extern "C" magma_int_t magma_c_applyprecond_right( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_preconditioner *precond, magma_queue_t queue ) { // set queue for old dense routines magma_queue_t orig_queue; magmablasGetKernelStream( &orig_queue ); if ( precond->solver == Magma_JACOBI ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1 ); // x = b } else if ( precond->solver == Magma_ILU || ( precond->solver == Magma_AILU && precond->maxiter == -1)) { magma_capplycumilu_r( b, x, precond, queue ); } else if ( precond->solver == Magma_ICC || ( precond->solver == Magma_AICC && precond->maxiter == -1) ) { magma_capplycumicc_r( b, x, precond, queue ); } else if ( precond->solver == Magma_NONE ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1 ); // x = b } else { printf( "error: preconditioner type not yet supported.\n" ); magmablasSetKernelStream( orig_queue ); return MAGMA_ERR_NOT_SUPPORTED; } magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; }
magma_int_t magma_c_applyprecond_right( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_preconditioner *precond ) { if( precond->solver == Magma_JACOBI ){ //magma_cjacobi_diagscal( A.num_rows, precond->d.val, b.val, x->val ); magma_ccopy( b.num_rows, b.val, 1, x->val, 1 ); // x = b return MAGMA_SUCCESS; } else if( precond->solver == Magma_ILU ){ magma_capplycuilu_r( b, x, precond ); return MAGMA_SUCCESS; } else if( precond->solver == Magma_AILU ){ magma_capplycuilu_r( b, x, precond ); // magma_capplyailu_r( b, x, precond ); return MAGMA_SUCCESS; } else if( precond->solver == Magma_ICC ){ magma_capplycuicc_r( b, x, precond ); // magma_capplycuilu_r( b, x, precond ); return MAGMA_SUCCESS; } else if( precond->solver == Magma_AICC ){ magma_capplycuicc_r( b, x, precond ); // magma_capplycuilu_r( b, x, precond ); return MAGMA_SUCCESS; } else{ printf( "error: preconditioner type not yet supported.\n" ); return MAGMA_ERR_NOT_SUPPORTED; } }
extern "C" magma_int_t magma_c_applyprecond( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_preconditioner *precond, magma_queue_t queue ) { // set queue for old dense routines magma_queue_t orig_queue; magmablasGetKernelStream( &orig_queue ); if ( precond->solver == Magma_JACOBI ) { magma_cjacobi_diagscal( A.num_rows, precond->d, b, x, queue ); } else if ( precond->solver == Magma_PASTIX ) { magma_capplypastix( b, x, precond, queue ); } else if ( precond->solver == Magma_ILU ) { magma_c_vector tmp; magma_c_vinit( &tmp, Magma_DEV, A.num_rows, MAGMA_C_ZERO, queue ); magma_c_vfree( &tmp, queue ); } else if ( precond->solver == Magma_ICC ) { magma_c_vector tmp; magma_c_vinit( &tmp, Magma_DEV, A.num_rows, MAGMA_C_ZERO, queue ); magma_c_vfree( &tmp, queue ); } else if ( precond->solver == Magma_NONE ) { magma_ccopy( b.num_rows, b.dval, 1, x->dval, 1 ); // x = b } else { printf( "error: preconditioner type not yet supported.\n" ); magmablasSetKernelStream( orig_queue ); return MAGMA_ERR_NOT_SUPPORTED; } magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; }
extern "C" magma_int_t magma_c_applyprecond( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_preconditioner *precond, magma_queue_t queue ) { magma_int_t info = 0; magma_c_matrix tmp={Magma_CSR}; if ( precond->solver == Magma_JACOBI ) { CHECK( magma_cjacobi_diagscal( b.num_rows, precond->d, b, x, queue )); } else if ( precond->solver == Magma_PASTIX ) { //CHECK( magma_capplypastix( b, x, precond, queue )); info = MAGMA_ERR_NOT_SUPPORTED; } else if ( precond->solver == Magma_ILU ) { CHECK( magma_cvinit( &tmp, Magma_DEV, b.num_rows, b.num_cols, MAGMA_C_ZERO, queue )); } else if ( precond->solver == Magma_ICC ) { CHECK( magma_cvinit( &tmp, Magma_DEV, b.num_rows, b.num_cols, MAGMA_C_ZERO, queue )); } else if ( precond->solver == Magma_NONE ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1, queue ); // x = b } else { printf( "error: preconditioner type not yet supported.\n" ); info = MAGMA_ERR_NOT_SUPPORTED; } cleanup: magma_cmfree( &tmp, queue ); return info; }
extern "C" magma_int_t magma_ccg_merge( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_CGMERGE; solver_par->numiter = 0; solver_par->spmv_count = 0; // solver variables magmaFloatComplex alpha, beta, gamma, rho, tmp1, *skp_h={0}; float nom, nom0, betanom, den, nomb; // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows*b.num_cols; magma_c_matrix r={Magma_CSR}, d={Magma_CSR}, z={Magma_CSR}, B={Magma_CSR}, C={Magma_CSR}; magmaFloatComplex *d1=NULL, *d2=NULL, *skp=NULL; // GPU workspace CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cmalloc( &d1, dofs*(1) )); CHECK( magma_cmalloc( &d2, dofs*(1) )); // array for the parameters CHECK( magma_cmalloc( &skp, 6 )); // skp = [alpha|beta|gamma|rho|tmp1|tmp2] // solver setup magma_cscal( dofs, c_zero, x->dval, 1, queue ); // x = 0 //CHECK( magma_cresidualvec( A, b, *x, &r, nom0, queue)); magma_ccopy( dofs, b.dval, 1, r.dval, 1, queue ); // r = b magma_ccopy( dofs, r.dval, 1, d.dval, 1, queue ); // d = r nom0 = betanom = magma_scnrm2( dofs, r.dval, 1, queue ); nom = nom0 * nom0; // nom = r' * r CHECK( magma_c_spmv( c_one, A, d, c_zero, z, queue )); // z = A d den = MAGMA_C_ABS( magma_cdotc( dofs, d.dval, 1, z.dval, 1, queue ) ); // den = d'* z solver_par->init_res = nom0; nomb = magma_scnrm2( dofs, b.dval, 1, queue ); if ( nomb == 0.0 ){ nomb=1.0; } // array on host for the parameters CHECK( magma_cmalloc_cpu( &skp_h, 6 )); alpha = rho = gamma = tmp1 = c_one; beta = magma_cdotc( dofs, r.dval, 1, r.dval, 1, queue ); skp_h[0]=alpha; skp_h[1]=beta; skp_h[2]=gamma; skp_h[3]=rho; skp_h[4]=tmp1; skp_h[5]=MAGMA_C_MAKE(nom, 0.0); magma_csetvector( 6, skp_h, 1, skp, 1, queue ); if( nom0 < solver_par->atol || nom0/nomb < solver_par->rtol ){ info = MAGMA_SUCCESS; goto cleanup; } 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] = (real_Double_t) nom0; solver_par->timing[0] = 0.0; } // check positive definite if (den <= 0.0) { info = MAGMA_NONSPD; 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++; // computes SpMV and dot product CHECK( magma_ccgmerge_spmv1( A, d1, d2, d.dval, z.dval, skp, queue )); solver_par->spmv_count++; // updates x, r, computes scalars and updates d CHECK( magma_ccgmerge_xrbeta( dofs, d1, d2, x->dval, r.dval, d.dval, z.dval, skp, queue )); // check stopping criterion (asynchronous copy) magma_cgetvector( 1 , skp+1, 1, skp_h+1, 1, queue ); betanom = sqrt(MAGMA_C_ABS(skp_h[1])); 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( betanom < solver_par->atol || betanom/nomb < solver_par->rtol ) { break; } } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue)); solver_par->iter_res = betanom; 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) betanom; 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->atol || solver_par->iter_res/solver_par->init_res < solver_par->rtol ){ 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_DIVERGENCE; } cleanup: magma_cmfree(&r, queue ); magma_cmfree(&z, queue ); magma_cmfree(&d, queue ); magma_cmfree(&B, queue ); magma_cmfree(&C, queue ); magma_free( d1 ); magma_free( d2 ); magma_free( skp ); magma_free_cpu( skp_h ); solver_par->info = info; return info; } /* magma_ccg_merge */
extern "C" magma_int_t magma_clsqr( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_LSQR; solver_par->numiter = 0; solver_par->spmv_count = 0; magma_int_t m = A.num_rows * b.num_cols; magma_int_t n = A.num_cols * b.num_cols; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; // solver variables float s, nom0, r0, res=0, nomb, phibar, beta, alpha, c, rho, rhot, phi, thet, normr, normar, norma, sumnormd2, normd; // need to transpose the matrix magma_c_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR}; // GPU workspace magma_c_matrix r={Magma_CSR}, v={Magma_CSR}, z={Magma_CSR}, zt={Magma_CSR}, d={Magma_CSR}, vt={Magma_CSR}, q={Magma_CSR}, w={Magma_CSR}, u={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &v, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &z, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &vt,Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &q, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &w, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // transpose the matrix magma_cmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue ); magma_cmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue ); magma_cmfree(&Ah1, queue ); magma_cmtransposeconjugate( Ah2, &Ah1, queue ); magma_cmfree(&Ah2, queue ); Ah2.blocksize = A.blocksize; Ah2.alignment = A.alignment; magma_cmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue ); magma_cmfree(&Ah1, queue ); magma_cmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue ); magma_cmfree(&Ah2, queue ); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); solver_par->init_res = nom0; nomb = magma_scnrm2( m, 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] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } if ( nom0 < r0 ) { info = MAGMA_SUCCESS; goto cleanup; } magma_ccopy( m, b.dval, 1, u.dval, 1, queue ); beta = magma_scnrm2( m, u.dval, 1, queue ); magma_cscal( m, MAGMA_C_MAKE(1./beta, 0.0 ), u.dval, 1, queue ); normr = beta; c = 1.0; s = 0.0; phibar = beta; CHECK( magma_c_spmv( c_one, AT, u, c_zero, v, queue )); if( precond_par->solver == Magma_NONE ){ ; } else { CHECK( magma_c_applyprecond_right( MagmaTrans, A, v, &zt, precond_par, queue )); CHECK( magma_c_applyprecond_left( MagmaTrans, A, zt, &v, precond_par, queue )); } alpha = magma_scnrm2( n, v.dval, 1, queue ); magma_cscal( n, MAGMA_C_MAKE(1./alpha, 0.0 ), v.dval, 1, queue ); normar = alpha * beta; norma = 0; sumnormd2 = 0; //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); solver_par->numiter = 0; // start iteration do { solver_par->numiter++; if( precond_par->solver == Magma_NONE || A.num_rows != A.num_cols ) { magma_ccopy( n, v.dval, 1 , z.dval, 1, queue ); } else { CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, v, &zt, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, zt, &z, precond_par, queue )); } //CHECK( magma_c_spmv( c_one, A, z, MAGMA_C_MAKE(-alpha,0.0), u, queue )); CHECK( magma_c_spmv( c_one, A, z, c_zero, zt, queue )); magma_cscal( m, MAGMA_C_MAKE(-alpha, 0.0 ), u.dval, 1, queue ); magma_caxpy( m, c_one, zt.dval, 1, u.dval, 1, queue ); solver_par->spmv_count++; beta = magma_scnrm2( m, u.dval, 1, queue ); magma_cscal( m, MAGMA_C_MAKE(1./beta, 0.0 ), u.dval, 1, queue ); // norma = norm([norma alpha beta]); norma = sqrt(norma*norma + alpha*alpha + beta*beta ); //lsvec( solver_par->numiter-1 ) = normar / norma; thet = -s * alpha; rhot = c * alpha; rho = sqrt( rhot * rhot + beta * beta ); c = rhot / rho; s = - beta / rho; phi = c * phibar; phibar = s * phibar; // d = (z - thet * d) / rho; magma_cscal( n, MAGMA_C_MAKE(-thet, 0.0 ), d.dval, 1, queue ); magma_caxpy( n, c_one, z.dval, 1, d.dval, 1, queue ); magma_cscal( n, MAGMA_C_MAKE(1./rho, 0.0 ), d.dval, 1, queue ); normd = magma_scnrm2( n, d.dval, 1, queue ); sumnormd2 = sumnormd2 + normd*normd; // convergence check res = normr; if ( solver_par->verbose > 0 ) { tempo2 = magma_sync_wtime( queue ); if ( (solver_par->numiter)%solver_par->verbose == c_zero ) { 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; } } // check for convergence in A*x=b if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){ info = MAGMA_SUCCESS; break; } // check for convergence in min{|b-A*x|} if ( A.num_rows != A.num_cols && ( normar/(norma*normr) <= solver_par->rtol || normar <= solver_par->atol ) ){ printf("%% warning: quit from minimization convergence check.\n"); info = MAGMA_SUCCESS; break; } magma_caxpy( n, MAGMA_C_MAKE( phi, 0.0 ), d.dval, 1, x->dval, 1, queue ); normr = fabs(s) * normr; CHECK( magma_c_spmv( c_one, AT, u, c_zero, vt, queue )); solver_par->spmv_count++; if( precond_par->solver == Magma_NONE ){ ; } else { CHECK( magma_c_applyprecond_right( MagmaTrans, A, vt, &zt, precond_par, queue )); CHECK( magma_c_applyprecond_left( MagmaTrans, A, zt, &vt, precond_par, queue )); } magma_cscal( n, MAGMA_C_MAKE(-beta, 0.0 ), v.dval, 1, queue ); magma_caxpy( n, c_one, vt.dval, 1, v.dval, 1, queue ); alpha = magma_scnrm2( n, v.dval, 1, queue ); magma_cscal( n, MAGMA_C_MAKE(1./alpha, 0.0 ), v.dval, 1, queue ); normar = alpha * fabs(s*phi); } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( 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 ) { 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 == c_zero ) { 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*solver_par->init_res || solver_par->iter_res < solver_par->atol ) { info = MAGMA_SUCCESS; } } else { if ( solver_par->verbose > 0 ) { if ( (solver_par->numiter)%solver_par->verbose == c_zero ) { 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_cmfree(&r, queue ); magma_cmfree(&v, queue ); magma_cmfree(&z, queue ); magma_cmfree(&zt, queue ); magma_cmfree(&d, queue ); magma_cmfree(&vt, queue ); magma_cmfree(&q, queue ); magma_cmfree(&u, queue ); magma_cmfree(&w, queue ); magma_cmfree(&AT, queue ); magma_cmfree(&Ah1, queue ); magma_cmfree(&Ah2, queue ); solver_par->info = info; return info; } /* magma_cqmr */
