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FLA_Hess_UT_blk_var4.c File Reference

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Functions

FLA_Error FLA_Hess_UT_blk_var4 (FLA_Obj A, FLA_Obj T)
 

Function Documentation

◆ FLA_Hess_UT_blk_var4()

FLA_Error FLA_Hess_UT_blk_var4 ( FLA_Obj A,
FLA_Obj T )
14{
15 FLA_Obj ATL, ATR, A00, A01, A02,
16 ABL, ABR, A10, A11, A12,
17 A20, A21, A22;
18 FLA_Obj UT, U0,
19 UB, U1,
20 U2;
21 FLA_Obj YT, Y0,
22 YB, Y1,
23 Y2;
24 FLA_Obj ZT, Z0,
25 ZB, Z1,
26 Z2;
27 FLA_Obj TL, TR, T0, T1, T2;
28
29 FLA_Obj U, Y, Z;
30 FLA_Obj ABR_l;
31 FLA_Obj UB_l, U2_l;
32 FLA_Obj YB_l, Y2_l;
33 FLA_Obj ZB_l, Z2_l;
34 FLA_Obj WT_l;
35 FLA_Obj T1_tl;
36 FLA_Obj none, none2, none3;
37 FLA_Obj UB_tl,
38 UB_bl;
39 FLA_Datatype datatype_A;
40 dim_t m_A;
41 dim_t b_alg, b, bb;
42
43 b_alg = FLA_Obj_length( T );
44
45 datatype_A = FLA_Obj_datatype( A );
46 m_A = FLA_Obj_length( A );
47
48 FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &U );
49 FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Y );
50 FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Z );
51
52 FLA_Part_2x2( A, &ATL, &ATR,
53 &ABL, &ABR, 0, 0, FLA_TL );
54 FLA_Part_2x1( U, &UT,
55 &UB, 0, FLA_TOP );
56 FLA_Part_2x1( Y, &YT,
57 &YB, 0, FLA_TOP );
58 FLA_Part_2x1( Z, &ZT,
59 &ZB, 0, FLA_TOP );
60 FLA_Part_1x2( T, &TL, &TR, 0, FLA_LEFT );
61
62 while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
63 {
64 b = min( FLA_Obj_length( ABR ), b_alg );
65
66 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
67 /* ************* */ /* ******************** */
68 &A10, /**/ &A11, &A12,
69 ABL, /**/ ABR, &A20, /**/ &A21, &A22,
70 b, b, FLA_BR );
71 FLA_Repart_2x1_to_3x1( UT, &U0,
72 /* ** */ /* ** */
73 &U1,
74 UB, &U2, b, FLA_BOTTOM );
75 FLA_Repart_2x1_to_3x1( YT, &Y0,
76 /* ** */ /* ** */
77 &Y1,
78 YB, &Y2, b, FLA_BOTTOM );
79 FLA_Repart_2x1_to_3x1( ZT, &Z0,
80 /* ** */ /* ** */
81 &Z1,
82 ZB, &Z2, b, FLA_BOTTOM );
83 FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, /**/ &T1, &T2,
84 b, FLA_RIGHT );
85
86 /*------------------------------------------------------------*/
87
88 FLA_Part_2x2( T1, &T1_tl, &none,
89 &none2, &none3, b, b, FLA_TL );
90
91 bb = min( FLA_Obj_length( ABR ) - 1, b_alg );
92
93 FLA_Part_1x2( ABR, &ABR_l, &none, bb, FLA_LEFT );
94 FLA_Part_1x2( UB, &UB_l, &none, bb, FLA_LEFT );
95 FLA_Part_1x2( YB, &YB_l, &none, bb, FLA_LEFT );
96 FLA_Part_1x2( ZB, &ZB_l, &none, bb, FLA_LEFT );
97
98 FLA_Part_2x1( UB_l, &none,
99 &U2_l, b, FLA_TOP );
100 FLA_Part_2x1( YB_l, &none,
101 &Y2_l, b, FLA_TOP );
102 FLA_Part_2x1( ZB_l, &none,
103 &Z2_l, b, FLA_TOP );
104
105 // [ ABR, YB, ZB, T1 ] = FLA_Hess_UT_step_unb_var4( ABR, YB, ZB, T1, b );
106 //FLA_Hess_UT_step_unb_var4( ABR, YB, ZB, T1_tl );
107 //FLA_Hess_UT_step_ofu_var4( ABR, YB, ZB, T1_tl );
108 FLA_Hess_UT_step_opt_var4( ABR, YB, ZB, T1_tl );
109
110 // Build UB from ABR, with explicit unit subdiagonal and zeros.
111 FLA_Copy_external( ABR_l, UB_l );
112 FLA_Part_2x1( UB_l, &UB_tl,
113 &UB_bl, 1, FLA_TOP );
114 FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_UNIT_DIAG, UB_bl );
115 FLA_Set( FLA_ZERO, UB_tl );
116
117 // ATR = ATR - ATR * UB * inv( triu( T ) ) * UB' );
118 if ( FLA_Obj_length( ATR ) > 0 )
119 {
120 // NOTE: We use ZT as temporary workspace.
