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FLA_Hess_UT_unb_var4.c File Reference

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Functions

FLA_Error FLA_Hess_UT_unb_var4 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Hess_UT_step_unb_var4 (FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T)
 

Function Documentation

◆ FLA_Hess_UT_step_unb_var4()

FLA_Error FLA_Hess_UT_step_unb_var4 ( FLA_Obj A,
FLA_Obj Y,
FLA_Obj Z,
FLA_Obj T )
30{
31 FLA_Obj ATL, ATR, A00, a01, A02,
32 ABL, ABR, a10t, alpha11, a12t,
33 A20, a21, A22;
34 FLA_Obj YTL, YTR, Y00, y01, Y02,
35 YBL, YBR, y10t, psi11, y12t,
36 Y20, y21, Y22;
37 FLA_Obj ZTL, ZTR, Z00, z01, Z02,
38 ZBL, ZBR, z10t, zeta11, z12t,
39 Z20, z21, Z22;
40 FLA_Obj TTL, TTR, T00, t01, T02,
41 TBL, TBR, t10t, tau11, t12t,
42 T20, t21, T22;
43 FLA_Obj dT, d0,
44 dB, delta1,
45 d2;
46 FLA_Obj eT, e0,
47 eB, epsilon1,
48 e2;
49 FLA_Obj fT, f0,
50 fB, phi1,
51 f2;
52 FLA_Obj d, e, f;
53
54 FLA_Obj inv_tau11;
55 FLA_Obj minus_inv_tau11;
56 FLA_Obj first_elem;
57 FLA_Obj last_elem;
58 FLA_Obj beta;
59 FLA_Obj conj_beta;
60 FLA_Obj dot_product;
61
62 FLA_Obj a10t_l, a10t_r;
63 FLA_Obj a21_t,
64 a21_b;
65 FLA_Obj a2;
66
67 FLA_Datatype datatype_A;
68 dim_t m_A;
69 dim_t b_alg;
70
71
72 b_alg = FLA_Obj_length( T );
73
74 datatype_A = FLA_Obj_datatype( A );
75 m_A = FLA_Obj_length( A );
76
77 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
78 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
79 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
80 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &last_elem );
81 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
82 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &conj_beta );
83 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &dot_product );
84 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
85 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
86 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
87
88 FLA_Set( FLA_ZERO, Y );
89 FLA_Set( FLA_ZERO, Z );
90
91 FLA_Part_2x2( A, &ATL, &ATR,
92 &ABL, &ABR, 0, 0, FLA_TL );
93 FLA_Part_2x2( Y, &YTL, &YTR,
94 &YBL, &YBR, 0, 0, FLA_TL );
95 FLA_Part_2x2( Z, &ZTL, &ZTR,
96 &ZBL, &ZBR, 0, 0, FLA_TL );
97 FLA_Part_2x2( T, &TTL, &TTR,
98 &TBL, &TBR, 0, 0, FLA_TL );
99 FLA_Part_2x1( d, &dT,
100 &dB, 0, FLA_TOP );
101 FLA_Part_2x1( e, &eT,
102 &eB, 0, FLA_TOP );
103 FLA_Part_2x1( f, &fT,
104 &fB, 0, FLA_TOP );
105
106 while ( FLA_Obj_length( ATL ) < b_alg )
107 {
108 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
109 /* ************* */ /* ************************** */
110 &a10t, /**/ &alpha11, &a12t,
111 ABL, /**/ ABR, &A20, /**/ &a21, &A22,
112 1, 1, FLA_BR );
113 FLA_Repart_2x2_to_3x3( YTL, /**/ YTR, &Y00, /**/ &y01, &Y02,
114 /* ************* */ /* ************************ */
115 &y10t, /**/ &psi11, &y12t,
116 YBL, /**/ YBR, &Y20, /**/ &y21, &Y22,
117 1, 1, FLA_BR );
118 FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR, &Z00, /**/ &z01, &Z02,
119 /* ************* */ /* ************************* */
120 &z10t, /**/ &zeta11, &z12t,
121 ZBL, /**/ ZBR, &Z20, /**/ &z21, &Z22,
122 1, 1, FLA_BR );
123 FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
124 /* ************* */ /* ************************** */
125 &t10t, /**/ &tau11, &t12t,
126 TBL, /**/ TBR, &T20, /**/ &t21, &T22,
127 1, 1, FLA_BR );
128 FLA_Repart_2x1_to_3x1( dT, &d0,
129 /* ** */ /* ****** */
130 &delta1,