extern "C" magma_int_t magma_cbicgstab( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { // set queue for old dense routines magma_queue_t orig_queue; magmablasGetKernelStream( &orig_queue ); // prepare solver feedback solver_par->solver = Magma_BICGSTAB; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE, c_mone = MAGMA_C_NEG_ONE; magma_int_t dofs = A.num_rows; // workspace magma_c_vector r,rr,p,v,s,t; magma_c_vinit( &r, Magma_DEV, dofs, c_zero, queue ); magma_c_vinit( &rr, Magma_DEV, dofs, c_zero, queue ); magma_c_vinit( &p, Magma_DEV, dofs, c_zero, queue ); magma_c_vinit( &v, Magma_DEV, dofs, c_zero, queue ); magma_c_vinit( &s, Magma_DEV, dofs, c_zero, queue ); magma_c_vinit( &t, Magma_DEV, dofs, c_zero, queue ); // solver variables magmaFloatComplex alpha, beta, omega, rho_old, rho_new; float nom, betanom, nom0, r0, den, res; // solver setup magma_cscal( dofs, c_zero, x->dval, 1) ; // x = 0 magma_ccopy( dofs, b.dval, 1, r.dval, 1 ); // r = b magma_ccopy( dofs, b.dval, 1, rr.dval, 1 ); // rr = b nom0 = betanom = magma_scnrm2( dofs, r.dval, 1 ); // nom = || r || nom = nom0*nom0; rho_old = omega = alpha = MAGMA_C_MAKE( 1.0, 0. ); solver_par->init_res = nom0; magma_c_spmv( c_one, A, r, c_zero, v, queue ); // z = A r den = MAGMA_C_REAL( magma_cdotc(dofs, v.dval, 1, r.dval, 1) ); // den = z' * r if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) r0 = ATOLERANCE; if ( nom < r0 ) { magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } // check positive definite if (den <= 0.0) { printf("Operator A is not postive definite. (Ar,r) = %f\n", den); magmablasSetKernelStream( orig_queue ); return MAGMA_NONSPD; solver_par->info = MAGMA_NONSPD;; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = nom0; solver_par->timing[0] = 0.0; } // start iteration for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; solver_par->numiter++ ) { rho_new = magma_cdotc( dofs, rr.dval, 1, r.dval, 1 ); // rho=<rr,r> beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega magma_cscal( dofs, beta, p.dval, 1 ); // p = beta*p magma_caxpy( dofs, c_mone * omega * beta, v.dval, 1 , p.dval, 1 ); // p = p-omega*beta*v magma_caxpy( dofs, c_one, r.dval, 1, p.dval, 1 ); // p = p+r magma_c_spmv( c_one, A, p, c_zero, v, queue ); // v = Ap alpha = rho_new / magma_cdotc( dofs, rr.dval, 1, v.dval, 1 ); magma_ccopy( dofs, r.dval, 1 , s.dval, 1 ); // s=r magma_caxpy( dofs, c_mone * alpha, v.dval, 1 , s.dval, 1 ); // s=s-alpha*v magma_c_spmv( c_one, A, s, c_zero, t, queue ); // t=As omega = magma_cdotc( dofs, t.dval, 1, s.dval, 1 ) // omega = <s,t>/<t,t> / magma_cdotc( dofs, t.dval, 1, t.dval, 1 ); magma_caxpy( dofs, alpha, p.dval, 1 , x->dval, 1 ); // x=x+alpha*p magma_caxpy( dofs, omega, s.dval, 1 , x->dval, 1 ); // x=x+omega*s magma_ccopy( dofs, s.dval, 1 , r.dval, 1 ); // r=s magma_caxpy( dofs, c_mone * omega, t.dval, 1 , r.dval, 1 ); // r=r-omega*t res = betanom = magma_scnrm2( dofs, r.dval, 1 ); nom = betanom*betanom; rho_old = rho_new; // rho_old=rho 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/nom0 < solver_par->epsilon ) { break; } } tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; magma_cresidual( A, b, *x, &residual, queue ); solver_par->iter_res = res; solver_par->final_res = residual; if ( solver_par->numiter < solver_par->maxiter) { solver_par->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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_SLOW_CONVERGENCE; } 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_DIVERGENCE; } magma_c_vfree(&r, queue ); magma_c_vfree(&rr, queue ); magma_c_vfree(&p, queue ); magma_c_vfree(&v, queue ); magma_c_vfree(&s, queue ); magma_c_vfree(&t, queue ); magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } /* magma_cbicgstab */
extern "C" magma_int_t magma_ccg( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { magma_int_t info = 0; // set queue for old dense routines magma_queue_t orig_queue=NULL; magmablasGetKernelStream( &orig_queue ); // prepare solver feedback solver_par->solver = Magma_CG; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows * b.num_cols; // GPU workspace magma_c_matrix r={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver variables magmaFloatComplex alpha, beta; float nom, nom0, r0, betanom, betanomsq, den; // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); magma_ccopy( dofs, r.dval, 1, p.dval, 1 ); // p = r betanom = nom0; nom = nom0 * nom0; // nom = r' * r CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p den = MAGMA_C_REAL( magma_cdotc(dofs, p.dval, 1, q.dval, 1) );// den = p dot q solver_par->init_res = nom0; if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) r0 = ATOLERANCE; if ( nom < r0 ) { solver_par->final_res = solver_par->init_res; solver_par->iter_res = solver_par->init_res; goto cleanup; } // check positive definite if (den <= 0.0) { printf("Operator A is not postive definite. (Ar,r) = %f\n", den); magmablasSetKernelStream( orig_queue ); info = MAGMA_NONSPD; goto cleanup; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } solver_par->numiter = 0; // start iteration do { solver_par->numiter++; alpha = MAGMA_C_MAKE(nom/den, 0.); magma_caxpy(dofs, alpha, p.dval, 1, x->dval, 1); // x = x + alpha p magma_caxpy(dofs, -alpha, q.dval, 1, r.dval, 1); // r = r - alpha q betanom = magma_scnrm2(dofs, r.dval, 1); // betanom = || r || betanomsq = betanom * betanom; // betanoms = r' * r 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( betanom < r0 ) { break; } beta = MAGMA_C_MAKE(betanomsq/nom, 0.); // beta = betanoms/nom magma_cscal(dofs, beta, p.dval, 1); // p = beta*p magma_caxpy(dofs, c_one, r.dval, 1, p.dval, 1); // p = p + r CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p den = MAGMA_C_REAL(magma_cdotc(dofs, p.dval, 1, q.dval, 1)); // den = p dot q nom = betanomsq; } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue)); solver_par->final_res = residual; if ( solver_par->numiter < solver_par->maxiter ) { solver_par->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) betanom; 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->epsilon*solver_par->init_res ){ 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } info = MAGMA_DIVERGENCE; } cleanup: magma_cmfree(&r, queue ); magma_cmfree(&p, queue ); magma_cmfree(&q, queue ); magmablasSetKernelStream( orig_queue ); solver_par->info = info; return info; } /* magma_ccg */
extern "C" magma_int_t magma_citerref( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = 0; // set queue for old dense routines magma_queue_t orig_queue=NULL; magmablasGetKernelStream( &orig_queue ); // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE, c_mone = MAGMA_C_NEG_ONE; // prepare solver feedback solver_par->solver = Magma_ITERREF; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; magma_int_t dofs = A.num_rows*b.num_cols; // solver variables float nom, nom0, r0; // workspace magma_c_matrix r={Magma_CSR}, z={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); float residual; CHECK( magma_cresidual( A, b, *x, &residual, queue )); solver_par->init_res = residual; // solver setup magma_cscal( dofs, c_zero, x->dval, 1) ; // x = 0 //CHECK( magma_cresidualvec( A, b, *x, &r, nom, queue)); magma_ccopy( dofs, b.dval, 1, r.dval, 1 ); // r = b nom0 = magma_scnrm2(dofs, r.dval, 1); // nom0 = || r || nom = nom0 * nom0; solver_par->init_res = nom0; if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) r0 = ATOLERANCE; if ( nom < r0 ) { solver_par->final_res = solver_par->init_res; solver_par->iter_res = solver_par->init_res; goto cleanup; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = nom0; solver_par->timing[0] = 0.0; } // start iteration for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; solver_par->numiter++ ) { magma_cscal( dofs, MAGMA_C_MAKE(1./nom, 0.), r.dval, 1) ; // scale it CHECK( magma_c_precond( A, r, &z, precond_par, queue )); // inner solver: A * z = r magma_cscal( dofs, MAGMA_C_MAKE(nom, 0.), z.dval, 1) ; // scale it magma_caxpy(dofs, c_one, z.dval, 1, x->dval, 1); // x = x + z CHECK( magma_c_spmv( c_mone, A, *x, c_zero, r, queue )); // r = - A x magma_caxpy(dofs, c_one, b.dval, 1, r.dval, 1); // r = r + b nom = magma_scnrm2(dofs, r.dval, 1); // nom = || r || 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) nom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( nom < r0 ) { break; } } tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue)); solver_par->final_res = residual; solver_par->iter_res = nom; if ( solver_par->numiter < solver_par->maxiter ) { solver_par->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) nom; 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->epsilon*solver_par->init_res ){ 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) nom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } info = MAGMA_DIVERGENCE; } cleanup: magma_cmfree(&r, queue ); magma_cmfree(&z, queue ); magmablasSetKernelStream( orig_queue ); solver_par->info = info; return info; } /* magma_citerref */
extern "C" magma_int_t magma_cpcgs_merge( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_PCGS; solver_par->numiter = 0; solver_par->spmv_count = 0; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; // solver variables float nom0, r0, res, nomb; magmaFloatComplex rho, rho_l = c_one, alpha, beta; magma_int_t dofs = A.num_rows* b.num_cols; // GPU workspace magma_c_matrix r={Magma_CSR}, rt={Magma_CSR}, r_tld={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}, u={Magma_CSR}, v={Magma_CSR}, t={Magma_CSR}, p_hat={Magma_CSR}, q_hat={Magma_CSR}, u_hat={Magma_CSR}, v_hat={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &r_tld,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); magma_ccopy( dofs, r.dval, 1, r_tld.dval, 1, queue ); solver_par->init_res = nom0; nomb = magma_scnrm2( 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] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } if ( nom0 < r0 ) { info = MAGMA_SUCCESS; goto cleanup; } //Chronometry real_Double_t tempo1, tempo2, tempop1, tempop2; tempo1 = magma_sync_wtime( queue ); solver_par->numiter = 0; solver_par->spmv_count = 0; // start iteration do { solver_par->numiter++; rho = magma_cdotc( dofs, r.dval, 1, r_tld.dval, 1, queue ); // rho = < r,r_tld> if ( MAGMA_C_ABS(rho) == 0.0 ) { goto cleanup; } if ( solver_par->numiter > 1 ) { // direction vectors beta = rho / rho_l; magma_ccgs_1( r.num_rows, r.num_cols, beta, r.dval, q.dval, u.dval, p.dval, queue ); //u = r + beta*q; //p = u + beta*( q + beta*p ); } else{ magma_ccgs_2( r.num_rows, r.num_cols, r.dval, u.dval, p.dval, queue ); // u = r // p = r } // preconditioner tempop1 = magma_sync_wtime( queue ); CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, p, &rt, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &p_hat, precond_par, queue )); tempop2 = magma_sync_wtime( queue ); precond_par->runtime += tempop2-tempop1; CHECK( magma_c_spmv( c_one, A, p_hat, c_zero, v_hat, queue )); // v = A p solver_par->spmv_count++; alpha = rho / magma_cdotc( dofs, r_tld.dval, 1, v_hat.dval, 1, queue ); magma_ccgs_3( r.num_rows, r.num_cols, alpha, v_hat.dval, u.dval, q.dval, t.dval, queue ); // q = u - alpha v_hat // t = u + q // preconditioner tempop1 = magma_sync_wtime( queue ); CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, t, &rt, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &u_hat, precond_par, queue )); tempop2 = magma_sync_wtime( queue ); precond_par->runtime += tempop2-tempop1; CHECK( magma_c_spmv( c_one, A, u_hat, c_zero, t, queue )); // t = A u_hat solver_par->spmv_count++; magma_ccgs_4( r.num_rows, r.num_cols, alpha, u_hat.dval, t.dval, x->dval, r.dval, queue ); // r = r -alpha*A u_hat // x = x + alpha u_hat res = magma_scnrm2( 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; } rho_l = rho; } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( 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*solver_par->init_res || 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_cmfree(&r, queue ); magma_cmfree(&rt, queue ); magma_cmfree(&r_tld, queue ); magma_cmfree(&p, queue ); magma_cmfree(&q, queue ); magma_cmfree(&u, queue ); magma_cmfree(&v, queue ); magma_cmfree(&t, queue ); magma_cmfree(&p_hat, queue ); magma_cmfree(&q_hat, queue ); magma_cmfree(&u_hat, queue ); magma_cmfree(&v_hat, queue ); solver_par->info = info; return info; } /* magma_cpcgs_merge */
extern "C" magma_int_t magma_cbombard( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // 1=QMR, 2=CGS, 3+BiCGSTAB magma_int_t flag = 0; // prepare solver feedback solver_par->solver = Magma_BOMBARD; solver_par->numiter = 0; solver_par->spmv_count = 0; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; // solver variables float nom0, r0, res, Q_res, T_res, C_res, B_res, nomb; //QMR magmaFloatComplex Q_rho = c_one, Q_rho1 = c_one, Q_eta = -c_one , Q_pds = c_one, Q_thet = c_one, Q_thet1 = c_one, Q_epsilon = c_one, Q_beta = c_one, Q_delta = c_one, Q_pde = c_one, Q_rde = c_one, Q_gamm = c_one, Q_gamm1 = c_one, Q_psi = c_one; //TFQMR magmaFloatComplex T_rho = c_one, T_rho_l = c_one, T_eta = c_zero , T_c = c_zero , T_theta = c_zero , T_tau = c_zero, T_alpha = c_one, T_beta = c_zero, T_sigma = c_zero; //CGS magmaFloatComplex C_rho, C_rho_l = c_one, C_alpha, C_beta = c_zero; //BiCGSTAB magmaFloatComplex B_alpha, B_beta, B_omega, B_rho_old, B_rho_new; magma_int_t dofs = A.num_rows* b.num_cols; // need to transpose the matrix // GPU workspace // QMR magma_c_matrix AT = {Magma_CSR}, Ah1 = {Magma_CSR}, Ah2 = {Magma_CSR}, Q_r={Magma_CSR}, r_tld={Magma_CSR}, Q_x={Magma_CSR}, Q_v={Magma_CSR}, Q_w={Magma_CSR}, Q_wt={Magma_CSR}, Q_d={Magma_CSR}, Q_s={Magma_CSR}, Q_z={Magma_CSR}, Q_q={Magma_CSR}, Q_p={Magma_CSR}, Q_pt={Magma_CSR}, Q_y={Magma_CSR}, d1={Magma_CSR}, d2={Magma_CSR}; //TFQMR // GPU workspace magma_c_matrix T_r={Magma_CSR}, T_pu_m={Magma_CSR}, T_x={Magma_CSR}, T_d={Magma_CSR}, T_w={Magma_CSR}, T_v={Magma_CSR}, T_u_mp1={Magma_CSR}, T_u_m={Magma_CSR}, T_Au={Magma_CSR}, T_Ad={Magma_CSR}, T_Au_new={Magma_CSR}; // CGS magma_c_matrix C_r={Magma_CSR}, C_rt={Magma_CSR}, C_x={Magma_CSR}, C_p={Magma_CSR}, C_q={Magma_CSR}, C_u={Magma_CSR}, C_v={Magma_CSR}, C_t={Magma_CSR}, C_p_hat={Magma_CSR}, C_q_hat={Magma_CSR}, C_u_hat={Magma_CSR}, C_v_hat={Magma_CSR}; //BiCGSTAB magma_c_matrix B_r={Magma_CSR}, B_x={Magma_CSR}, B_p={Magma_CSR}, B_v={Magma_CSR}, B_s={Magma_CSR}, B_t={Magma_CSR}; CHECK( magma_cvinit( &r_tld, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d1, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d2, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // QMR CHECK( magma_cvinit( &Q_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Q_x, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // TFQMR CHECK( magma_cvinit( &T_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &T_u_mp1,Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &T_u_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &T_pu_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &T_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &T_d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &T_w, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &T_Ad, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &T_Au_new, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &T_Au, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &T_x, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // CGS CHECK( magma_cvinit( &C_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_x,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &C_t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // BiCGSTAB CHECK( magma_cvinit( &B_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &B_x,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &B_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &B_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &B_s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &B_t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r_tld, &nom0, queue)); solver_par->init_res = nom0; res = nom0; // QMR magma_ccopy( dofs, r_tld.dval, 1, Q_r.dval, 1, queue ); magma_ccopy( dofs, r_tld.dval, 1, Q_y.dval, 1, queue ); magma_ccopy( dofs, r_tld.dval, 1, Q_v.dval, 1, queue ); magma_ccopy( dofs, r_tld.dval, 1, Q_wt.dval, 1, queue ); magma_ccopy( dofs, r_tld.dval, 1, Q_z.dval, 1, queue ); magma_ccopy( dofs, x->dval, 1, Q_x.dval, 1, queue ); // transpose the matrix // transpose the matrix