Ejemplo n.º 1
0
/* ////////////////////////////////////////////////////////////////////////////
   -- testing any solver
*/
int main(  int argc, char** argv )
{
    magma_int_t info = 0;
    /* Initialize */
    TESTING_INIT();
    magma_queue_t queue=NULL;
    magma_queue_create( &queue );
    magmablasSetKernelStream( queue );

    magma_int_t j, n=1000000, FLOPS;
    
    float one = MAGMA_S_MAKE( 1.0, 0.0 );
    float two = MAGMA_S_MAKE( 2.0, 0.0 );

    magma_s_matrix a={Magma_CSR}, ad={Magma_CSR}, bd={Magma_CSR}, cd={Magma_CSR};
    CHECK( magma_svinit( &a, Magma_CPU, n, 1, one, queue ));
    CHECK( magma_svinit( &bd, Magma_DEV, n, 1, two, queue ));
    CHECK( magma_svinit( &cd, Magma_DEV, n, 1, one, queue ));
    
    CHECK( magma_smtransfer( a, &ad, Magma_CPU, Magma_DEV, queue ));

    real_Double_t start, end, res;
    
    FLOPS = 2*n;
    start = magma_sync_wtime( queue );
    for (j=0; j<100; j++)
        res = magma_snrm2(n, ad.dval, 1);
    end = magma_sync_wtime( queue );
    printf( " > MAGMA nrm2: %.2e seconds %.2e GFLOP/s\n",
                                    (end-start)/100, FLOPS*100/1e9/(end-start) );
    FLOPS = n;
    start = magma_sync_wtime( queue );
    for (j=0; j<100; j++)
        magma_sscal( n, two, ad.dval, 1 );
    end = magma_sync_wtime( queue );
    printf( " > MAGMA scal: %.2e seconds %.2e GFLOP/s\n",
                                    (end-start)/100, FLOPS*100/1e9/(end-start) );
    FLOPS = 2*n;
    start = magma_sync_wtime( queue );
    for (j=0; j<100; j++)
        magma_saxpy( n, one, ad.dval, 1, bd.dval, 1 );
    end = magma_sync_wtime( queue );
    printf( " > MAGMA axpy: %.2e seconds %.2e GFLOP/s\n",
                                    (end-start)/100, FLOPS*100/1e9/(end-start) );
    FLOPS = n;
    start = magma_sync_wtime( queue );
    for (j=0; j<100; j++)
        magma_scopy( n, bd.dval, 1, ad.dval, 1 );
    end = magma_sync_wtime( queue );
    printf( " > MAGMA copy: %.2e seconds %.2e GFLOP/s\n",
                                    (end-start)/100, FLOPS*100/1e9/(end-start) );
    FLOPS = 2*n;
    start = magma_sync_wtime( queue );
    for (j=0; j<100; j++)
        res = MAGMA_S_REAL( magma_sdot(n, ad.dval, 1, bd.dval, 1) );
    end = magma_sync_wtime( queue );
    printf( " > MAGMA dotc: %.2e seconds %.2e GFLOP/s\n",
                                    (end-start)/100, FLOPS*100/1e9/(end-start) );

    printf("# tester BLAS:  ok\n");


    magma_smfree( &a, queue);
    magma_smfree(&ad, queue);
    magma_smfree(&bd, queue);
    magma_smfree(&cd, queue);

    
cleanup:
    magma_smfree( &a, queue);
    magma_smfree(&ad, queue);
    magma_smfree(&bd, queue);
    magma_smfree(&cd, queue);
    magmablasSetKernelStream( NULL );
    magma_queue_destroy( queue );
    magma_finalize();
    return info;
}
Ejemplo n.º 2
0
extern "C" magma_int_t
magma_spidr(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_s_preconditioner *precond_par,
    magma_queue_t queue )
{
    magma_int_t info = MAGMA_NOTCONVERGED;

    // prepare solver feedback
    solver_par->solver = Magma_PIDR;
    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 float c_zero = MAGMA_S_ZERO;
    const float c_one = MAGMA_S_ONE;
    const float c_n_one = MAGMA_S_NEG_ONE;

    // internal user parameters
    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;
    float residual;
    float nrm;
    float nrmb;
    float nrmr;
    float nrmt;
    float rho;
    float om;
    float tt;
    float tr;
    float gamma;
    float alpha;
    float mkk;
    float fk;

    // matrices and vectors
    magma_s_matrix dxs = {Magma_CSR};
    magma_s_matrix dr = {Magma_CSR}, drs = {Magma_CSR};
    magma_s_matrix dP = {Magma_CSR}, dP1 = {Magma_CSR};
    magma_s_matrix dG = {Magma_CSR};
    magma_s_matrix dU = {Magma_CSR};
    magma_s_matrix dM = {Magma_CSR};
    magma_s_matrix df = {Magma_CSR};
    magma_s_matrix dt = {Magma_CSR};
    magma_s_matrix dc = {Magma_CSR};
    magma_s_matrix dv = {Magma_CSR};
    magma_s_matrix dbeta = {Magma_CSR}, hbeta = {Magma_CSR};
    magma_s_matrix dlu = {Magma_CSR};

    // chronometry
    real_Double_t tempo1, tempo2;

    // 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_snrm2( b.num_rows, b.dval, 1, queue );
    if ( nrmb == 0.0 ) {
        magma_sscal( x->num_rows, MAGMA_S_ZERO, x->dval, 1, queue );
        info = MAGMA_SUCCESS;
        goto cleanup;
    }

    // r = b - A x
    CHECK( magma_svinit( &dr, Magma_DEV, b.num_rows, 1, c_zero, queue ));
    CHECK( magma_sresidualvec( 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_svinit( &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_slarnv( &distr, iseed, &dof, dP.val );

    // transfer P to device
    CHECK( magma_smtransfer( dP, &dP1, Magma_CPU, Magma_DEV, queue ));
    magma_smfree( &dP, queue );

    // P = ortho(P1)
    if ( dP1.num_cols > 1 ) {
        // P = magma_sqr(P1), QR factorization
        CHECK( magma_sqr( dP1.num_rows, dP1.num_cols, dP1, dP1.ld, &dP, NULL, queue ));
    } else {
        // P = P1 / |P1|
        nrm = magma_snrm2( dof, dP1.dval, 1, queue );
        nrm = 1.0 / nrm;
        magma_sscal( dof, nrm, dP1.dval, 1, queue );
        CHECK( magma_smtransfer( dP1, &dP, Magma_DEV, Magma_DEV, queue ));
    }
    magma_smfree( &dP1, queue );
//---------------------------------------

    // allocate memory for the scalar products
    CHECK( magma_svinit( &hbeta, Magma_CPU, s, 1, c_zero, queue ));
    CHECK( magma_svinit( &dbeta, Magma_DEV, s, 1, c_zero, queue ));

    // smoothing enabled
    if ( smoothing > 0 ) {
        // set smoothing solution vector
        CHECK( magma_smtransfer( *x, &dxs, Magma_DEV, Magma_DEV, queue ));

        // set smoothing residual vector
        CHECK( magma_smtransfer( dr, &drs, Magma_DEV, Magma_DEV, queue ));
    }

    // G(n,s) = 0
    CHECK( magma_svinit( &dG, Magma_DEV, A.num_cols, s, c_zero, queue ));

    // U(n,s) = 0
    CHECK( magma_svinit( &dU, Magma_DEV, A.num_cols, s, c_zero, queue ));

    // M(s,s) = I
    CHECK( magma_svinit( &dM, Magma_DEV, s, s, c_zero, queue ));
    magmablas_slaset( MagmaFull, s, s, c_zero, c_one, dM.dval, s, queue );

    // f = 0
    CHECK( magma_svinit( &df, Magma_DEV, dP.num_cols, 1, c_zero, queue ));

    // t = 0
    CHECK( magma_svinit( &dt, Magma_DEV, dr.num_rows, 1, c_zero, queue ));

    // c = 0
    CHECK( magma_svinit( &dc, Magma_DEV, dM.num_cols, 1, c_zero, queue ));

    // v = 0
    CHECK( magma_svinit( &dv, Magma_DEV, dr.num_rows, 1, c_zero, queue ));

    // lu = 0
    CHECK( magma_svinit( &dlu, Magma_DEV, A.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_S_ONE;
    innerflag = 0;

    // start iteration
    do
    {
        solver_par->numiter++;
    
        // new RHS for small systems
        // f = P' r
        magmablas_sgemv( MagmaConjTrans, dP.num_rows, dP.num_cols, c_one, dP.dval, dP.ld, dr.dval, 1, c_zero, df.dval, 1, queue );

        // shadow space loop
        for ( k = 0; k < s; ++k ) {
            sk = s - k;
    
            // f(k:s) = M(k:s,k:s) c(k:s)
            magma_scopyvector( sk, &df.dval[k], 1, &dc.dval[k], 1, queue );
            magma_strsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, sk, &dM.dval[k*dM.ld+k], dM.ld, &dc.dval[k], 1, queue );

            // v = r - G(:,k:s) c(k:s)
            magma_scopyvector( dr.num_rows, dr.dval, 1, dv.dval, 1, queue );
            magmablas_sgemv( MagmaNoTrans, dG.num_rows, sk, c_n_one, &dG.dval[k*dG.ld], dG.ld, &dc.dval[k], 1, c_one, dv.dval, 1, queue );

            // preconditioning operation 
            // v = L \ v;
            // v = U \ v;
            CHECK( magma_s_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queue )); 
            CHECK( magma_s_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queue )); 

            // U(:,k) = om * v + U(:,k:s) c(k:s)
            magmablas_sgemv( MagmaNoTrans, dU.num_rows, sk, c_one, &dU.dval[k*dU.ld], dU.ld, &dc.dval[k], 1, om, dv.dval, 1, queue );
            magma_scopyvector( dU.num_rows, dv.dval, 1, &dU.dval[k*dU.ld], 1, queue );

            // G(:,k) = A U(:,k)
            CHECK( magma_s_spmv( c_one, A, dv, c_zero, dv, queue ));
            solver_par->spmv_count++;
            magma_scopyvector( dG.num_rows, dv.dval, 1, &dG.dval[k*dG.ld], 1, queue );

            // bi-orthogonalize the new basis vectors
            for ( i = 0; i < k; ++i ) {
                // alpha = P(:,i)' G(:,k)
                alpha = magma_sdot( dP.num_rows, &dP.dval[i*dP.ld], 1, &dG.dval[k*dG.ld], 1, queue );

