B, b, FLA_TOP );
166
167 FLA_Part_2x2( W, &WTL, &WTR,
168 &WBL, &WBR, b, FLA_Obj_width( B1 ), FLA_TL );
169
170 // WTL = B1;
171
172 FLA_Copyt_internal( FLA_NO_TRANSPOSE, B1, WTL,
173 FLA_Cntl_sub_copyt( cntl ) );
174
175 // U11 = trilu( A11 );
176 // U21 = A21;
177 //
178 // WTL = inv( triu(T1T) ) * ( U11' * B1 + U21' * B2 );
179
180 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
181 FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG,
182 FLA_ONE, A11, WTL,
183 FLA_Cntl_sub_trmm1( cntl ) );
184
185 FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_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_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
191 FLA_ONE, T1T, WTL,
192 FLA_Cntl_sub_trsm( cntl ) );
193
194 // B2 = B2 - U21 * WTL;
195 // B1 = B1 - U11 * WTL;
196
197 FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
198 FLA_MINUS_ONE, A21, WTL, FLA_ONE, B2,
199 FLA_Cntl_sub_gemm2( cntl ) );
200
201 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
202 FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
203 FLA_MINUS_ONE, A11, WTL,
204 FLA_Cntl_sub_trmm2( cntl ) );
205
206 FLA_Axpyt_internal( FLA_NO_TRANSPOSE, FLA_ONE, WTL, B1,
207 FLA_Cntl_sub_axpyt( cntl ) );
208
209 /*------------------------------------------------------------*/
210
211 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02,
212 /* ************** */ /* ****************** */
213 A10, /**/ A11, A12,
214 &ABL, /**/ &ABR, A20, /**/ A21, A22,
215 FLA_BR );
216
217 FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, /**/ T1, T2,
218 FLA_RIGHT );
219
220 FLA_Cont_with_3x1_to_2x1( &BT, B0,
221 /* ** */ /* ** */
222 B1,
223 &BB, B2, FLA_BOTTOM );
224 }
225
226 return FLA_SUCCESS;
227}
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_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_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_3x1_to_2x1(), 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_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), FLA_Trsm_internal(), and i.

Referenced by FLA_Apply_Q_UT_lnfc().

◆ FLA_Apply_Q_UT_lnfc_blk_var2()

FLA_Error FLA_Apply_Q_UT_lnfc_blk_var2 ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  W,
FLA_Obj  B,
fla_apqut_t *  cntl 
)
14{
15 FLA_Obj BL, BR, B0, B1, B2;
16
17 FLA_Obj WL, WR, W0, W1, W2;
18
19 dim_t b;
20
21 FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT );
22
23 FLA_Part_1x2( W, &WL, &WR, 0, FLA_LEFT );
24
25 while ( FLA_Obj_width( BL ) < FLA_Obj_width( B ) ){
26
27 b = FLA_Determine_blocksize( BR, FLA_RIGHT, FLA_Cntl_blocksize( cntl ) );
28
29 FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2,
30 b, FLA_RIGHT );
31
32 FLA_Repart_1x2_to_1x3( WL, /**/ WR, &W0, /**/ &W1, &W2,
33 b, FLA_RIGHT );
34
35 /*------------------------------------------------------------*/
36
37 // B1 = Q * B1;
38 FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
39 A, T, W1, B1,
40 FLA_Cntl_sub_apqut( cntl ) );
41
42 /*------------------------------------------------------------*/
43
44 FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2,
45 FLA_LEFT );
46
47 FLA_Cont_with_1x3_to_1x2( &WL, /**/ &WR, W0, W1, /**/ W2,
48 FLA_LEFT );
49 }
50
51 return FLA_SUCCESS;
52}
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_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_Determine_blocksize(), FLA_Obj_width(), FLA_Part_1x2(), FLA_Repart_1x2_to_1x3(), and i.

Referenced by FLA_Apply_Q_UT_lnfc().