magma_cmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue ); magma_cmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue ); magma_cmfree(&Ah1, queue ); magma_cmtransposeconjugate( Ah2, &Ah1, queue ); magma_cmfree(&Ah2, queue ); Ah2.blocksize = A.blocksize; Ah2.alignment = A.alignment; magma_cmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue ); magma_cmfree(&Ah1, queue ); magma_cmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue ); magma_cmfree(&Ah2, queue ); // TFQMR solver_par->init_res = nom0; magma_ccopy( dofs, r_tld.dval, 1, T_r.dval, 1, queue ); magma_ccopy( dofs, T_r.dval, 1, T_w.dval, 1, queue ); magma_ccopy( dofs, T_r.dval, 1, T_u_m.dval, 1, queue ); magma_ccopy( dofs, T_r.dval, 1, T_u_mp1.dval, 1, queue ); magma_ccopy( dofs, T_u_m.dval, 1, T_pu_m.dval, 1, queue ); CHECK( magma_c_spmv( c_one, A, T_pu_m, c_zero, T_v, queue )); magma_ccopy( dofs, T_v.dval, 1, T_Au.dval, 1, queue ); // CGS magma_ccopy( dofs, r_tld.dval, 1, C_r.dval, 1, queue ); magma_ccopy( dofs, x->dval, 1, C_x.dval, 1, queue ); // BiCGSTAB magma_ccopy( dofs, r_tld.dval, 1, B_r.dval, 1, queue ); magma_ccopy( dofs, x->dval, 1, B_x.dval, 1, queue ); CHECK( magma_c_spmv( c_one, A, B_r, c_zero, B_v, queue )); nomb = magma_scnrm2( 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] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } if ( nom0 < r0 ) { info = MAGMA_SUCCESS; goto cleanup; } T_tau = magma_csqrt( magma_cdotc( dofs, T_r.dval, 1, r_tld.dval, 1, queue) ); T_rho = magma_cdotc( dofs, T_r.dval, 1, r_tld.dval, 1, queue ); T_rho_l = T_rho; Q_psi = magma_csqrt( magma_cdotc( dofs, Q_z.dval, 1, Q_z.dval, 1, queue )); Q_rho = magma_csqrt( magma_cdotc( dofs, Q_y.dval, 1, Q_y.dval, 1, queue )); // BiCGSTAB B_rho_new = magma_cdotc( dofs, B_r.dval, 1, B_r.dval, 1, queue ); B_rho_old = B_omega = B_alpha = MAGMA_C_MAKE( 1.0, 0. ); // v = y / rho // y = y / rho // w = wt / psi // z = z / psi magma_cqmr_1( b.num_rows, b.num_cols, Q_rho, Q_psi, Q_y.dval, Q_z.dval, Q_v.dval, Q_w.dval, queue ); //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++; //QMR: delta = z' * y; Q_delta = magma_cdotc( dofs, Q_z.dval, 1, Q_y.dval, 1, queue ); // TFQMR T_alpha = T_rho / magma_cdotc( dofs, T_v.dval, 1, r_tld.dval, 1, queue ); T_sigma = T_theta * T_theta / T_alpha * T_eta; //CGS: rho = r' * r_tld C_rho = magma_cdotc( dofs, C_r.dval, 1, r_tld.dval, 1, queue ); // BiCGSTAB B_rho_old = B_rho_new; B_rho_new = magma_cdotc( dofs, r_tld.dval, 1, B_r.dval, 1, queue ); // rho=<rr,r> B_beta = B_rho_new/B_rho_old * B_alpha/B_omega; // beta=rho/rho_old *alpha/omega if( solver_par->numiter == 1 ){ //QMR: p = y; //QMR: q = z; magma_ccopy( dofs, Q_y.dval, 1, Q_p.dval, 1, queue ); magma_ccopy( dofs, Q_z.dval, 1, Q_q.dval, 1, queue ); //QMR: u = r; //QMR: p = r; magma_ccgs_2( b.num_rows, b.num_cols, C_r.dval, C_u.dval, C_p.dval, queue ); } else{ Q_pde = Q_psi * Q_delta / Q_epsilon; Q_rde = Q_rho * MAGMA_C_CONJ(Q_delta/Q_epsilon); C_beta = C_rho / C_rho_l; //QMR p = y - pde * p //QMR q = z - rde * q magma_cqmr_2( b.num_rows, b.num_cols, Q_pde, Q_rde, Q_y.dval, Q_z.dval, Q_p.dval, Q_q.dval, queue ); //CGS: u = r + beta*q; //CGS: p = u + beta*( q + beta*p ); magma_ccgs_1( b.num_rows, b.num_cols, C_beta, C_r.dval, C_q.dval, C_u.dval, C_p.dval, queue ); } // TFQMR magma_ctfqmr_1( b.num_rows, b.num_cols, T_alpha, T_sigma, T_v.dval, T_Au.dval, T_u_m.dval, T_pu_m.dval, T_u_mp1.dval, T_w.dval, T_d.dval, T_Ad.dval, queue ); T_theta = magma_csqrt( magma_cdotc(dofs, T_w.dval, 1, T_w.dval, 1, queue) ) / T_tau; T_c = c_one / magma_csqrt( c_one + T_theta*T_theta ); T_tau = T_tau * T_theta *T_c; T_eta = T_c * T_c * T_alpha; T_sigma = T_theta * T_theta / T_alpha * T_eta; magma_ctfqmr_2( b.num_rows, b.num_cols, T_eta, T_d.dval, T_Ad.dval, T_x.dval, T_r.dval, queue ); magma_ccopy( dofs, T_u_mp1.dval, 1, T_pu_m.dval, 1, queue ); // BiCGSTAB: p = r + beta * ( p - omega * v ) magma_cbicgstab_1( b.num_rows, b.num_cols, B_beta, B_omega, B_r.dval, B_v.dval, B_p.dval, queue ); //QMR CHECK( magma_c_spmv( c_one, A, Q_p, c_zero, Q_pt, queue )); //TFQMR CHECK( magma_c_spmv( c_one, A, T_pu_m, c_zero, T_Au_new, queue )); //CGS CHECK( magma_c_spmv( c_one, A, C_p, c_zero, C_v_hat, queue )); // BiCGSTAB CHECK( magma_c_spmv( c_one, A, B_p, c_zero, B_v, queue )); // v = Ap solver_par->spmv_count++; //QMR: epsilon = q' * pt; Q_epsilon = magma_cdotc( dofs, Q_q.dval, 1, Q_pt.dval, 1, queue ); Q_beta = Q_epsilon / Q_delta; //TFQMR magma_ccopy( dofs, T_Au_new.dval, 1, T_Au.dval, 1, queue ); magma_ccopy( dofs, T_u_mp1.dval, 1, T_u_m.dval, 1, queue ); //CGS: alpha = r_tld' * v_hat C_alpha = C_rho / magma_cdotc( dofs, r_tld.dval, 1, C_v_hat.dval, 1, queue ); //BiCGSTAB B_alpha = B_rho_new / magma_cdotc( dofs, r_tld.dval, 1, B_v.dval, 1, queue ); //QMR: v = pt - beta * v //QMR: y = v magma_cqmr_3( b.num_rows, b.num_cols, Q_beta, Q_pt.dval, Q_v.dval, Q_y.dval, queue ); // TFQMR magma_ctfqmr_5( b.num_rows, b.num_cols, T_alpha, T_sigma, T_v.dval, T_Au.dval, T_pu_m.dval, T_w.dval, T_d.dval, T_Ad.dval, queue ); // TFQMR T_sigma = T_theta * T_theta / T_alpha * T_eta; T_theta = magma_csqrt( magma_cdotc(dofs, T_w.dval, 1, T_w.dval, 1, queue) ) / T_tau; T_c = c_one / magma_csqrt( c_one + T_theta*T_theta ); T_tau = T_tau * T_theta *T_c; T_eta = T_c * T_c * T_alpha; // TFQMR magma_ctfqmr_2( b.num_rows, b.num_cols, T_eta, T_d.dval, T_Ad.dval, T_x.dval, T_r.dval, queue ); T_rho = magma_cdotc( dofs, T_w.dval, 1, r_tld.dval, 1, queue ); T_beta = T_rho / T_rho_l; T_rho_l = T_rho; magma_ctfqmr_3( b.num_rows, b.num_cols, T_beta, T_w.dval, T_u_m.dval, T_u_mp1.dval, queue ); magma_ccopy( dofs, T_u_mp1.dval, 1, T_pu_m.dval, 1, queue ); //CGS: q = u - alpha v_hat //CGS: t = u + q magma_ccgs_3( b.num_rows, b.num_cols, C_alpha, C_v_hat.dval, C_u.dval, C_q.dval, C_t.dval, queue ); // BiCGSTAB: s = r - alpha v magma_cbicgstab_2( b.num_rows, b.num_cols, B_alpha, B_r.dval, B_v.dval, B_s.dval, queue ); Q_rho1 = Q_rho; //QMR rho = norm(y); Q_rho = magma_csqrt( magma_cdotc( dofs, Q_y.dval, 1, Q_y.dval, 1, queue ) ); //QMR wt = A' * q - beta' * w; CHECK( magma_c_spmv( c_one, AT, Q_q, c_zero, Q_wt, queue )); //TFQMR CHECK( magma_c_spmv( c_one, A, T_pu_m, c_zero, T_Au_new, queue )); //CGS t = A u_hat CHECK( magma_c_spmv( c_one, A, C_t, c_zero, C_rt, queue )); //BiCGSTAB CHECK( magma_c_spmv( c_one, A, B_s, c_zero, B_t, queue )); // t=As solver_par->spmv_count++; //BiCGSTAB B_omega = magma_cdotc( dofs, B_t.dval, 1, B_s.dval, 1, queue ) // omega = <s,t>/<t,t> / magma_cdotc( dofs, B_t.dval, 1, B_t.dval, 1, queue ); // QMR magma_caxpy( dofs, - MAGMA_C_CONJ( Q_beta ), Q_w.dval, 1, Q_wt.dval, 1, queue ); // no precond: z = wt magma_ccopy( dofs, Q_wt.dval, 1, Q_z.dval, 1, queue ); //TFQMR magma_ctfqmr_4( b.num_rows, b.num_cols, T_beta, T_Au_new.dval, T_v.dval, T_Au.dval, queue ); magma_ccopy( dofs, T_u_mp1.dval, 1, T_u_m.dval, 1, queue ); // QMR Q_thet1 = Q_thet; Q_thet = Q_rho / (Q_gamm * MAGMA_C_MAKE( MAGMA_C_ABS(Q_beta), 0.0 )); Q_gamm1 = Q_gamm; Q_gamm = c_one / magma_csqrt(c_one + Q_thet*Q_thet); Q_eta = - Q_eta * Q_rho1 * Q_gamm * Q_gamm / (Q_beta * Q_gamm1 * Q_gamm1); if ( solver_par->numiter == 1 ) { //QMR: d = eta * p + pds * d; //QMR: s = eta * pt + pds * d; //QMR: x = x + d; //QMR: r = r - s; magma_cqmr_4( b.num_rows, b.num_cols, Q_eta, Q_p.dval, Q_pt.dval, Q_d.dval, Q_s.dval, Q_x.dval, Q_r.dval, queue ); } else { Q_pds = (Q_thet1 * Q_gamm) * (Q_thet1 * Q_gamm); // d = eta * p + pds * d; // s = eta * pt + pds * d; // x = x + d; // r = r - s; magma_cqmr_5( b.num_rows, b.num_cols, Q_eta, Q_pds, Q_p.dval, Q_pt.dval, Q_d.dval, Q_s.dval, Q_x.dval, Q_r.dval, queue ); } // CGS: r = r -alpha*A u_hat // CGS: x = x + alpha u_hat magma_ccgs_4( b.num_rows, b.num_cols, C_alpha, C_t.dval, C_rt.dval, C_x.dval, C_r.dval, queue ); C_rho_l = C_rho; // BiCGSTAB: x = x + alpha * p + omega * s // BiCGSTAB: r = s - omega * t magma_cbicgstab_3( b.num_rows, b.num_cols, B_alpha, B_omega, B_p.dval, B_s.dval, B_t.dval, B_x.dval, B_r.dval, queue ); //QMR: psi = norm(z); Q_psi = magma_csqrt( magma_cdotc( dofs, Q_z.dval, 1, Q_z.dval, 1, queue ) ); //QMR: v = y / rho //QMR: y = y / rho //QMR: w = wt / psi //QMR: z = z / psi magma_cqmr_1( b.num_rows, b.num_cols, Q_rho, Q_psi, Q_y.dval, Q_z.dval, Q_v.dval, Q_w.dval, queue ); Q_res = magma_scnrm2( dofs, Q_r.dval, 1, queue ); T_res = magma_scnrm2( dofs, T_r.dval, 1, queue ); C_res = magma_scnrm2( dofs, C_r.dval, 1, queue ); B_res = magma_scnrm2( dofs, B_r.dval, 1, queue ); // printf(" %e %e %e\n", Q_res, C_res, B_res); if( Q_res < res ){ res = Q_res; flag = 1; } if( T_res < res ){ res = Q_res; flag = 2; } if( C_res < res ){ res = C_res; flag = 3; } if( B_res < res ){ res = B_res; flag = 4; } if ( solver_par->verbose > 0 ) { tempo2 = magma_sync_wtime( queue ); if ( (solver_par->numiter)%solver_par->verbose == c_zero ) { 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 ){ info = MAGMA_SUCCESS; break; } if( magma_c_isnan_inf( Q_beta ) && magma_c_isnan_inf( C_beta ) && magma_c_isnan_inf( B_beta ) ){ info = MAGMA_DIVERGENCE; break; } } while ( solver_par->numiter+1 <= solver_par->maxiter ); // copy back the best solver switch ( flag ) { case 1: printf("%% QMR fastest solver.\n"); magma_ccopy( dofs, Q_x.dval, 1, x->dval, 1, queue ); break; case 2: printf("%% TFQMR fastest solver.\n"); magma_ccopy( dofs, T_x.dval, 1, x->dval, 1, queue ); break; case 3: printf("%% CGS fastest solver.\n"); magma_ccopy( dofs, C_x.dval, 1, x->dval, 1, queue ); break; case 4: printf("%% BiCGSTAB fastest solver.\n"); magma_ccopy( dofs, B_x.dval, 1, x->dval, 1, queue ); break; } tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( A, b, *x, &r_tld, &residual, queue)); solver_par->iter_res = res; solver_par->final_res = residual; if ( solver_par->numiter < solver_par->maxiter && info == MAGMA_SUCCESS ) { 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 == c_zero ) { 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*solver_par->init_res || solver_par->iter_res < solver_par->atol ) { info = MAGMA_SUCCESS; } } else { if ( solver_par->verbose > 0 ) { if ( (solver_par->numiter)%solver_par->verbose == c_zero ) { 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_cmfree(&r_tld, queue ); magma_cmfree(&d1, queue ); magma_cmfree(&d2, queue ); magma_cmfree(&AT, queue ); // QMR magma_cmfree(&Q_r, queue ); magma_cmfree(&Q_v, queue ); magma_cmfree(&Q_w, queue ); magma_cmfree(&Q_wt, queue ); magma_cmfree(&Q_d, queue ); magma_cmfree(&Q_s, queue ); magma_cmfree(&Q_z, queue ); magma_cmfree(&Q_q, queue ); magma_cmfree(&Q_p, queue ); magma_cmfree(&Q_pt, queue ); magma_cmfree(&Q_y, queue ); magma_cmfree(&Q_x, queue ); magma_cmfree(&Ah1, queue ); magma_cmfree(&Ah2, queue ); // TFQMR magma_cmfree(&T_r, queue ); magma_cmfree(&T_x, queue ); magma_cmfree(&T_d, queue ); magma_cmfree(&T_w, queue ); magma_cmfree(&T_v, queue ); magma_cmfree(&T_u_m, queue ); magma_cmfree(&T_u_mp1, queue ); magma_cmfree(&T_pu_m, queue ); magma_cmfree(&T_d, queue ); magma_cmfree(&T_Au, queue ); magma_cmfree(&T_Au_new, queue ); magma_cmfree(&T_Ad, queue ); // CGS magma_cmfree(&C_r, queue ); magma_cmfree(&C_rt, queue ); magma_cmfree(&C_x, queue ); magma_cmfree(&C_p, queue ); magma_cmfree(&C_q, queue ); magma_cmfree(&C_u, queue ); magma_cmfree(&C_v, queue ); magma_cmfree(&C_t, queue ); magma_cmfree(&C_p_hat, queue ); magma_cmfree(&C_q_hat, queue ); magma_cmfree(&C_u_hat, queue ); magma_cmfree(&C_v_hat, queue ); // BiCGSTAB magma_cmfree(&B_r, queue ); magma_cmfree(&B_x, queue ); magma_cmfree(&B_p, queue ); magma_cmfree(&B_v, queue ); magma_cmfree(&B_s, queue ); magma_cmfree(&B_t, queue ); solver_par->info = info; return info; } /* magma_cbombard */
extern "C" magma_int_t magma_cbpcg( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { // set queue for old dense routines magma_queue_t orig_queue; magmablasGetKernelStream( &orig_queue ); magma_int_t stat_dev = 0, stat_cpu = 0; magma_int_t i, num_vecs = b.num_rows/A.num_rows; // prepare solver feedback solver_par->solver = Magma_PCG; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows; // GPU workspace magma_c_vector r, rt, p, q, h; magma_c_vinit( &r, Magma_DEV, dofs*num_vecs, c_zero, queue ); magma_c_vinit( &rt, Magma_DEV, dofs*num_vecs, c_zero, queue ); magma_c_vinit( &p, Magma_DEV, dofs*num_vecs, c_zero, queue ); magma_c_vinit( &q, Magma_DEV, dofs*num_vecs, c_zero, queue ); magma_c_vinit( &h, Magma_DEV, dofs*num_vecs, c_zero, queue ); // solver variables magmaFloatComplex *alpha, *beta; alpha = NULL; beta = NULL; stat_cpu += magma_cmalloc_cpu(&alpha, num_vecs); stat_cpu += magma_cmalloc_cpu(&beta, num_vecs); float *nom, *nom0, *r0, *gammaold, *gammanew, *den, *res, *residual; nom = NULL; nom0 = NULL; r0 = NULL; gammaold = NULL; gammanew = NULL; den = NULL; res = NULL; residual = NULL; stat_cpu += magma_smalloc_cpu(&residual, num_vecs); stat_cpu += magma_smalloc_cpu(&nom, num_vecs); stat_cpu += magma_smalloc_cpu(&nom0, num_vecs); stat_cpu += magma_smalloc_cpu(&r0, num_vecs); stat_cpu += magma_smalloc_cpu(&gammaold, num_vecs); stat_cpu += magma_smalloc_cpu(&gammanew, num_vecs); stat_cpu += magma_smalloc_cpu(&den, num_vecs); stat_cpu += magma_smalloc_cpu(&res, num_vecs); stat_cpu += magma_smalloc_cpu(&residual, num_vecs); if( stat_cpu != 0 ){ magma_free_cpu( nom ); magma_free_cpu( nom0 ); magma_free_cpu( r0 ); magma_free_cpu( gammaold ); magma_free_cpu( gammanew ); magma_free_cpu( den ); magma_free_cpu( res ); magma_free_cpu( alpha ); magma_free_cpu( beta ); magma_free_cpu( residual ); magmablasSetKernelStream( orig_queue ); printf("error: memory allocation.