                // alpha = alpha / M(i,i)
                magma_sgetvector( 1, &dM.dval[i*dM.ld+i], 1, &mkk, 1, queue );
                alpha = alpha / mkk;

                // G(:,k) = G(:,k) - alpha * G(:,i)
                magma_saxpy( dG.num_rows, -alpha, &dG.dval[i*dG.ld], 1, &dG.dval[k*dG.ld], 1, queue );

                // U(:,k) = U(:,k) - alpha * U(:,i)
                magma_saxpy( dU.num_rows, -alpha, &dU.dval[i*dU.ld], 1, &dU.dval[k*dU.ld], 1, queue );
            }

            // new column of M = P'G, first k-1 entries are zero
            // M(k:s,k) = P(:,k:s)' G(:,k)
            magmablas_sgemv( MagmaConjTrans, dP.num_rows, sk, c_one, &dP.dval[k*dP.ld], dP.ld, &dG.dval[k*dG.ld], 1, c_zero, &dM.dval[k*dM.ld+k], 1, queue );

            // check M(k,k) == 0
            magma_sgetvector( 1, &dM.dval[k*dM.ld+k], 1, &mkk, 1, queue );
            if ( MAGMA_S_EQUAL(mkk, MAGMA_S_ZERO) ) {
                innerflag = 1;
                info = MAGMA_DIVERGENCE;
                break;
            }

            // beta = f(k) / M(k,k)
            magma_sgetvector( 1, &df.dval[k], 1, &fk, 1, queue );
            hbeta.val[k] = fk / mkk;

            // check for nan
            if ( magma_s_isnan( hbeta.val[k] ) || magma_s_isinf( hbeta.val[k] )) {
                innerflag = 1;
                info = MAGMA_DIVERGENCE;
                break;
            }

            // r = r - beta * G(:,k)
            magma_saxpy( dr.num_rows, -hbeta.val[k], &dG.dval[k*dG.ld], 1, dr.dval, 1, queue );

            // smoothing disabled
            if ( smoothing <= 0 ) {
                // |r|
                nrmr = magma_snrm2( dr.num_rows, dr.dval, 1, queue );

            // smoothing enabled
            } else {
                // x = x + beta * U(:,k)
                magma_saxpy( x->num_rows, hbeta.val[k], &dU.dval[k*dU.ld], 1, x->dval, 1, queue );

                // smoothing operation
//---------------------------------------
                // t = rs - r
                magma_scopyvector( drs.num_rows, drs.dval, 1, dt.dval, 1, queue );
                magma_saxpy( dt.num_rows, c_n_one, dr.dval, 1, dt.dval, 1, queue );

                // t't
                // t'rs 
                tt = magma_sdot( dt.num_rows, dt.dval, 1, dt.dval, 1, queue );
                tr = magma_sdot( dt.num_rows, dt.dval, 1, drs.dval, 1, queue );

                // gamma = (t' * rs) / (t' * t)
                gamma = tr / tt;

                // rs = rs - gamma * (rs - r) 
                magma_saxpy( drs.num_rows, -gamma, dt.dval, 1, drs.dval, 1, queue );

                // xs = xs - gamma * (xs - x) 
                magma_scopyvector( dxs.num_rows, dxs.dval, 1, dt.dval, 1, queue );
                magma_saxpy( dt.num_rows, c_n_one, x->dval, 1, dt.dval, 1, queue );
                magma_saxpy( dxs.num_rows, -gamma, dt.dval, 1, dxs.dval, 1, queue );

                // |rs|
                nrmr = magma_snrm2( drs.num_rows, drs.dval, 1, queue );           
//---------------------------------------
            }

            // 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
            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;
            }

            // non-last s iteration
            if ( (k + 1) < s ) {
                // f(k+1:s) = f(k+1:s) - beta * M(k+1:s,k)
                magma_saxpy( sk-1, -hbeta.val[k], &dM.dval[k*dM.ld+(k+1)], 1, &df.dval[k+1], 1, queue );
            }

        }

        // smoothing disabled
        if ( smoothing <= 0 && innerflag != 1 ) {
            // update solution approximation x
            // x = x + U(:,1:s) * beta(1:s)
            magma_ssetvector( s, hbeta.val, 1, dbeta.dval, 1, queue );
            magmablas_sgemv( MagmaNoTrans, dU.num_rows, s, c_one, dU.dval, dU.ld, dbeta.dval, 1, c_one, x->dval, 1, queue );
        }

        // check convergence or iteration limit or invalid result of inner loop
        if ( innerflag > 0 ) {
            break;
        }

        // v = r
        magma_scopyvector( dr.num_rows, dr.dval, 1, dv.dval, 1, queue );

        // preconditioning operation 
        // v = L \ v;
        // v = U \ v;
        CHECK( magma_s_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queue )); 
        CHECK( magma_s_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queue )); 

        // t = A v
        CHECK( magma_s_spmv( c_one, A, dv, c_zero, dt, queue ));
        solver_par->spmv_count++;

        // computation of a new omega
//---------------------------------------
        // |t|
        nrmt = magma_snrm2( dt.num_rows, dt.dval, 1, queue );

        // t'r 
        tr = magma_sdot( dt.num_rows, dt.dval, 1, dr.dval, 1, queue );

        // rho = abs(t' * r) / (|t| * |r|))
        rho = MAGMA_D_ABS( MAGMA_S_REAL(tr) / (nrmt * nrmr) );

        // om = (t' * r) / (|t| * |t|)
        om = tr / (nrmt * nrmt);
        if ( rho < angle ) {
            om = (om * angle) / rho;
        }
//---------------------------------------
        if ( MAGMA_S_EQUAL(om, MAGMA_S_ZERO) ) {
            info = MAGMA_DIVERGENCE;
            break;
        }

        // update approximation vector
        // x = x + om * v
        magma_saxpy( x->num_rows, om, dv.dval, 1, x->dval, 1, queue );

        // update residual vector
        // r = r - om * t
        magma_saxpy( dr.num_rows, -om, dt.dval, 1, dr.dval, 1, queue );

        // smoothing disabled
        if ( smoothing <= 0 ) {
            // residual norm
            nrmr = magma_snrm2( b.num_rows, dr.dval, 1, queue );

        // smoothing enabled
        } else {
            // smoothing operation
//---------------------------------------
            // t = rs - r
            magma_scopyvector( drs.num_rows, drs.dval, 1, dt.dval, 1, queue );
            magma_saxpy( dt.num_rows, c_n_one, dr.dval, 1, dt.dval, 1, queue );

            // t't
            // t'rs
            tt = magma_sdot( dt.num_rows, dt.dval, 1, dt.dval, 1, queue );
            tr = magma_sdot( dt.num_rows, dt.dval, 1, drs.dval, 1, queue );

            // gamma = (t' * rs) / (|t| * |t|)
            gamma = tr / tt;

            // rs = rs - gamma * (rs - r) 
            magma_saxpy( drs.num_rows, -gamma, dt.dval, 1, drs.dval, 1, queue );

            // xs = xs - gamma * (xs - x) 
            magma_scopyvector( dxs.num_rows, dxs.dval, 1, dt.dval, 1, queue );
            magma_saxpy( dt.num_rows, c_n_one, x->dval, 1, dt.dval, 1, queue );
            magma_saxpy( dxs.num_rows, -gamma, dt.dval, 1, dxs.dval, 1, queue );

            // |rs|
            nrmr = magma_snrm2( b.num_rows, drs.dval, 1, queue );           
//---------------------------------------
        }

        // 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
        if ( nrmr <= solver_par->atol ||
            nrmr/nrmb <= solver_par->rtol ) { 
            info = MAGMA_SUCCESS;
            break;
        }
    }
    while ( solver_par->numiter + 1 <= solver_par->maxiter );

    // smoothing enabled
    if ( smoothing > 0 ) {
        // x = xs
        magma_scopyvector( x->num_rows, dxs.dval, 1, x->dval, 1, queue );

        // r = rs
        magma_scopyvector( dr.num_rows, drs.dval, 1, dr.dval, 1, queue );
    }

    // get last iteration timing
    tempo2 = magma_sync_wtime( queue );
    solver_par->runtime = (real_Double_t)tempo2 - tempo1;
//--------------STOP TIME----------------

    // get final stats
    solver_par->iter_res = nrmr;
    CHECK( magma_sresidualvec( 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
    // smoothing enabled
    if ( smoothing > 0 ) {
        magma_smfree( &dxs, queue );
        magma_smfree( &drs, queue );
    }
    magma_smfree( &dr, queue );
    magma_smfree( &dP, queue );
    magma_smfree( &dP1, queue );
    magma_smfree( &dG, queue );
    magma_smfree( &dU, queue );
    magma_smfree( &dM, queue );
    magma_smfree( &df, queue );
    magma_smfree( &dt, queue );
    magma_smfree( &dc, queue );
    magma_smfree( &dv, queue );
    magma_smfree(&dlu, queue);
    magma_smfree( &dbeta, queue );
    magma_smfree( &hbeta, queue );

    solver_par->info = info;
    return info;
    /* magma_spidr */
}
Ejemplo n.º 3
0
magma_int_t
magma_spgmres( magma_s_sparse_matrix A, magma_s_vector b, magma_s_vector *x,  
               magma_s_solver_par *solver_par, 
               magma_s_preconditioner *precond_par ){

    // prepare solver feedback
    solver_par->solver = Magma_PGMRES;
    solver_par->numiter = 0;
    solver_par->info = 0;

    // local variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE, 
                                                c_mone = MAGMA_S_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);
    float *H, *HH, *y, *h1;
    magma_smalloc_pinned( &H, (ldh+1)*ldh );
    magma_smalloc_pinned( &y, ldh );
    magma_smalloc_pinned( &HH, ldh*ldh );
    magma_smalloc_pinned( &h1, ldh );

    // GPU workspace
    magma_s_vector r, q, q_t, z, z_t, t;
    magma_s_vinit( &t, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &r, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &q, Magma_DEV, dofs*(ldh+1), c_zero );
    magma_s_vinit( &z, Magma_DEV, dofs*(ldh+1), c_zero );
    magma_s_vinit( &z_t, Magma_DEV, dofs, c_zero );
    q_t.memory_location = Magma_DEV; 
    q_t.val = NULL; 
    q_t.num_rows = q_t.nnz = dofs;

    float *dy, *dH = NULL;
    if (MAGMA_SUCCESS != magma_smalloc( &dy, ldh )) 
        return MAGMA_ERR_DEVICE_ALLOC;
    if (MAGMA_SUCCESS != magma_smalloc( &dH, (ldh+1)*ldh )) 
        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_sscal( dofs, c_zero, x->val, 1 );              //  x = 0
    magma_scopy( dofs, b.val, 1, r.val, 1 );             //  r = b
    nom0 = betanom = magma_snrm2( dofs, r.val, 1 );     //  nom0= || r||
    nom = nom0  * nom0;
    solver_par->init_res = nom0;
    H(1,0) = MAGMA_S_MAKE( nom0, 0. ); 
    magma_ssetvector(1, &H(1,0), 1, &dH(1,0), 1);
    if ( (r0 = nom0 * RTOLERANCE ) < ATOLERANCE ) 
        r0 = solver_par->epsilon;
    if ( nom < r0 )
        return MAGMA_SUCCESS;