131 dB, &d2, 1, FLA_BOTTOM );
132 FLA_Repart_2x1_to_3x1( eT, &e0,
133 /* ** */ /* ******** */
134 &epsilon1,
135 eB, &e2, 1, FLA_BOTTOM );
136 FLA_Repart_2x1_to_3x1( fT, &f0,
137 /* ** */ /* **** */
138 &phi1,
139 fB, &f2, 1, FLA_BOTTOM );
140
141 /*------------------------------------------------------------*/
142
143 // Save first element of a10_r and set it to one so we can use a10t as
144 // u10t in subsequent computations. We will restore a10_r later on.
145 if ( FLA_Obj_length( ATL ) > 0 )
146 {
147 FLA_Part_1x2( a10t, &a10t_l, &a10t_r, 1, FLA_RIGHT );
148 FLA_Copy( a10t_r, last_elem );
149 FLA_Set( FLA_ONE, a10t_r );
150 }
151
152 FLA_Merge_2x1( alpha11,
153 a21, &a2 );
154
155 // alpha11 = alpha11 - u10t * y10t' - z10t * u10t';
156 // a21 = a21 - U20 * y10t' - Z20 * u10t';
157 FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
158 FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
159
160 // a12t = a12t - u10t * Y20' - z10t * U20';
161 FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
162 FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
163
164 // Restore last element of a10t.
165 if ( FLA_Obj_length( ATL ) > 0 )
166 {
167 FLA_Copy( last_elem, a10t_r );
168 }
169
170 if ( FLA_Obj_length( A22 ) > 0 )
171 {
172 FLA_Part_2x1( a21, &a21_t,
173 &a21_b, 1, FLA_TOP );
174
175 // [ u21, tau11, a21 ] = House( a21 );
176 FLA_Househ2_UT( FLA_LEFT,
177 a21_t,
178 a21_b, tau11 );
179
180 // inv_tau11 = 1 / tau11;
181 // minus_inv_tau11 = -1 / tau11;
182 FLA_Set( FLA_ONE, inv_tau11 );
183 FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
184 FLA_Copy( inv_tau11, minus_inv_tau11 );
185 FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
186
187 // Save first element of a21_t and set it to one.
188 FLA_Copy( a21_t, first_elem );
189 FLA_Set( FLA_ONE, a21_t );
190
191 // y21 = A22' * u21;
192 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
193
194 // z21 = A22 * u21;
195 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
196
197 // y21 = y21 - Y20 * ( U20' * u21 ) - U20 * ( Z20' * u21 );
198 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
199 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
200 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
201
202 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
203 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
204
205 // t01 = U20' * u21;
206 FLA_Copy( d0, t01 );
207
208 // z21 = z21 - U20 * ( Y20' * u21 ) - Z20 * ( U20' * u21 );
209 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
210 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
211
212 // beta = u21' * z21 / 2;
213 // conj_beta = conj(beta);
214 FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
215 FLA_Inv_scal( FLA_TWO, beta );
216 FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
217
218 // y21' = ( y21' - beta / tau * u21' ) / tau;
219 // y21 = ( y21 - conj(beta) / tau * u21 ) / tau;
220 FLA_Scal( minus_inv_tau11, conj_beta );
221 FLA_Axpy( conj_beta, a21, y21 );
222 FLA_Scal( inv_tau11, y21 );
223
224 // z21 = ( z21 - beta / tau * u21 ) / tau;
225 FLA_Scal( minus_inv_tau11, beta );
226 FLA_Axpy( beta, a21, z21 );
227 FLA_Scal( inv_tau11, z21 );
228
229 // a12t = a12t * ( I - u21 * u21' / tau );
230 // = a12t - ( a12t * u21 ) * u21' / tau;
231 FLA_Dot( a12t, a21, dot_product );
232 FLA_Scal( minus_inv_tau11, dot_product );
233 FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
234
235 // A02 = A02 * ( I - u21 * u21' / tau );