\n"); return MAGMA_ERR_HOST_ALLOC; } // solver setup magma_cscal( dofs*num_vecs, c_zero, x->dval, 1) ; // x = 0 magma_ccopy( dofs*num_vecs, b.dval, 1, r.dval, 1 ); // r = b // preconditioner magma_c_applyprecond_left( A, r, &rt, precond_par, queue ); magma_c_applyprecond_right( A, rt, &h, precond_par, queue ); magma_ccopy( dofs*num_vecs, h.dval, 1, p.dval, 1 ); // p = h for( i=0; i<num_vecs; i++) { nom[i] = MAGMA_C_REAL( magma_cdotc(dofs, r(i), 1, h(i), 1) ); nom0[i] = magma_scnrm2( dofs, r(i), 1 ); } magma_c_spmv( c_one, A, p, c_zero, q, queue ); // q = A p for( i=0; i<num_vecs; i++) den[i] = MAGMA_C_REAL( magma_cdotc(dofs, p(i), 1, q(i), 1) ); // den = p dot q solver_par->init_res = nom0[0]; if ( (r0[0] = nom[0] * solver_par->epsilon) < ATOLERANCE ) r0[0] = ATOLERANCE; // check positive definite if (den[0] <= 0.0) { printf("Operator A is not postive definite. (Ar,r) = %f\n", den[0]); magmablasSetKernelStream( orig_queue ); return MAGMA_NONSPD; solver_par->info = MAGMA_NONSPD;; } if ( nom[0] < r0[0] ) { magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = (real_Double_t)nom0[0]; solver_par->timing[0] = 0.0; } // start iteration for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; solver_par->numiter++ ) { // preconditioner magma_c_applyprecond_left( A, r, &rt, precond_par, queue ); magma_c_applyprecond_right( A, rt, &h, precond_par, queue ); for( i=0; i<num_vecs; i++) gammanew[i] = MAGMA_C_REAL( magma_cdotc(dofs, r(i), 1, h(i), 1) ); // gn = < r,h> if ( solver_par->numiter==1 ) { magma_ccopy( dofs*num_vecs, h.dval, 1, p.dval, 1 ); // p = h } else { for( i=0; i<num_vecs; i++) { beta[i] = MAGMA_C_MAKE(gammanew[i]/gammaold[i], 0.); // beta = gn/go magma_cscal(dofs, beta[i], p(i), 1); // p = beta*p magma_caxpy(dofs, c_one, h(i), 1, p(i), 1); // p = p + h } } magma_c_spmv( c_one, A, p, c_zero, q, queue ); // q = A p // magma_c_bspmv_tuned( dofs, num_vecs, c_one, A, p.dval, c_zero, q.dval, queue ); for( i=0; i<num_vecs; i++) { den[i] = MAGMA_C_REAL(magma_cdotc(dofs, p(i), 1, q(i), 1)); // den = p dot q alpha[i] = MAGMA_C_MAKE(gammanew[i]/den[i], 0.); magma_caxpy(dofs, alpha[i], p(i), 1, x->dval+dofs*i, 1); // x = x + alpha p magma_caxpy(dofs, -alpha[i], q(i), 1, r(i), 1); // r = r - alpha q gammaold[i] = gammanew[i]; res[i] = magma_scnrm2( dofs, r(i), 1 ); } 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[0]; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( res[0]/nom0[0] < solver_par->epsilon ) { break; } } tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; magma_cresidual( A, b, *x, residual, queue ); solver_par->iter_res = res[0]; solver_par->final_res = residual[0]; if ( solver_par->numiter < solver_par->maxiter) { solver_par->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[0]; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_SLOW_CONVERGENCE; } 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[0]; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_DIVERGENCE; } for( i=0; i<num_vecs; i++) { printf("%.4e ",res[i]); } printf("\n"); for( i=0; i<num_vecs; i++) { printf("%.4e ",residual[i]); } printf("\n"); magma_c_vfree(&r, queue ); magma_c_vfree(&rt, queue ); magma_c_vfree(&p, queue ); magma_c_vfree(&q, queue ); magma_c_vfree(&h, queue ); magma_free_cpu(alpha); magma_free_cpu(beta); magma_free_cpu(nom); magma_free_cpu(nom0); magma_free_cpu(r0); magma_free_cpu(gammaold); magma_free_cpu(gammanew); magma_free_cpu(den); magma_free_cpu(res); magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } /* magma_cbpcg */
extern "C" magma_int_t magma_ctfqmr( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_TFQMR; solver_par->numiter = 0; solver_par->spmv_count = 0; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; // solver variables float nom0, r0, res, nomb; //, normx, normd, normr_act; magmaFloatComplex rho = c_one, rho_l = c_one, eta = c_zero , c = c_zero , theta = c_zero , tau = c_zero, alpha = c_one, beta = c_zero, sigma = c_zero; magma_int_t dofs = A.num_rows* b.num_cols; // magma_int_t stag = 0; // GPU workspace magma_c_matrix r={Magma_CSR}, r_tld={Magma_CSR}, pu_m={Magma_CSR}, d={Magma_CSR}, w={Magma_CSR}, v={Magma_CSR}, u_mp1={Magma_CSR}, u_m={Magma_CSR}, Au={Magma_CSR}, Ad={Magma_CSR}, Au_new={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &u_mp1,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &r_tld,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &u_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &pu_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &w, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); CHECK( magma_cvinit( &Ad, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Au_new, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &Au, Magma_DEV, A.num_rows, b.num_cols, c_one, queue )); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); solver_par->init_res = nom0; magma_ccopy( dofs, r.dval, 1, r_tld.dval, 1, queue ); magma_ccopy( dofs, r.dval, 1, w.dval, 1, queue ); magma_ccopy( dofs, r.dval, 1, u_m.dval, 1, queue ); magma_ccopy( dofs, u_m.dval, 1, pu_m.dval, 1, queue ); CHECK( magma_c_spmv( c_one, A, pu_m, c_zero, v, queue )); // v = A u magma_ccopy( dofs, v.dval, 1, Au.dval, 1, queue ); nomb = magma_scnrm2( 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] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } if ( nom0 < r0 ) { info = MAGMA_SUCCESS; goto cleanup; } tau = magma_csqrt( magma_cdotc( dofs, r.dval, 1, r_tld.dval, 1, queue )); rho = magma_cdotc( dofs, r.dval, 1, r_tld.dval, 1, queue ); rho_l = rho; //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++; if( solver_par->numiter%2 == 1 ){ alpha = rho / magma_cdotc( dofs, v.dval, 1, r_tld.dval, 1, queue ); magma_ccopy( dofs, u_m.dval, 1, u_mp1.dval, 1, queue ); magma_caxpy( dofs, -alpha, v.dval, 1, u_mp1.dval, 1, queue ); // u_mp1 = u_m - alpha*v; } magma_caxpy( dofs, -alpha, Au.dval, 1, w.dval, 1, queue ); // w = w - alpha*Au; sigma = theta * theta / alpha * eta; magma_cscal( dofs, sigma, d.dval, 1, queue ); magma_caxpy( dofs, c_one, pu_m.dval, 1, d.dval, 1, queue ); // d = pu_m + sigma*d; magma_cscal( dofs, sigma, Ad.dval, 1, queue ); magma_caxpy( dofs, c_one, Au.dval, 1, Ad.dval, 1, queue ); // Ad = Au + sigma*Ad; theta = magma_csqrt( magma_cdotc(dofs, w.dval, 1, w.dval, 1, queue) ) / tau; c = c_one / magma_csqrt( c_one + theta*theta ); tau = tau * theta *c; eta = c * c * alpha; // normd = magma_scnrm2( dofs, d.dval, 1, queue ); // normx = magma_scnrm2( dofs, x->dval, 1, queue ); // // // if ( MAGMA_C_ABS(eta)*normd < 1e-15*normx ){ // stag = stag + 1; // } else { // stag = 0; // } magma_caxpy( dofs, eta, d.dval, 1, x->dval, 1, queue ); // x = x + eta * d magma_caxpy( dofs, -eta, Ad.dval, 1, r.dval, 1, queue ); // r = r - eta * Ad res = magma_scnrm2( dofs, r.dval, 1, queue ); // normr_act = res; 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 ){ info = MAGMA_SUCCESS; break; } // if (normr_act < normrmin){ //update minimal norm quantities // normrmin = normr_act; // //xmin = x; // } // if ( stag >= maxstagsteps ){ // 3 iterates are the same // break; // } if( solver_par->numiter%2 == 0 ){ rho = magma_cdotc( dofs, w.dval, 1, r_tld.dval, 1, queue ); beta = rho / rho_l; rho_l = rho; magma_ccopy( dofs, w.dval, 1, u_mp1.dval, 1, queue ); magma_caxpy( dofs, beta, u_m.dval, 1, u_mp1.dval, 1, queue ); // u_mp1 = w + beta*u_m; } magma_ccopy( dofs, u_mp1.dval, 1, pu_m.dval, 1, queue ); CHECK( magma_c_spmv( c_one, A, pu_m, c_zero, Au_new, queue )); // Au_new = A pu_m solver_par->spmv_count++; if( solver_par->numiter%2 == 0 ){ magma_cscal( dofs, beta*beta, v.dval, 1, queue ); magma_caxpy( dofs, beta, Au.dval, 1, v.dval, 1, queue ); magma_caxpy( dofs, c_one, Au_new.dval, 1, v.dval, 1, queue ); // v = Au_new + beta*(Au+beta*v); } magma_ccopy( dofs, Au_new.dval, 1, Au.dval, 1, queue ); magma_ccopy( dofs, u_mp1.dval, 1, u_m.dval, 1, queue ); } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( 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*solver_par->init_res || 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_cmfree(&r, queue ); magma_cmfree(&r_tld, queue ); magma_cmfree(&d, queue ); magma_cmfree(&w, queue ); magma_cmfree(&v, queue ); magma_cmfree(&pu_m, queue ); magma_cmfree(&u_m, queue ); magma_cmfree(&u_mp1, queue ); magma_cmfree(&d, queue ); magma_cmfree(&Au, queue ); magma_cmfree(&Au_new, queue ); magma_cmfree(&Ad, queue ); solver_par->info = info; return info; } /* magma_ctfqmr */
extern "C" int calc_bounding_box(magmaFloatComplex *M, magma_int_t M_lead_dim, float *wReEig, float *wImEig) { magma_int_t rslt = 0; //magmaFloatComplex *AT = nullptr; magmaFloatComplex *dA = nullptr, *dAT = nullptr, *dreA = nullptr, *dimA = nullptr; float *dreEig = nullptr; float *dimEig = nullptr; //magma_int_t *ipiv = NULL; magma_int_t lda = M_lead_dim; //magma_int_t ldx = lda; magma_int_t info = 0; magma_int_t nb = 0; //magma_vec_t jobvl; //magma_vec_t jobvr; magmaFloatComplex *work = nullptr; magma_int_t lwork = 0; float *rwork = nullptr; magma_int_t lrwork = 0; magma_int_t *iwork = nullptr; magma_int_t liwork = 0; nb = magma_get_cgehrd_nb( M_lead_dim ); lwork = 2 * (M_lead_dim + M_lead_dim*nb); // MagmaNoVec //lwork = 2 * max(M_lead_dim + M_lead_dim*nb, 2*M_lead_dim + M_lead_dim*M_lead_dim); // MagmaVec lrwork = M_lead_dim; // MagmaNoVec //lrwork = 1 + 5 * M_lead_dim + 2*M_lead_dim*M_lead_dim; // MagmaVec liwork = 1; // MagmaNoVec //liwork = 3 + 5*M_lead_dim; // MagmaVec magma_imalloc_cpu(&iwork, liwork); magma_smalloc_cpu(&rwork, lrwork); //magma_cmalloc_cpu(&A, lda*M_lead_dim); //magma_cmalloc_cpu(&AT, lda*M_lead_dim); //magma_smalloc_cpu(&reEig, M_lead_dim); //magma_smalloc_cpu(&imEig, M_lead_dim); magma_cmalloc_pinned(&dA, lda*M_lead_dim); magma_cmalloc_pinned(&dAT, lda*M_lead_dim); magma_cmalloc_pinned(&dreA, lda*M_lead_dim); magma_cmalloc_pinned(&dimA, lda*M_lead_dim); //magma_cmalloc_pinned(&VL, lda*M_lead_dim); //magma_cmalloc_pinned(&VR, lda*M_lead_dim); magma_cmalloc_pinned(&work, lwork); magma_smalloc_pinned(&dreEig, M_lead_dim); magma_smalloc_pinned(&dimEig, M_lead_dim); //matrix_fillzero(AT, M_lead_dim); //vector_fillzero(reEig, M_lead_dim); //vector_fillzero(imEig, M_lead_dim); //prepare_matrix_2(M); magma_csetmatrix(M_lead_dim, M_lead_dim, M, lda, dA, M_lead_dim, queue); //magma_csetmatrix(M_lead_dim, M_lead_dim, AT, lda, dAT, M_lead_dim, queue); //magma_ssetvector(M_lead_dim, wReEig, 1, dreEig, 1, queue); //magma_ssetvector(M_lead_dim, wImEig, 1, dimEig, 1, queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dA, lda); // reA = ( (A + A')/2.0 ) // A' magmablas_ctranspose(M_lead_dim, M_lead_dim, dA, M_lead_dim, dAT, M_lead_dim, queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda); // AT = A + A' magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dA, M_lead_dim, dAT, M_lead_dim, queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda); // AT=AT*0.5 magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.5f, 0.0f), dAT, 1, queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda); // reA = AT magma_ccopy(lda*M_lead_dim, dAT, 1, dreA, 1, queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dreA, lda); magma_sync_wtime(queue); // imA = ( -1im*(A - A')/2.0 ) // A' magmablas_ctranspose(M_lead_dim, M_lead_dim, dA, M_lead_dim, dAT, M_lead_dim, queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda); // AT = A + A' magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(-1.0f, 0.0f), dAT, M_lead_dim, dA, M_lead_dim, queue); // A=A*-1j*0.5 magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.0f, -0.5f), dA, 1, queue); // imA = A magma_ccopy(lda*M_lead_dim, dA, 1, dimA, 1, queue); magma_sync_wtime(queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dreA, lda); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dimA, lda); // reEig::Vector=eigvals(reA) rslt = magma_cheevd(MagmaNoVec, MagmaLower, M_lead_dim, dreA, lda, dreEig, work, lwork, rwork, lrwork, iwork, liwork, &info); // imEig::Vector=eigvals(imA) rslt = magma_cheevd(MagmaNoVec, MagmaLower, M_lead_dim, dimA, lda, dimEig, work, lwork, rwork, lrwork, iwork, liwork, &info); //magma_sprint_gpu(M_lead_dim, 1, dreEig, M_lead_dim); //magma_sprint_gpu(M_lead_dim, 1, dimEig, M_lead_dim); magma_sgetvector(M_lead_dim, dreEig, 1, wReEig, 1, queue); //magma_sync_wtime(queue); magma_sgetvector(M_lead_dim, dimEig, 1, wImEig, 1, queue); //magma_sync_wtime(queue); /* maxReIdx = magma_isamax(M_lead_dim, dreEig, 1, queue) - 1; minReIdx = magma_isamin(M_lead_dim, dreEig, 1, queue) - 1; maxImIdx = magma_isamax(M_lead_dim, dimEig, 1, queue) - 1; minImIdx = magma_isamin(M_lead_dim, dimEig, 1, queue) - 1; printf("max re idx = %d\nmin re idx = %d\n", maxReIdx, minReIdx); printf("%f %f\n", wReEig[maxReIdx], wReEig[minReIdx]); printf("max im idx = %d\nmin im idx = %d\n", maxImIdx, minImIdx); printf("%f %f\n", wImEig[maxImIdx], wImEig[minImIdx]); */ //printf("test wReEig: %f %f\n", wReEig[0], wReEig[1]); //printf("test wImEig: %f %f\n", wImEig[0], wImEig[1]); magma_free_cpu(iwork); magma_free_cpu(rwork); //magma_free_cpu(AT); magma_free_pinned(dA); magma_free_pinned(dAT); magma_free_pinned(dreA); magma_free_pinned(dimA); magma_free_pinned(work); magma_free_pinned(dreEig); magma_free_pinned(dimEig); return rslt; }
extern "C" int calc_numerical_range(magmaFloatComplex *M, magma_int_t M_lead_dim, float _from, float _step, magma_int_t _steps, magmaFloatComplex *pts) { magma_int_t idx = 0, rslt = 0; magmaFloatComplex p, scalar; std::complex<float> vtmp; float j; magmaFloatComplex *dA = nullptr; magmaFloatComplex *dAth = NULL, *dAthT = NULL, *dX = NULL, *dY = NULL; float *dE = NULL; //float *hE = NULL; //magma_int_t *ipiv = NULL; magma_int_t lda = M_lead_dim; //magma_int_t ldx = lda; magma_int_t info = 0; magma_int_t nb = 0; //magma_vec_t jobvl; //magma_vec_t jobvr; magmaFloatComplex *work = nullptr; magma_int_t lwork = 0; float *rwork = nullptr; magma_int_t lrwork = 0; magma_int_t *iwork = nullptr; magma_int_t liwork = 0; nb = magma_get_cgehrd_nb( M_lead_dim ); lwork = 2 * max(M_lead_dim + M_lead_dim*nb, 2 * M_lead_dim + M_lead_dim*M_lead_dim); // MagmaVec lrwork = 1 + 5 * M_lead_dim + 2 * M_lead_dim*M_lead_dim; // MagmaVec liwork = (3 + 5 * M_lead_dim); // MagmaVec magma_imalloc_cpu(&iwork, liwork); magma_smalloc_cpu(&rwork, lrwork); magma_cmalloc_pinned(&work, lwork); magma_cmalloc_pinned(&dA, lda*M_lead_dim); magma_cmalloc_pinned(&dAth, lda*M_lead_dim); magma_cmalloc_pinned(&dAthT, lda*M_lead_dim); magma_smalloc_pinned(&dE, M_lead_dim); //magma_smalloc_cpu(&hE, M_lead_dim); magma_cmalloc_pinned(&dX, M_lead_dim); magma_cmalloc_pinned(&dY, M_lead_dim); magma_csetmatrix(M_lead_dim, M_lead_dim, M, lda, dA, M_lead_dim, queue); // th=[0:resolution:2*pi] j = _from; for (idx = 0; idx < _steps; idx++) { //scalar = exp( 1im * -j); vtmp.real( 0.0f ); vtmp.imag( -j ); //vtmp = _FCbuild(0.0f, -j); //printf("vtmp = %f + i%f\n", vtmp._Val[0], vtmp._Val[1]); vtmp = exp(vtmp); scalar.x = vtmp.real(); scalar.y = vtmp.imag(); //printf("scalar = %f + i%f\n", scalar.x, scalar.y); magma_ccopy(lda * M_lead_dim, dA, 1, dAth, 1, queue); // Ath = exp(1im * -j) * As magma_cscal(lda * M_lead_dim, scalar, dAth, 1, queue); //magma_cprint_gpu(N, N, dA, lda); //magma_cprint_gpu(N, N, dAth, lda); // AthT = (Ath + Ath') magmablas_ctranspose_conj(M_lead_dim, M_lead_dim, dAth, M_lead_dim, dAthT, M_lead_dim, queue); magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dAth, M_lead_dim, dAthT, M_lead_dim, queue); // AthT = AthT / 2 magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.5f, 0.0f), dAthT, 1, queue); magma_sync_wtime(queue); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dAthT, lda); // e, r = eig(AthT) rslt = magma_cheevd(MagmaVec, MagmaLower, M_lead_dim, dAthT, lda, dE, work, lwork, rwork, lrwork, iwork, liwork, &info); magma_sync_wtime(queue); //printf("magma_cheevd info=%d\n", info); //magma_cprint_gpu(M_lead_dim, M_lead_dim, dAthT, lda); //magma_sprint_gpu(M_lead_dim, 1, dE, M_lead_dim); //magma_sgetvector(M_lead_dim, dE, 1, hE, 1, queue); //printf("%f %f\n", hE[0], hE[1]); // p = r[:,s]' * A * r[:,s] // r = r[:,s] magma_ccopy( M_lead_dim, dAthT + (M_lead_dim*(M_lead_dim-1)), 1, // dAthT + (N), where (N) is a column offset dX, 1, queue); magma_sync_wtime(queue); //magma_cprint_gpu(M_lead_dim, 1, dX, M_lead_dim); // pp = A * r[:,s] magma_cgemv(MagmaNoTrans, M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dA, lda, dX, 1, MAGMA_C_MAKE(0.0f, 0.0f), dY, 1, queue); magma_sync_wtime(queue); //magma_cprint_gpu(M_lead_dim, 1, dY, M_lead_dim); // p = r' * pp p = magma_cdotc(M_lead_dim, dX, 1, dY, 1, queue); magma_sync_wtime(queue); pts[idx] = p; //printf("p = %f %fi\n", p.x, p.y); j += _step; } // end of for (idx = 0; idx < _steps; idx++) magma_free_pinned(dY); magma_free_pinned(dX); //magma_free_cpu(hE); magma_free_pinned(dE); magma_free_pinned(dAthT); magma_free_pinned(dAth); magma_free_pinned(dA); magma_free_pinned(work); magma_free_cpu(rwork); magma_free_cpu(iwork); //magma_free_cpu(w); //magma_free_cpu(A); return rslt; }
