/** Purpose ------- CLAHR2 reduces the first NB columns of a complex general n-BY-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero. The reduction is performed by an orthogonal similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V', and also the matrix Y = A * V. (Note this is different than LAPACK, which computes Y = A * V * T.) This is an auxiliary routine called by CGEHRD. Arguments --------- @param[in] n INTEGER The order of the matrix A. @param[in] k INTEGER The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. K < N. @param[in] nb INTEGER The number of columns to be reduced. @param[in,out] A COMPLEX array, dimension (LDA,N-K+1) On entry, the n-by-(n-k+1) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A are unchanged. See Further Details. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[out] tau COMPLEX array, dimension (NB) The scalar factors of the elementary reflectors. See Further Details. @param[out] T COMPLEX array, dimension (LDT,NB) The upper triangular matrix T. @param[in] ldt INTEGER The leading dimension of the array T. LDT >= NB. @param[out] Y COMPLEX array, dimension (LDY,NB) The n-by-nb matrix Y. @param[in] ldy INTEGER The leading dimension of the array Y. LDY >= N. @param[in,out] data Structure with pointers to dA, dT, dV, dW, dY which are distributed across multiple GPUs. Further Details --------------- The matrix Q is represented as a product of nb elementary reflectors Q = H(1) H(2) . . . H(nb). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in A(i+k+1:n,i), and tau in TAU(i). The elements of the vectors v together form the (n-k+1)-by-nb matrix V which is needed, with T and Y, to apply the transformation to the unreduced part of the matrix, using an update of the form: A := (I - V*T*V') * (A - Y*T*V'). The contents of A on exit are illustrated by the following example with n = 7, k = 3 and nb = 2: @verbatim ( a a a a a ) ( a a a a a ) ( a a a a a ) ( h h a a a ) ( v1 h a a a ) ( v1 v2 a a a ) ( v1 v2 a a a ) @endverbatim where "a" denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). This implementation follows the hybrid algorithm and notations described in S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009. @ingroup magma_cgeev_aux ********************************************************************/ extern "C" magma_int_t magma_clahr2_m( magma_int_t n, magma_int_t k, magma_int_t nb, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *T, magma_int_t ldt, magmaFloatComplex *Y, magma_int_t ldy, struct cgehrd_data *data ) { #define A( i, j ) ( A + (i) + (j)*lda) #define Y( i, j ) ( Y + (i) + (j)*ldy) #define T( i, j ) ( T + (i) + (j)*ldt) #define dA( d, i, j ) (data->A [d] + (i) + (j)*ldda) #define dTi( d ) (data->Ti[d]) #define dV( d, i, j ) (data->V [d] + (i) + (j)*ldv ) #define dVd( d, i, j ) (data->Vd[d] + (i) + (j)*ldvd) #define dY( d, i, j ) (data->Y [d] + (i) + (j)*ldda) magmaFloatComplex c_zero = MAGMA_C_ZERO; magmaFloatComplex c_one = MAGMA_C_ONE; magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE; magmaFloatComplex tmp; magma_int_t ngpu = data->ngpu; magma_int_t ldda = data->ldda; magma_int_t ldv = data->ldv; magma_int_t ldvd = data->ldvd; magma_int_t ione = 1; magma_int_t d, dki1, dn, nblocks, gblock, lblock, lgid; magma_int_t n_k_i_1, n_k; magmaFloatComplex scale; magma_int_t i; magmaFloatComplex ei = MAGMA_C_ZERO; magma_int_t info_data = 0; magma_int_t *info = &info_data; if (n < 0) { *info = -1; } else if (k < 0 || k >= n) { *info = -2; } else if (nb < 1 || nb > n) { *info = -3; } else if (lda < max(1,n)) { *info = -5; } else if (ldt < nb) { *info = -8; } else if (ldy < max(1,n)) { *info = -10; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } // adjust from 1-based indexing k -= 1; // Function Body if (n <= 1) return *info; magma_device_t orig_dev; magma_getdevice( &orig_dev ); magma_queue_t orig_stream; magmablasGetKernelStream( &orig_stream ); // zero out current top block of V on all GPUs for( d = 0; d < ngpu; ++d ) { magma_setdevice( d ); magmablasSetKernelStream( data->streams[d] ); magmablas_claset( MagmaFull, nb, nb, c_zero, c_zero, dV(d,k,0), ldv ); } // set all Y=0 lapackf77_claset( "Full", &n, &nb, &c_zero, &c_zero, Y, &ldy ); for (i = 0; i < nb; ++i) { n_k_i_1 = n - k - i - 1; n_k = n - k; if (i > 0) { // Finish applying I - V * T * V' on right tmp = MAGMA_C_NEGATE( tau[i-1] ); blasf77_caxpy( &n_k, &tmp, Y(k,i-1), &ione, A(k,i), &ione ); // Apply I - V * T' * V' to this column (call it b) from the // left, using the last column of T as workspace, w. // // Let V = ( V1 ) and b = ( b1 ) (first i-1 rows) // ( V2 ) ( b2 ) // where V1 is unit lower