121 FLA_Part_1x2( ZT, &WT_l, &none, bb, FLA_LEFT );
122 FLA_Part_2x2( T1, &T1_tl, &none,
123 &none2, &none3, bb, bb, FLA_TL );
124
125 // WT_l = ATR * UB_l * inv( triu( T ) ).
126 FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
127 FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
128 FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
129 FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );
130
131 // ATR = ATR - WT_l * UB_l'
132 FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
133 FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
134 }
135
136 // A22 = A22 - U2 * Y2' - Z2 * U2';
137 FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
138 FLA_MINUS_ONE, U2_l, Y2_l, FLA_ONE, A22 );
139 FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
140 FLA_MINUS_ONE, Z2_l, U2_l, FLA_ONE, A22 );
141
142 /*------------------------------------------------------------*/
143
144 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
145 A10, A11, /**/ A12,
146 /* ************** */ /* ****************** */
147 &ABL, /**/ &ABR, A20, A21, /**/ A22,
148 FLA_TL );
149 FLA_Cont_with_3x1_to_2x1( &UT, U0,
150 U1,
151 /* ** */ /* ** */
152 &UB, U2, FLA_TOP );
153 FLA_Cont_with_3x1_to_2x1( &YT, Y0,
154 Y1,
155 /* ** */ /* ** */
156 &YB, Y2, FLA_TOP );
157 FLA_Cont_with_3x1_to_2x1( &ZT, Z0,
158 Z1,
159 /* ** */ /* ** */
160 &ZB, Z2, FLA_TOP );
161 FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, T1, /**/ T2,
162 FLA_LEFT );
163 }
164
165 FLA_Obj_free( &U );
166 FLA_Obj_free( &Y );
167 FLA_Obj_free( &Z );
168
169 return FLA_SUCCESS;
170}
FLA_Hess_UT_step_opt_var4
FLA_Error FLA_Hess_UT_step_opt_var4(FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T)
Definition FLA_Hess_UT_opt_var4.c:29
FLA_Copy_external
FLA_Error FLA_Copy_external(FLA_Obj A, FLA_Obj B)
Definition FLA_Copy_external.c:13
FLA_Gemm_external
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_Trsm_external
FLA_Error FLA_Trsm_external(FLA_Side side, FLA_Uplo uplo, FLA_Trans trans, FLA_Diag diag, FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition FLA_Trsm_external.c:13
FLA_MINUS_ONE
FLA_Obj FLA_MINUS_ONE
Definition FLA_Init.c:22
FLA_ZERO
FLA_Obj FLA_ZERO
Definition FLA_Init.c:20
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_create
FLA_Error FLA_Obj_create(FLA_Datatype datatype, dim_t m, dim_t n, dim_t rs, dim_t cs, FLA_Obj *obj)
Definition FLA_Obj.c:55
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_free
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition FLA_Obj.c:588
FLA_Obj_datatype
FLA_Datatype FLA_Obj_datatype(FLA_Obj obj)
Definition FLA_Query.c:13
FLA_Datatype
int FLA_Datatype
Definition FLA_type_defs.h:49
dim_t
unsigned long dim_t
Definition FLA_type_defs.h:71
FLA_Triangularize
FLA_Error FLA_Triangularize(FLA_Uplo uplo, FLA_Diag diag, FLA_Obj A)
Definition FLA_Triangularize.c:13
FLA_Set
FLA_Error FLA_Set(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Set.c:13
FLA_Obj_view
Definition FLA_type_defs.h:159

References FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var4(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), 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_Set(), FLA_Triangularize(), FLA_Trsm_external(), and FLA_ZERO.

Referenced by FLA_Hess_UT_internal().

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