extern "C" magma_int_t magma_c_applyprecond_right( magma_trans_t trans, magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_preconditioner *precond, magma_queue_t queue ) { magma_int_t info = 0; if( trans == MagmaNoTrans ) { if ( precond->solver == Magma_JACOBI ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1, queue ); // x = b } else if ( ( precond->solver == Magma_ILU || precond->solver == Magma_AILU ) && precond->maxiter >= 50 ) { CHECK( magma_capplycumilu_r( b, x, precond, queue )); } else if ( ( precond->solver == Magma_ILU || precond->solver == Magma_AILU ) && precond->maxiter < 50 ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, b.num_cols, x->dval, b.num_cols, queue ); magma_c_solver_par solver_par; solver_par.maxiter = precond->maxiter; magma_cjacobiiter_sys( precond->U, b, precond->d2, precond->work2, x, &solver_par, queue ); // CHECK( magma_cjacobispmvupdate_bw(precond->maxiter, precond->U, precond->work2, b, precond->d2, x, queue )); } else if ( ( precond->solver == Magma_ICC || precond->solver == Magma_AICC ) && precond->maxiter >= 50 ) { CHECK( magma_capplycumicc_r( b, x, precond, queue )); } else if ( ( precond->solver == Magma_ICC || precond->solver == Magma_AICC ) && precond->maxiter < 50 ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, b.num_cols, x->dval, b.num_cols, queue ); magma_c_solver_par solver_par; solver_par.maxiter = precond->maxiter; magma_cjacobiiter_sys( precond->U, b, precond->d2, precond->work2, x, &solver_par, queue ); // CHECK( magma_cjacobispmvupdate_bw(precond->maxiter, precond->U, precond->work2, b, precond->d2, x, queue )); } else if ( precond->solver == Magma_NONE ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1, queue ); // x = b } else if ( precond->solver == Magma_FUNCTION ) { CHECK( magma_capplycustomprecond_r( b, x, precond, queue )); } else { printf( "error: preconditioner type not yet supported.\n" ); info = MAGMA_ERR_NOT_SUPPORTED; } } else if ( trans == MagmaTrans ){ if ( precond->solver == Magma_JACOBI ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1, queue ); // x = b } else if ( ( precond->solver == Magma_ILU || precond->solver == Magma_AILU ) && precond->maxiter >= 50 ) { CHECK( magma_capplycumilu_r_transpose( b, x, precond, queue )); } else if ( ( precond->solver == Magma_ILU || precond->solver == Magma_AILU ) && precond->maxiter < 50 ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, b.num_cols, x->dval, b.num_cols, queue ); magma_c_solver_par solver_par; solver_par.maxiter = precond->maxiter; magma_cjacobiiter_sys( precond->UT, b, precond->d2, precond->work2, x, &solver_par, queue ); // CHECK( magma_cjacobispmvupdate_bw(precond->maxiter, precond->U, precond->work2, b, precond->d2, x, queue )); } else if ( ( precond->solver == Magma_ICC || precond->solver == Magma_AICC ) && precond->maxiter >= 50 ) { CHECK( magma_capplycumicc_r( b, x, precond, queue )); } else if ( ( precond->solver == Magma_ICC || precond->solver == Magma_AICC ) && precond->maxiter < 50 ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, b.num_cols, x->dval, b.num_cols, queue ); magma_c_solver_par solver_par; solver_par.maxiter = precond->maxiter; magma_cjacobiiter_sys( precond->UT, b, precond->d2, precond->work2, x, &solver_par, queue ); // CHECK( magma_cjacobispmvupdate_bw(precond->maxiter, precond->U, precond->work2, b, precond->d2, x, queue )); } else if ( precond->solver == Magma_NONE ) { magma_ccopy( b.num_rows*b.num_cols, b.dval, 1, x->dval, 1, queue ); // x = b } else if ( precond->solver == Magma_FUNCTION ) { CHECK( magma_capplycustomprecond_r( b, x, precond, queue )); } else { printf( "error: preconditioner type not yet supported.\n" ); info = MAGMA_ERR_NOT_SUPPORTED; } } cleanup: return info; }
extern "C" magma_int_t magma_cbicgstab_merge3( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_BICGSTABMERGE; solver_par->numiter = 0; solver_par->spmv_count = 0; // solver variables magmaFloatComplex alpha, beta, omega, rho_old, rho_new, *skp_h={0}; float nom, nom0, betanom, nomb; // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows; // workspace magma_c_matrix q={Magma_CSR}, r={Magma_CSR}, rr={Magma_CSR}, p={Magma_CSR}, v={Magma_CSR}, s={Magma_CSR}, t={Magma_CSR}; magmaFloatComplex *d1=NULL, *d2=NULL, *skp=NULL; d1 = NULL; d2 = NULL; skp = NULL; CHECK( magma_cmalloc( &d1, dofs*(2) )); CHECK( magma_cmalloc( &d2, dofs*(2) )); // array for the parameters CHECK( magma_cmalloc( &skp, 8 )); // skp = [alpha|beta|omega|rho_old|rho|nom|tmp1|tmp2] CHECK( magma_cvinit( &q, Magma_DEV, dofs*6, 1, c_zero, queue )); // q = rr|r|p|v|s|t rr.memory_location = Magma_DEV; rr.dval = NULL; rr.num_rows = rr.nnz = dofs; rr.num_cols = 1; rr.storage_type = Magma_DENSE; r.memory_location = Magma_DEV; r.dval = NULL; r.num_rows = r.nnz = dofs; r.num_cols = 1; r.storage_type = Magma_DENSE; p.memory_location = Magma_DEV; p.dval = NULL; p.num_rows = p.nnz = dofs; p.num_cols = 1; p.storage_type = Magma_DENSE; v.memory_location = Magma_DEV; v.dval = NULL; v.num_rows = v.nnz = dofs; v.num_cols = 1; v.storage_type = Magma_DENSE; s.memory_location = Magma_DEV; s.dval = NULL; s.num_rows = s.nnz = dofs; s.num_cols = 1; s.storage_type = Magma_DENSE; t.memory_location = Magma_DEV; t.dval = NULL; t.num_rows = t.nnz = dofs; t.num_cols = 1; t.storage_type = Magma_DENSE; rr.dval = q(0); r.dval = q(1); p.dval = q(2); v.dval = q(3); s.dval = q(4); t.dval = q(5); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); magma_ccopy( dofs, r.dval, 1, q(0), 1, queue ); // rr = r magma_ccopy( dofs, r.dval, 1, q(1), 1, queue ); // q = r betanom = nom0; nom = nom0*nom0; rho_new = magma_cdotc( dofs, r.dval, 1, r.dval, 1, queue ); // rho=<rr,r> rho_old = omega = alpha = MAGMA_C_MAKE( 1.0, 0. ); beta = rho_new; solver_par->init_res = nom0; // array on host for the parameters CHECK( magma_cmalloc_cpu( &skp_h, 8 )); nomb = magma_scnrm2( dofs, b.dval, 1, queue ); if ( nomb == 0.0 ){ nomb=1.0; } 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; } skp_h[0]=alpha; skp_h[1]=beta; skp_h[2]=omega; skp_h[3]=rho_old; skp_h[4]=rho_new; skp_h[5]=MAGMA_C_MAKE(nom, 0.0); magma_csetvector( 8, skp_h, 1, skp, 1, queue ); CHECK( magma_c_spmv( c_one, A, r, c_zero, v, queue )); // z = A r nomb = magma_scnrm2( dofs, b.dval, 1, queue ); if( nom0 < solver_par->atol || nom0/nomb < solver_par->rtol ){ 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++; // computes p=r+beta*(p-omega*v) CHECK( magma_cbicgmerge1( dofs, skp, v.dval, r.dval, p.dval, queue )); CHECK( magma_c_spmv( c_one, A, p, c_zero, v, queue )); // v = Ap solver_par->spmv_count++; CHECK( magma_cmdotc( dofs, 1, q.dval, v.dval, d1, d2, skp, queue )); CHECK( magma_cbicgmerge4( 1, skp, queue )); CHECK( magma_cbicgmerge2( dofs, skp, r.dval, v.dval, s.dval, queue )); // s=r-alpha*v CHECK( magma_c_spmv( c_one, A, s, c_zero, t, queue )); // t=As solver_par->spmv_count++; CHECK( magma_cmdotc( dofs, 2, q.dval+4*dofs, t.dval, d1, d2, skp+6, queue )); CHECK( magma_cbicgmerge4( 2, skp, queue )); CHECK( magma_cbicgmerge_xrbeta( dofs, d1, d2, q.dval, r.dval, p.dval, s.dval, t.dval, x->dval, skp, queue )); // check stopping criterion magma_cgetvector_async( 1 , skp+5, 1, skp_h+5, 1, queue ); betanom = sqrt(MAGMA_C_REAL(skp_h[5])); 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( betanom < solver_par->atol || betanom/nomb < solver_par->rtol ) { break; } } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue)); solver_par->iter_res = betanom; 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) betanom; 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->atol || solver_par->iter_res/solver_par->init_res < solver_par->rtol ){ 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } info = MAGMA_DIVERGENCE; } cleanup: magma_cmfree(&q, queue ); // frees all vectors magma_free(d1); magma_free(d2); magma_free( skp ); magma_free_cpu( skp_h ); solver_par->info = info; return info; } /* cbicgstab_merge */
extern "C" magma_int_t magma_cbicgstab_merge( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { // set queue for old dense routines magma_queue_t orig_queue; magmablasGetKernelStream( &orig_queue ); // prepare solver feedback solver_par->solver = Magma_BICGSTABMERGE; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows; // GPU stream magma_queue_t stream[2]; magma_event_t event[1]; magma_queue_create( &stream[0] ); magma_queue_create( &stream[1] ); magma_event_create( &event[0] ); // workspace magma_c_vector q, r,rr,p,v,s,t; magmaFloatComplex *d1, *d2, *skp; d1 = NULL; d2 = NULL; skp = NULL; magma_int_t stat_dev = 0, stat_cpu = 0; stat_dev += magma_cmalloc( &d1, dofs*(2) ); stat_dev += magma_cmalloc( &d2, dofs*(2) ); // array for the parameters stat_dev += magma_cmalloc( &skp, 8 ); if( stat_dev != 0 ){ magma_free( d1 ); magma_free( d2 ); magma_free( skp ); printf("error: memory allocation.\n"); return MAGMA_ERR_DEVICE_ALLOC; } // skp = [alpha|beta|omega|rho_old|rho|nom|tmp1|tmp2] magma_c_vinit( &q, Magma_DEV, dofs*6, c_zero, queue ); // q = rr|r|p|v|s|t rr.memory_location = Magma_DEV; rr.dval = NULL; rr.num_rows = rr.nnz = dofs; rr.num_cols = 1; r.memory_location = Magma_DEV; r.dval = NULL; r.num_rows = r.nnz = dofs; r.num_cols = 1; p.memory_location = Magma_DEV; p.dval = NULL; p.num_rows = p.nnz = dofs; p.num_cols = 1; v.memory_location = Magma_DEV; v.dval = NULL; v.num_rows = v.nnz = dofs; v.num_cols = 1; s.memory_location = Magma_DEV; s.dval = NULL; s.num_rows = s.nnz = dofs; s.num_cols = 1; t.memory_location = Magma_DEV; t.dval = NULL; t.num_rows = t.nnz = dofs; t.num_cols = 1; rr.dval = q(0); r.dval = q(1); p.dval = q(2); v.dval = q(3); s.dval = q(4); t.dval = q(5); // solver variables magmaFloatComplex alpha, beta, omega, rho_old, rho_new, *skp_h; float nom, nom0, betanom, r0, den; // solver setup magma_cscal( dofs, c_zero, x->dval, 1) ; // x = 0 magma_ccopy( dofs, b.dval, 1, q(0), 1 ); // rr = b magma_ccopy( dofs, b.dval, 1, q(1), 1 ); // r = b rho_new = magma_cdotc( dofs, r.dval, 1, r.dval, 1 ); // rho=<rr,r> nom = MAGMA_C_REAL(magma_cdotc( dofs, r.dval, 1, r.dval, 1 )); nom0 = betanom = sqrt(nom); // nom = || r || rho_old = omega = alpha = MAGMA_C_MAKE( 1.0, 0. ); beta = rho_new; solver_par->init_res = nom0; // array on host for the parameters stat_cpu = magma_cmalloc_cpu( &skp_h, 8 ); if( stat_cpu != 0 ){ magma_free( d1 ); magma_free( d2 ); magma_free( skp ); magma_free_cpu( skp_h ); printf("error: memory allocation.\n"); return MAGMA_ERR_HOST_ALLOC; } skp_h[0]=alpha; skp_h[1]=beta; skp_h[2]=omega; skp_h[3]=rho_old; skp_h[4]=rho_new; skp_h[5]=MAGMA_C_MAKE(nom, 0.0); magma_csetvector( 8, skp_h, 1, skp, 1 ); magma_c_spmv( c_one, A, r, c_zero, v, queue ); // z = A r den = MAGMA_C_REAL( magma_cdotc(dofs, v.dval, 1, r.dval, 1) );// den = z dot r if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) r0 = ATOLERANCE; if ( nom < r0 ) { magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } // check positive definite if (den <= 0.0) { printf("Operator A is not postive definite. (Ar,r) = %f\n", den); magmablasSetKernelStream( orig_queue ); return MAGMA_NONSPD; solver_par->info = MAGMA_NONSPD;; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = nom0; solver_par->timing[0] = 0.0; } // start iteration for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; solver_par->numiter++ ) { magmablasSetKernelStream(stream[0]); // computes p=r+beta*(p-omega*v) magma_cbicgmerge1( dofs, skp, v.dval, r.dval, p.dval, queue ); magma_c_spmv( c_one, A, p, c_zero, v, queue ); // v = Ap magma_cmdotc( dofs, 1, q.dval, v.dval, d1, d2, skp, queue ); magma_cbicgmerge4( 1, skp, queue ); magma_cbicgmerge2( dofs, skp, r.dval, v.dval, s.dval, queue ); // s=r-alpha*v magma_c_spmv( c_one, A, s, c_zero, t, queue ); // t=As magma_cmdotc( dofs, 2, q.dval+4*dofs, t.dval, d1, d2, skp+6, queue ); magma_cbicgmerge4( 2, skp, queue ); magma_cbicgmerge_xrbeta( dofs, d1, d2, q.dval, r.dval, p.dval, s.dval, t.dval, x->dval, skp, queue ); // check stopping criterion (asynchronous copy) magma_cgetvector_async( 1 , skp+5, 1, skp_h+5, 1, stream[1] ); betanom = sqrt(MAGMA_C_REAL(skp_h[5])); 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( betanom < r0 ) { break; } } tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; magma_cresidual( A, b, *x, &residual, queue ); solver_par->iter_res = betanom; solver_par->final_res = residual; if ( solver_par->numiter < solver_par->maxiter) { solver_par->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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_SLOW_CONVERGENCE; } 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_DIVERGENCE; } magma_c_vfree(&q, queue ); // frees all vectors magma_free(d1); magma_free(d2); magma_free( skp ); magma_free_cpu( skp_h ); magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } /* cbicgstab_merge */