triangular // w := b1 = A(k+1:k+i, i) blasf77_ccopy( &i, A(k+1,i), &ione, T(0,nb-1), &ione ); // w := V1' * b1 = VA(k+1:k+i, 0:i-1)' * w blasf77_ctrmv( "Lower", "Conj", "Unit", &i, A(k+1,0), &lda, T(0,nb-1), &ione ); // w := w + V2'*b2 = w + VA(k+i+1:n-1, 0:i-1)' * A(k+i+1:n-1, i) blasf77_cgemv( "Conj", &n_k_i_1, &i, &c_one, A(k+i+1,0), &lda, A(k+i+1,i), &ione, &c_one, T(0,nb-1), &ione ); // w := T'*w = T(0:i-1, 0:i-1)' * w blasf77_ctrmv( "Upper", "Conj", "Non-unit", &i, T(0,0), &ldt, T(0,nb-1), &ione ); // b2 := b2 - V2*w = A(k+i+1:n-1, i) - VA(k+i+1:n-1, 0:i-1) * w blasf77_cgemv( "No trans", &n_k_i_1, &i, &c_neg_one, A(k+i+1,0), &lda, T(0,nb-1), &ione, &c_one, A(k+i+1,i), &ione ); // w := V1*w = VA(k+1:k+i, 0:i-1) * w blasf77_ctrmv( "Lower", "No trans", "Unit", &i, A(k+1,0), &lda, T(0,nb-1), &ione ); // b1 := b1 - w = A(k+1:k+i-1, i) - w blasf77_caxpy( &i, &c_neg_one, T(0,nb-1), &ione, A(k+1,i), &ione ); // Restore diagonal element, saved below during previous iteration *A(k+i,i-1) = ei; } // Generate the elementary reflector H(i) to annihilate A(k+i+1:n-1,i) lapackf77_clarfg( &n_k_i_1, A(k+i+1,i), A(k+i+2,i), &ione, &tau[i] ); // Save diagonal element and set to one, to simplify multiplying by V ei = *A(k+i+1,i); *A(k+i+1,i) = c_one; // compute yi = A vi = sum_g A{d} vi{d} nblocks = (n-1) / nb / ngpu + 1; for( d = 0; d < ngpu; ++d ) { magma_setdevice( d ); magmablasSetKernelStream( data->streams[d] ); // dV(k+i+1:n-1, i) = VA(k+i:n, i) magma_csetvector_async( n_k_i_1, A(k+i+1,i), 1, dV(d, k+i+1, i), 1, data->streams[d] ); // copy column of dV -> dVd, using block cyclic distribution. // This assumes V and Vd have been padded so that // a 2D matrix copy doesn't access them out-of-bounds gblock = k / nb; lblock = gblock / ngpu; lgid = gblock % ngpu; if ( d < lgid ) { lblock += 1; } // treat V as (nb*ngpu) x nblock matrix, and Vd as nb x nblock matrix magmablas_clacpy( MagmaFull, nb, nblocks-lblock, dV (d, d*nb + lblock*nb*ngpu, i), nb*ngpu, dVd(d, 0 + lblock*nb, i), nb ); // convert global indices (k) to local indices (dk) magma_indices_1D_bcyclic( nb, ngpu, d, k+i+1, n, &dki1, &dn ); // dY(k:n, i) = dA(k:n, k+i+1:n) * dV(k+i+1:n, i) // skip if matrix is empty // each GPU copies to different temporary vector in Y, // which are summed in separate loop below if ( dn-dki1 > 0 ) { magma_cgemv( MagmaNoTrans, n-k, dn-dki1, c_one, dA (d, k, dki1), ldda, dVd(d, dki1, i), 1, c_zero, dY (d, k, i), 1 ); // copy vector to host, storing in column nb+d of Y // as temporary space (Y has >= nb+ngpu columns) magma_cgetvector_async( n-k, dY(d, k, i), 1, Y(k, nb+d), 1, data->streams[d] ); } } // while GPU is doing above Ag*v... // Compute T(0:i,i) = [ -tau T V' vi ] // [ tau ] // T(0:i-1, i) = -tau VA(k+i+1:n-1, 0:i-1)' VA(k+i+1:n-1, i) scale = MAGMA_C_NEGATE( tau[i] ); blasf77_cgemv( "Conj", &n_k_i_1, &i, &scale, A(k+i+1,0), &lda, A(k+i+1,i), &ione, &c_zero, T(0,i), &ione ); // T(0:i-1, i) = T(0:i-1, 0:i-1) * T(0:i-1, i) blasf77_ctrmv( "Upper", "No trans", "Non-unit", &i, T(0,0), &ldt, T(0,i), &ione ); *T(i,i) = tau[i]; // apply reflectors to next column, A(i+1), on right only. // one axpy will be required to finish this, in the next iteration above if ( i > 0 && i+1 < nb ) { // Update next column, A(k:n,i+1), applying Q on right. // One axpy will be required to finish this, in the next iteration // above, after yi is computed. // This updates one more row than LAPACK does (row k), // making block above panel an even multiple of nb. // Use last column of T as workspace, w. magma_int_t i1 = i+1; // If complex, conjugate row of V, and undo afterwards #if defined(PRECISION_z) || defined(PRECISION_c) lapackf77_clacgv( &i1, A(k+i1,0), &lda ); #endif // w = T(0:i, 0:i+1) * VA(k+i+1, 0:i+1)' // T is now rectangular, so we use gemv instead of trmv as in lapack. blasf77_cgemv( "No trans", &i, &i1, &c_one, T(0,0), &ldt, A(k+i1,0), &lda, &c_zero, T(0,nb-1), &ione ); #if defined(PRECISION_z) || defined(PRECISION_c) lapackf77_clacgv( &i1, A(k+i1,0), &lda ); #endif // A(k:n, i+1) -= Y(k:n, 0:i) * w blasf77_cgemv( "No trans", &n_k, &i, &c_neg_one, Y(k,0), &ldy, T(0,nb-1), &ione, &c_one, A(k,i1), &ione ); } // yi = sum_g yi{d} for( d = 0; d < ngpu; ++d ) { magma_setdevice( d ); magma_queue_sync( data->streams[d] ); magma_indices_1D_bcyclic( nb, ngpu, d, k+i+1, n, &dki1, &dn ); if ( dn-dki1 > 0 ) { // yi = yi + yi{d} blasf77_caxpy( &n_k, &c_one, Y(k,nb+d), &ione, Y(k,i), &ione ); } } } // Restore diagonal element *A(k+nb,nb-1) = ei; // compute Y = Am V = sum_g Am{d} V{d} --- top part, Y(0:k-1,:) for( d = 0; d < ngpu; ++d ) { magma_setdevice( d ); magmablasSetKernelStream( data->streams[d] ); // convert