    //Chronometry
    real_Double_t tempo1, tempo2;
    magma_device_sync(); tempo1=magma_wtime();
    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_scopy(dofs, r.val, 1, q(k-1), 1);       //  q[0]    = 1.0/||r||
        magma_sscal(dofs, 1./H(k,k-1), q(k-1), 1);    //  (to be fused)
            q_t.val = q(k-1);
            magmablasSetKernelStream(stream[0]);
            // preconditioner
            //  z[k] = M^(-1) q(k)
            magma_s_applyprecond_left( A, q_t, &t, precond_par );      
            magma_s_applyprecond_right( A, t, &z_t, precond_par );     
  
            magma_scopy(dofs, z_t.val, 1, z(k-1), 1);                  

            // r = A q[k] 
            magma_s_spmv( c_one, A, z_t, c_zero, r );


    //      if (solver_par->ortho == Magma_MGS ) {
                // modified Gram-Schmidt
                for (i=1; i<=k; i++) {
                    H(i,k) =magma_sdot(dofs, q(i-1), 1, r.val, 1);            
                        //  H(i,k) = q[i] . r
                    magma_saxpy(dofs,-H(i,k), q(i-1), 1, r.val, 1);            
                       //  r = r - H(i,k) q[i]
                }
                H(k+1,k) = MAGMA_S_MAKE( magma_snrm2(dofs, r.val, 1), 0. ); // H(k+1,k) = ||r|| 


            /*}else if (solver_par->ortho == Magma_FUSED_CGS ) {
                // fusing sgemv with snrm2 in classical Gram-Schmidt
                magmablasSetKernelStream(stream[0]);
                magma_scopy(dofs, r.val, 1, q(k), 1);  
                    // dH(1:k+1,k) = q[0:k] . r
                magmablas_sgemv(MagmaTrans, dofs, k+1, c_one, q(0), 
                                dofs, r.val, 1, c_zero, &dH(1,k), 1);
                    // r = r - q[0:k-1] dH(1:k,k)
                magmablas_sgemv(MagmaNoTrans, dofs, k, c_mone, q(0), 
                                dofs, &dH(1,k), 1, c_one, r.val, 1);
                   // 1) dH(k+1,k) = sqrt( dH(k+1,k) - dH(1:k,k) )
                magma_scopyscale(  dofs, k, r.val, 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_sgetvector_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_sgemv(MagmaTrans, dofs, k, c_one, q(0), 
                                dofs, r.val, 1, c_zero, &dH(1,k), 1); 
                                // dH(1:k,k) = q[0:k-1] . r
                #ifndef SNRM2SCALE 
                // 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_sgetvector_async(k, &dH(1,k), 1, &H(1,k), 
                                                    1, stream[1]);
                #endif
                                  // r = r - q[0:k-1] dH(1:k,k)
                magmablas_sgemv(MagmaNoTrans, dofs, k, c_mone, q(0), 
                                    dofs, &dH(1,k), 1, c_one, r.val, 1);
                #ifdef SNRM2SCALE
                magma_scopy(dofs, r.val, 1, q(k), 1);                 
                    //  q[k] = r / H(k,k-1) 
                magma_snrm2scale(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_sgetvector_async(k+1, &dH(1,k), 1, &H(1,k), 1, stream[1]);
                #else
                H(k+1,k) = MAGMA_S_MAKE( magma_snrm2(dofs, r.val, 1), 0. );   
                            //  H(k+1,k) = sqrt(r . r) 
                if( k<solver_par->restart ){
                        magmablasSetKernelStream(stream[0]);
                        magma_scopy(dofs, r.val, 1, q(k), 1);                  
                            //  q[k]    = 1.0/H[k][k-1] r
                        magma_sscal(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_sdot( 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_S_REAL(H(k+1,k)));
        }/*     Minimization done       */ 
        // compute solution approximation
        magma_ssetmatrix(m, 1, y+1, m, dy, m );

        magma_sgemv(MagmaNoTrans, dofs, m, c_one, z(0), dofs, dy, 1, 
                                                    c_one, x->val, 1); 

        // compute residual
        magma_s_spmv( c_mone, A, *x, c_zero, r );      //  r = - A * x
        magma_saxpy(dofs, c_one, b.val, 1, r.val, 1);  //  r = r + b
        H(1,0) = MAGMA_S_MAKE( magma_snrm2(dofs, r.val, 1), 0. ); 
                                            //  RNorm = H[1][0] = || r ||
        RNorm = MAGMA_S_REAL( H(1,0) );
        betanom = fabs(RNorm);  

        if( solver_par->verbose > 0 ){
            magma_device_sync(); tempo2=magma_wtime();
            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;
        } 
    }

    magma_device_sync(); tempo2=magma_wtime();
    solver_par->runtime = (real_Double_t) tempo2-tempo1;
    float residual;
    magma_sresidual( A, b, *x, &residual );
    solver_par->iter_res = betanom;
    solver_par->final_res = residual;

    if( solver_par->numiter < solver_par->maxiter){
        solver_par->info = 0;
    }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 = -2;
    }
    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 = -1;
    }
    // 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_s_vfree(&t);
    magma_s_vfree(&r);
    magma_s_vfree(&q);
    magma_s_vfree(&z);
    magma_s_vfree(&z_t);

    // free GPU streams and events
    magma_queue_destroy( stream[0] );
    magma_queue_destroy( stream[1] );
    magma_event_destroy( event[0] );
    magmablasSetKernelStream(NULL);

    return MAGMA_SUCCESS;
}   /* magma_spgmres */
Ejemplo n.º 4
0
magma_int_t
magma_sbicgstab( magma_s_sparse_matrix A, magma_s_vector b, magma_s_vector *x,  
                    magma_s_solver_par *solver_par ){

    // prepare solver feedback
    solver_par->solver = Magma_BICGSTAB;
    solver_par->numiter = 0;
    solver_par->info = 0;

    // some useful variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE, 
                                            c_mone = MAGMA_S_NEG_ONE;
    
    magma_int_t dofs = A.num_rows;

    // workspace
    magma_s_vector r,rr,p,v,s,t;
    magma_s_vinit( &r, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &rr, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &p, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &v, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &s, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &t, Magma_DEV, dofs, c_zero );

    
    // solver variables
    float alpha, beta, omega, rho_old, rho_new;
    float nom, betanom, nom0, r0, den, res;

    // solver setup
    magma_sscal( dofs, c_zero, x->val, 1) ;                    // x = 0
    magma_scopy( dofs, b.val, 1, r.val, 1 );                   // r = b
    magma_scopy( dofs, b.val, 1, rr.val, 1 );                  // rr = b
    nom0 = betanom = magma_snrm2( dofs, r.val, 1 );           // nom = || r ||
    nom = nom0*nom0;
    rho_old = omega = alpha = MAGMA_S_MAKE( 1.0, 0. );
    solver_par->init_res = nom0;

    magma_s_spmv( c_one, A, r, c_zero, v );                      // z = A r
    den = MAGMA_S_REAL( magma_sdot(dofs, v.val, 1, r.val, 1) ); // den = z' * r

    if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) 
        r0 = ATOLERANCE;
    if ( nom < r0 )
        return MAGMA_SUCCESS;
    // check positive definite  
    if (den <= 0.0) {
        printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
        return -100;
    }

    //Chronometry
    real_Double_t tempo1, tempo2;
    magma_device_sync(); tempo1=magma_wtime();
    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_sdot( dofs, rr.val, 1, r.val, 1 );  // rho=<rr,r>
        beta = rho_new/rho_old * alpha/omega;   // beta=rho/rho_old *alpha/omega
        magma_sscal( dofs, beta, p.val, 1 );                 // p = beta*p
        magma_saxpy( dofs, c_mone * omega * beta, v.val, 1 , p.val, 1 );        
                                                        // p = p-omega*beta*v
        magma_saxpy( dofs, c_one, r.val, 1, p.val, 1 );      // p = p+r
        magma_s_spmv( c_one, A, p, c_zero, v );              // v = Ap

        alpha = rho_new / magma_sdot( dofs, rr.val, 1, v.val, 1 );
        magma_scopy( dofs, r.val, 1 , s.val, 1 );            // s=r
        magma_saxpy( dofs, c_mone * alpha, v.val, 1 , s.val, 1 ); // s=s-alpha*v

        magma_s_spmv( c_one, A, s, c_zero, t );               // t=As
        omega = magma_sdot( dofs, t.val, 1, s.val, 1 )   // omega = <s,t>/<t,t>
                   / magma_sdot( dofs, t.val, 1, t.val, 1 );

        magma_saxpy( dofs, alpha, p.val, 1 , x->val, 1 );     // x=x+alpha*p
        magma_saxpy( dofs, omega, s.val, 1 , x->val, 1 );     // x=x+omega*s

        magma_scopy( dofs, s.val, 1 , r.val, 1 );             // r=s
        magma_saxpy( dofs, c_mone * omega, t.val, 1 , r.val, 1 ); // r=r-omega*t
        res = betanom = magma_snrm2( dofs, r.val, 1 );

        nom = betanom*betanom;
        rho_old = rho_new;                                    // rho_old=rho

        if( solver_par->verbose > 0 ){
            magma_device_sync(); tempo2=magma_wtime();
            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;
        }
    }
    magma_device_sync(); tempo2=magma_wtime();
    solver_par->runtime = (real_Double_t) tempo2-tempo1;
    float residual;
    magma_sresidual( A, b, *x, &residual );
    solver_par->iter_res = res;
    solver_par->final_res = residual;

    if( solver_par->numiter < solver_par->maxiter){
        solver_par->info = 0;
    }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 = -2;
    }
    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 = -1;
    }
    magma_s_vfree(&r);
    magma_s_vfree(&rr);
    magma_s_vfree(&p);
    magma_s_vfree(&v);
    magma_s_vfree(&s);
    magma_s_vfree(&t);

    return MAGMA_SUCCESS;
}   /* magma_sbicgstab */
Ejemplo n.º 5
0
/**
    Purpose
    -------
    SGEGQR orthogonalizes the N vectors given by a real M-by-N matrix A:
           
            A = Q * R.