extern "C" magma_int_t magma_cgmres( magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x, magma_c_solver_par *solver_par, magma_queue_t queue ) { magma_int_t stat = 0; // set queue for old dense routines magma_queue_t orig_queue; magmablasGetKernelStream( &orig_queue ); magma_int_t stat_cpu = 0, stat_dev = 0; // prepare solver feedback solver_par->solver = Magma_GMRES; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE, c_mone = MAGMA_C_NEG_ONE; magma_int_t dofs = A.num_rows; magma_int_t i, j, k, m = 0; magma_int_t restart = min( dofs-1, solver_par->restart ); magma_int_t ldh = restart+1; float nom, rNorm, RNorm, nom0, betanom, r0 = 0.; // CPU workspace //magma_setdevice(0); magmaFloatComplex *H, *HH, *y, *h1; stat_cpu += magma_cmalloc_pinned( &H, (ldh+1)*ldh ); stat_cpu += magma_cmalloc_pinned( &y, ldh ); stat_cpu += magma_cmalloc_pinned( &HH, ldh*ldh ); stat_cpu += magma_cmalloc_pinned( &h1, ldh ); if( stat_cpu != 0){ magma_free_pinned( H ); magma_free_pinned( y ); magma_free_pinned( HH ); magma_free_pinned( h1 ); magmablasSetKernelStream( orig_queue ); return MAGMA_ERR_HOST_ALLOC; } // GPU workspace magma_c_vector r, q, q_t; magma_c_vinit( &r, Magma_DEV, dofs, c_zero, queue ); magma_c_vinit( &q, Magma_DEV, dofs*(ldh+1), c_zero, queue ); q_t.memory_location = Magma_DEV; q_t.dval = NULL; q_t.num_rows = q_t.nnz = dofs; q_t.num_cols = 1; magmaFloatComplex *dy = NULL, *dH = NULL; stat_dev += magma_cmalloc( &dy, ldh ); stat_dev += magma_cmalloc( &dH, (ldh+1)*ldh ); if( stat_dev != 0){ magma_free_pinned( H ); magma_free_pinned( y ); magma_free_pinned( HH ); magma_free_pinned( h1 ); magma_free( dH ); magma_free( dy ); magma_free( dH ); magma_free( dy ); magmablasSetKernelStream( orig_queue ); return MAGMA_ERR_DEVICE_ALLOC; } // GPU stream magma_queue_t stream[2]; magma_event_t event[1]; magma_queue_create( &stream[0] ); magma_queue_create( &stream[1] ); magma_event_create( &event[0] ); //magmablasSetKernelStream(stream[0]); magma_cscal( dofs, c_zero, x->dval, 1 ); // x = 0 magma_ccopy( dofs, b.dval, 1, r.dval, 1 ); // r = b nom0 = betanom = magma_scnrm2( dofs, r.dval, 1 ); // nom0= || r|| nom = nom0 * nom0; solver_par->init_res = nom0; H(1,0) = MAGMA_C_MAKE( nom0, 0. ); magma_csetvector(1, &H(1,0), 1, &dH(1,0), 1); if ( (r0 = nom0 * solver_par->epsilon ) < ATOLERANCE ){ r0 = solver_par->epsilon; } if ( nom < r0 ) { magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = nom0; solver_par->timing[0] = 0.0; } // start iteration for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; solver_par->numiter++ ) { for(k=1; k<=restart; k++) { magma_ccopy(dofs, r.dval, 1, q(k-1), 1); // q[0] = 1.0/||r|| magma_cscal(dofs, 1./H(k,k-1), q(k-1), 1); // (to be fused) q_t.dval = q(k-1); //magmablasSetKernelStream(stream[0]); magma_c_spmv( c_one, A, q_t, c_zero, r, queue ); // r = A q[k] // if (solver_par->ortho == Magma_MGS ) { // modified Gram-Schmidt for (i=1; i<=k; i++) { H(i,k) =magma_cdotc(dofs, q(i-1), 1, r.dval, 1); // H(i,k) = q[i] . r magma_caxpy(dofs,-H(i,k), q(i-1), 1, r.dval, 1); // r = r - H(i,k) q[i] } H(k+1,k) = MAGMA_C_MAKE( magma_scnrm2(dofs, r.dval, 1), 0. ); // H(k+1,k) = ||r|| /*} else if (solver_par->ortho == Magma_FUSED_CGS ) { // fusing cgemv with scnrm2 in classical Gram-Schmidt magmablasSetKernelStream(stream[0]); magma_ccopy(dofs, r.dval, 1, q(k), 1); // dH(1:k+1,k) = q[0:k] . r magmablas_cgemv(MagmaTrans, dofs, k+1, c_one, q(0), dofs, r.dval, 1, c_zero, &dH(1,k), 1); // r = r - q[0:k-1] dH(1:k,k) magmablas_cgemv(MagmaNoTrans, dofs, k, c_mone, q(0), dofs, &dH(1,k), 1, c_one, r.dval, 1); // 1) dH(k+1,k) = sqrt( dH(k+1,k) - dH(1:k,k) ) magma_ccopyscale( dofs, k, r.dval, q(k), &dH(1,k) ); // 2) q[k] = q[k] / dH(k+1,k) magma_event_record( event[0], stream[0] ); magma_queue_wait_event( stream[1], event[0] ); magma_cgetvector_async(k+1, &dH(1,k), 1, &H(1,k), 1, stream[1]); // asynch copy dH(1:(k+1),k) to H(1:(k+1),k) } else { // classical Gram-Schmidt (default) // > explicitly calling magmabls magmablasSetKernelStream(stream[0]); magmablas_cgemv(MagmaTrans, dofs, k, c_one, q(0), dofs, r.dval, 1, c_zero, &dH(1,k), 1, queue ); // dH(1:k,k) = q[0:k-1] . r #ifndef SCNRM2SCALE // start copying dH(1:k,k) to H(1:k,k) magma_event_record( event[0], stream[0] ); magma_queue_wait_event( stream[1], event[0] ); magma_cgetvector_async(k, &dH(1,k), 1, &H(1,k), 1, stream[1]); #endif // r = r - q[0:k-1] dH(1:k,k) magmablas_cgemv(MagmaNoTrans, dofs, k, c_mone, q(0), dofs, &dH(1,k), 1, c_one, r.dval, 1); #ifdef SCNRM2SCALE magma_ccopy(dofs, r.dval, 1, q(k), 1); // q[k] = r / H(k,k-1) magma_scnrm2scale(dofs, q(k), dofs, &dH(k+1,k) ); // dH(k+1,k) = sqrt(r . r) and r = r / dH(k+1,k) magma_event_record( event[0], stream[0] ); // start sending dH(1:k,k) to H(1:k,k) magma_queue_wait_event( stream[1], event[0] ); // can we keep H(k+1,k) on GPU and combine? magma_cgetvector_async(k+1, &dH(1,k), 1, &H(1,k), 1, stream[1]); #else H(k+1,k) = MAGMA_C_MAKE( magma_scnrm2(dofs, r.dval, 1), 0. ); // H(k+1,k) = sqrt(r . r) if ( k<solver_par->restart ) { magmablasSetKernelStream(stream[0]); magma_ccopy(dofs, r.dval, 1, q(k), 1); // q[k] = 1.0/H[k][k-1] r magma_cscal(dofs, 1./H(k+1,k), q(k), 1); // (to be fused) } #endif }*/ /* Minimization of || b-Ax || in H_k */ for (i=1; i<=k; i++) { HH(k,i) = magma_cblas_cdotc( i+1, &H(1,k), 1, &H(1,i), 1 ); } h1[k] = H(1,k)*H(1,0); if (k != 1) { for (i=1; i<k; i++) { HH(k,i) = HH(k,i)/HH(i,i);// for (m=i+1; m<=k; m++) { HH(k,m) -= HH(k,i) * HH(m,i) * HH(i,i); } h1[k] -= h1[i] * HH(k,i); } } y[k] = h1[k]/HH(k,k); if (k != 1) for (i=k-1; i>=1; i--) { y[i] = h1[i]/HH(i,i); for (j=i+1; j<=k; j++) y[i] -= y[j] * HH(j,i); } m = k; rNorm = fabs(MAGMA_C_REAL(H(k+1,k))); }/* Minimization done */ // compute solution approximation magma_csetmatrix(m, 1, y+1, m, dy, m ); magma_cgemv(MagmaNoTrans, dofs, m, c_one, q(0), dofs, dy, 1, c_one, x->dval, 1); // compute residual magma_c_spmv( c_mone, A, *x, c_zero, r, queue ); // r = - A * x magma_caxpy(dofs, c_one, b.dval, 1, r.dval, 1); // r = r + b H(1,0) = MAGMA_C_MAKE( magma_scnrm2(dofs, r.dval, 1), 0. ); // RNorm = H[1][0] = || r || RNorm = MAGMA_C_REAL( H(1,0) ); betanom = fabs(RNorm); 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } if ( betanom < r0 ) { break; } } tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; magma_cresidual( A, b, *x, &residual, queue ); solver_par->iter_res = betanom; solver_par->final_res = residual; if ( solver_par->numiter < solver_par->maxiter) { solver_par->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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_SLOW_CONVERGENCE; } 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } solver_par->info = MAGMA_DIVERGENCE; } // free pinned memory magma_free_pinned( H ); magma_free_pinned( y ); magma_free_pinned( HH ); magma_free_pinned( h1 ); // free GPU memory magma_free(dy); if (dH != NULL ) magma_free(dH); magma_c_vfree(&r, queue ); magma_c_vfree(&q, queue ); // free GPU streams and events magma_queue_destroy( stream[0] ); magma_queue_destroy( stream[1] ); magma_event_destroy( event[0] ); //magmablasSetKernelStream(NULL); magmablasSetKernelStream( orig_queue ); return MAGMA_SUCCESS; } /* magma_cgmres */
extern "C" magma_int_t magma_cpcg( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_PCG; solver_par->numiter = 0; solver_par->spmv_count = 0; // solver variables magmaFloatComplex alpha, beta; float nom0, r0, res, nomb; magmaFloatComplex den, gammanew, gammaold = MAGMA_C_MAKE(1.0,0.0); // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows* b.num_cols; // GPU workspace magma_c_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}, h={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &h, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); // preconditioner CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue )); magma_ccopy( dofs, h.dval, 1, p.dval, 1, queue ); // p = h CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p den = magma_cdotc( dofs, p.dval, 1, q.dval, 1, queue ); // den = p dot q solver_par->init_res = nom0; nomb = magma_scnrm2( 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] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } if ( nomb < r0 ) { info = MAGMA_SUCCESS; goto cleanup; } // check positive definite if ( MAGMA_C_ABS(den) <= 0.0 ) { info = MAGMA_NONSPD; 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++; // preconditioner CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue )); gammanew = magma_cdotc( dofs, r.dval, 1, h.dval, 1, queue ); // gn = < r,h> if ( solver_par->numiter == 1 ) { magma_ccopy( dofs, h.dval, 1, p.dval, 1, queue ); // p = h } else { beta = (gammanew/gammaold); // beta = gn/go magma_cscal( dofs, beta, p.dval, 1, queue ); // p = beta*p magma_caxpy( dofs, c_one, h.dval, 1, p.dval, 1, queue ); // p = p + h } CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p den = magma_cdotc( dofs, p.dval, 1, q.dval, 1, queue ); // den = p dot q alpha = gammanew / den; magma_caxpy( dofs, alpha, p.dval, 1, x->dval, 1, queue ); // x = x + alpha p magma_caxpy( dofs, -alpha, q.dval, 1, r.dval, 1, queue ); // r = r - alpha q gammaold = gammanew; res = magma_scnrm2( 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; float residual; CHECK( magma_cresidualvec( 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*solver_par->init_res || 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_cmfree(&r, queue ); magma_cmfree(&rt, queue ); magma_cmfree(&p, queue ); magma_cmfree(&q, queue ); magma_cmfree(&h, queue ); solver_par->info = info; return info; } /* magma_ccg */
extern "C" magma_int_t magma_cpqmr_merge( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_QMR; solver_par->numiter = 0; solver_par->spmv_count = 0; // local variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE; // solver variables float nom0, r0, res=0.0, nomb; magmaFloatComplex rho = c_one, rho1 = c_one, eta = -c_one , pds = c_one, thet = c_one, thet1 = c_one, epsilon = c_one, beta = c_one, delta = c_one, pde = c_one, rde = c_one, gamm = c_one, gamm1 = c_one, psi = c_one; magma_int_t dofs = A.num_rows* b.num_cols; // need to transpose the matrix magma_c_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR}; // GPU workspace magma_c_matrix r={Magma_CSR}, r_tld={Magma_CSR}, v={Magma_CSR}, w={Magma_CSR}, wt={Magma_CSR}, d={Magma_CSR}, s={Magma_CSR}, z={Magma_CSR}, q={Magma_CSR}, p={Magma_CSR}, pt={Magma_CSR}, y={Magma_CSR}, vt={Magma_CSR}, yt={Magma_CSR}, zt={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &r_tld, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &yt, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &vt, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &zt, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); solver_par->init_res = nom0; magma_ccopy( dofs, r.dval, 1, r_tld.dval, 1, queue ); magma_ccopy( dofs, r.dval, 1, vt.dval, 1, queue ); magma_ccopy( dofs, r.dval, 1, wt.dval, 1, queue ); // transpose the matrix magma_cmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue ); magma_cmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue ); magma_cmfree(&Ah1, queue ); magma_cmtransposeconjugate( Ah2, &Ah1, queue ); magma_cmfree(&Ah2, queue ); Ah2.blocksize = A.blocksize; Ah2.alignment = A.alignment; magma_cmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue ); magma_cmfree(&Ah1, queue ); magma_cmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue ); magma_cmfree(&Ah2, queue ); nomb = magma_scnrm2( 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] = (real_Double_t)nom0; solver_par->timing[0] = 0.0; } if ( nom0 < r0 ) { info = MAGMA_SUCCESS; goto cleanup; } // no precond: y = vt, z = wt // magma_ccopy( dofs, vt.dval, 1, y.dval, 1, queue ); // magma_ccopy( dofs, wt.dval, 1, z.dval, 1, queue ); CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, vt, &y, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaTrans, A, wt, &z, precond_par, queue )); psi = magma_csqrt( magma_cdotc( dofs, z.dval, 1, z.dval, 1, queue )); rho = magma_csqrt( magma_cdotc( dofs, y.dval, 1, y.dval, 1, queue )); // v = vt / rho // y = y / rho // w = wt / psi // z = z / psi magma_cqmr_8( r.num_rows, r.num_cols, rho, psi, vt.dval, wt.dval, y.dval, z.dval, v.dval, w.dval, queue ); //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); solver_par->numiter = 0; // start iteration do { solver_par->numiter++; if( magma_c_isnan_inf( rho ) || magma_c_isnan_inf( psi ) ){ info = MAGMA_DIVERGENCE; break; } // delta = z' * y; delta = magma_cdotc( dofs, z.dval, 1, y.dval, 1, queue ); if( magma_c_isnan_inf( delta ) ){ info = MAGMA_DIVERGENCE; break; } // no precond: yt = y, zt = z // magma_ccopy( dofs, y.dval, 1, yt.dval, 1, queue ); // magma_ccopy( dofs, z.dval, 1, zt.dval, 1, queue ); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, y, &yt, precond_par, queue )); CHECK( magma_c_applyprecond_left( MagmaTrans, A, z, &zt, precond_par, queue )); if( solver_par->numiter == 1 ){ // p = y; // q = z; magma_ccopy( dofs, yt.dval, 1, p.dval, 1, queue ); magma_ccopy( dofs, zt.dval, 1, q.dval, 1, queue ); } else{ pde = psi * delta / epsilon; rde = rho * MAGMA_C_CONJ(delta/epsilon); // p = yt - pde * p // q = zt - rde * q magma_cqmr_2( r.num_rows, r.num_cols, pde, rde, yt.dval, zt.dval, p.dval, q.dval, queue ); } if( magma_c_isnan_inf( rho ) || magma_c_isnan_inf( psi ) ){ info = MAGMA_DIVERGENCE; break; } CHECK( magma_c_spmv( c_one, A, p, c_zero, pt, queue )); solver_par->spmv_count++; // epsilon = q' * pt; epsilon = magma_cdotc( dofs, q.dval, 1, pt.dval, 1, queue ); beta = epsilon / delta; if( magma_c_isnan_inf( epsilon ) || magma_c_isnan_inf( beta ) ){ info = MAGMA_DIVERGENCE; break; } // vt = pt - beta * v; magma_cqmr_7( r.num_rows, r.num_cols, beta, pt.dval, v.dval, vt.dval, queue ); magma_ccopy( dofs, v.dval, 1, vt.dval, 1, queue ); magma_cscal( dofs, -beta, vt.dval, 1, queue ); magma_caxpy( dofs, c_one, pt.dval, 1, vt.dval, 1, queue ); // no precond: y = vt // magma_ccopy( dofs, vt.dval, 1, y.dval, 1, queue ); CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, vt, &y, precond_par, queue )); rho1 = rho; // rho = norm(y); rho = magma_csqrt( magma_cdotc( dofs, y.dval, 1, y.dval, 1, queue )); // wt = A' * q - beta' * w; CHECK( magma_c_spmv( c_one, AT, q, c_zero, wt, queue )); solver_par->spmv_count++; magma_caxpy( dofs, - MAGMA_C_CONJ( beta ), w.dval, 1, wt.dval, 1, queue ); // no precond: z = wt // magma_ccopy( dofs, wt.dval, 1, z.dval, 1, queue ); CHECK( magma_c_applyprecond_right( MagmaTrans, A, wt, &z, precond_par, queue )); thet1 = thet; thet = rho / (gamm * MAGMA_C_MAKE( MAGMA_C_ABS(beta), 0.0 )); gamm1 = gamm; gamm = c_one / magma_csqrt(c_one + thet*thet); eta = - eta * rho1 * gamm * gamm / (beta * gamm1 * gamm1); if( magma_c_isnan_inf( thet ) || magma_c_isnan_inf( gamm ) || magma_c_isnan_inf( eta ) ){ info = MAGMA_DIVERGENCE; break; } if( solver_par->numiter == 1 ){ // d = eta * p + pds * d; // s = eta * pt + pds * d; // x = x + d; // r = r - s; magma_cqmr_4( r.num_rows, r.num_cols, eta, p.dval, pt.dval, d.dval, s.dval, x->dval, r.dval, queue ); } else{ // pds = (thet1 * gamm)^2; pds = (thet1 * gamm) * (thet1 * gamm); // d = eta * p + pds * d; // s = eta * pt + pds * d; // x = x + d; // r = r - s; magma_cqmr_5( r.num_rows, r.num_cols, eta, pds, p.dval, pt.dval, d.dval, s.dval, x->dval, r.dval, queue ); } // psi = norm(z); psi = magma_csqrt( magma_cdotc( dofs, z.dval, 1, z.dval, 1, queue ) ); res = magma_scnrm2( dofs, r.dval, 1, queue ); if ( solver_par->verbose > 0 ) { tempo2 = magma_sync_wtime( queue ); if ( (solver_par->numiter)%solver_par->verbose == c_zero ) { 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; } } // v = vt / rho // y = y / rho // w = wt / psi // z = z / psi magma_cqmr_8( r.num_rows, r.num_cols, rho, psi, vt.dval, wt.dval, y.dval, z.dval, v.dval, w.dval, queue ); 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; float residual; CHECK( magma_cresidualvec( 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 ) { 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 == c_zero ) { 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*solver_par->init_res || solver_par->iter_res < solver_par->atol ) { info = MAGMA_SUCCESS; } } else { if ( solver_par->verbose > 0 ) { if ( (solver_par->numiter)%solver_par->verbose == c_zero ) { 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_cmfree(&r, queue ); magma_cmfree(&r_tld, queue ); magma_cmfree(&v, queue ); magma_cmfree(&w, queue ); magma_cmfree(&wt, queue ); magma_cmfree(&d, queue ); magma_cmfree(&s, queue ); magma_cmfree(&z, queue ); magma_cmfree(&q, queue ); magma_cmfree(&p, queue ); magma_cmfree(&zt, queue ); magma_cmfree(&vt, queue ); magma_cmfree(&yt, queue ); magma_cmfree(&pt, queue ); magma_cmfree(&y, queue ); magma_cmfree(&AT, queue ); magma_cmfree(&Ah1, queue ); magma_cmfree(&Ah2, queue ); solver_par->info = info; return info; } /* magma_cqmr */