global indices (k) to local indices (dk) magma_indices_1D_bcyclic( nb, ngpu, d, k+1, n, &dki1, &dn ); // dY(0:k, :) = dA(0:k, k+i+1:n-1) * dV(k+i+1:n-1, :) // skip if matrix is empty // each GPU copies to different temporary block in Y, // which are summed in separate loop below if ( dn-dki1 > 0 ) { magma_cgemm( MagmaNoTrans, MagmaNoTrans, k, nb, dn-dki1, c_one, dA (d, 0, dki1), ldda, dVd(d, dki1, 0), ldvd, c_zero, dY (d, 0, 0), ldda ); // copy result to host, storing in columns [nb + nb*d : nb + nb*(d+1)] of Y // as temporary space (Y has nb + nb*ngpu columns) magma_cgetmatrix_async( k, nb, dY(d, 0, 0), ldda, Y(0,nb+nb*d), ldy, data->streams[d] ); } } // Y = sum_g Y{d} for( d = 0; d < ngpu; ++d ) { magma_setdevice( d ); magma_queue_sync( 0 ); magma_indices_1D_bcyclic( nb, ngpu, d, k+1, n, &dki1, &dn ); if ( dn-dki1 > 0 ) { // Y = Y + Am V for( i = 0; i < nb; ++i ) { blasf77_caxpy( &k, &c_one, Y(0,nb+nb*d+i), &ione, Y(0,i), &ione ); } } } // copy Y and T matrices to GPUs for( d = 0; d < ngpu; ++d ) { magma_setdevice( d ); magma_csetmatrix_async( n, nb, Y, ldy, dY(d, 0, 0), ldda, data->streams[d] ); magma_csetmatrix_async( nb, nb, T, nb, dTi(d), nb, data->streams[d] ); } magma_setdevice( orig_dev ); magmablasSetKernelStream( orig_stream ); return *info; } /* magma_clahr2 */
extern "C" magma_int_t magma_cpidr_strms( 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_PIDRMERGE; solver_par->numiter = 0; solver_par->spmv_count = 0; solver_par->init_res = 0.0; solver_par->final_res = 0.0; solver_par->iter_res = 0.0; solver_par->runtime = 0.0; // constants const magmaFloatComplex c_zero = MAGMA_C_ZERO; const magmaFloatComplex c_one = MAGMA_C_ONE; const magmaFloatComplex c_n_one = MAGMA_C_NEG_ONE; // internal user options const magma_int_t smoothing = 1; // 0 = disable, 1 = enable const float angle = 0.7; // [0-1] // local variables magma_int_t iseed[4] = {0, 0, 0, 1}; magma_int_t dof; magma_int_t s; magma_int_t distr; magma_int_t k, i, sk; magma_int_t innerflag; magma_int_t ldd; magma_int_t q; float residual; float nrm; float nrmb; float nrmr; float nrmt; float rho; magmaFloatComplex om; magmaFloatComplex gamma; // matrices and vectors magma_c_matrix dxs = {Magma_CSR}; magma_c_matrix dr = {Magma_CSR}, drs = {Magma_CSR}; magma_c_matrix dP = {Magma_CSR}, dP1 = {Magma_CSR}; magma_c_matrix dG = {Magma_CSR}, dGcol = {Magma_CSR}; magma_c_matrix dU = {Magma_CSR}; magma_c_matrix dM = {Magma_CSR}; magma_c_matrix df = {Magma_CSR}; magma_c_matrix dt = {Magma_CSR}, dtt = {Magma_CSR}; magma_c_matrix dc = {Magma_CSR}; magma_c_matrix dv = {Magma_CSR}; magma_c_matrix dlu = {Magma_CSR}; magma_c_matrix dskp = {Magma_CSR}; magma_c_matrix dalpha = {Magma_CSR}; magma_c_matrix dbeta = {Magma_CSR}; magmaFloatComplex *hMdiag = NULL; magmaFloatComplex *hskp = NULL; magmaFloatComplex *halpha = NULL; magmaFloatComplex *hbeta = NULL; magmaFloatComplex *d1 = NULL, *d2 = NULL; // queue variables const magma_int_t nqueues = 3; // number of queues magma_queue_t queues[nqueues]; // chronometry real_Double_t tempo1, tempo2; // create additional queues queues[0] = queue; for ( q = 1; q < nqueues; q++ ) { magma_queue_create( queue->device(), &(queues[q]) ); } // initial s space // TODO: add option for 's' (shadow space number) // Hack: uses '--restart' option as the shadow space number. // This is not a good idea because the default value of restart option is used to detect // if the user provided a custom restart. This means that if the default restart value // is changed then the code will think it was the user (unless the default value is // also updated in the 'if' statement below. s = 1; if ( solver_par->restart != 50 ) { if ( solver_par->restart > A.num_cols ) { s = A.num_cols; } else { s = solver_par->restart; } } solver_par->restart = s; // set max iterations solver_par->maxiter = min( 2 * A.num_cols, solver_par->maxiter ); // check if matrix A is square if ( A.num_rows != A.num_cols ) { //printf("Matrix A is not square.