    On exit, if successful, the orthogonal vectors Q overwrite A
    and R is given in work (on the CPU memory).
    The routine is designed for tall-and-skinny matrices: M >> N, N <= 128.
    
    This version uses normal equations and SVD in an iterative process that
    makes the computation numerically accurate.
    
    Arguments
    ---------
    @param[in]
    ikind   INTEGER
            Several versions are implemented indiceted by the ikind value:  
            1:  This version uses normal equations and SVD in an iterative process 
                that makes the computation numerically accurate.
            2:  This version uses a standard LAPACK-based orthogonalization through
                MAGMA's QR panel factorization (magma_sgeqr2x3_gpu) and magma_sorgqr
            3:  MGS
            4.  Cholesky QR [ Note: this method uses the normal equations which 
                                    squares the condition number of A, therefore 
                                    ||I - Q'Q|| < O(eps cond(A)^2)               ]

    @param[in]
    m       INTEGER
            The number of rows of the matrix A.  m >= n >= 0.

    @param[in]
    n       INTEGER
            The number of columns of the matrix A. 128 >= n >= 0.

    @param[in,out]
    dA      REAL array on the GPU, dimension (ldda,n)
            On entry, the m-by-n matrix A.
            On exit, the m-by-n matrix Q with orthogonal columns.

    @param[in]
    ldda     INTEGER
            The leading dimension of the array dA.  LDDA >= max(1,m).
            To benefit from coalescent memory accesses LDDA must be
            divisible by 16.

    @param
    dwork   (GPU workspace) REAL array, dimension: 
            n^2                    for ikind = 1
            3 n^2 + min(m, n) + 2  for ikind = 2 
            0 (not used)           for ikind = 3
            n^2                    for ikind = 4           

    @param[out]
    work    (CPU workspace) REAL array, dimension 3 n^2.
            On exit, work(1:n^2) holds the rectangular matrix R.
            Preferably, for higher performance, work should be in pinned memory.
 
    @param[out]
    info    INTEGER
      -     = 0:  successful exit
      -     < 0:  if INFO = -i, the i-th argument had an illegal value
                  or another error occured, such as memory allocation failed.


    @ingroup magma_sgeqrf_comp
    ********************************************************************/
extern "C" magma_int_t
magma_sgegqr_gpu( magma_int_t ikind, magma_int_t m, magma_int_t n,
                  float *dA,   magma_int_t ldda,
                  float *dwork, float *work,
                  magma_int_t *info )
{
    #define work(i_,j_) (work + (i_) + (j_)*n)
    #define dA(i_,j_)   (dA   + (i_) + (j_)*ldda)
    
    magma_int_t i = 0, j, k, n2 = n*n;
    magma_int_t ione = 1;
    float c_zero = MAGMA_S_ZERO;
    float c_one  = MAGMA_S_ONE;
    float cn = 200., mins, maxs;

    /* check arguments */
    *info = 0;
    if (ikind < 1 || ikind > 4) {
        *info = -1;
    } else if (m < 0 || m < n) {
        *info = -2;
    } else if (n < 0 || n > 128) {
        *info = -3;
    } else if (ldda < max(1,m)) {
        *info = -5;
    }
    if (*info != 0) {
        magma_xerbla( __func__, -(*info) );
        return *info;
    }

    if (ikind == 1) {
        // === Iterative, based on SVD ============================================================
        float *U, *VT, *vt, *R, *G, *hwork, *tau;
        float *S;

        R    = work;             // Size n * n
        G    = R    + n*n;       // Size n * n
        VT   = G    + n*n;       // Size n * n
        
        magma_smalloc_cpu( &hwork, 32 + 2*n*n + 2*n);
        if ( hwork == NULL ) {
            *info = MAGMA_ERR_HOST_ALLOC;
            return *info;
        }
        
        magma_int_t lwork=n*n+32; // First part f hwork; used as workspace in svd
        
        U    = hwork + n*n + 32;  // Size n*n
        S    = (float *)(U+n*n); // Size n
        tau  = U + n*n + n;       // Size n
        
#if defined(PRECISION_c) || defined(PRECISION_z)
        float *rwork;
        magma_smalloc_cpu( &rwork, 5*n);
        if ( rwork == NULL ) {
            *info = MAGMA_ERR_HOST_ALLOC;
            return *info;
        }
#endif
        
        do {
            i++;
            
            magma_sgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, dA, ldda, dA, ldda, c_zero, dwork, n );
            magma_sgetmatrix(n, n, dwork, n, G, n);
            
#if defined(PRECISION_s) || defined(PRECISION_d)
            lapackf77_sgesvd("n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
                             hwork, &lwork, info);
#else
            lapackf77_sgesvd("n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
                             hwork, &lwork, rwork, info);
#endif
            
            mins = 100.f, maxs = 0.f;
            for (k=0; k < n; k++) {
                S[k] = magma_ssqrt( S[k] );
                
                if (S[k] < mins)  mins = S[k];
                if (S[k] > maxs)  maxs = S[k];
            }
            
            for (k=0; k < n; k++) {
                vt = VT + k*n;
                for (j=0; j < n; j++)
                    vt[j] *= S[j];
            }
            lapackf77_sgeqrf(&n, &n, VT, &n, tau, hwork, &lwork, info);
            
            if (i == 1)
                blasf77_scopy(&n2, VT, &ione, R, &ione);
            else
                blasf77_strmm("l", "u", "n", "n", &n, &n, &c_one, VT, &n, R, &n);
            
            magma_ssetmatrix(n, n, VT, n, dwork, n);
            magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, n, c_one, dwork, n, dA, ldda);
            if (mins > 0.00001f)
                cn = maxs/mins;
            
            //fprintf(stderr, "Iteration %d, cond num = %f \n", i, cn);
        } while (cn > 10.f);
        
        magma_free_cpu( hwork );
#if defined(PRECISION_c) || defined(PRECISION_z)
        magma_free_cpu( rwork );
#endif
        // ================== end of ikind == 1 ===================================================
    }
    else if (ikind == 2) {
        // ================== LAPACK based      ===================================================
        magma_int_t min_mn = min(m, n);
        magma_int_t nb = n;

        float *dtau = dwork + 2*n*n, *d_T = dwork, *ddA = dwork + n*n;
        float *tau  = work+n*n;

        magmablas_slaset( MagmaFull, n, n, c_zero, c_zero, d_T, n );
        magma_sgeqr2x3_gpu(m, n, dA, ldda, dtau, d_T, ddA,
                           (float *)(dwork+min_mn+2*n*n), info);
        magma_sgetmatrix( min_mn, 1, dtau, min_mn, tau, min_mn);
        magma_sgetmatrix( n, n, ddA, n, work, n);
        magma_sorgqr_gpu( m, n, n, dA, ldda, tau, d_T, nb, info );
        // ================== end of ikind == 2 ===================================================       
    }
    else if (ikind == 3) {
        // ================== MGS               ===================================================
        for(magma_int_t j = 0; j<n; j++){
            for(magma_int_t i = 0; i<j; i++){
                *work(i, j) = magma_sdot(m, dA(0,i), 1, dA(0,j), 1);
                magma_saxpy(m, -(*work(i,j)),  dA(0,i), 1, dA(0,j), 1);
            }
            for(magma_int_t i = j; i<n; i++)
                *work(i, j) = MAGMA_S_ZERO;
            //*work(j,j) = MAGMA_S_MAKE( magma_snrm2(m, dA(0,j), 1), 0. );
            *work(j,j) = magma_sdot(m, dA(0,j), 1, dA(0,j), 1);
            *work(j,j) = MAGMA_S_MAKE( sqrt(MAGMA_S_REAL( *work(j,j) )), 0.);
            magma_sscal(m, 1./ *work(j,j), dA(0,j), 1);
        }
        // ================== end of ikind == 3 ===================================================
    }
    else if (ikind == 4) {
        // ================== Cholesky QR       ===================================================
        magma_sgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, dA, ldda, dA, ldda, c_zero, dwork, n );
        magma_sgetmatrix(n, n, dwork, n, work, n);
        lapackf77_spotrf("u", &n, work, &n, info);
        magma_ssetmatrix(n, n, work, n, dwork, n);
        magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, n, c_one, dwork, n, dA, ldda);
        // ================== end of ikind == 4 ===================================================
    }
             
    return *info;
} /* magma_sgegqr_gpu */
Ejemplo n.º 6
0
extern "C" magma_int_t
magma_scg_merge(
    magma_s_sparse_matrix A, magma_s_vector b, magma_s_vector *x,  
    magma_s_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_CGMERGE;
    solver_par->numiter = 0;
    solver_par->info = MAGMA_SUCCESS; 

    // some useful variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_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] );

    // GPU workspace
    magma_s_vector r, d, z;
    magma_s_vinit( &r, Magma_DEV, dofs, c_zero, queue );
    magma_s_vinit( &d, Magma_DEV, dofs, c_zero, queue );
    magma_s_vinit( &z, Magma_DEV, dofs, c_zero, queue );
    
    float *d1, *d2, *skp;
    d1 = NULL;
    d2 = NULL;
    skp = NULL;
    magma_int_t stat_dev = 0, stat_cpu = 0;
    stat_dev += magma_smalloc( &d1, dofs*(1) );
    stat_dev += magma_smalloc( &d2, dofs*(1) );
    // array for the parameters
    stat_dev += magma_smalloc( &skp, 6 );       
    // skp = [alpha|beta|gamma|rho|tmp1|tmp2]
    if( stat_dev != 0 ){
        magma_free( d1 );
        magma_free( d2 );
        magma_free( skp );
        printf("error: memory allocation.\n");
        return MAGMA_ERR_DEVICE_ALLOC;
    }

    // solver variables
    float alpha, beta, gamma, rho, tmp1, *skp_h;
    float nom, nom0, r0, betanom, den;

    // solver setup
    magma_sscal( dofs, c_zero, x->dval, 1) ;                     // x = 0
    magma_scopy( dofs, b.dval, 1, r.dval, 1 );                    // r = b
    magma_scopy( dofs, b.dval, 1, d.dval, 1 );                    // d = b
    nom0 = betanom = magma_snrm2( dofs, r.dval, 1 );               
    nom = nom0 * nom0;                                           // nom = r' * r
    magma_s_spmv( c_one, A, d, c_zero, z, queue );                      // z = A d
    den = MAGMA_S_REAL( magma_sdot(dofs, d.dval, 1, z.dval, 1) ); // den = d'* z
    solver_par->init_res = nom0;
    
