1 /*
2
3 Copyright (C) 2014, The University of Texas at Austin
4
5 This file is part of libflame and is available under the 3-Clause
6 BSD license, which can be found in the LICENSE file at the top-level
7 directory, or at http://opensource.org/licenses/BSD-3-Clause
8
9 */
10
11 #include "FLAME.h"
12
FLA_Bidiag_UT_u_unb_var5(FLA_Obj A,FLA_Obj TU,FLA_Obj TV)13 FLA_Error FLA_Bidiag_UT_u_unb_var5( FLA_Obj A, FLA_Obj TU, FLA_Obj TV )
14 {
15 FLA_Error r_val;
16 FLA_Obj Y, Z;
17 FLA_Datatype datatype_A;
18 dim_t m_A, n_A;
19
20 datatype_A = FLA_Obj_datatype( A );
21 m_A = FLA_Obj_length( A );
22 n_A = FLA_Obj_width( A );
23
24 FLA_Obj_create( datatype_A, n_A, n_A, 0, 0, &Y );
25 FLA_Obj_create( datatype_A, m_A, n_A, 0, 0, &Z );
26
27 r_val = FLA_Bidiag_UT_u_step_unb_var5( A, Y, Z, TU, TV );
28
29 FLA_Obj_free( &Y );
30 FLA_Obj_free( &Z );
31
32 return r_val;
33 }
34
FLA_Bidiag_UT_u_step_unb_var5(FLA_Obj A,FLA_Obj Y,FLA_Obj Z,FLA_Obj T,FLA_Obj S)35 FLA_Error FLA_Bidiag_UT_u_step_unb_var5( FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T, FLA_Obj S )
36 {
37 FLA_Obj ATL, ATR, A00, a01, A02,
38 ABL, ABR, a10t, alpha11, a12t,
39 A20, a21, A22;
40 FLA_Obj YTL, YTR, Y00, y01, Y02,
41 YBL, YBR, y10t, psi11, y12t,
42 Y20, y21, Y22;
43 FLA_Obj ZTL, ZTR, Z00, z01, Z02,
44 ZBL, ZBR, z10t, zeta11, z12t,
45 Z20, z21, Z22;
46 FLA_Obj TTL, TTR, T00, t01, T02,
47 TBL, TBR, t10t, tau11, t12t,
48 T20, t21, T22;
49 FLA_Obj STL, STR, S00, s01, S02,
50 SBL, SBR, s10t, sigma11, s12t,
51 S20, s21, S22;
52 FLA_Obj uT, u01,
53 uB, upsilon11,
54 u21;
55 FLA_Obj vT, v01,
56 vB, nu11,
57 v21;
58 FLA_Obj dT, d0,
59 dB, delta1,
60 d2;
61 FLA_Obj eT, e0,
62 eB, epsilon1,
63 e2;
64 FLA_Obj fT, f0,
65 fB, phi1,
66 f2;
67 FLA_Obj gT, g0,
68 gB, ghi1,
69 g2;
70 FLA_Obj u, v;
71 FLA_Obj d, e, f, g;
72
73 FLA_Obj last_elem;
74 FLA_Obj beta;
75 FLA_Obj minus_upsilon11;
76 FLA_Obj minus_zeta11;
77
78 FLA_Obj a01_t,
79 a01_b;
80 FLA_Obj a12t_l, a12t_r;
81 FLA_Obj v21_t,
82 v21_b;
83 FLA_Obj a2;
84
85 FLA_Datatype datatype_A;
86 dim_t m_A, n_A;
87 dim_t b_alg;
88
89
90 b_alg = FLA_Obj_length( T );
91
92 datatype_A = FLA_Obj_datatype( A );
93 m_A = FLA_Obj_length( A );
94 n_A = FLA_Obj_width( A );
95
96 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &last_elem );
97 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
98 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_upsilon11 );
99 FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_zeta11 );
100 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
101 FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &v );
102 FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &d );
103 FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &e );
104 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
105 FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &g );
106
107 FLA_Set( FLA_ZERO, Y );
108 FLA_Set( FLA_ZERO, Z );
109
110 FLA_Part_2x2( A, &ATL, &ATR,
111 &ABL, &ABR, 0, 0, FLA_TL );
112 FLA_Part_2x2( Y, &YTL, &YTR,
113 &YBL, &YBR, 0, 0, FLA_TL );
114 FLA_Part_2x2( Z, &ZTL, &ZTR,
115 &ZBL, &ZBR, 0, 0, FLA_TL );
116 FLA_Part_2x2( T, &TTL, &TTR,
