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FLA_Hess_UT_unb_var2.c File Reference

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Functions

FLA_Error FLA_Hess_UT_unb_var2 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Hess_UT_step_unb_var2 (FLA_Obj A, FLA_Obj T)
 

Function Documentation

◆ FLA_Hess_UT_step_unb_var2()

FLA_Error FLA_Hess_UT_step_unb_var2 ( FLA_Obj A,
FLA_Obj T )
19{
20 FLA_Obj ATL, ATR, A00, a01, A02,
21 ABL, ABR, a10t, alpha11, a12t,
22 A20, a21, A22;
23 FLA_Obj TTL, TTR, T00, t01, T02,
24 TBL, TBR, t10t, tau11, t12t,
25 T20, t21, T22;
26 FLA_Obj yT, y0,
27 yB, psi1,
28 y2;
29 FLA_Obj zT, z0,
30 zB, zeta1,
31 z2;
32 FLA_Obj y, z;
33
34 FLA_Obj inv_tau11;
35 FLA_Obj minus_inv_tau11;
36 FLA_Obj first_elem;
37 FLA_Obj beta;
38 FLA_Obj conj_beta;
39 FLA_Obj dot_product;
40
41 FLA_Obj a21_t,
42 a21_b;
43
44 FLA_Datatype datatype_A;
45 dim_t m_A;
46 dim_t b_alg;
47
48
49 b_alg = FLA_Obj_length( T );
50
51 datatype_A = FLA_Obj_datatype( A );
52 m_A = FLA_Obj_length( A );
53
54 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
55 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
56 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
57 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
58 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &conj_beta );
59 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &dot_product );
60 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
61 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
62
63 FLA_Part_2x2( A, &ATL, &ATR,
64 &ABL, &ABR, 0, 0, FLA_TL );
65 FLA_Part_2x2( T, &TTL, &TTR,
66 &TBL, &TBR, 0, 0, FLA_TL );
67 FLA_Part_2x1( y, &yT,
68 &yB, 0, FLA_TOP );
69 FLA_Part_2x1( z, &zT,
70 &zB, 0, FLA_TOP );
71
72 while ( FLA_Obj_length( ATL ) < b_alg )
73 {
74 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
75 /* ************* */ /* ************************** */
76 &a10t, /**/ &alpha11, &a12t,
77 ABL, /**/ ABR, &A20, /**/ &a21, &A22,
78 1, 1, FLA_BR );
79 FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
80 /* ************* */ /* ************************** */
81 &t10t, /**/ &tau11, &t12t,
82 TBL, /**/ TBR, &T20, /**/ &t21, &T22,
83 1, 1, FLA_BR );
84 FLA_Repart_2x1_to_3x1( yT, &y0,
85 /* ** */ /* **** */
86 &psi1,
87 yB, &y2, 1, FLA_BOTTOM );
88 FLA_Repart_2x1_to_3x1( zT, &z0,
89 /* ** */ /* ***** */
90 &zeta1,
91 zB, &z2, 1, FLA_BOTTOM );
92
93 /*------------------------------------------------------------*/
94
95 if ( FLA_Obj_length( A22 ) > 0 )
96 {
97 FLA_Part_2x1( a21, &a21_t,
98 &a21_b, 1, FLA_TOP );
99
100 // [ u21, tau11, a21 ] = House( a21 );
101 FLA_Househ2_UT( FLA_LEFT,
102 a21_t,
103 a21_b, tau11 );
104
105 // inv_tau11 = 1 / tau11;
106 // minus_inv_tau11 = -1 / tau11;
107 FLA_Set( FLA_ONE, inv_tau11 );
108 FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
109 FLA_Copy( inv_tau11, minus_inv_tau11 );
110 FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
111
112 // Save first element of a21_t and set it to one so we can use a21 as
113 // u21 in subsequent computations. We will restore a21_t later on.
114 FLA_Copy( a21_t, first_elem );
115 FLA_Set( FLA_ONE, a21_t );
116
117 // y21 = A22' * u21;
118 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
119
120 // z21 = A22 * u21;
121 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
122
123 // beta = u21' * z21 / 2;
124 // conj_beta = conj(beta);
125 FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
126 FLA_Inv_scal( FLA_TWO, beta );
127 FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
128
129 // y21' = ( y21' - beta / tau * u21' ) / tau;
130 // y21 = ( y21 - conj(beta) / tau * u21 ) / tau;
131 FLA_Scal( minus_inv_tau11, conj_beta );
132 FLA_Axpy( conj_beta, a21, y2 );
133 FLA_Scal( inv_tau11, y2 );
134
135 // z21 = ( z21 - beta / tau * u21 ) / tau;
136 FLA_Scal( minus_inv_tau11, beta );
137 FLA_Axpy( beta, a21, z2 );
138 FLA_Scal( inv_tau11, z2 );
139
140 // a12t = a12t * ( I - u21 * u21' / tau );
141 // = a12t - ( a12t * u21 ) * u21' / tau;
142 FLA_Dot( a12t, a21, dot_product );
