1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
|
/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@precisions normal z -> s d c
@author Hartwig Anzt
*/
#include "magmasparse_internal.h"
#define RTOLERANCE lapackf77_dlamch( "E" )
#define ATOLERANCE lapackf77_dlamch( "E" )
/**
Purpose
-------
Solves a system of linear equations
A * X = B
where A is a general matrix.
This is a GPU implementation of the preconditioned Biconjugate Gradient method.
Arguments
---------
@param[in]
A magma_z_matrix
input matrix A
@param[in]
b magma_z_matrix
RHS b
@param[in,out]
x magma_z_matrix*
solution approximation
@param[in,out]
solver_par magma_z_solver_par*
solver parameters
@param[in,out]
precond_par magma_z_preconditioner*
preconditioner
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magmasparse_zgesv
********************************************************************/
extern "C" magma_int_t
magma_zpbicg(
magma_z_matrix A, magma_z_matrix b, magma_z_matrix *x,
magma_z_solver_par *solver_par,
magma_z_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_PBICG;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// some useful variables
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t dofs = A.num_rows * b.num_cols;
// workspace
magma_z_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, pt={Magma_CSR},
z={Magma_CSR}, zt={Magma_CSR}, q={Magma_CSR}, y={Magma_CSR},
yt={Magma_CSR}, qt={Magma_CSR};
// need to transpose the matrix
magma_z_matrix AT={Magma_CSR};
CHECK( magma_zvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &qt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &yt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver variables
magmaDoubleComplex alpha, rho, beta, rho_new, ptq;
double res, nomb, nom0, r0;
// transpose the matrix
magma_zmtransposeconjugate( A, &AT, queue );
// solver setup
CHECK( magma_zresidualvec( A, b, *x, &r, &nom0, queue));
res = nom0;
solver_par->init_res = nom0;
magma_zcopy( dofs, r.dval, 1, rt.dval, 1, queue ); // rr = r
rho_new = magma_zdotc( dofs, rt.dval, 1, r.dval, 1, queue ); // rho=<rr,r>
rho = alpha = MAGMA_Z_MAKE( 1.0, 0. );
nomb = magma_dznrm2( dofs, b.dval, 1, queue );
if ( nomb == 0.0 ){
nomb=1.0;
}
if ( (r0 = nomb * solver_par->rtol) < ATOLERANCE ){
r0 = ATOLERANCE;
}
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = nom0;
solver_par->timing[0] = 0.0;
}
if ( nom0 < r0 ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, r, &y, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, y, &z, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaTrans, A, rt, &yt, precond_par, queue ));
CHECK( magma_z_applyprecond_left( MagmaTrans, A, yt, &zt, precond_par, queue ));
//magma_zcopy( dofs, r.dval, 1 , y.dval, 1, queue ); // y=r
//magma_zcopy( dofs, y.dval, 1 , z.dval, 1, queue ); // z=y
//magma_zcopy( dofs, rt.dval, 1 , yt.dval, 1, queue ); // yt=rt
//magma_zcopy( dofs, yt.dval, 1 , zt.dval, 1, queue ); // yt=rt
rho= rho_new;
rho_new = magma_zdotc( dofs, rt.dval, 1, z.dval, 1, queue ); // rho=<rt,z>
if( magma_z_isnan_inf( rho_new ) ){
info = MAGMA_DIVERGENCE;
break;
}
if( solver_par->numiter==1 ){
magma_zcopy( dofs, z.dval, 1 , p.dval, 1, queue ); // yt=rt
magma_zcopy( dofs, zt.dval, 1 , pt.dval, 1, queue ); // zt=yt
} else {
beta = rho_new/rho;
magma_zscal( dofs, beta, p.dval, 1, queue ); // p = beta*p
magma_zaxpy( dofs, c_one , z.dval, 1 , p.dval, 1, queue ); // p = z+beta*p
magma_zscal( dofs, MAGMA_Z_CONJ(beta), pt.dval, 1, queue ); // pt = beta*pt
magma_zaxpy( dofs, c_one , zt.dval, 1 , pt.dval, 1, queue ); // pt = zt+beta*pt
}
CHECK( magma_z_spmv( c_one, A, p, c_zero, q, queue )); // v = Ap
CHECK( magma_z_spmv( c_one, AT, pt, c_zero, qt, queue )); // v = Ap
solver_par->spmv_count++;
solver_par->spmv_count++;
ptq = magma_zdotc( dofs, pt.dval, 1, q.dval, 1, queue );
alpha = rho_new /ptq;
magma_zaxpy( dofs, alpha, p.dval, 1 , x->dval, 1, queue ); // x=x+alpha*p
magma_zaxpy( dofs, c_neg_one * alpha, q.dval, 1 , r.dval, 1, queue ); // r=r+alpha*q
magma_zaxpy( dofs, c_neg_one * MAGMA_Z_CONJ(alpha), qt.dval, 1 , rt.dval, 1, queue ); // r=r+alpha*q
res = magma_dznrm2( dofs, r.dval, 1, queue );
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
CHECK( magma_zresidualvec( A, b, *x, &r, &residual, queue));
solver_par->iter_res = res;
solver_par->final_res = residual;
if ( solver_par->numiter < solver_par->maxiter ) {
info = MAGMA_SUCCESS;
} else if ( solver_par->init_res > solver_par->final_res ) {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_SLOW_CONVERGENCE;
if( solver_par->iter_res < solver_par->rtol*nomb ||
solver_par->iter_res < solver_par->atol ) {
info = MAGMA_SUCCESS;
}
}
else {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_zmfree(&r, queue );
magma_zmfree(&rt, queue );
magma_zmfree(&p, queue );
magma_zmfree(&pt, queue );
magma_zmfree(&q, queue );
magma_zmfree(&qt, queue );
magma_zmfree(&y, queue );
magma_zmfree(&yt, queue );
magma_zmfree(&z, queue );
magma_zmfree(&zt, queue );
magma_zmfree(&AT, queue );
solver_par->info = info;
return info;
} /* magma_zpbicg */
|