\n"); info = MAGMA_ERR_NOT_SUPPORTED; goto cleanup; } // |b| nrmb = magma_scnrm2( b.num_rows, b.dval, 1, queue ); if ( nrmb == 0.0 ) { magma_cscal( x->num_rows, MAGMA_C_ZERO, x->dval, 1, queue ); info = MAGMA_SUCCESS; goto cleanup; } // t = 0 // make t twice as large to contain both, dt and dr ldd = magma_roundup( b.num_rows, 32 ); CHECK( magma_cvinit( &dt, Magma_DEV, ldd, 2, c_zero, queue )); dt.num_rows = b.num_rows; dt.num_cols = 1; dt.nnz = dt.num_rows; // redirect the dr.dval to the second part of dt CHECK( magma_cvinit( &dr, Magma_DEV, b.num_rows, 1, c_zero, queue )); magma_free( dr.dval ); dr.dval = dt.dval + ldd; // r = b - A x CHECK( magma_cresidualvec( A, b, *x, &dr, &nrmr, queue )); // |r| solver_par->init_res = nrmr; 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)nrmr; } // check if initial is guess good enough if ( nrmr <= solver_par->atol || nrmr/nrmb <= solver_par->rtol ) { info = MAGMA_SUCCESS; goto cleanup; } // P = randn(n, s) // P = ortho(P) //--------------------------------------- // P = 0.0 CHECK( magma_cvinit( &dP, Magma_CPU, A.num_cols, s, c_zero, queue )); // P = randn(n, s) distr = 3; // 1 = unif (0,1), 2 = unif (-1,1), 3 = normal (0,1) dof = dP.num_rows * dP.num_cols; lapackf77_clarnv( &distr, iseed, &dof, dP.val ); // transfer P to device CHECK( magma_cmtransfer( dP, &dP1, Magma_CPU, Magma_DEV, queue )); magma_cmfree( &dP, queue ); // P = ortho(P1) if ( dP1.num_cols > 1 ) { // P = magma_cqr(P1), QR factorization CHECK( magma_cqr( dP1.num_rows, dP1.num_cols, dP1, dP1.ld, &dP, NULL, queue )); } else { // P = P1 / |P1| nrm = magma_scnrm2( dof, dP1.dval, 1, queue ); nrm = 1.0 / nrm; magma_csscal( dof, nrm, dP1.dval, 1, queue ); CHECK( magma_cmtransfer( dP1, &dP, Magma_DEV, Magma_DEV, queue )); } magma_cmfree( &dP1, queue ); //--------------------------------------- // allocate memory for the scalar products CHECK( magma_cmalloc_pinned( &hskp, 5 )); CHECK( magma_cvinit( &dskp, Magma_DEV, 4, 1, c_zero, queue )); CHECK( magma_cmalloc_pinned( &halpha, s )); CHECK( magma_cvinit( &dalpha, Magma_DEV, s, 1, c_zero, queue )); CHECK( magma_cmalloc_pinned( &hbeta, s )); CHECK( magma_cvinit( &dbeta, Magma_DEV, s, 1, c_zero, queue )); // workspace for merged dot product CHECK( magma_cmalloc( &d1, max(2, s) * b.num_rows )); CHECK( magma_cmalloc( &d2, max(2, s) * b.num_rows )); // smoothing enabled if ( smoothing > 0 ) { // set smoothing solution vector CHECK( magma_cmtransfer( *x, &dxs, Magma_DEV, Magma_DEV, queue )); // tt = 0 // make tt twice as large to contain both, dtt and drs ldd = magma_roundup( b.num_rows, 32 ); CHECK( magma_cvinit( &dtt, Magma_DEV, ldd, 2, c_zero, queue )); dtt.num_rows = dr.num_rows; dtt.num_cols = 1; dtt.nnz = dtt.num_rows; // redirect the drs.dval to the second part of dtt CHECK( magma_cvinit( &drs, Magma_DEV, dr.num_rows, 1, c_zero, queue )); magma_free( drs.dval ); drs.dval = dtt.dval + ldd; // set smoothing residual vector magma_ccopyvector( dr.num_rows, dr.dval, 1, drs.dval, 1, queue ); } // G(n,s) = 0 if ( s > 1 ) { ldd = magma_roundup( A.num_rows, 32 ); CHECK( magma_cvinit( &dG, Magma_DEV, ldd, s, c_zero, queue )); dG.num_rows = A.num_rows; } else { CHECK( magma_cvinit( &dG, Magma_DEV, A.num_rows, s, c_zero, queue )); } // dGcol represents a single column of dG, array pointer is set inside loop CHECK( magma_cvinit( &dGcol, Magma_DEV, dG.num_rows, 1, c_zero, queue )); magma_free( dGcol.dval ); // U(n,s) = 0 if ( s > 1 ) { ldd = magma_roundup( A.num_cols, 32 ); CHECK( magma_cvinit( &dU, Magma_DEV, ldd, s, c_zero, queue )); dU.num_rows = A.num_cols; } else { CHECK( magma_cvinit( &dU, Magma_DEV, A.num_cols, s, c_zero, queue )); } // M(s,s) = I CHECK( magma_cvinit( &dM, Magma_DEV, s, s, c_zero, queue )); CHECK( magma_cmalloc_pinned( &hMdiag, s )); magmablas_claset( MagmaFull, dM.num_rows, dM.num_cols, c_zero, c_one, dM.dval, dM.ld, queue ); // f = 0 CHECK( magma_cvinit( &df, Magma_DEV, dP.num_cols, 1, c_zero, queue )); // c = 0 CHECK( magma_cvinit( &dc, Magma_DEV, dM.num_cols, 1, c_zero, queue )); // v = r CHECK( magma_cmtransfer( dr, &dv, Magma_DEV, Magma_DEV, queue )); // lu = 0 CHECK( magma_cvinit( &dlu, Magma_DEV, dr.num_rows, 1, c_zero, queue )); //--------------START TIME--------------- // chronometry tempo1 = magma_sync_wtime( queue ); if ( solver_par->verbose > 0 ) { solver_par->timing[0] = 0.0; } om = MAGMA_C_ONE; gamma = MAGMA_C_ZERO; innerflag = 0; // start iteration do { solver_par->numiter++; // new RHS for small systems // f = P' r // Q1 magma_cgemvmdot_shfl( dP.num_rows, dP.num_cols, dP.dval, dr.dval, d1, d2, df.dval, queues[1] ); // skp[4] = f(k) // Q1 magma_cgetvector_async( 1, df.dval, 1, &hskp[4], 1, queues[1] ); // c(k:s) = f(k:s) // Q1 magma_ccopyvector_async( s, df.dval, 1, dc.dval, 1, queues[1] ); // c(k:s) = M(k:s,k:s) \ f(k:s) // Q1 magma_ctrsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, s, dM.dval, dM.ld, dc.dval, 1, queues[1] ); // shadow space loop for ( k = 0; k < s; ++k ) { sk = s - k; dGcol.dval = dG.dval + k * dG.ld; // v = r - G(:,k:s) c(k:s) // Q1 magmablas_cgemv( MagmaNoTrans, dG.num_rows, sk, c_n_one, dGcol.dval, dG.ld, &dc.dval[k], 1, c_one, dv.dval, 1, queues[1] ); // preconditioning operation // v = L \ v; // v = U \ v; // Q1 CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queues[1] )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queues[1] )); // sync