143 FLA_Scal( minus_inv_tau11, dot_product );
144 FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
145
146 // A02 = A02 * ( I - u21 * u21' / tau );
147 // = A02 - ( A02 * u21 ) * u21' / tau;
148 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
149 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
150
151 // A22 = A22 - u21 * y21' - z21 * u21';
152 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
153 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
154
155 // t01 = U20' * u21;
156 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
157
158 // Restore first element of a21.
159 FLA_Copy( first_elem, a21_t );
160 }
161
162 /*------------------------------------------------------------*/
163
164 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
165 a10t, alpha11, /**/ a12t,
166 /* ************** */ /* ************************ */
167 &ABL, /**/ &ABR, A20, a21, /**/ A22,
168 FLA_TL );
169 FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
170 t10t, tau11, /**/ t12t,
171 /* ************** */ /* ************************ */
172 &TBL, /**/ &TBR, T20, t21, /**/ T22,
173 FLA_TL );
174 FLA_Cont_with_3x1_to_2x1( &yT, y0,
175 psi1,
176 /* ** */ /* **** */
177 &yB, y2, FLA_TOP );
178 FLA_Cont_with_3x1_to_2x1( &zT, z0,
179 zeta1,
180 /* ** */ /* ***** */
181 &zB, z2, FLA_TOP );
182 }
183
184 FLA_Obj_free( &inv_tau11 );
185 FLA_Obj_free( &minus_inv_tau11 );
186 FLA_Obj_free( &first_elem );
187 FLA_Obj_free( &beta );
188 FLA_Obj_free( &conj_beta );
189 FLA_Obj_free( &dot_product );
190 FLA_Obj_free( &y );
191 FLA_Obj_free( &z );
192
193 return FLA_SUCCESS;
194}
FLA_Copy
FLA_Error FLA_Copy(FLA_Obj A, FLA_Obj B)
Definition FLA_Copy.c:15
FLA_Scal
FLA_Error FLA_Scal(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Scal.c:15
FLA_Dot
FLA_Error FLA_Dot(FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition FLA_Dot.c:13
FLA_Dotc
FLA_Error FLA_Dotc(FLA_Conj conj, FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition FLA_Dotc.c:13
FLA_Axpy
FLA_Error FLA_Axpy(FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition FLA_Axpy.c:15
FLA_Axpyt
FLA_Error FLA_Axpyt(FLA_Trans trans, FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition FLA_Axpyt.c:15
FLA_Inv_scal
FLA_Error FLA_Inv_scal(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Inv_scal.c:13
FLA_Copyt
FLA_Error FLA_Copyt(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition FLA_Copyt.c:15
FLA_Inv_scalc
FLA_Error FLA_Inv_scalc(FLA_Conj conjalpha, FLA_Obj alpha, FLA_Obj A)
Definition FLA_Inv_scalc.c:13
FLA_Gerc
FLA_Error FLA_Gerc(FLA_Conj conjx, FLA_Conj conjy, FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj A)
Definition FLA_Gerc.c:13
FLA_Gemv
FLA_Error FLA_Gemv(FLA_Trans transa, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition FLA_Gemv.c:15
FLA_TWO
FLA_Obj FLA_TWO
Definition FLA_Init.c:17
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_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_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_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_Set
FLA_Error FLA_Set(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Set.c:13
FLA_Househ2_UT
FLA_Error FLA_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition FLA_Househ2_UT.c:16
zeta1
double *restrict zeta1
Definition bl1_axmyv2.c:142
psi1
double *restrict psi1
Definition bl1_axmyv2.c:141
FLA_Obj_view
Definition FLA_type_defs.h:159

References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dotc(), FLA_Gemv(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Set(), FLA_TWO, FLA_ZERO, psi1, and zeta1.

Referenced by FLA_Hess_UT_unb_var2().

◆ FLA_Hess_UT_unb_var2()

FLA_Error FLA_Hess_UT_unb_var2 ( FLA_Obj A,
FLA_Obj T )
14{
15 return FLA_Hess_UT_step_unb_var2( A, T );
16}
FLA_Hess_UT_step_unb_var2
FLA_Error FLA_Hess_UT_step_unb_var2(FLA_Obj A, FLA_Obj T)
Definition FLA_Hess_UT_unb_var2.c:18

References FLA_Hess_UT_step_unb_var2().

Referenced by FLA_Hess_UT_internal().

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