    // array on host for the parameters
    stat_cpu += magma_smalloc_cpu( &skp_h, 6 );
    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;
    }
    
    alpha = rho = gamma = tmp1 = c_one; 
    beta =  magma_sdot(dofs, r.dval, 1, r.dval, 1);
    skp_h[0]=alpha; 
    skp_h[1]=beta; 
    skp_h[2]=gamma; 
    skp_h[3]=rho; 
    skp_h[4]=tmp1; 
    skp_h[5]=MAGMA_S_MAKE(nom, 0.0);

    magma_ssetvector( 6, skp_h, 1, skp, 1 );
    
    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] = (real_Double_t) 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 SpMV and dot product
        magma_scgmerge_spmv1(  A, d1, d2, d.dval, z.dval, skp, queue ); 
            
        // updates x, r, computes scalars and updates d
        magma_scgmerge_xrbeta( dofs, d1, d2, x->dval, r.dval, d.dval, z.dval, skp, queue ); 

        // check stopping criterion (asynchronous copy)
        magma_sgetvector_async( 1 , skp+1, 1, 
                                                    skp_h+1, 1, stream[1] );
        betanom = sqrt(MAGMA_S_REAL(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  < r0 ) {
            break;
        }

    } 
    tempo2 = magma_sync_wtime( queue );
    solver_par->runtime = (real_Double_t) tempo2-tempo1;
    float residual;
    magma_sresidual( 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_s_vfree(&r, queue );
    magma_s_vfree(&z, queue );
    magma_s_vfree(&d, queue );

    magma_free( d1 );
    magma_free( d2 );
    magma_free( skp );
    magma_free_cpu( skp_h );

    magmablasSetKernelStream( orig_queue );
    return MAGMA_SUCCESS;
}   /* magma_scg_merge */
Ejemplo n.º 7
0
extern "C" magma_int_t
magma_sbicg(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_queue_t queue )
{
    magma_int_t info = MAGMA_NOTCONVERGED;
    
    // prepare solver feedback
    solver_par->solver = Magma_BICG;
    solver_par->numiter = 0;
    solver_par->spmv_count = 0;

    // some useful variables
    float c_zero = MAGMA_S_ZERO;
    float c_one  = MAGMA_S_ONE;
    float c_neg_one = MAGMA_S_NEG_ONE;
    
    magma_int_t dofs = A.num_rows * b.num_cols;

    // workspace
    magma_s_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, pt={Magma_CSR}, 
                z={Magma_CSR}, zt={Magma_CSR}, q={Magma_CSR}, y={Magma_CSR}, 
                yt={Magma_CSR},  qt={Magma_CSR};
                
    // need to transpose the matrix
    magma_s_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
    
    CHECK( magma_svinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &qt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &yt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));

    
    // solver variables
    float alpha, rho, beta, rho_new, ptq;
    float res, nomb, nom0, r0;

        // transpose the matrix
    magma_smtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
    magma_smconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
    magma_smfree(&Ah1, queue );
    magma_smtransposeconjugate( Ah2, &Ah1, queue );
    magma_smfree(&Ah2, queue );
    Ah2.blocksize = A.blocksize;
    Ah2.alignment = A.alignment;
    magma_smconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
    magma_smfree(&Ah1, queue );
    magma_smtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
    magma_smfree(&Ah2, queue );
    
    // solver setup
    CHECK(  magma_sresidualvec( A, b, *x, &r, &nom0, queue));
    res = nom0;
    solver_par->init_res = nom0;
    magma_scopy( dofs, r.dval, 1, rt.dval, 1, queue );                  // rr = r
    rho_new = magma_sdot( dofs, rt.dval, 1, r.dval, 1, queue );             // rho=<rr,r>
    rho = alpha = MAGMA_S_MAKE( 1.0, 0. );

    nomb = magma_snrm2( dofs, b.dval, 1, queue );
    if ( nomb == 0.0 ){
        nomb=1.0;
    }       
    if ( (r0 = nomb * solver_par->rtol) < ATOLERANCE ){
        r0 = ATOLERANCE;
    }
    
    solver_par->final_res = solver_par->init_res;
    solver_par->iter_res = solver_par->init_res;
    if ( solver_par->verbose > 0 ) {
        solver_par->res_vec[0] = nom0;
        solver_par->timing[0] = 0.0;
    }
    if ( nom0 < r0 ) {
        info = MAGMA_SUCCESS;
        goto cleanup;
    }

    //Chronometry
    real_Double_t tempo1, tempo2;
    tempo1 = magma_sync_wtime( queue );


    solver_par->numiter = 0;
    solver_par->spmv_count = 0;
    // start iteration
    do
    {
        solver_par->numiter++;

        magma_scopy( dofs, r.dval, 1 , y.dval, 1, queue );             // y=r
        magma_scopy( dofs, y.dval, 1 , z.dval, 1, queue );             // z=y
        magma_scopy( dofs, rt.dval, 1 , yt.dval, 1, queue );           // yt=rt
        magma_scopy( dofs, yt.dval, 1 , zt.dval, 1, queue );           // zt=yt
        
        rho= rho_new;
        rho_new = magma_sdot( dofs, rt.dval, 1, z.dval, 1, queue );  // rho=<rt,z>
        if( magma_s_isnan_inf( rho_new ) ){
            info = MAGMA_DIVERGENCE;
            break;
        }
        
        if( solver_par->numiter==1 ){
            magma_scopy( dofs, z.dval, 1 , p.dval, 1, queue );           // yt=rt
            magma_scopy( dofs, zt.dval, 1 , pt.dval, 1, queue );           // zt=yt
        } else {
            beta = rho_new/rho;
            magma_sscal( dofs, beta, p.dval, 1, queue );                 // p = beta*p
            magma_saxpy( dofs, c_one , z.dval, 1 , p.dval, 1, queue );   // p = z+beta*p
            magma_sscal( dofs, MAGMA_S_CONJ(beta), pt.dval, 1, queue );   // pt = beta*pt
            magma_saxpy( dofs, c_one , zt.dval, 1 , pt.dval, 1, queue );  // pt = zt+beta*pt
        }
        CHECK( magma_s_spmv( c_one, A, p, c_zero, q, queue ));      // v = Ap
        CHECK( magma_s_spmv( c_one, AT, pt, c_zero, qt, queue ));   // v = Ap
        solver_par->spmv_count++;
        solver_par->spmv_count++;
        ptq = magma_sdot( dofs, pt.dval, 1, q.dval, 1, queue );
        alpha = rho_new /ptq;
        
        
        magma_saxpy( dofs, alpha, p.dval, 1 , x->dval, 1, queue );                // x=x+alpha*p
        magma_saxpy( dofs, c_neg_one * alpha, q.dval, 1 , r.dval, 1, queue );     // r=r+alpha*q
        magma_saxpy( dofs, c_neg_one * MAGMA_S_CONJ(alpha), qt.dval, 1 , rt.dval, 1, queue );     // r=r+alpha*q

        res = magma_snrm2( 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_sresidualvec( 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_smfree(&r, queue );
    magma_smfree(&rt, queue );
    magma_smfree(&p, queue );
    magma_smfree(&pt, queue );
    magma_smfree(&q, queue );
    magma_smfree(&qt, queue );
    magma_smfree(&y, queue );
    magma_smfree(&yt, queue );
    magma_smfree(&z, queue );
    magma_smfree(&zt, queue );
    magma_smfree(&AT, queue );
    magma_smfree(&Ah1, queue );
    magma_smfree(&Ah2, queue );

    solver_par->info = info;
    return info;
}   /* magma_sbicg */
Ejemplo n.º 8
0
extern "C" magma_int_t
magma_sbpcg(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_s_preconditioner *precond_par,
    magma_queue_t queue )
{
    magma_int_t info = 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->spmv_count = 0;
    solver_par->info = MAGMA_SUCCESS;

    // local variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE;
    
    magma_int_t dofs = A.num_rows;

    // GPU workspace
    magma_s_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}, h={Magma_CSR};

    
    // solver variables
    float *alpha={0}, *beta={0};
    alpha = NULL;
    beta = NULL;


    float *nom={0}, *nom0={0}, *r0={0}, *gammaold={0}, *gammanew={0}, *den={0}, *res={0}, *residual={0};
    nom        = NULL;
    nom0       = NULL;
    r0         = NULL;
    gammaold   = NULL;
    gammanew   = NULL;
    den        = NULL;
    res        = NULL;
    residual   = NULL;
    
    CHECK( magma_smalloc_cpu(&alpha, num_vecs));
    CHECK( magma_smalloc_cpu(&beta, num_vecs));
    CHECK( magma_smalloc_cpu(&residual, num_vecs));
    CHECK( magma_smalloc_cpu(&nom, num_vecs));
    CHECK( magma_smalloc_cpu(&nom0, num_vecs));
    CHECK( magma_smalloc_cpu(&r0, num_vecs));
    CHECK( magma_smalloc_cpu(&gammaold, num_vecs));
    CHECK( magma_smalloc_cpu(&gammanew, num_vecs));
    CHECK( magma_smalloc_cpu(&den, num_vecs));
    CHECK( magma_smalloc_cpu(&res, num_vecs));
    CHECK( magma_smalloc_cpu(&residual, num_vecs));
    
    CHECK( magma_svinit( &r, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
    CHECK( magma_svinit( &rt, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
    CHECK( magma_svinit( &p, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
    CHECK( magma_svinit( &q, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
    CHECK( magma_svinit( &h, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));

    // solver setup
    CHECK(  magma_sresidualvec( A, b, *x, &r, nom0, queue));

    // preconditioner
    CHECK( magma_s_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
    CHECK( magma_s_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));

    magma_scopy( dofs*num_vecs, h.dval, 1, p.dval, 1, queue );                 // p = h

    for( i=0; i<num_vecs; i++) {
        nom[i] = MAGMA_S_REAL( magma_sdot( dofs, r(i), 1, h(i), 1, queue ) );
        nom0[i] = magma_snrm2( dofs, r(i), 1, queue );
    }
                                          