Q0 --> U(:,k) = U(:,k) - U(:,1:k) * alpha(1:k) magma_queue_sync( queues[0] ); // U(:,k) = om * v + U(:,k:s) c(k:s) // Q1 magmablas_cgemv( MagmaNoTrans, dU.num_rows, sk, c_one, &dU.dval[k*dU.ld], dU.ld, &dc.dval[k], 1, om, dv.dval, 1, queues[1] ); // G(:,k) = A U(:,k) // Q1 CHECK( magma_c_spmv( c_one, A, dv, c_zero, dGcol, queues[1] )); solver_par->spmv_count++; // bi-orthogonalize the new basis vectors for ( i = 0; i < k; ++i ) { // alpha = P(:,i)' G(:,k) // Q1 halpha[i] = magma_cdotc( dP.num_rows, &dP.dval[i*dP.ld], 1, dGcol.dval, 1, queues[1] ); // implicit sync Q1 --> alpha = P(:,i)' G(:,k) // alpha = alpha / M(i,i) halpha[i] = halpha[i] / hMdiag[i]; // G(:,k) = G(:,k) - alpha * G(:,i) // Q1 magma_caxpy( dG.num_rows, -halpha[i], &dG.dval[i*dG.ld], 1, dGcol.dval, 1, queues[1] ); } // sync Q1 --> compute new G, skp[4] = f(k magma_queue_sync( queues[1] ); // new column of M = P'G, first k-1 entries are zero // M(k:s,k) = P(:,k:s)' G(:,k) // Q2 magma_cgemvmdot_shfl( dP.num_rows, sk, &dP.dval[k*dP.ld], dGcol.dval, d1, d2, &dM.dval[k*dM.ld+k], queues[2] ); // U(:,k) = v // Q0 magma_ccopyvector_async( dU.num_rows, dv.dval, 1, &dU.dval[k*dU.ld], 1, queues[0] ); // non-first s iteration if ( k > 0 ) { // alpha = dalpha // Q0 magma_csetvector_async( k, halpha, 1, dalpha.dval, 1, queues[0] ); // U update outside of loop using GEMV // U(:,k) = U(:,k) - U(:,1:k) * alpha(1:k) // Q0 magmablas_cgemv( MagmaNoTrans, dU.num_rows, k, c_n_one, dU.dval, dU.ld, dalpha.dval, 1, c_one, &dU.dval[k*dU.ld], 1, queues[0] ); } // Mdiag(k) = M(k,k) // Q2 magma_cgetvector( 1, &dM.dval[k*dM.ld+k], 1, &hMdiag[k], 1, queues[2] ); // implicit sync Q2 --> Mdiag(k) = M(k,k) // check M(k,k) == 0 if ( MAGMA_C_EQUAL(hMdiag[k], MAGMA_C_ZERO) ) { innerflag = 1; info = MAGMA_DIVERGENCE; break; } // beta = f(k) / M(k,k) hbeta[k] = hskp[4] / hMdiag[k]; // check for nan if ( magma_c_isnan( hbeta[k] ) || magma_c_isinf( hbeta[k] )) { innerflag = 1; info = MAGMA_DIVERGENCE; break; } // non-last s iteration if ( (k + 1) < s ) { // f(k+1:s) = f(k+1:s) - beta * M(k+1:s,k) // Q1 magma_caxpy( sk-1, -hbeta[k], &dM.dval[k*dM.ld+(k+1)], 1, &df.dval[k+1], 1, queues[1] ); // c(k+1:s) = f(k+1:s) // Q1 magma_ccopyvector_async( sk-1, &df.dval[k+1], 1, &dc.dval[k+1], 1, queues[1] ); // c(k+1:s) = M(k+1:s,k+1:s) \ f(k+1:s) // Q1 magma_ctrsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, sk-1, &dM.dval[(k+1)*dM.ld+(k+1)], dM.ld, &dc.dval[k+1], 1, queues[1] ); // skp[4] = f(k+1) // Q1 magma_cgetvector_async( 1, &df.dval[k+1], 1, &hskp[4], 1, queues[1] ); } // r = r - beta * G(:,k) // Q2 magma_caxpy( dr.num_rows, -hbeta[k], dGcol.dval, 1, dr.dval, 1, queues[2] ); // smoothing disabled if ( smoothing <= 0 ) { // |r| // Q2 nrmr = magma_scnrm2( dr.num_rows, dr.dval, 1, queues[2] ); // implicit sync Q2 --> |r| // v = r // Q1 magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] ); // smoothing enabled } else { // x = x + beta * U(:,k) // Q0 magma_caxpy( x->num_rows, hbeta[k], &dU.dval[k*dU.ld], 1, x->dval, 1, queues[0] ); // smoothing operation //--------------------------------------- // t = rs - r // Q2 magma_cidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queues[2] ); // t't // t'rs // Q2 CHECK( magma_cgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queues[2] )); // skp[2-3] = dskp[2-3] // Q2 magma_cgetvector( 2, &dskp.dval[2], 1, &hskp[2], 1, queues[2] ); // implicit sync Q2 --> skp = dskp // gamma = (t' * rs) / (t' * t) gamma = hskp[3] / hskp[2]; // xs = xs - gamma * (xs - x) // Q0 magma_cidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queues[0] ); // v = r // Q1 magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] ); // rs = rs - gamma * t // Q2 magma_caxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queues[2] ); // |rs| // Q2 nrmr = magma_scnrm2( drs.num_rows, drs.dval, 1, queues[2] ); // implicit sync Q2 --> |r| //--------------------------------------- } // store current timing and residual 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)nrmr; solver_par->timing[(solver_par->numiter) / solver_par->verbose] = (real_Double_t)tempo2 - tempo1; } } // check convergence or iteration limit if ( nrmr <= solver_par->atol || nrmr/nrmb <= solver_par->rtol ) { s = k + 1; // for the x-update outside the loop innerflag = 2; info = MAGMA_SUCCESS; break; } } // smoothing disabled if ( smoothing <= 0 && innerflag != 1 ) { // dbeta(1:s) = beta(1:s) // Q0 magma_csetvector_async( s, hbeta, 1, dbeta.dval, 1, queues[0] ); // x = x + U(:,1:s) * beta(1:s) // Q0 magmablas_cgemv( MagmaNoTrans, dU.num_rows, s, c_one, dU.dval, dU.ld, dbeta.dval, 