extern "C" magma_int_t magma_cpbicgstab_merge( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = MAGMA_NOTCONVERGED; // prepare solver feedback solver_par->solver = Magma_BICGSTAB; solver_par->numiter = 0; solver_par->spmv_count = 0; // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO; magmaFloatComplex c_one = MAGMA_C_ONE; magma_int_t dofs = A.num_rows * b.num_cols; // workspace magma_c_matrix r={Magma_CSR}, rr={Magma_CSR}, p={Magma_CSR}, v={Magma_CSR}, z={Magma_CSR}, y={Magma_CSR}, ms={Magma_CSR}, mt={Magma_CSR}, s={Magma_CSR}, t={Magma_CSR}, d1={Magma_CSR}, d2={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &rr,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &ms,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &mt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d1, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &d2, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver variables magmaFloatComplex alpha, beta, omega, rho_old, rho_new; float betanom, nom0, r0, res, nomb; res=0; //float den; // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); magma_ccopy( dofs, r.dval, 1, rr.dval, 1, queue ); // rr = r betanom = nom0; rho_new = magma_cdotc( dofs, r.dval, 1, r.dval, 1, queue ); // rho=<rr,r> rho_old = omega = alpha = MAGMA_C_MAKE( 1.0, 0. ); solver_par->init_res = nom0; CHECK( magma_c_spmv( c_one, A, r, c_zero, v, queue )); // z = A r nomb = magma_scnrm2( 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 ( nomb < 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++; rho_old = rho_new; // rho_old=rho rho_new = magma_cdotc( dofs, rr.dval, 1, r.dval, 1, queue ); // rho=<rr,r> beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega if( magma_c_isnan_inf( beta ) ){ info = MAGMA_DIVERGENCE; break; } // p = r + beta * ( p - omega * v ) magma_cbicgstab_1( r.num_rows, r.num_cols, beta, omega, r.dval, v.dval, p.dval, queue ); // preconditioner CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, p, &mt, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, mt, &y, precond_par, queue )); CHECK( magma_c_spmv( c_one, A, y, c_zero, v, queue )); // v = Ap solver_par->spmv_count++; //alpha = rho_new / tmpval; alpha = rho_new /magma_cdotc( dofs, rr.dval, 1, v.dval, 1, queue ); if( magma_c_isnan_inf( alpha ) ){ info = MAGMA_DIVERGENCE; break; } // s = r - alpha v magma_cbicgstab_2( r.num_rows, r.num_cols, alpha, r.dval, v.dval, s.dval, queue ); // preconditioner CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, s, &ms, precond_par, queue )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, ms, &z, precond_par, queue )); CHECK( magma_c_spmv( c_one, A, z, c_zero, t, queue )); // t=As solver_par->spmv_count++; omega = magma_cdotc( dofs, t.dval, 1, s.dval, 1, queue ) // omega = <s,t>/<t,t> / magma_cdotc( dofs, t.dval, 1, t.dval, 1, queue ); // x = x + alpha * y + omega * z // r = s - omega * t magma_cbicgstab_4( r.num_rows, r.num_cols, alpha, omega, y.dval, z.dval, s.dval, t.dval, x->dval, r.dval, queue ); res = betanom = magma_scnrm2( 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; float residual; CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue)); solver_par->final_res = residual; solver_par->iter_res = res; if ( solver_par->numiter < solver_par->maxiter && info == MAGMA_SUCCESS ) { 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) betanom; 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*solver_par->init_res || 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } info = MAGMA_DIVERGENCE; } cleanup: magma_cmfree(&r, queue ); magma_cmfree(&rr, queue ); magma_cmfree(&p, queue ); magma_cmfree(&v, queue ); magma_cmfree(&s, queue ); magma_cmfree(&y, queue ); magma_cmfree(&z, queue ); magma_cmfree(&t, queue ); magma_cmfree(&ms, queue ); magma_cmfree(&mt, queue ); magma_cmfree(&d1, queue ); magma_cmfree(&d2, queue ); solver_par->info = info; return info; } /* magma_cbicgstab_merge */
extern "C" magma_int_t magma_cpbicgstab( magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x, magma_c_solver_par *solver_par, magma_c_preconditioner *precond_par, magma_queue_t queue ) { magma_int_t info = 0; // set queue for old dense routines magma_queue_t orig_queue=NULL; magmablasGetKernelStream( &orig_queue ); // prepare solver feedback solver_par->solver = Magma_PBICGSTAB; solver_par->numiter = 0; solver_par->info = MAGMA_SUCCESS; // some useful variables magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE, c_mone = MAGMA_C_NEG_ONE; magma_int_t dofs = A.num_rows*b.num_cols; // workspace magma_c_matrix r={Magma_CSR}, rr={Magma_CSR}, p={Magma_CSR}, v={Magma_CSR}, s={Magma_CSR}, t={Magma_CSR}, ms={Magma_CSR}, mt={Magma_CSR}, y={Magma_CSR}, z={Magma_CSR}; CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &rr,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &ms,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &mt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue )); // solver variables magmaFloatComplex alpha, beta, omega, rho_old, rho_new; float nom, betanom, nom0, r0, den, res; // solver setup CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue)); magma_ccopy( dofs, r.dval, 1, rr.dval, 1 ); // rr = r betanom = nom0; nom = nom0*nom0; rho_new = omega = alpha = MAGMA_C_MAKE( 1.0, 0. ); solver_par->init_res = nom0; CHECK( magma_c_spmv( c_one, A, r, c_zero, v, queue )); // z = A r den = MAGMA_C_REAL( magma_cdotc(dofs, v.dval, 1, r.dval, 1) ); // den = z' * r if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) r0 = ATOLERANCE; if ( nom < r0 ) { solver_par->final_res = solver_par->init_res; solver_par->iter_res = solver_par->init_res; goto cleanup; } //Chronometry real_Double_t tempo1, tempo2; tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->res_vec[0] = nom0; solver_par->timing[0] = 0.0; } solver_par->numiter = 0; // start iteration do { solver_par->numiter++; rho_old = rho_new; // rho_old=rho rho_new = magma_cdotc( dofs, rr.dval, 1, r.dval, 1 ); // rho=<rr,r> beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega magma_cscal( dofs, beta, p.dval, 1 ); // p = beta*p magma_caxpy( dofs, c_mone * omega * beta, v.dval, 1 , p.dval, 1 ); // p = p-omega*beta*v magma_caxpy( dofs, c_one, r.dval, 1, p.dval, 1 ); // p = p+r // preconditioner CHECK( magma_c_applyprecond_left( A, p, &mt, precond_par, queue )); CHECK( magma_c_applyprecond_right( A, mt, &y, precond_par, queue )); CHECK( magma_c_spmv( c_one, A, y, c_zero, v, queue )); // v = Ap alpha = rho_new / magma_cdotc( dofs, rr.dval, 1, v.dval, 1 ); magma_ccopy( dofs, r.dval, 1 , s.dval, 1 ); // s=r magma_caxpy( dofs, c_mone * alpha, v.dval, 1 , s.dval, 1 ); // s=s-alpha*v // preconditioner CHECK( magma_c_applyprecond_left( A, s, &ms, precond_par, queue )); CHECK( magma_c_applyprecond_right( A, ms, &z, precond_par, queue )); CHECK( magma_c_spmv( c_one, A, z, c_zero, t, queue )); // t=As // preconditioner CHECK( magma_c_applyprecond_left( A, s, &ms, precond_par, queue )); CHECK( magma_c_applyprecond_left( A, t, &mt, precond_par, queue )); // omega = <ms,mt>/<mt,mt> omega = magma_cdotc( dofs, mt.dval, 1, ms.dval, 1 ) / magma_cdotc( dofs, mt.dval, 1, mt.dval, 1 ); magma_caxpy( dofs, alpha, y.dval, 1 , x->dval, 1 ); // x=x+alpha*p magma_caxpy( dofs, omega, z.dval, 1 , x->dval, 1 ); // x=x+omega*s magma_ccopy( dofs, s.dval, 1 , r.dval, 1 ); // r=s magma_caxpy( dofs, c_mone * omega, t.dval, 1 , r.dval, 1 ); // r=r-omega*t res = betanom = magma_scnrm2( dofs, r.dval, 1 ); nom = betanom*betanom; 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/nom0 < solver_par->epsilon ) { break; } } while ( solver_par->numiter+1 <= solver_par->maxiter ); tempo2 = magma_sync_wtime( queue ); solver_par->runtime = (real_Double_t) tempo2-tempo1; float residual; CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue)); solver_par->final_res = residual; solver_par->iter_res = res; 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) betanom; 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->epsilon*solver_par->init_res ){ 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) betanom; solver_par->timing[(solver_par->numiter)/solver_par->verbose] = (real_Double_t) tempo2-tempo1; } } info = MAGMA_DIVERGENCE; } cleanup: magma_cmfree(&r, queue ); magma_cmfree(&rr, queue ); magma_cmfree(&p, queue ); magma_cmfree(&v, queue ); magma_cmfree(&s, queue ); magma_cmfree(&t, queue ); magma_cmfree(&ms, queue ); magma_cmfree(&mt, queue ); magma_cmfree(&y, queue ); magma_cmfree(&z, queue ); magmablasSetKernelStream( orig_queue ); solver_par->info = info; return info; } /* magma_cbicgstab */
/** Purpose ======= CLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12' U22' ) A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U' denotes the conjugate transpose of U. CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). Arguments --------- @param[in] UPLO CHARACTER Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: - = 'U': Upper triangular - = 'L': Lower triangular @param[in] N INTEGER The order of the matrix A. N >= 0. @param[in] NB INTEGER The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks. @param[out] KB INTEGER The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. @param[in,out] A COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, A contains details of the partial factorization. @param[in] LDA INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[out] ipiv INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = 'U', only the last KB elements of ipiv are set; if UPLO = 'L', only the first KB elements are set. \n If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and ipiv(k) = ipiv(k-1) < 0, then rows and columns k-1 and -ipiv(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and ipiv(k) = ipiv(k+1) < 0, then rows and columns k+1 and -ipiv(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. @param[out] W (workspace) COMPLEX array, dimension (LDW,NB) @param[in] LDW INTEGER The leading dimension of the array W. LDW >= max(1,N). @param[out] INFO INTEGER - = 0: successful exit - > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular. @ingroup magma_chetrf_comp ********************************************************************/ extern "C" magma_int_t magma_clahef_gpu( magma_uplo_t uplo, magma_int_t n, magma_int_t nb, magma_int_t *kb, magmaFloatComplex *hA, magma_int_t lda, magmaFloatComplex_ptr dA, size_t dA_offset, magma_int_t ldda, magma_int_t *ipiv, magmaFloatComplex_ptr dW, size_t dW_offset, magma_int_t lddw, magma_queue_t queue, magma_int_t *info) { /* .. Parameters .. */ float d_one = 1.0; float d_zero = 0.0; float d_eight = 8.0; float d_seven = 7.0; #if defined(PRECISION_c) float f_zero = 0.0; #endif magmaFloatComplex c_one = MAGMA_C_ONE; magmaFloatComplex c_mone = -MAGMA_C_ONE; magma_int_t upper = (uplo == MagmaUpper); magma_int_t ione = 1; /* .. Local Scalars .. */ magma_int_t imax = 0, jmax = 0, kk, kkW, kp, kstep, iinfo; float abs_akk, alpha, colmax, R1, rowmax; magmaFloatComplex Zimax, Z; #define dA(i, j) dA, dA_offset + (j)*ldda + (i) #define dW(i, j) dW, dW_offset + (j)*lddw + (i) #define A(i, j) (hA + (j)*lda + (i)) /* .. Executable Statements .. */ *info = 0; /* Initialize alpha for use in choosing pivot block size. */ alpha = ( d_one+sqrt( d_seven ) ) / d_eight; magma_event_t event = NULL; if( upper ) { /* Factorize the trailing columns of A using the upper triangle of A and working backwards, and compute the matrix W = U12*D for use in updating A11 (note that conjg(W) is actually stored) K is the main loop index, decreasing from N in steps of 1 or 2 KW is the column of W which corresponds to column K of A */ int k, kw = 0; for (k = n-1; k+1 > max(n-nb+1, nb); k -= kstep) { kw = nb - (n-k); /* Copy column K of A to column KW of W and update it */ magma_ccopy( k+1, dA( 0, k ), 1, dW( 0, kw ), 1, queue ); // set imaginary part of diagonal to be zero #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*(k+ kw*lddw+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*(k+ kw*lddw+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #endif if (k+1 < n) { magma_cgemv( MagmaNoTrans, k+1, n-(k+1), c_mone, dA( 0, k+1 ), ldda, dW( k, kw+1 ), lddw, c_one, dW( 0, kw ), ione, queue ); // set imaginary part of diagonal to be zero #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*(k+ kw*lddw+dW_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*(k+ kw*lddw+dW_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #endif } kstep = 1; /* Determine rows and columns to be interchanged and whether a 1-by-1 or 2-by-2 pivot block will be used */ magma_cgetvector_async( 1, dW( k, kw ), 1, &Z, 1, queue, &event ); magma_queue_sync( queue ); abs_akk = fabs( MAGMA_C_REAL( Z ) ); /* imax is the row-index of the largest off-diagonal element in column K, and colmax is its absolute value */ if( k > 0 ) { // magma is one-base imax = magma_icamax( k, dW( 0, kw ), 1, queue ) - 1; magma_cgetvector( 1, dW( imax, kw ), 1, &Z, 1, queue ); colmax = MAGMA_C_ABS1( Z ); } else { colmax = d_zero; } if( max( abs_akk, colmax ) == 0.0 ) { /* Column K is zero: set INFO and continue */ if ( *info == 0 ) *info = k; kp = k; #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dA, 2*(k+ k*ldda+dA_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dA, 2*(k+ k*ldda+dA_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #endif } else { if( abs_akk >= alpha*colmax ) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else { /* Copy column imax to column KW-1 of W and update it */ magma_ccopy( imax+1, dA( 0, imax ), 1, dW( 0, kw-1 ), 1, queue ); #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*(imax+ (kw-1)*lddw+dW_offset)+1, 1, queue, &event ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*(imax+ (kw-1)*lddw+dW_offset)+1, 1, queue, &event ); #endif #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( k-imax, dA(imax,imax+1), ldda, dW(imax+1,kw-1), 1, queue ); #else magma_ccopy( k-imax, dA(imax,imax+1), ldda, dW(imax+1,kw-1), 1, queue ); #endif if( k+1 < n ) { magma_cgemv( MagmaNoTrans, k+1, n-(k+1), c_mone, dA( 0, k+1 ), ldda, dW( imax, kw+1 ), lddw, c_one, dW( 0, kw-1 ), ione, queue ); #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*(imax+ (kw-1)*lddw+dW_offset)+1, 1, queue, &event ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*(imax+ (kw-1)*lddw+dW_offset)+1, 1, queue, &event ); #endif } magma_cgetvector_async( 1, dW( imax, kw-1 ), 1, &Zimax, 1, queue, &event ); magma_queue_sync( queue ); /* jmax is the column-index of the largest off-diagonal element in row imax, and rowmax is its absolute value */ jmax = imax + magma_icamax( k-imax, dW( imax+1, kw-1 ), 1, queue ); magma_cgetvector( 1, dW( jmax, kw-1 ), 1, &Z, 1, queue ); rowmax = MAGMA_C_ABS1( Z ); if ( imax > 0 ) { // magma is one-base jmax = magma_icamax( imax, dW( 0, kw-1 ), 1, queue ) - 1; magma_cgetvector( 1, dW( jmax, kw-1 ), 1, &Z, 1, queue ); rowmax = max( rowmax, MAGMA_C_ABS1( Z ) ); } if( abs_akk >= alpha*colmax*( colmax / rowmax ) ) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else if ( fabs( MAGMA_C_REAL( Zimax ) ) >= alpha*rowmax ) { /* interchange rows and columns K and imax, use 1-by-1 pivot block */ kp = imax; /* copy column KW-1 of W to column KW */ magma_ccopy( k+1, dW( 0, kw-1 ), 1, dW( 0, kw ), 1, queue ); } else { /* interchange rows and columns K-1 and imax, use 2-by-2 pivot block */ kp = imax; kstep = 2; } } kk = k - kstep + 1; kkW = nb - (n - kk); /* Updated column kp is already stored in column kkW of W */ if( kp != kk ) { /* Interchange rows kk and kp in last kk columns of A and W */ // note: row-swap A(:,kk) magmablas_cswap( n-kk, dA( kk, kk ), ldda, dA( kp, kk ), ldda, queue ); magmablas_cswap( n-kk, dW( kk, kkW), lddw, dW( kp, kkW), lddw, queue ); /* Copy non-updated column kk to column kp */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( kk-kp-1, dA( kp+1, kk ), 1, dA( kp, kp+1 ), ldda, queue ); #else magma_ccopy( kk-kp-1, dA( kp+1, kk ), 1, dA( kp, kp+1 ), ldda, queue ); #endif // now A(kp,kk) should be A(kk,kk), and copy to A(kp,kp) magma_ccopy( kp+1, dA( 0, kk ), 1, dA( 0, kp ), 1, queue ); #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dA, 2*(kp+ kp*ldda+dA_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dA, 2*(kp+ kp*ldda+dA_offset)+1, 1, queue, &event ); #endif } if( kstep == 1 ) { /* 1-by-1 pivot block D(k): column KW of W now holds W(k) = U(k)*D(k) where U(k) is the k-th column of U Store U(k) in column k of A */ magma_ccopy( k+1, dW( 0, kw ), 1, dA( 0, k ), 1, queue ); if ( k > 0 ) { magma_cgetvector_async( 1, dA( k, k ), 1, &Z, 1, queue, &event ); magma_queue_sync( queue ); R1 = d_one / MAGMA_C_REAL( Z ); magma_csscal( k, R1, dA( 0, k ), 1, queue ); /* Conjugate W(k) */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( k, dW( 0, kw ), 1, dW( 0, kw ), 1, queue ); #endif } } else { /* 2-by-2 pivot block D(k): columns KW and KW-1 of W now hold ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) where U(k) and U(k-1) are the k-th and (k-1)-th columns of U */ if( k > 1 ) { /* Store U(k) and U(k-1) in columns k and k-1 of A */ magmablas_clascl_2x2( MagmaUpper, k-1, dW(0, kw-1), lddw, dA(0,k-1), ldda, &iinfo, queue ); } /* Copy D(k) to A */ magma_ccopymatrix( 2, 2, dW( k-1, kw-1 ), lddw, dA( k-1, k-1 ), ldda, queue ); /* Conjugate W(k) and W(k-1) */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( k, dW( 0, kw ), 1, dW( 0, kw ), 1, queue ); magmablas_clacpy_cnjg( k-1, dW( 0, kw-1 ), 1, dW( 0, kw-1 ), 1, queue ); #endif } } /* Store details of the interchanges in ipiv */ if( kstep == 1 ) { ipiv[ k ] = 1+kp; } else { ipiv[ k ] = -(1+kp); ipiv[ k-1 ] = -(1+kp); } } /* Update the upper triangle of A11 (= A(1:k,1:k)) as A11 := A11 - U12*D*U12' = A11 - U12*W' computing blocks of NB columns at a time (note that conjg(W) is actually stored) */ kw = nb - (n-k); for (int j = ( k / nb )*nb; j >= 0; j -= nb ) { int jb = min( nb, k-j+1 ); #ifdef SYMMETRIC_UPDATE /* Update the upper triangle of the diagonal block */ for (int jj = j; jj < j + jb; jj++) { #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dA, 2*(jj+ jj*ldda+dA_offset)+1, 1, queue, &event ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dA, 2*(jj+ jj*ldda+dA_offset)+1, 1, queue, &event ); #endif magma_cgemv( MagmaNoTrans, jj-j+1, n-(k+1), c_mone, dA( j, k+1 ), ldda, dW( jj, kw+1 ), lddw, c_one, dA( j, jj ), 1, queue ); #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dA, 2*(jj+ jj*ldda+dA_offset)+1, 1, queue, &event ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dA, 2*(jj+ jj*ldda+dA_offset)+1, 1, queue, &event ); #endif } /* Update the rectangular superdiagonal block */ magma_cgemm( MagmaNoTrans, MagmaTrans, j, jb, n-(k+1), c_mone, dA( 0, k+1 ), ldda, dW( j, kw+1 ), lddw, c_one, dA( 0, j ), ldda, queue ); #else #if defined(PRECISION_z) magmablas_dlaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j+ j*ldda+dA_offset)+1, 2*(1+ldda), queue ); #elif defined(PRECISION_c) magmablas_slaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j+ j*ldda+dA_offset)+1, 2*(1+ldda), queue ); #endif magma_cgemm( MagmaNoTrans, MagmaTrans, j+jb, jb, n-(k+1), c_mone, dA( 0, k+1 ), ldda, dW( j, kw+1 ), lddw, c_one, dA( 0, j ), ldda, queue ); #if defined(PRECISION_z) magmablas_dlaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j+ j*ldda+dA_offset)+1, 2*(1+ldda), queue ); #elif defined(PRECISION_c) magmablas_slaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j+ j*ldda+dA_offset)+1, 2*(1+ldda), queue ); #endif #endif } /* Put U12 in standard form by partially undoing the interchanges in columns k+1:n */ for (int j = k+1; j < n;) { int jj = j; int jp = ipiv[ j ]; if( jp < 0 ) { jp = -jp; j = j + 1; } j = j + 1; jp = jp - 1; if( jp != jj && j < n ) magmablas_cswap( n-j, dA( jp, j ), ldda, dA( jj, j ), ldda, queue ); } // copying the panel back to CPU magma_cgetmatrix_async( n, n-(k+1), dA(0,k+1), ldda, A(0,k+1), lda, queue, &event ); magma_queue_sync( queue ); /* Set KB to the number of columns factorized */ *kb = n - (k+1); } else { /* Factorize the leading columns of A using the lower triangle of A and working forwards, and compute the matrix W = L21*D for use in updating A22 (note that conjg(W) is actually stored) K is the main loop index, increasing from 1 in steps of 1 or 2 */ int k; for (k = 0; k < min(nb-1,n); k += kstep) { /* Copy column K of A to column K of W and update it */ /* -------------------------------------------------------------- */ magma_ccopy( n-k, dA( k, k ), 1, dW( k, k ), 1, queue ); // set imaginary part of diagonal to be zero #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*(k*lddw+k+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*(k*lddw+k+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #endif /* -------------------------------------------------------------- */ magma_cgemv( MagmaNoTrans, n-k, k, c_mone, dA( k, 0 ), ldda, dW( k, 0 ), lddw, c_one, dW( k, k ), ione, queue ); // re-set imaginary part of diagonal to be zero #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*(k*lddw+k+dW_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*(k*lddw+k+dW_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #endif kstep = 1; /* Determine rows and columns to be interchanged and whether a 1-by-1 or 2-by-2 pivot block will be used */ magma_cgetvector_async( 1, dW( k, k ), 1, &Z, 1, queue, &event ); magma_queue_sync( queue ); abs_akk = fabs( MAGMA_C_REAL( Z ) ); /* imax is the row-index of the largest off-diagonal element in column K, and colmax is its absolute value */ if( k < n-1 ) { // magmablas is one-base imax = k + magma_icamax( n-k-1, dW(k+1,k), 1, queue ); magma_cgetvector( 1, dW( imax,k ), 1, &Z, 1, queue ); colmax = MAGMA_C_ABS1( Z ); } else { colmax = d_zero; } if ( max( abs_akk, colmax ) == 0.0 ) { /* Column K is zero: set INFO and continue */ if( *info == 0 ) *info = k; kp = k; // make sure the imaginary part of diagonal is zero #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dA, 2*(k*ldda+k+dA_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dA, 2*(k*ldda+k+dA_offset)+1, 1, queue, &event ); magma_queue_sync( queue ); #endif } else { if ( abs_akk >= alpha*colmax ) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else { /* Copy column imax to column K+1 of W and update it */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( imax-k, dA(imax,k), ldda, dW(k,k+1), 1, queue ); #else magma_ccopy( imax-k, dA( imax, k ), ldda, dW( k, k+1 ), 1, queue ); #endif magma_ccopy( n-imax, dA( imax, imax ), 1, dW( imax, k+1 ), 1, queue ); #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*((k+1)*lddw+imax+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*((k+1)*lddw+imax+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #endif magma_cgemv( MagmaNoTrans, n-k, k, c_mone, dA( k, 0 ), ldda, dW( imax, 0 ), lddw, c_one, dW( k, k+1 ), ione, queue ); #if defined(PRECISION_z) magma_dsetvector_async( 1, &d_zero, 1, dW, 2*((k+1)*lddw+imax+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #elif defined(PRECISION_c) magma_ssetvector_async( 1, &f_zero, 1, dW, 2*((k+1)*lddw+imax+dW_offset)+1, 1, queue, &event); magma_queue_sync( queue ); #endif magma_cgetvector_async( 1, dW(imax,k+1), 1, &Zimax, 1, queue, &event); magma_queue_sync( queue ); /* jmax is the column-index of the largest off-diagonal element in row imax, and rowmax is its absolute value */ // magmablas is one-base jmax = k-1 + magma_icamax( imax-k, dW(k, k+1), 1, queue ); magma_cgetvector( 1, dW(jmax,k+1), 1, &Z, 1, queue ); rowmax = MAGMA_C_ABS1( Z ); if( imax < n-1 ) { // magmablas is one-base jmax = imax + magma_icamax( (n-1)-imax, dW(imax+1,k+1), 1, queue); magma_cgetvector( 1, dW(jmax,k+1), 1, &Z, 1, queue ); rowmax = max( rowmax, MAGMA_C_ABS1( Z ) ); } if( abs_akk >= alpha*colmax*( colmax / rowmax ) ) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else if( fabs( MAGMA_C_REAL( Zimax ) ) >= alpha*rowmax ) { /* interchange rows and columns K and imax, use 1-by-1 pivot block */ kp = imax; /* copy column K+1 of W to column K */ magma_ccopy( n-k, dW( k, k+1 ), 1, dW( k, k ), 1, queue ); } else { /* interchange rows and columns K+1 and imax, use 2-by-2 pivot block */ kp = imax; kstep = 2; } } kk = k + kstep - 1; /* Updated column kp is already stored in column kk of W */ if( kp != kk ) { /* Copy non-updated column kk to column kp */ /* ------------------------------------------------------------------ */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( kp-kk, dA( kk, kk ), 1, dA( kp, kk ), ldda, queue ); #else magma_ccopy( kp-kk, dA( kk, kk ), 1, dA( kp, kk ), ldda, queue ); #endif if ( kp < n ) { magma_ccopy( n-kp, dA( kp, kk), 1, dA( kp, kp ), 1, queue ); } /* ------------------------------------------------------------------ */ /* Interchange rows kk and kp in first kk columns of A and W */ magmablas_cswap( kk+1, dA( kk, 0 ), ldda, dA( kp, 0 ), ldda, queue ); magmablas_cswap( kk+1, dW( kk, 0 ), lddw, dW( kp, 0 ), lddw, queue ); } if ( kstep == 1 ) { /* 1-by-1 pivot block D(k): column k of W now holds W(k) = L(k)*D(k) where L(k) is the k-th column of L Store L(k) in column k of A */ magma_ccopy( n-k, dW( k, k ), 1, dA( k, k ), 1, queue ); if ( k < n-1 ) { magma_cgetvector_async( 1, dA(k,k), 1, &Z, 1, queue, &event ); magma_queue_sync( queue ); R1 = d_one / MAGMA_C_REAL( Z ); magma_csscal((n-1)-k, R1, dA( k+1,k ), 1, queue); /* Conjugate W(k) */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( (n-1)-k, dW( k+1,k ), 1, dW( k+1,k ), 1, queue ); #endif } } else { /* 2-by-2 pivot block D(k): columns k and k+1 of W now hold ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) where L(k) and L(k+1) are the k-th and (k+1)-th columns of L */ magmablas_clascl_2x2( MagmaLower, n-(k+2), dW(k,k), lddw, dA(k+2,k), ldda, &iinfo, queue ); /* Copy D(k) to A */ magma_ccopymatrix( 2, 2, dW( k, k ), lddw, dA( k, k ), ldda, queue ); /* Conjugate W(k) and W(k+1) */ #if defined(PRECISION_z) || defined(PRECISION_c) magmablas_clacpy_cnjg( (n-1)-k, dW( k+1,k ), 1, dW( k+1,k ), 1, queue ); magmablas_clacpy_cnjg( (n-1)-k-1, dW( k+2,k+1), 1, dW( k+2,k+1 ), 1, queue ); #endif } } /* Store details of the interchanges in ipiv */ if ( kstep == 1 ) { ipiv[k] = kp+1; } else { ipiv[k] = -kp-1; ipiv[k+1] = -kp-1; } } /* Update the lower triangle of A22 (= A(k:n,k:n)) as A22 := A22 - L21*D*L21' = A22 - L21*W' computing blocks of NB columns at a time (note that conjg(W) is actually stored) */ for( int j = k; j < n; j += nb ) { int jb = min( nb, n-j ); /* Update the lower triangle of the diagonal block */ #ifdef SYMMETRIC_UPDATE for (int jj = j; jj < j + jb; jj++) { int jnb = j + jb - jj; /* -------------------------------------------------------- */ magma_cgemv( MagmaNoTrans, jnb, k, c_mone, dA( jj, 0 ), ldda, dW( jj, 0 ), lddw, c_one, dA( jj, jj ), ione, queue ); /* -------------------------------------------------------- */ } /* Update the rectangular subdiagonal block */ if( j+jb < n ) { int nk = n - (j+jb); /* -------------------------------------------- */ magma_cgemm( MagmaNoTrans, MagmaTrans, nk, jb, k, c_mone, dA( j+jb, 0 ), ldda, dW( j, 0 ), lddw, c_one, dA( j+jb, j ), ldda, queue ); /* ------------------------------------------- */ } #else #if defined(PRECISION_z) magmablas_dlaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j*ldda+j+dA_offset)+1, 2*(1+ldda), queue ); #elif defined(PRECISION_c) magmablas_slaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j*ldda+j+dA_offset)+1, 2*(1+ldda), queue ); #endif magma_cgemm( MagmaNoTrans, MagmaTrans, n-j, jb, k, c_mone, dA( j, 0 ), ldda, dW( j, 0 ), lddw, c_one, dA( j, j ), ldda, queue ); #if defined(PRECISION_z) magmablas_dlaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j*ldda+j+dA_offset)+1, 2*(1+ldda), queue ); #elif defined(PRECISION_c) magmablas_slaset(MagmaUpperLower, 1, jb, 0, 0, dA, 2*(j*ldda+j+dA_offset)+1, 2*(1+ldda), queue ); #endif #endif } /* Put L21 in standard form by partially undoing the interchanges in columns 1:k-1 */ for (int j = k; j > 0;) { int jj = j; int jp = ipiv[j-1]; if( jp < 0 ) { jp = -jp; j--; } j--; if ( jp != jj && j >= 1 ) { magmablas_cswap( j, dA( jp-1,0 ), ldda, dA( jj-1,0 ), ldda, queue ); } } // copying the panel back to CPU magma_cgetmatrix_async( n, k, dA(0,0), ldda, A(0,0), lda, queue, &event ); magma_queue_sync( queue ); /* Set KB to the number of columns factorized */ *kb = k; } return *info; /* End of CLAHEF */ }