◆ FLA_Apply_Q_UT_lnfc_blk_var3()

FLA_Error FLA_Apply_Q_UT_lnfc_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 BT, B0,
27 BB, B1,
28 B2;
29
30 dim_t b, m_BR, n_BR;
31
32 // If m < n, then we have to initialize our partitionings carefully so
33 // that we begin in the proper location in A and B (since we traverse
34 // matrix A from BR to TL).
35 if ( FLA_Obj_length( A ) < FLA_Obj_width( A ) )
36 {
37 m_BR = 0;
38 n_BR = FLA_Obj_width( A ) - FLA_Obj_length( A );
39 }
40 else
41 {
42 m_BR = 0;
43 n_BR = 0;
44 }
45
46 FLA_Part_2x2( A, &ATL, &ATR,
47 &ABL, &ABR, m_BR, n_BR, FLA_BR );
48
49 FLA_Part_2x2( TW, &TWTL, &TWTR,
50 &TWBL, &TWBR, 0, 0, FLA_BR );
51
52 FLA_Part_2x1( B, &BT,
53 &BB, n_BR, FLA_BOTTOM );
54
55 while ( FLA_Obj_min_dim( ATL ) > 0 ){
56
57 b = FLA_Determine_blocksize( ATL, FLA_TL, FLA_Cntl_blocksize( cntl ) );
58
59 // Since T was filled from TL to BR, and since we need to access them in
60 // reverse order, we need to handle the case where the bottom-right-most
61 // block is smaller than the other b x b blocks.
62 if ( FLA_Obj_width( TWBR ) == 0 &&
63 FLA_Obj_width( TW ) % b > 0 )
64 b = FLA_Obj_width( TW ) % b;
65
66 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02,
67 &A10, &A11, /**/ &A12,
68 /* ************* */ /* ******************** */
69 ABL, /**/ ABR, &A20, &A21, /**/ &A22,
70 b, b, FLA_TL );
71
72 FLA_Repart_2x2_to_3x3( TWTL, /**/ TWTR, &TW00, &TW01, /**/ &TW02,
73 &TW10, &T11, /**/ &W12,
74 /* *************** */ /* *********************** */
75 TWBL, /**/ TWBR, &TW20, &TW21, /**/ &TW22,
76 b, b, FLA_TL );
77
78 FLA_Repart_2x1_to_3x1( BT, &B0,
79 &B1,
80 /* ** */ /* ** */
81 BB, &B2, b, FLA_TOP );
82
83 /*------------------------------------------------------------*/
84
85 FLA_Part_2x2( W, &WTL, &WTR,
86 &WBL, &WBR, b, FLA_Obj_width( B1 ), FLA_TL );
87
88 // WTL = B1;
89
90 FLA_Copyt_internal( FLA_NO_TRANSPOSE, B1, WTL,
91 FLA_Cntl_sub_copyt( cntl ) );
92
93 // U11 = trilu( A11 );
94 // U21 = A21;
95 //
96 // WTL = inv( triu(T11) ) * ( U11' * B1 + U21' * B2 );
97
98 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
99 FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG,
100 FLA_ONE, A11, WTL,
101 FLA_Cntl_sub_trmm1( cntl ) );
102
103 FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
104 FLA_ONE, A21, B2, FLA_ONE, WTL,
105 FLA_Cntl_sub_gemm1( cntl ) );
106
107 FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
108 FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
109 FLA_ONE, T11, WTL,
110 FLA_Cntl_sub_trsm( cntl ) );
111
112 // B2 = B2 - U21 * WTL;
113 // B1 = B1 - U11 * WTL;
114
115 FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
116 FLA_MINUS_ONE, A21, WTL, FLA_ONE, B2,
117 FLA_Cntl_sub_gemm2( cntl ) );
118
119 FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
120 FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
121 FLA_MINUS_ONE, A11, WTL,
122 FLA_Cntl_sub_trmm2( cntl ) );
123
124 FLA_Axpyt_internal( FLA_NO_TRANSPOSE, FLA_ONE, WTL, B1,
125 FLA_Cntl_sub_axpyt( cntl ) );
126
127 /*------------------------------------------------------------*/
128
129 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02,
130 /* ************** */ /* ****************** */
131 A10, /**/ A11, A12,
132 &ABL, /**/ &ABR, A20, /**/ A21, A22,
133 FLA_BR );
134
135 FLA_Cont_with_3x3_to_2x2( &TWTL, /**/ &TWTR, TW00, /**/ TW01, TW02,
136 /* **************** */ /* ********************* */
137 TW10, /**/ T11, W12,
138 &TWBL, /**/ &TWBR, TW20, /**/ TW21, TW22,
139 FLA_BR );
140
141 FLA_Cont_with_3x1_to_2x1( &BT, B0,
142 /* ** */ /* ** */
143 B1,
144 &BB, B2, FLA_BOTTOM );
145 }
146
147 return FLA_SUCCESS;
148}

References FLA_Axpyt_internal(), FLA_Cont_with_3x1_to_2x1(), 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_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), FLA_Trsm_internal(), and i.

Referenced by FLA_Apply_Q_UT_lnfc().

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