1, c_one, x->dval, 1, queues[0] ); } // check convergence or iteration limit or invalid result of inner loop if ( innerflag > 0 ) { break; } // preconditioning operation // v = L \ v; // v = U \ v; // Q2 CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queues[2] )); CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queues[2] )); // t = A v // Q2 CHECK( magma_c_spmv( c_one, A, dv, c_zero, dt, queues[2] )); solver_par->spmv_count++; // computation of a new omega //--------------------------------------- // t't // t'r // Q2 CHECK( magma_cgemvmdot_shfl( dt.ld, 2, dt.dval, dt.dval, d1, d2, dskp.dval, queues[2] )); // skp[0-2] = dskp[0-2] // Q2 magma_cgetvector( 2, dskp.dval, 1, hskp, 1, queues[2] ); // implicit sync Q2 --> skp = dskp // |t| nrmt = magma_ssqrt( MAGMA_C_REAL(hskp[0]) ); // rho = abs((t' * r) / (|t| * |r|)) rho = MAGMA_D_ABS( MAGMA_C_REAL(hskp[1]) / (nrmt * nrmr) ); // om = (t' * r) / (|t| * |t|) om = hskp[1] / hskp[0]; if ( rho < angle ) { om = (om * angle) / rho; } //--------------------------------------- if ( MAGMA_C_EQUAL(om, MAGMA_C_ZERO) ) { info = MAGMA_DIVERGENCE; break; } // sync Q1 --> v = r magma_queue_sync( queues[1] ); // r = r - om * t // Q2 magma_caxpy( dr.num_rows, -om, dt.dval, 1, dr.dval, 1, queues[2] ); // x = x + om * v // Q0 magma_caxpy( x->num_rows, om, dv.dval, 1, x->dval, 1, queues[0] ); // smoothing disabled if ( smoothing <= 0 ) { // |r| // Q2 nrmr = magma_scnrm2( dr.num_rows, dr.dval, 1, queues[2] ); // implicit sync Q2 --> |r| // v = r // Q1 magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] ); // smoothing enabled } else { // smoothing operation //--------------------------------------- // t = rs - r // Q2 magma_cidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queues[2] ); // t't // t'rs // Q2 CHECK( magma_cgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queues[2] )); // skp[2-3] = dskp[2-3] // Q2 magma_cgetvector( 2, &dskp.dval[2], 1, &hskp[2], 1, queues[2] ); // implicit sync Q2 --> skp = dskp // gamma = (t' * rs) / (t' * t) gamma = hskp[3] / hskp[2]; // xs = xs - gamma * (xs - x) // Q0 magma_cidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queues[0] ); // v = r // Q1 magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] ); // rs = rs - gamma * (rs - r) // Q2 magma_caxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queues[2] ); // |rs| // Q2 nrmr = magma_scnrm2( drs.num_rows, drs.dval, 1, queues[2] ); // implicit sync Q2 --> |r| //--------------------------------------- } // store current timing and residual if ( solver_par->verbose > 0 ) { tempo2 = magma_sync_wtime( queue ); magma_queue_sync( queue ); if ( (solver_par->numiter) % solver_par->verbose == 0 ) { solver_par->res_vec[(solver_par->numiter) / solver_par->verbose] = (real_Double_t)nrmr; solver_par->timing[(solver_par->numiter) / solver_par->verbose] = (real_Double_t)tempo2 - tempo1; } } // check convergence or iteration limit if ( nrmr <= solver_par->atol || nrmr/nrmb <= solver_par->rtol ) { info = MAGMA_SUCCESS; break; } } while ( solver_par->numiter + 1 <= solver_par->maxiter ); // sync all queues for ( q = 0; q < nqueues; q++ ) { magma_queue_sync( queues[q] ); } // smoothing enabled if ( smoothing > 0 ) { // x = xs magma_ccopyvector_async( x->num_rows, dxs.dval, 1, x->dval, 1, queue ); // r = rs magma_ccopyvector_async( dr.num_rows, drs.dval, 1, dr.dval, 1, queue ); } // get last iteration timing tempo2 = magma_sync_wtime( queue ); magma_queue_sync( queue ); solver_par->runtime = (real_Double_t)tempo2 - tempo1; //--------------STOP TIME---------------- // get final stats solver_par->iter_res = nrmr; CHECK( magma_cresidualvec( A, b, *x, &dr, &residual, queue )); solver_par->final_res = residual; // set solver conclusion if ( info != MAGMA_SUCCESS && info != MAGMA_DIVERGENCE ) { if ( solver_par->init_res > solver_par->final_res ) { info = MAGMA_SLOW_CONVERGENCE; } } cleanup: // free resources // sync all queues, destory additional queues magma_queue_sync( queues[0] ); for ( q = 1; q < nqueues; q++ ) { magma_queue_sync( queues[q] ); magma_queue_destroy( queues[q] ); } // smoothing enabled if ( smoothing > 0 ) { drs.dval = NULL; // needed because its pointer is redirected to dtt magma_cmfree( &dxs, queue ); magma_cmfree( &drs, queue ); magma_cmfree( &dtt, queue ); } dr.dval = NULL; // needed because its pointer is redirected to dt dGcol.dval = NULL; // needed because its pointer is redirected to dG magma_cmfree( &dr, queue ); magma_cmfree( &dP, queue ); magma_cmfree( &dP1, queue ); magma_cmfree( &dG, queue ); magma_cmfree( &dGcol, queue ); magma_cmfree( &dU, queue ); magma_cmfree( &dM, queue ); magma_cmfree( &df, queue ); magma_cmfree( &dt, queue ); magma_cmfree( &dc, queue ); magma_cmfree( &dv, queue ); magma_cmfree( &dlu, queue ); magma_cmfree( &dskp, queue ); magma_cmfree( &dalpha, queue ); magma_cmfree( &dbeta, queue ); magma_free_pinned( hMdiag ); magma_free_pinned( hskp ); magma_free_pinned( halpha ); magma_free_pinned( hbeta ); magma_free( d1 ); magma_free( d2 ); solver_par->info = info; return info; /* magma_cpidr_strms */ }