236 // = A02 - ( A02 * u21 ) * u21' / tau;
237 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
238 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
239
240 // Restore first element of a21.
241 FLA_Copy( first_elem, a21_t );
242 }
243
244 /*------------------------------------------------------------*/
245
246 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
247 a10t, alpha11, /**/ a12t,
248 /* ************** */ /* ************************ */
249 &ABL, /**/ &ABR, A20, a21, /**/ A22,
250 FLA_TL );
251 FLA_Cont_with_3x3_to_2x2( &YTL, /**/ &YTR, Y00, y01, /**/ Y02,
252 y10t, psi11, /**/ y12t,
253 /* ************** */ /* ********************** */
254 &YBL, /**/ &YBR, Y20, y21, /**/ Y22,
255 FLA_TL );
256 FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR, Z00, z01, /**/ Z02,
257 z10t, zeta11, /**/ z12t,
258 /* ************** */ /* *********************** */
259 &ZBL, /**/ &ZBR, Z20, z21, /**/ Z22,
260 FLA_TL );
261 FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
262 t10t, tau11, /**/ t12t,
263 /* ************** */ /* ************************ */
264 &TBL, /**/ &TBR, T20, t21, /**/ T22,
265 FLA_TL );
266 FLA_Cont_with_3x1_to_2x1( &dT, d0,
267 delta1,
268 /* ** */ /* ****** */
269 &dB, d2, FLA_TOP );
270 FLA_Cont_with_3x1_to_2x1( &eT, e0,
271 epsilon1,
272 /* ** */ /* ******** */
273 &eB, e2, FLA_TOP );
274 FLA_Cont_with_3x1_to_2x1( &fT, f0,
275 phi1,
276 /* ** */ /* **** */
277 &fB, f2, FLA_TOP );
278 }
279
280 FLA_Obj_free( &inv_tau11 );
281 FLA_Obj_free( &minus_inv_tau11 );
282 FLA_Obj_free( &first_elem );
283 FLA_Obj_free( &last_elem );
284 FLA_Obj_free( &beta );
285 FLA_Obj_free( &conj_beta );
286 FLA_Obj_free( &dot_product );
287 FLA_Obj_free( &d );
288 FLA_Obj_free( &e );
289 FLA_Obj_free( &f );
290
291 return FLA_SUCCESS;
292}
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_Gemvc
FLA_Error FLA_Gemvc(FLA_Trans transa, FLA_Conj conjx, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition FLA_Gemvc.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_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_Merge_2x1
FLA_Error FLA_Merge_2x1(FLA_Obj AT, FLA_Obj AB, FLA_Obj *A)
Definition FLA_View.c:541
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
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_Gemvc(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_Merge_2x1(), 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_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Set(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var4().

◆ FLA_Hess_UT_unb_var4()

FLA_Error FLA_Hess_UT_unb_var4 ( FLA_Obj A,
FLA_Obj T )
14{
15 FLA_Error r_val;
16 FLA_Obj Y, Z;
17
18 FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Y );
19 FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );
20
21 r_val = FLA_Hess_UT_step_unb_var4( A, Y, Z, T );
22
23 FLA_Obj_free( &Y );
24 FLA_Obj_free( &Z );
25
26 return r_val;
27}
FLA_Hess_UT_step_unb_var4
FLA_Error FLA_Hess_UT_step_unb_var4(FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T)
Definition FLA_Hess_UT_unb_var4.c:29
FLA_Obj_create_conf_to
FLA_Error FLA_Obj_create_conf_to(FLA_Trans trans, FLA_Obj old, FLA_Obj *obj)
Definition FLA_Obj.c:286
FLA_Error
int FLA_Error
Definition FLA_type_defs.h:47

References FLA_Hess_UT_step_unb_var4(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

Referenced by FLA_Hess_UT_internal().

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