    CHECK( magma_s_spmv( c_one, A, p, c_zero, q, queue ));             // q = A p

    for( i=0; i<num_vecs; i++)
        den[i] = MAGMA_S_REAL( magma_sdot( dofs, p(i), 1, q(i), 1, queue ) );  // den = p dot q

    solver_par->init_res = nom0[0];
    
    if ( (r0[0] = nom[0] * solver_par->rtol) < 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]);
        info = MAGMA_NONSPD; 
        goto cleanup;
    }
    if ( nom[0] < r0[0] ) {
        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] = (real_Double_t)nom0[0];
        solver_par->timing[0] = 0.0;
    }
    
    solver_par->numiter = 0;
    solver_par->spmv_count = 0;
    // start iteration
    do
    {
        solver_par->numiter++;
        // preconditioner
        CHECK( magma_s_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
        CHECK( magma_s_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));


        for( i=0; i<num_vecs; i++)
            gammanew[i] = MAGMA_S_REAL( magma_sdot( dofs, r(i), 1, h(i), 1, queue ) );  // gn = < r,h>


        if ( solver_par->numiter==1 ) {
            magma_scopy( dofs*num_vecs, h.dval, 1, p.dval, 1, queue );                    // p = h
        } else {
            for( i=0; i<num_vecs; i++) {
                beta[i] = MAGMA_S_MAKE(gammanew[i]/gammaold[i], 0.);       // beta = gn/go
                magma_sscal( dofs, beta[i], p(i), 1, queue );            // p = beta*p
                magma_saxpy( dofs, c_one, h(i), 1, p(i), 1, queue ); // p = p + h
            }
        }

        CHECK( magma_s_spmv( c_one, A, p, c_zero, q, queue ));   // q = A p
        solver_par->spmv_count++;
     //   magma_s_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_S_REAL(magma_sdot( dofs, p(i), 1, q(i), 1, queue) );
                // den = p dot q

            alpha[i] = MAGMA_S_MAKE(gammanew[i]/den[i], 0.);
            magma_saxpy( dofs,  alpha[i], p(i), 1, x->dval+dofs*i, 1, queue ); // x = x + alpha p
            magma_saxpy( dofs, -alpha[i], q(i), 1, r(i), 1, queue );      // r = r - alpha q
            gammaold[i] = gammanew[i];

            res[i] = magma_snrm2( dofs, r(i), 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[0];
                solver_par->timing[(solver_par->numiter)/solver_par->verbose]
                        = (real_Double_t) tempo2-tempo1;
            }
        }


        if (  res[0]/nom0[0]  < 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;
    CHECK( magma_sresidual( 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;
            }
        }
        info = MAGMA_SLOW_CONVERGENCE;
        if( solver_par->iter_res < solver_par->rtol*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) res[0];
                solver_par->timing[(solver_par->numiter)/solver_par->verbose]
                        = (real_Double_t) tempo2-tempo1;
            }
        }
        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");

cleanup:
    magma_smfree(&r, queue );
    magma_smfree(&rt, queue );
    magma_smfree(&p, queue );
    magma_smfree(&q, queue );
    magma_smfree(&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);

    solver_par->info = info;
    return info;
}   /* magma_sbpcg */
Ejemplo n.º 9
0
magma_int_t
magma_sbicgstab_merge( magma_s_sparse_matrix A, magma_s_vector b, 
        magma_s_vector *x, magma_s_solver_par *solver_par ){

    // prepare solver feedback
    solver_par->solver = Magma_BICGSTABMERGE;
    solver_par->numiter = 0;
    solver_par->info = 0;

    // some useful variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_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_s_vector q, r,rr,p,v,s,t;
    float *d1, *d2, *skp;
    magma_smalloc( &d1, dofs*(2) );
    magma_smalloc( &d2, dofs*(2) );
    // array for the parameters
    magma_smalloc( &skp, 8 );       
    // skp = [alpha|beta|omega|rho_old|rho|nom|tmp1|tmp2]
    magma_s_vinit( &q, Magma_DEV, dofs*6, c_zero );

    // q = rr|r|p|v|s|t
    rr.memory_location = Magma_DEV; rr.val = NULL; rr.num_rows = rr.nnz = dofs;
    r.memory_location = Magma_DEV; r.val = NULL; r.num_rows = r.nnz = dofs;
    p.memory_location = Magma_DEV; p.val = NULL; p.num_rows = p.nnz = dofs;
    v.memory_location = Magma_DEV; v.val = NULL; v.num_rows = v.nnz = dofs;
    s.memory_location = Magma_DEV; s.val = NULL; s.num_rows = s.nnz = dofs;
    t.memory_location = Magma_DEV; t.val = NULL; t.num_rows = t.nnz = dofs;

    rr.val = q(0);
    r.val = q(1);
    p.val = q(2);
    v.val = q(3);
    s.val = q(4);
    t.val = q(5);
    
    // solver variables
    float alpha, beta, omega, rho_old, rho_new, *skp_h;
    float nom, nom0, betanom, r0, den;

    // solver setup
    magma_sscal( dofs, c_zero, x->val, 1) ;                            // x = 0
    magma_scopy( dofs, b.val, 1, q(0), 1 );                            // rr = b
    magma_scopy( dofs, b.val, 1, q(1), 1 );                            // r = b

    rho_new = magma_sdot( dofs, r.val, 1, r.val, 1 );             // rho=<rr,r>
    nom = MAGMA_S_REAL(magma_sdot( dofs, r.val, 1, r.val, 1 ));    
    nom0 = betanom = sqrt(nom);                                 // nom = || r ||                            
    rho_old = omega = alpha = MAGMA_S_MAKE( 1.0, 0. );
    beta = rho_new;
    solver_par->init_res = nom0;
    // array on host for the parameters    
    magma_smalloc_cpu( &skp_h, 8 );
    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_S_MAKE(nom, 0.0);
    magma_ssetvector( 8, skp_h, 1, skp, 1 );
    magma_s_spmv( c_one, A, r, c_zero, v );                     // z = A r
    den = MAGMA_S_REAL( magma_sdot(dofs, v.val, 1, r.val, 1) );// den = z dot r

    if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) 
        r0 = ATOLERANCE;
    if ( nom < r0 )
        return MAGMA_SUCCESS;
    // check positive definite  
    if (den <= 0.0) {
        printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
        return -100;
    }

    //Chronometry
    real_Double_t tempo1, tempo2;
    magma_device_sync(); tempo1=magma_wtime();
    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_sbicgmerge1( dofs, skp, v.val, r.val, p.val );

        magma_s_spmv( c_one, A, p, c_zero, v );                 // v = Ap

        magma_smdotc( dofs, 1, q.val, v.val, d1, d2, skp );                     
        magma_sbicgmerge4(  1, skp );
        magma_sbicgmerge2( dofs, skp, r.val, v.val, s.val );    // s=r-alpha*v

        magma_s_spmv( c_one, A, s, c_zero, t );                 // t=As

        magma_smdotc( dofs, 2, q.val+4*dofs, t.val, d1, d2, skp+6 );
        magma_sbicgmerge4(  2, skp );
        magma_sbicgmerge3( dofs, skp, p.val, s.val,     // x=x+alpha*p+omega*s
                            t.val, x->val, r.val );     // r=s-omega*t
        magma_smdotc( dofs, 2, q.val, r.val, d1, d2, skp+4);
        magma_sbicgmerge4(  3, skp );

        // check stopping criterion (asynchronous copy)
        magma_sgetvector_async( 1 , skp+5, 1, 
                                                        skp_h+5, 1, stream[1] );
        betanom = sqrt(MAGMA_S_REAL(skp_h[5]));

        if( solver_par->verbose > 0 ){
            magma_device_sync(); tempo2=magma_wtime();
            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;
        }
    }
    magma_device_sync(); tempo2=magma_wtime();
    solver_par->runtime = (real_Double_t) tempo2-tempo1;
    float residual;
    magma_sresidual( A, b, *x, &residual );
    solver_par->iter_res = betanom;
    solver_par->final_res = residual;

    if( solver_par->numiter < solver_par->maxiter){
        solver_par->info = 0;
    }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 = -2;
    }
    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 = -1;
    }
    magma_s_vfree(&q);  // frees all vectors

    magma_free(d1);
    magma_free(d2);
    magma_free( skp );
    magma_free_cpu( skp_h );

    return MAGMA_SUCCESS;
}   /* sbicgstab_merge */
Ejemplo n.º 10
0
extern "C" magma_int_t
magma_scg_res(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_queue_t queue )
{
    magma_int_t info = MAGMA_NOTCONVERGED;
    
    // prepare solver feedback
    solver_par->solver = Magma_CG;
    solver_par->numiter = 0;
    solver_par->spmv_count = 0;
    
    // solver variables
    float alpha, beta;
    float nom0, r0,  res, nomb;
    float den, gammanew, gammaold = MAGMA_S_MAKE(1.0,0.0);
    // local variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE;
    
    magma_int_t dofs = A.num_rows* b.num_cols;

    // GPU workspace
    magma_s_matrix r={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR};
    CHECK( magma_svinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    

    // solver setup
    CHECK(  magma_sresidualvec( A, b, *x, &r, &nom0, queue));

    magma_scopy( dofs, r.dval, 1, p.dval, 1, queue );                    // p = h
    CHECK( magma_s_spmv( c_one, A, p, c_zero, q, queue ));             // q = A p
    solver_par->spmv_count++;
    den =  magma_sdot( dofs, p.dval, 1, q.dval, 1, queue ); // den = p dot q
    solver_par->init_res = nom0;
            
    nomb = magma_snrm2( 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_S_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++;

        gammanew = magma_sdot( dofs, r.dval, 1, r.dval, 1, queue );
                                                            // gn = < r,r>

        if ( solver_par->numiter == 1 ) {
            magma_scopy( dofs, r.dval, 1, p.dval, 1, queue );                    // p = r
        } else {
            beta = (gammanew/gammaold);       // beta = gn/go
            magma_sscal( dofs, beta, p.dval, 1, queue );            // p = beta*p
            magma_saxpy( dofs, c_one, r.dval, 1, p.dval, 1, queue ); // p = p + r
        }

        CHECK( magma_s_spmv( c_one, A, p, c_zero, q, queue ));   // q = A p
        solver_par->spmv_count++;
        den = magma_sdot( dofs, p.dval, 1, q.dval, 1, queue );
                // den = p dot q

        alpha = gammanew / den;
        magma_saxpy( dofs,  alpha, p.dval, 1, x->dval, 1, queue );     // x = x + alpha p
        magma_saxpy( dofs, -alpha, q.dval, 1, r.dval, 1, queue );      // r = r - alpha q
        gammaold = gammanew;

        res = magma_snrm2( 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_sresidualvec( 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_smfree(&r, queue );
    magma_smfree(&p, queue );
    magma_smfree(&q, queue );

    solver_par->info = info;
    return info;
}   /* magma_scg */
Ejemplo n.º 11
0
extern "C" magma_int_t
magma_scgs(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_queue_t queue )
{
    magma_int_t info = MAGMA_NOTCONVERGED;
    
