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FLA_Hess_UT_unb_var3.c File Reference

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Functions

FLA_Error FLA_Hess_UT_unb_var3 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Hess_UT_step_unb_var3 (FLA_Obj A, FLA_Obj T)
 

Function Documentation

◆ FLA_Hess_UT_step_unb_var3()

FLA_Error FLA_Hess_UT_step_unb_var3 ( 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 uT, u0,
27 uB, upsilon1,
28 u2;
29 FLA_Obj yT, y0,
30 yB, psi1,
31 y2;
32 FLA_Obj zT, z0,
33 zB, zeta1,
34 z2;
35 FLA_Obj vT, v0,
36 vB, nu1,
37 v2;
38 FLA_Obj wT, w0,
39 wB, omega1,
40 w2;
41 FLA_Obj u, y, z, v, w;
42
43 FLA_Obj inv_tau11;
44 FLA_Obj minus_inv_tau11;
45 FLA_Obj first_elem;
46 FLA_Obj beta;
47 FLA_Obj conj_beta;
48 FLA_Obj dot_product;
49 FLA_Obj minus_upsilon1;
50 FLA_Obj minus_conj_upsilon1;
51 FLA_Obj minus_psi1;
52 FLA_Obj minus_conj_psi1;
53 FLA_Obj minus_zeta1;
54
55 FLA_Obj a21_t,
56 a21_b;
57
58 FLA_Datatype datatype_A;
59 dim_t m_A;
60 dim_t b_alg;
61
62
63 b_alg = FLA_Obj_length( T );
64
65 datatype_A = FLA_Obj_datatype( A );
66 m_A = FLA_Obj_length( A );
67
68 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
69 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
70 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
71 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
72 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &conj_beta );
73 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &dot_product );
74 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_upsilon1 );
75 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_upsilon1 );
76 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_psi1 );
77 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_psi1 );
78 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_zeta1 );
79 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
80 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
81 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
82 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
83 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
84
85 FLA_Part_2x2( A, &ATL, &ATR,
86 &ABL, &ABR, 0, 0, FLA_TL );
87 FLA_Part_2x2( T, &TTL, &TTR,
88 &TBL, &TBR, 0, 0, FLA_TL );
89 FLA_Part_2x1( u, &uT,
90 &uB, 0, FLA_TOP );
91 FLA_Part_2x1( y, &yT,
92 &yB, 0, FLA_TOP );
93 FLA_Part_2x1( z, &zT,
94 &zB, 0, FLA_TOP );
95 FLA_Part_2x1( v, &vT,
96 &vB, 0, FLA_TOP );
97 FLA_Part_2x1( w, &wT,
98 &wB, 0, FLA_TOP );
99
100 while ( FLA_Obj_length( ATL ) < b_alg )
101 {
102 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
103 /* ************* */ /* ************************** */
104 &a10t, /**/ &alpha11, &a12t,
105 ABL, /**/ ABR, &A20, /**/ &a21, &A22,
106 1, 1, FLA_BR );
107 FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
108 /* ************* */ /* ************************** */
109 &t10t, /**/ &tau11, &t12t,
110 TBL, /**/ TBR, &T20, /**/ &t21, &T22,
111 1, 1, FLA_BR );
112 FLA_Repart_2x1_to_3x1( uT, &u0,
113 /* ** */ /* ******** */
114 &upsilon1,
115 uB, &u2, 1, FLA_BOTTOM );
116 FLA_Repart_2x1_to_3x1( yT, &y0,
117 /* ** */ /* **** */
118 &psi1,
119 yB, &y2, 1, FLA_BOTTOM );
120 FLA_Repart_2x1_to_3x1( zT, &z0,
121 /* ** */ /* ***** */
122 &zeta1,
123 zB, &z2, 1, FLA_BOTTOM );
124 FLA_Repart_2x1_to_3x1( vT, &v0,
125 /* ** */ /* *** */
126 &nu1,
127 vB, &v2, 1, FLA_BOTTOM );
128 FLA_Repart_2x1_to_3x1( wT, &w0,
129 /* ** */ /* ****** */
130 &omega1,
131 wB, &w2, 1, FLA_BOTTOM );
132
133 /*------------------------------------------------------------*/
134
135 if ( FLA_Obj_length( ATL ) > 0 )
136 {
137 FLA_Copy( upsilon1, minus_upsilon1 );
138 FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
139 FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
140
141 FLA_Copy( psi1, minus_psi1 );
142 FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
143 FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
144
145 FLA_Copy( zeta1, minus_zeta1 );
146 FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
147
148 // alpha11 = alpha11 - upsilon11 * conj(psi11) - zeta11 * conj(upsilon11);
149 FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1, alpha11 );
150 FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1, upsilon1, alpha11 );
151
152 // a12t = a12t - upsilon11 * y21' - zeta11 * u21';
153 FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
154 FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1, u2, a12t );
155
156 // a21 = a21 - conj(psi11) * u21 - conj(upsilon11) * z21;
157 FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1, u2, a21 );
158 FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
159 }
160
161 if ( FLA_Obj_length( A22 ) > 0 )
162 {
163 FLA_Part_2x1( a21, &a21_t,
164 &a21_b, 1, FLA_TOP );
165
166 // [ x21, tau11, a21 ] = House( a21 );
167 FLA_Househ2_UT( FLA_LEFT,
168 a21_t,
169 a21_b, tau11 );
170
171 // inv_tau11 = 1 / tau11;