/** Purpose ------- CLATRD2 reduces NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A. If UPLO = MagmaUpper, CLATRD reduces the last NB rows and columns of a matrix, of which the upper triangle is supplied; if UPLO = MagmaLower, CLATRD reduces the first NB rows and columns of a matrix, of which the lower triangle is supplied. This is an auxiliary routine called by CHETRD2_GPU. It uses an accelerated HEMV that needs extra memory. Arguments --------- @param[in] uplo magma_uplo_t Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: - = MagmaUpper: Upper triangular - = MagmaLower: Lower triangular @param[in] n INTEGER The order of the matrix A. @param[in] nb INTEGER The number of rows and columns to be reduced. @param[in,out] A COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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: - if UPLO = MagmaUpper, the last NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements above the diagonal with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; - if UPLO = MagmaLower, the first NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements below the diagonal with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. @param[in] lda INTEGER The leading dimension of the array A. LDA >= (1,N). @param[out] e COMPLEX array, dimension (N-1) If UPLO = MagmaUpper, E(n-nb:n-1) contains the superdiagonal elements of the last NB columns of the reduced matrix; if UPLO = MagmaLower, E(1:nb) contains the subdiagonal elements of the first NB columns of the reduced matrix. @param[out] tau COMPLEX array, dimension (N-1) The scalar factors of the elementary reflectors, stored in TAU(n-nb:n-1) if UPLO = MagmaUpper, and in TAU(1:nb) if UPLO = MagmaLower. See Further Details. @param[out] W COMPLEX array, dimension (LDW,NB) The n-by-nb matrix W required to update the unreduced part of A. @param[in] ldw INTEGER The leading dimension of the array W. LDW >= max(1,N). @param dA TODO: dimension (ldda, n) ?? @param ldda TODO: ldda >= n ?? @param dW TODO: dimension (lddw, 2*nb) ?? @param lddw TODO: lddw >= n ?? @param dwork TODO: dimension (ldwork) ?? @param ldwork TODO: ldwork >= ceil(n/64)*ldda ?? @param[in] queue magma_queue_t Queue to execute in. Further Details --------------- If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors Q = H(n) H(n-1) . . . H(n-nb+1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), and tau in TAU(i-1). If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(nb). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), and tau in TAU(i). The elements of the vectors v together form the n-by-nb matrix V which is needed, with W, to apply the transformation to the unreduced part of the matrix, using a Hermitian rank-2k update of the form: A := A - V*W' - W*V'. The contents of A on exit are illustrated by the following examples with n = 5 and nb = 2: if UPLO = MagmaUpper: if UPLO = MagmaLower: ( a a a v4 v5 ) ( d ) ( a a v4 v5 ) ( 1 d ) ( a 1 v5 ) ( v1 1 a ) ( d 1 ) ( v1 v2 a a ) ( d ) ( v1 v2 a a a ) where d denotes a diagonal element of the reduced matrix, a denotes an element of the original matrix that is unchanged, and vi denotes an element of the vector defining H(i). @ingroup magma_cheev_aux ********************************************************************/ extern "C" magma_int_t magma_clatrd2( magma_uplo_t uplo, magma_int_t n, magma_int_t nb, magmaFloatComplex *A, magma_int_t lda, float *e, magmaFloatComplex *tau, magmaFloatComplex *W, magma_int_t ldw, magmaFloatComplex *work, magma_int_t lwork, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dW, magma_int_t lddw, magmaFloatComplex_ptr dwork, magma_int_t ldwork, magma_queue_t queue ) { #define A(i_, j_) (A + (i_) + (j_)*lda) #define W(i_, j_) (W + (i_) + (j_)*ldw) #define dA(i_, j_) (dA + (i_) + (j_)*ldda) #define dW(i_, j_) (dW + (i_) + (j_)*lddw) /* Constants */ const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE; const magmaFloatComplex c_one = MAGMA_C_ONE; const magmaFloatComplex c_zero = MAGMA_C_ZERO; const magma_int_t ione = 1; /* Local variables */ magmaFloatComplex alpha, value; magma_int_t i, i_n, i_1, iw; /* Check arguments */ magma_int_t info = 0; if ( uplo != MagmaLower && uplo != MagmaUpper ) { info = -1; } else if ( n < 0 ) { info = -2; } else if ( nb < 1 ) { info = -3; } else if ( lda < max(1,n) ) { info = -5; } else if ( ldw < max(1,n) ) { info = -9; } else if ( lwork < max(1,n) ) { info = -11; } else if ( ldda < max(1,n) ) { info = -13; } else if ( lddw < max(1,n) ) { info = -15; } else if ( ldwork < ldda*magma_ceildiv(n,64) ) { info = -17; } if (info != 0) { magma_xerbla( __func__, -(info) ); return info; } /* Quick return if possible */ if (n == 0) { return info; } if (uplo == MagmaUpper) { /* Reduce last NB columns of upper triangle */ for (i = n-1; i >= n - nb; --i) { i_1 = i + 1; i_n = n - i - 1; iw = i - n + nb; if (i < n-1) { /* Update A(1:i,i) */ #ifdef COMPLEX lapackf77_clacgv( &i_n, W(i, iw+1), &ldw ); #endif blasf77_cgemv( "No transpose", &i_1, &i_n, &c_neg_one, A(0, i+1), &lda, W(i, iw+1), &ldw, &c_one, A(0, i), &ione ); #ifdef COMPLEX lapackf77_clacgv( &i_n, W(i, iw+1), &ldw ); lapackf77_clacgv( &i_n, A(i, i+1), &lda ); #endif blasf77_cgemv( "No transpose", &i_1, &i_n, &c_neg_one, W(0, iw+1), &ldw, A(i, i+1), &lda, &c_one, A(0, i), &ione ); #ifdef COMPLEX lapackf77_clacgv( &i_n, A(i, i+1), &lda ); #endif } if (i > 0) { /* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */ alpha = *A(i-1, i); lapackf77_clarfg( &i, &alpha, A(0, i), &ione, &tau[i - 1] ); e[i-1] = MAGMA_C_REAL( alpha ); *A(i-1,i) = MAGMA_C_ONE; /* Compute W(1:i-1,i) */ // 1. Send the block reflector A(0:n-i-1,i) to the GPU magma_csetvector_async( i, A(0, i), 1, dA(0, i), 1, queue ); magmablas_chemv_work( MagmaUpper, i, c_one, dA(0, 0), ldda, dA(0, i), ione, c_zero, dW(0, iw), ione, dwork, ldwork, queue ); // 2. Start getting the result back (asynchronously) magma_cgetmatrix_async( i, 1, dW(0, iw), lddw, W(0, iw), ldw, queue ); if (i < n-1) { blasf77_cgemv( MagmaConjTransStr, &i, &i_n, &c_one, W(0, iw+1), &ldw, A(0, i), &ione, &c_zero, W(i+1, iw), &ione ); } // 3. Here we need chemv result W(0, iw) magma_queue_sync( queue ); if (i < n-1) { blasf77_cgemv( "No transpose", &i, &i_n, &c_neg_one, A(0, i+1), &lda, W(i+1, iw), &ione, &c_one, W(0, iw), &ione ); blasf77_cgemv( MagmaConjTransStr, &i, &i_n, &c_one, A(0, i+1), &lda, A(0, i), &ione, &c_zero, W(i+1, iw), &ione ); blasf77_cgemv( "No transpose", &i, &i_n, &c_neg_one, W(0, iw+1), &ldw, W(i+1, iw), &ione, &c_one, W(0, iw), &ione ); } blasf77_cscal( &i, &tau[i - 1], W(0, iw), &ione ); value = magma_cblas_cdotc( i, W(0,iw), ione, A(0,i), ione ); alpha = tau[i - 1] * -0.5f * value; blasf77_caxpy( &i, &alpha, A(0, i), &ione, W(0, iw), &ione ); } } } else { /* Reduce first NB columns of lower triangle */ for (i = 0; i < nb; ++i) { /* Update A(i:n,i) */ i_n = n - i; #ifdef COMPLEX lapackf77_clacgv( &i, W(i, 0), &ldw ); #endif blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, A(i, 0), &lda, W(i, 0), &ldw, &c_one, A(i, i), &ione ); #ifdef COMPLEX lapackf77_clacgv( &i, W(i, 0), &ldw ); lapackf77_clacgv( &i, A(i, 0), &lda ); #endif blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, W(i, 0), &ldw, A(i, 0), &lda, &c_one, A(i, i), &ione ); #ifdef COMPLEX lapackf77_clacgv( &i, A(i, 0), &lda ); #endif if (i < n-1) { /* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */ i_n = n - i - 1; alpha = *A(i+1, i); lapackf77_clarfg( &i_n, &alpha, A(min(i+2,n-1), i), &ione, &tau[i] ); e[i] = MAGMA_C_REAL( alpha ); *A(i+1,i) = MAGMA_C_ONE; /* Compute W(i+1:n,i) */ // 1. Send the block reflector A(i+1:n,i) to the GPU magma_csetvector_async( i_n, A(i+1, i), 1, dA(i+1, i), 1, queue ); magmablas_chemv_work( MagmaLower, i_n, c_one, dA(i+1, i+1), ldda, dA(i+1, i), ione, c_zero, dW(i+1, i), ione, dwork, ldwork, queue ); // 2. Start getting the result back (asynchronously) magma_cgetmatrix_async( i_n, 1, dW(i+1, i), lddw, W(i+1, i), ldw, queue ); blasf77_cgemv( MagmaConjTransStr, &i_n, &i, &c_one, W(i+1, 0), &ldw, A(i+1, i), &ione, &c_zero, W(0, i), &ione ); blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, A(i+1, 0), &lda, W(0, i), &ione, &c_zero, work, &ione ); blasf77_cgemv( MagmaConjTransStr, &i_n, &i, &c_one, A(i+1, 0), &lda, A(i+1, i), &ione, &c_zero, W(0, i), &ione ); // 3. Here we need chemv result W(i+1, i) magma_queue_sync( queue ); if (i != 0) blasf77_caxpy( &i_n, &c_one, work, &ione, W(i+1, i), &ione ); blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, W(i+1, 0), &ldw, W(0, i), &ione, &c_one, W(i+1, i), &ione ); blasf77_cscal( &i_n, &tau[i], W(i+1,i), &ione ); value = magma_cblas_cdotc( i_n, W(i+1,i), ione, A(i+1,i), ione ); alpha = tau[i] * -0.5f * value; blasf77_caxpy( &i_n, &alpha, A(i+1, i), &ione, W(i+1,i), &ione ); } } } return info; } /* magma_clatrd */