    // prepare solver feedback
    solver_par->solver = Magma_CGS;
    solver_par->numiter = 0;
    solver_par->spmv_count = 0;
    
    // constants
    const float c_zero    = MAGMA_S_ZERO;
    const float c_one     = MAGMA_S_ONE;
    const float c_neg_one = MAGMA_S_NEG_ONE;
    
    // solver variables
    float nom0, r0, res=0, nomb;
    float rho, rho_l = c_one, alpha, beta;
    
    magma_int_t dofs = A.num_rows* b.num_cols;

    // GPU workspace
    magma_s_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_svinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &r_tld,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));

    // solver setup
    CHECK(  magma_sresidualvec( A, b, *x, &r, &nom0, queue));
    magma_scopy( dofs, r.dval, 1, r_tld.dval, 1, queue );   

    solver_par->init_res = nom0;
            
    nomb = magma_snrm2( 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;
    tempo1 = magma_sync_wtime( queue );
    
    solver_par->numiter = 0;
    solver_par->spmv_count = 0;
    // start iteration
    do
    {
        solver_par->numiter++;
        
        rho = magma_sdot( dofs, r.dval, 1, r_tld.dval, 1, queue );
                                                            // rho = < r,r_tld>    
        if( magma_s_isnan_inf( rho ) ){
            info = MAGMA_DIVERGENCE;
            break;
        }
        
        if ( solver_par->numiter > 1 ) {                        // direction vectors
            beta = rho / rho_l;            
            magma_scopy( dofs, r.dval, 1, u.dval, 1, queue );          // u = r
            magma_saxpy( dofs,  beta, q.dval, 1, u.dval, 1, queue );     // u = u + beta q
            magma_sscal( dofs, beta, p.dval, 1, queue );                 // p = beta*p
            magma_saxpy( dofs, c_one, q.dval, 1, p.dval, 1, queue );      // p = q + beta*p
            magma_sscal( dofs, beta, p.dval, 1, queue );                 // p = beta*(q + beta*p)
            magma_saxpy( dofs, c_one, u.dval, 1, p.dval, 1, queue );     // p = u + beta*(q + beta*p)
        //u = r + beta*q;
        //p = u + beta*( q + beta*p );
        }
        else{
            magma_scopy( dofs, r.dval, 1, u.dval, 1, queue );          // u = r
            magma_scopy( dofs, r.dval, 1, p.dval, 1, queue );          // p = r
        }
        
        CHECK( magma_s_spmv( c_one, A, p, c_zero, v_hat, queue ));   // v = A p
        solver_par->spmv_count++;
        alpha = rho / magma_sdot( dofs, r_tld.dval, 1, v_hat.dval, 1, queue );
        magma_scopy( dofs, u.dval, 1, q.dval, 1, queue );              // q = u
        magma_saxpy( dofs,  -alpha, v_hat.dval, 1, q.dval, 1, queue );   // q = u - alpha v_hat
        
        magma_scopy( dofs, u.dval, 1, t.dval, 1, queue );             // t = q
        magma_saxpy( dofs,  c_one, q.dval, 1, t.dval, 1, queue );       // t = u + q


        CHECK( magma_s_spmv( c_one, A, t, c_zero, rt, queue ));   // t = A u_hat
        solver_par->spmv_count++;
        magma_saxpy( dofs,  c_neg_one*alpha, rt.dval, 1, r.dval, 1, queue );       // r = r -alpha*A u_hat
        magma_saxpy( dofs,  alpha, t.dval, 1, x->dval, 1, queue );      // x = x + alpha u_hat
        rho_l = rho;
        
        res = magma_snrm2( 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_sresidualvec( 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 == 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_smfree(&r, queue );
    magma_smfree(&rt, queue );
    magma_smfree(&r_tld, queue );
    magma_smfree(&p, queue );
    magma_smfree(&q, queue );
    magma_smfree(&u, queue );
    magma_smfree(&v, queue );
    magma_smfree(&t, queue );
    magma_smfree(&p_hat, queue );
    magma_smfree(&q_hat, queue );
    magma_smfree(&u_hat, queue );
    magma_smfree(&v_hat, queue );

    solver_par->info = info;
    return info;
}   /* magma_scgs */
Ejemplo n.º 12
0
extern "C" magma_int_t
magma_scg(
    magma_s_sparse_matrix A, magma_s_vector b, magma_s_vector *x,  
    magma_s_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_CG;
    solver_par->numiter = 0;
    solver_par->info = MAGMA_SUCCESS; 

    // local variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE;
    
    magma_int_t dofs = A.num_rows;

    // GPU workspace
    magma_s_vector r, p, q;
    magma_s_vinit( &r, Magma_DEV, dofs, c_zero, queue );
    magma_s_vinit( &p, Magma_DEV, dofs, c_zero, queue );
    magma_s_vinit( &q, Magma_DEV, dofs, c_zero, queue );
    
    // solver variables
    float alpha, beta;
    float nom, nom0, r0, betanom, betanomsq, den;

    // solver setup
    magma_sscal( dofs, c_zero, x->dval, 1) ;                     // x = 0
    magma_scopy( dofs, b.dval, 1, r.dval, 1 );                    // r = b
    magma_scopy( dofs, b.dval, 1, p.dval, 1 );                    // p = b
    nom0 = betanom = magma_snrm2( dofs, r.dval, 1 );           
    nom  = nom0 * nom0;                                // nom = r' * r
    magma_s_spmv( c_one, A, p, c_zero, q, queue );                     // q = A p
    den = MAGMA_S_REAL( magma_sdot(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 ) {
        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] = (real_Double_t)nom0;
        solver_par->timing[0] = 0.0;
    }
    
    // start iteration
    for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; 
                                                    solver_par->numiter++ ) {
        alpha = MAGMA_S_MAKE(nom/den, 0.);
        magma_saxpy(dofs,  alpha, p.dval, 1, x->dval, 1);     // x = x + alpha p
        magma_saxpy(dofs, -alpha, q.dval, 1, r.dval, 1);      // r = r - alpha q
        betanom = magma_snrm2(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_S_MAKE(betanomsq/nom, 0.);           // beta = betanoms/nom
        magma_sscal(dofs, beta, p.dval, 1);                // p = beta*p
        magma_saxpy(dofs, c_one, r.dval, 1, p.dval, 1);     // p = p + r 
        magma_s_spmv( c_one, A, p, c_zero, q, queue );           // q = A p
        den = MAGMA_S_REAL(magma_sdot(dofs, p.dval, 1, q.dval, 1));    
                // den = p dot q
        nom = betanomsq;
    } 
    tempo2 = magma_sync_wtime( queue );
    solver_par->runtime = (real_Double_t) tempo2-tempo1;
    float residual;
    magma_sresidual( A, b, *x, &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;
            }
        }
        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_s_vfree(&r, queue );
    magma_s_vfree(&p, queue );
    magma_s_vfree(&q, queue );

    magmablasSetKernelStream( orig_queue );
    return MAGMA_SUCCESS;
}   /* magma_scg */
Ejemplo n.º 13
0
extern "C" magma_int_t
magma_sidr_strms(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_queue_t queue )
{
    magma_int_t info = MAGMA_NOTCONVERGED;

    // prepare solver feedback
    solver_par->solver = Magma_IDRMERGE;
    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 float c_zero = MAGMA_S_ZERO;
    const float c_one = MAGMA_S_ONE;
    const float c_n_one = MAGMA_S_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;
    float om;
    float gamma;

    // matrices and vectors
    magma_s_matrix dxs = {Magma_CSR};
    magma_s_matrix dr = {Magma_CSR}, drs = {Magma_CSR};
    magma_s_matrix dP = {Magma_CSR}, dP1 = {Magma_CSR};
    magma_s_matrix dG = {Magma_CSR}, dGcol = {Magma_CSR};
    magma_s_matrix dU = {Magma_CSR};
    magma_s_matrix dM = {Magma_CSR};
    magma_s_matrix df = {Magma_CSR};
    magma_s_matrix dt = {Magma_CSR}, dtt = {Magma_CSR};
    magma_s_matrix dc = {Magma_CSR};
    magma_s_matrix dv = {Magma_CSR};
    magma_s_matrix dskp = {Magma_CSR};
    magma_s_matrix dalpha = {Magma_CSR};
    magma_s_matrix dbeta = {Magma_CSR};
    float *hMdiag = NULL;
    float *hskp = NULL;
    float *halpha = NULL;
    float *hbeta = NULL;
    float *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_snrm2( b.num_rows, b.dval, 1, queue );
    if ( nrmb == 0.0 ) {
        magma_sscal( x->num_rows, MAGMA_S_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_svinit( &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_svinit( &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_sresidualvec( 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_svinit( &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_slarnv( &distr, iseed, &dof, dP.val );

    // transfer P to device
    CHECK( magma_smtransfer( dP, &dP1, Magma_CPU, Magma_DEV, queue ));
    magma_smfree( &dP, queue );

    // P = ortho(P1)
    if ( dP1.num_cols > 1 ) {
        // P = magma_sqr(P1), QR factorization
        CHECK( magma_sqr( dP1.num_rows, dP1.num_cols, dP1, dP1.ld, &dP, NULL, queue ));
    } else {
        // P = P1 / |P1|
        nrm = magma_snrm2( dof, dP1.dval, 1, queue );
        nrm = 1.0 / nrm;
        magma_sscal( dof, nrm, dP1.dval, 1, queue );
        CHECK( magma_smtransfer( dP1, &dP, Magma_DEV, Magma_DEV, queue ));
    }
    magma_smfree( &dP1, queue );
//---------------------------------------

    // allocate memory for the scalar products
    CHECK( magma_smalloc_pinned( &hskp, 5 ));
    CHECK( magma_svinit( &dskp, Magma_DEV, 4, 1, c_zero, queue ));

    CHECK( magma_smalloc_pinned( &halpha, s ));
    CHECK( magma_svinit( &dalpha, Magma_DEV, s, 1, c_zero, queue ));

    CHECK( magma_smalloc_pinned( &hbeta, s ));
    CHECK( magma_svinit( &dbeta, Magma_DEV, s, 1, c_zero, queue ));
    
    // workspace for merged dot product
    CHECK( magma_smalloc( &d1, max(2, s) * b.num_rows ));
    CHECK( magma_smalloc( &d2, max(2, s) * b.num_rows ));