117 &TBL, &TBR, 0, 0, FLA_TL );
118 FLA_Part_2x2( S, &STL, &STR,
119 &SBL, &SBR, 0, 0, FLA_TL );
120 FLA_Part_2x1( u, &uT,
121 &uB, 0, FLA_TOP );
122 FLA_Part_2x1( v, &vT,
123 &vB, 0, FLA_TOP );
124 FLA_Part_2x1( d, &dT,
125 &dB, 0, FLA_TOP );
126 FLA_Part_2x1( e, &eT,
127 &eB, 0, FLA_TOP );
128 FLA_Part_2x1( f, &fT,
129 &fB, 0, FLA_TOP );
130 FLA_Part_2x1( g, &gT,
131 &gB, 0, FLA_TOP );
132
133 while ( FLA_Obj_length( ATL ) < b_alg )
134 {
135 FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
136 /* ************* */ /* ************************** */
137 &a10t, /**/ &alpha11, &a12t,
138 ABL, /**/ ABR, &A20, /**/ &a21, &A22,
139 1, 1, FLA_BR );
140 FLA_Repart_2x2_to_3x3( YTL, /**/ YTR, &Y00, /**/ &y01, &Y02,
141 /* ************* */ /* ************************ */
142 &y10t, /**/ &psi11, &y12t,
143 YBL, /**/ YBR, &Y20, /**/ &y21, &Y22,
144 1, 1, FLA_BR );
145 FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR, &Z00, /**/ &z01, &Z02,
146 /* ************* */ /* ************************* */
147 &z10t, /**/ &zeta11, &z12t,
148 ZBL, /**/ ZBR, &Z20, /**/ &z21, &Z22,
149 1, 1, FLA_BR );
150 FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
151 /* ************* */ /* ************************** */
152 &t10t, /**/ &tau11, &t12t,
153 TBL, /**/ TBR, &T20, /**/ &t21, &T22,
154 1, 1, FLA_BR );
155 FLA_Repart_2x2_to_3x3( STL, /**/ STR, &S00, /**/ &s01, &S02,
156 /* ************* */ /* ************************** */
157 &s10t, /**/ &sigma11, &s12t,
158 SBL, /**/ SBR, &S20, /**/ &s21, &S22,
159 1, 1, FLA_BR );
160 FLA_Repart_2x1_to_3x1( uT, &u01,
161 /* ** */ /* ***** */
162 &upsilon11,
163 uB, &u21, 1, FLA_BOTTOM );
164 FLA_Repart_2x1_to_3x1( vT, &v01,
165 /* ** */ /* ***** */
166 &nu11,
167 vB, &v21, 1, FLA_BOTTOM );
168 FLA_Repart_2x1_to_3x1( dT, &d0,
169 /* ** */ /* ****** */
170 &delta1,
171 dB, &d2, 1, FLA_BOTTOM );
172 FLA_Repart_2x1_to_3x1( eT, &e0,
173 /* ** */ /* ******** */
174 &epsilon1,
175 eB, &e2, 1, FLA_BOTTOM );
176 FLA_Repart_2x1_to_3x1( fT, &f0,
177 /* ** */ /* **** */
178 &phi1,
179 fB, &f2, 1, FLA_BOTTOM );
180 FLA_Repart_2x1_to_3x1( gT, &g0,
181 /* ** */ /* **** */
182 &ghi1,
183 gB, &g2, 1, FLA_BOTTOM );
184
185 /*------------------------------------------------------------*/
186
187 // Save last element of a01 and set it to one so we can use a01 as
188 // v10t^T in subsequent computations. We will restore a01_b later on.
189 // Also note: V20^T is stored in A02.
190 if ( FLA_Obj_length( ATL ) > 0 )
191 {
192 FLA_Part_2x1( a01, &a01_t,
193 &a01_b, 1, FLA_BOTTOM );
194 FLA_Copy( a01_b, last_elem );
195 FLA_Set( FLA_ONE, a01_b );
196 }
197
198 FLA_Merge_2x1( alpha11,
199 a21, &a2 );
200
201 // alpha11 = alpha11 - u10t * y10t' - z10t * v10t';
202 // a21 = a21 - U20 * y10t' - Z20 * v10t';
203 FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
204 FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a01, FLA_ONE, a2 );
205
206 // a12t = a12t - u10t * Y20' - z10t * V20';
207 FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
208 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, A02, z10t, FLA_ONE, a12t );
209
210 // Restore last element of a01.