172 // minus_inv_tau11 = -1 / tau11;
173 FLA_Set( FLA_ONE, inv_tau11 );
174 FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
175 FLA_Copy( inv_tau11, minus_inv_tau11 );
176 FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
177
178 // Save first element of a21_t and set it to one so we can use a21 as
179 // u21 in subsequent computations. We will restore a21_t later on.
180 FLA_Copy( a21_t, first_elem );
181 FLA_Set( FLA_ONE, a21_t );
182 }
183
184 if ( FLA_Obj_length( ATL ) > 0 )
185 {
186 // A22 = A22 - u21 * y21' - z21 * u21';
187 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
188 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
189 }
190
191 if ( FLA_Obj_length( A22 ) > 0 )
192 {
193 // v2 = A22' * x21;
194 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
195
196 // w2 = A22 * x21;
197 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
198
199 // u21 = x21;
200 // y21 = v2;
201 // z21 = w2;
202 FLA_Copy( a21, u2 );
203 FLA_Copy( v2, y2 );
204 FLA_Copy( w2, z2 );
205
206 // beta = u21' * z21 / 2;
207 // conj_beta = conj(beta);
208 FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
209 FLA_Inv_scal( FLA_TWO, beta );
210 FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
211
212 // y21' = ( y21' - beta / tau * u21' ) / tau;
213 // y21 = ( y21 - conj(beta) / tau * u21 ) / tau;
214 FLA_Scal( minus_inv_tau11, conj_beta );
215 FLA_Axpy( conj_beta, a21, y2 );
216 FLA_Scal( inv_tau11, y2 );
217
218 // z21 = ( z21 - beta / tau * u21 ) / tau;
219 FLA_Scal( minus_inv_tau11, beta );
220 FLA_Axpy( beta, a21, z2 );
221 FLA_Scal( inv_tau11, z2 );
222
223 // a12t = a12t * ( I - u21 * u21' / tau );
224 // = a12t - ( a12t * u21 ) * u21' / tau;
225 FLA_Dot( a12t, a21, dot_product );
226 FLA_Scal( minus_inv_tau11, dot_product );
227 FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
228
229 // A02 = A02 * ( I - u21 * u21' / tau );
230 // = A02 - ( A02 * u21 ) * u21' / tau;
231 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
232 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
233
234 // t01 = U20' * u21;
235 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
236
237 // Restore first element of a21.
238 FLA_Copy( first_elem, a21_t );
239 }
240
241 // Update A22 if this is the last iteration; this is needed when we're
242 // being called from the blocked routine so A22 is left in a valid state.
243 if ( FLA_Obj_length( ATL ) + 1 == b_alg &&
244 FLA_Obj_length( A22 ) > 0 )
245 {
246 // A22 = A22 - u21 * y21' - z21 * u21';
247 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
248 FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
249 }
250
251 /*------------------------------------------------------------*/
252
253 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
254 a10t, alpha11, /**/ a12t,
255 /* ************** */ /* ************************ */
256 &ABL, /**/ &ABR, A20, a21, /**/ A22,
257 FLA_TL );
258 FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
259 t10t, tau11, /**/ t12t,
260 /* ************** */ /* ************************ */
261 &TBL, /**/ &TBR, T20, t21, /**/ T22,
262 FLA_TL );
263 FLA_Cont_with_3x1_to_2x1( &uT, u0,
264 upsilon1,
265 /* ** */ /* ******** */
266 &uB, u2, FLA_TOP );
267 FLA_Cont_with_3x1_to_2x1( &yT, y0,
268 psi1,
269 /* ** */ /* **** */
270 &yB, y2, FLA_TOP );
271 FLA_Cont_with_3x1_to_2x1( &zT, z0,
272 zeta1,
273 /* ** */ /* ***** */
274 &zB, z2, FLA_TOP );
275 FLA_Cont_with_3x1_to_2x1( &vT, v0,
276 nu1,
277 /* ** */ /* *** */
278 &vB, v2, FLA_TOP );
279 FLA_Cont_with_3x1_to_2x1( &wT, w0,
280 omega1,
281 /* ** */ /* ****** */
282 &wB, w2, FLA_TOP );
283 }
284
285 FLA_Obj_free( &inv_tau11 );
286 FLA_Obj_free( &minus_inv_tau11 );
287 FLA_Obj_free( &first_elem );
288 FLA_Obj_free( &beta );
289 FLA_Obj_free( &conj_beta );
290 FLA_Obj_free( &dot_product );
291 FLA_Obj_free( &minus_upsilon1 );
292 FLA_Obj_free( &minus_conj_upsilon1 );
293 FLA_Obj_free( &minus_psi1 );
294 FLA_Obj_free( &minus_conj_psi1 );
295 FLA_Obj_free( &minus_zeta1 );
296 FLA_Obj_free( &u );
297 FLA_Obj_free( &y );
298 FLA_Obj_free( &z );
299 FLA_Obj_free( &v );
300 FLA_Obj_free( &w );
301
302 return FLA_SUCCESS;
303}
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
i
int i
Definition bl1_axmyv2.c:145
upsilon1
upsilon1
Definition bl1_axpyv2bdotaxpy.c:225
omega1
double *restrict omega1
Definition bl1_axpyv2bdotaxpy.c:200
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, i, omega1, psi1, upsilon1, and zeta1.

Referenced by FLA_Hess_UT_unb_var3().

◆ FLA_Hess_UT_unb_var3()

FLA_Error FLA_Hess_UT_unb_var3 ( FLA_Obj  A,
FLA_Obj  T 
)
14{
15 return FLA_Hess_UT_step_unb_var3( A, T );
16}
FLA_Hess_UT_step_unb_var3
FLA_Error FLA_Hess_UT_step_unb_var3(FLA_Obj A, FLA_Obj T)
Definition FLA_Hess_UT_unb_var3.c:18

References FLA_Hess_UT_step_unb_var3(), and i.

Referenced by FLA_Hess_UT_internal().

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