211 if ( FLA_Obj_length( ATL ) > 0 )
212 {
213 FLA_Copy( last_elem, a01_b );
214 }
215
216 // [ alpha11, u21, tau11 ] = House2( alpha11, a21 );
217 FLA_Househ2_UT( FLA_LEFT,
218 alpha11,
219 a21, tau11 );
220 FLA_Copy( a21, u21 );
221
222 if ( FLA_Obj_width( A22 ) > 0 )
223 {
224 // y21' = a12t + u21' * A22;
225 // y21 = conj(a12t) + A22' * u21;
226 FLA_Copyt( FLA_CONJ_TRANSPOSE, a12t, y21 );
227 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, u21, FLA_ONE, y21 );
228
229 // y21 = y21 - Y20 * ( U20' * u21 ) - V20 * ( Z20' * u21 );
230 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, u21, FLA_ZERO, d0 );
231 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, u21, FLA_ZERO, e0 );
232
233 // t01 = a10t' + U20' * u21;
234 FLA_Copyt( FLA_CONJ_TRANSPOSE, a10t, t01 );
235 FLA_Axpy( FLA_ONE, d0, t01 );
236
237 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
238 FLA_Gemv( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, e0, FLA_ONE, y21 );
239
240 // y21 = y21 / tau11;
241 FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, y21 );
242
243 // a12t = a12t - conj(y21)^T;
244 FLA_Axpyt( FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, y21, a12t );
245
246 FLA_Part_1x2( a12t, &a12t_l, &a12t_r, 1, FLA_LEFT );
247 FLA_Part_2x1( v21, &v21_t,
248 &v21_b, 1, FLA_TOP );
249
250 // [ a12t_l, v21_b, sigma11 ] = House2( a12t_l, a12t_r );
251 FLA_Househ2_UT( FLA_RIGHT, a12t_l, a12t_r, sigma11 );
252
253 // v21_t = 1;
254 // v21_b = a12t_r^T;
255 FLA_Set( FLA_ONE, v21_t );
256 FLA_Copyt( FLA_TRANSPOSE, a12t_r, v21_b );
257
258 // beta = - y21' * v21;
259 FLA_Dotc( FLA_CONJUGATE, y21, v21, beta );
260 FLA_Scal( FLA_MINUS_ONE, beta );
261
262 // z21 = A22 * v21 + beta * u21;
263 FLA_Copy( u21, z21 );
264 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, v21, beta, z21 );
265
266 // z21 = z21 - U20 * ( Y20' * v21 ) - Z20 * ( V20' * v21 );
267 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, v21, FLA_ZERO, f0 );
268 FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_ONE, A02, v21, FLA_ZERO, g0 );
269
270 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, z21 );
271 FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, g0, FLA_ONE, z21 );
272
273 // z21 = z21 / sigma11;
274 FLA_Inv_scalc( FLA_NO_CONJUGATE, sigma11, z21 );
275
276 // s01 = conj(V02) * v21;
277 FLA_Copy( g0, s01 );
278 }
279 else // if ( FLA_Obj_width( A22 ) == 0 )
280 {
281 // t01 = a10t' + U20' * u21;
282 FLA_Copyt( FLA_CONJ_TRANSPOSE, a10t, t01 );
283 FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, u21, FLA_ONE, t01 );
284 }
285
286 /*------------------------------------------------------------*/
287
288 FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
289 a10t, alpha11, /**/ a12t,
290 /* ************** */ /* ************************ */
291 &ABL, /**/ &ABR, A20, a21, /**/ A22,
292 FLA_TL );
293 FLA_Cont_with_3x3_to_2x2( &YTL, /**/ &YTR, Y00, y01, /**/ Y02,
294 y10t, psi11, /**/ y12t,
295 /* ************** */ /* ********************** */
296 &YBL, /**/ &YBR, Y20, y21, /**/ Y22,
297 FLA_TL );
298 FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR, Z00, z01, /**/ Z02,
299 z10t, zeta11, /**/ z12t,
300 /* ************** */ /* *********************** */
301 &ZBL, /**/ &ZBR, Z20, z21, /**/ Z22,
302 FLA_TL );
303 FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
304 t10t, tau11, /**/ t12t,
305 /* ************** */ /* ************************ */
306 &TBL, /**/ &TBR, T20, t21, /**/ T22,
307 FLA_TL );
308 FLA_Cont_with_3x3_to_2x2( &STL, /**/ &STR, S00, s01, /**/ S02,
309 s10t, sigma11, /**/ s12t,
310 /* ************** */ /* ************************ */
311 &SBL, /**/ &SBR, S20, s21, /**/ S22,
312 FLA_TL );
313 FLA_Cont_with_3x1_to_2x1( &uT, u01,
314 upsilon11,
315 /* ** */ /* ***** */
316 &uB, u21, FLA_TOP );
317 FLA_Cont_with_3x1_to_2x1( &vT, v01,
318 nu11,
319 /* ** */ /* ***** */
320 &vB, v21, FLA_TOP );
321 FLA_Cont_with_3x1_to_2x1( &dT, d0,
322 delta1,
323 /* ** */ /* ****** */
324 &dB, d2, FLA_TOP );
325 FLA_Cont_with_3x1_to_2x1( &eT, e0,
326 epsilon1,
327 /* ** */ /* ******** */
328 &eB, e2, FLA_TOP );
329 FLA_Cont_with_3x1_to_2x1( &fT, f0,
330 phi1,
331 /* ** */ /* **** */
332 &fB, f2, FLA_TOP );
333 FLA_Cont_with_3x1_to_2x1( &gT, g0,
334 ghi1,
335 /* ** */ /* **** */
336 &gB, g2, FLA_TOP );
337 }
338
339 FLA_Obj_free( &last_elem );
340 FLA_Obj_free( &beta );
341 FLA_Obj_free( &minus_upsilon11 );
342 FLA_Obj_free( &minus_zeta11 );
343 FLA_Obj_free( &u );
344 FLA_Obj_free( &v );
345 FLA_Obj_free( &d );
346 FLA_Obj_free( &e );
347 FLA_Obj_free( &f );
348 FLA_Obj_free( &g );
349
350 return FLA_SUCCESS;
351 }
352
353