    // smoothing enabled
    if ( smoothing > 0 ) {
        // set smoothing solution vector
        CHECK( magma_smtransfer( *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_svinit( &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_svinit( &drs, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
        magma_free( drs.dval );
        drs.dval = dtt.dval + ldd;

        // set smoothing residual vector
        magma_scopyvector( 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_svinit( &dG, Magma_DEV, ldd, s, c_zero, queue ));
        dG.num_rows = A.num_rows;
    } else {
        CHECK( magma_svinit( &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_svinit( &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_svinit( &dU, Magma_DEV, ldd, s, c_zero, queue ));
        dU.num_rows = A.num_cols;
    } else {
        CHECK( magma_svinit( &dU, Magma_DEV, A.num_cols, s, c_zero, queue ));
    }

    // M(s,s) = I
    CHECK( magma_svinit( &dM, Magma_DEV, s, s, c_zero, queue ));
    CHECK( magma_smalloc_pinned( &hMdiag, s ));
    magmablas_slaset( MagmaFull, dM.num_rows, dM.num_cols, c_zero, c_one, dM.dval, dM.ld, queue );

    // f = 0
    CHECK( magma_svinit( &df, Magma_DEV, dP.num_cols, 1, c_zero, queue ));

    // c = 0
    CHECK( magma_svinit( &dc, Magma_DEV, dM.num_cols, 1, c_zero, queue ));

    // v = r
    CHECK( magma_smtransfer( dr, &dv, Magma_DEV, Magma_DEV, queue ));

    //--------------START TIME---------------
    // chronometry
    tempo1 = magma_sync_wtime( queue );
    if ( solver_par->verbose > 0 ) {
        solver_par->timing[0] = 0.0;
    }

cudaProfilerStart();

    om = MAGMA_S_ONE;
    gamma = MAGMA_S_ZERO;
    innerflag = 0;

    // new RHS for small systems
    // f = P' r
    // Q1
    magma_sgemvmdot_shfl( dP.num_rows, dP.num_cols, dP.dval, dr.dval, d1, d2, df.dval, queues[1] );

    // skp[4] = f(k)
    // Q1
    magma_sgetvector_async( 1, df.dval, 1, &hskp[4], 1, queues[1] );

    // c(k:s) = f(k:s)
    // Q1
    magma_scopyvector_async( s, df.dval, 1, dc.dval, 1, queues[1] );

    // c(k:s) = M(k:s,k:s) \ f(k:s)
    // Q1
    magma_strsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, s, dM.dval, dM.ld, dc.dval, 1, queues[1] );

    // start iteration
    do
    {
        solver_par->numiter++;

        // 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_sgemv( MagmaNoTrans, dG.num_rows, sk, c_n_one, dGcol.dval, dG.ld, &dc.dval[k], 1, c_one, dv.dval, 1, queues[1] );

            // U(:,k) = om * v + U(:,k:s) c(k:s)
            // Q1
            magmablas_sgemv( 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_s_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_sdot( 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_saxpy( dG.num_rows, -halpha[i], &dG.dval[i*dG.ld], 1, dGcol.dval, 1, queues[1] );
            }

            // sync Q1 --> G(:,k) = G(:,k) - alpha * G(:,i), 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_sgemvmdot_shfl( dP.num_rows, sk, &dP.dval[k*dP.ld], dGcol.dval, d1, d2, &dM.dval[k*dM.ld+k], queues[2] );

            // non-first s iteration
            if ( k > 0 ) {
                // alpha = dalpha
                // Q0
                magma_ssetvector_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_sgemv( MagmaNoTrans, dU.num_rows, k, c_n_one, dU.dval, dU.ld, dalpha.dval, 1, c_one, dv.dval, 1, queues[0] );
            }

            // Mdiag(k) = M(k,k)
            // Q2
            magma_sgetvector( 1, &dM.dval[k*dM.ld+k], 1, &hMdiag[k], 1, queues[2] );
            // implicit sync Q2 --> Mdiag(k) = M(k,k)

            // U(:,k) = v
            // Q0
            magma_scopyvector_async( dU.num_rows, dv.dval, 1, &dU.dval[k*dU.ld], 1, queues[0] );

            // check M(k,k) == 0
            if ( MAGMA_S_EQUAL(hMdiag[k], MAGMA_S_ZERO) ) {
                innerflag = 1;
                info = MAGMA_DIVERGENCE;
                break;
            }

            // beta = f(k) / M(k,k)
            hbeta[k] = hskp[4] / hMdiag[k];

            // check for nan
            if ( magma_s_isnan( hbeta[k] ) || magma_s_isinf( hbeta[k] )) {
                innerflag = 1;
                info = MAGMA_DIVERGENCE;
                break;
            }

            // r = r - beta * G(:,k)
            // Q2
            magma_saxpy( dr.num_rows, -hbeta[k], dGcol.dval, 1, dr.dval, 1, queues[2] );

            // non-last s iteration 
            if ( (k + 1) < s ) {
                // f(k+1:s) = f(k+1:s) - beta * M(k+1:s,k)
                // Q1
                magma_saxpy( 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_scopyvector_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_strsv( 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_sgetvector_async( 1, &df.dval[k+1], 1, &hskp[4], 1, queues[1] ); 
            }

            // smoothing disabled
            if ( smoothing <= 0 ) {
                // |r|
                // Q2
                nrmr = magma_snrm2( dr.num_rows, dr.dval, 1, queues[2] );           
                // implicit sync Q2 --> |r|

            // smoothing enabled
            } else {
                // smoothing operation
//---------------------------------------
                // t = rs - r
                // Q2
                magma_sidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queues[2] );

                // x = x + beta * U(:,k)
                // Q0
                magma_saxpy( x->num_rows, hbeta[k], &dU.dval[k*dU.ld], 1, x->dval, 1, queues[0] );

                // t't
                // t'rs
                // Q2
                CHECK( magma_sgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queues[2] ));

                // skp[2-3] = dskp[2-3]
                // Q2
                magma_sgetvector( 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];
                
                // rs = rs - gamma * t 
                // Q1
                magma_saxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queues[1] );

                // xs = xs - gamma * (xs - x) 
                // Q0
                magma_sidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queues[0] );

                // |rs|
                // Q1
                nrmr = magma_snrm2( drs.num_rows, drs.dval, 1, queues[1] );       
                // implicit sync Q0 --> |r|
//---------------------------------------
            }

            // v = r
            // Q1
            magma_scopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] );

            // last s iteration
            if ( (k + 1) == s ) {
               // t = A r
               // Q2
               CHECK( magma_s_spmv( c_one, A, dr, c_zero, dt, queues[2] ));
               solver_par->spmv_count++;

               // t't
               // t'r
               // Q2
               CHECK( magma_sgemvmdot_shfl( dt.ld, 2, dt.dval, dt.dval, d1, d2, dskp.dval, queues[2] ));
            }

            // 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_ssetvector_async( s, hbeta, 1, dbeta.dval, 1, queues[0] );

            // x = x + U(:,1:s) * beta(1:s)
            // Q0
            magmablas_sgemv( 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;
        }

        // computation of a new omega
//---------------------------------------
        // skp[0-2] = dskp[0-2]
        // Q2
        magma_sgetvector( 2, dskp.dval, 1, hskp, 1, queues[2] );
        // implicit sync Q2 --> skp = dskp

        // |t|
        nrmt = magma_ssqrt( MAGMA_S_REAL(hskp[0]) );
        
        // rho = abs((t' * r) / (|t| * |r|))
        rho = MAGMA_D_ABS( MAGMA_S_REAL(hskp[1]) / (nrmt * nrmr) );

        // om = (t' * r) / (|t| * |t|)
        om = hskp[1] / hskp[0]; 
        if ( rho < angle ) {
            om = (om * angle) / rho;
        }
//---------------------------------------
        if ( MAGMA_S_EQUAL(om, MAGMA_S_ZERO) ) {
            info = MAGMA_DIVERGENCE;
            break;
        }

        // sync Q1 --> v = r
        magma_queue_sync( queues[1] );

        // r = r - om * t
        // Q2
        magma_saxpy( dr.num_rows, -om, dt.dval, 1, dr.dval, 1, queues[2] );

        // x = x + om * v
        // Q0
        magma_saxpy( x->num_rows, om, dv.dval, 1, x->dval, 1, queues[0] );

        // smoothing disabled
        if ( smoothing <= 0 ) {
            // |r|
            // Q2
            nrmr = magma_snrm2( dr.num_rows, dr.dval, 1, queues[2] );           
            // implicit sync Q2 --> |r|

            // v = r
            // Q0
            magma_scopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[0] );

            // new RHS for small systems
            // f = P' r
            // Q1
            magma_sgemvmdot_shfl( dP.num_rows, dP.num_cols, dP.dval, dr.dval, d1, d2, df.dval, queues[1] );

            // skp[4] = f(k)
            // Q1
            magma_sgetvector_async( 1, df.dval, 1, &hskp[4], 1, queues[1] );

            // c(k:s) = f(k:s)
            // Q1
            magma_scopyvector_async( s, df.dval, 1, dc.dval, 1, queues[1] );

            // c(k:s) = M(k:s,k:s) \ f(k:s)
            // Q1
            magma_strsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, s, dM.dval, dM.ld, dc.dval, 1, queues[1] );

        // smoothing enabled
        } else {
            // smoothing operation
//---------------------------------------
            // t = rs - r
            // Q2
            magma_sidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queues[2] );

            // t't
            // t'rs
            // Q2
            CHECK( magma_sgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queues[2] ));

            // skp[2-3] = dskp[2-3]
            // Q2
            magma_sgetvector( 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];

            // rs = rs - gamma * (rs - r) 
            // Q2
            magma_saxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queues[2] );

            // xs = xs - gamma * (xs - x) 
            // Q0
            magma_sidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queues[0] );

            // v = r
            // Q0
            magma_scopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[0] );

            // new RHS for small systems
            // f = P' r
            // Q1
            magma_sgemvmdot_shfl( dP.num_rows, dP.num_cols, dP.dval, dr.dval, d1, d2, df.dval, queues[1] );

            // skp[4] = f(k)
            // Q1
            magma_sgetvector_async( 1, df.dval, 1, &hskp[4], 1, queues[1] );

            // c(k:s) = f(k:s)
            // Q1
            magma_scopyvector_async( s, df.dval, 1, dc.dval, 1, queues[1] );

            // |rs|
            // Q2
            nrmr = magma_snrm2( drs.num_rows, drs.dval, 1, queues[2] );           
            // implicit sync Q2 --> |r|

            // c(k:s) = M(k:s,k:s) \ f(k:s)
            // Q1
            magma_strsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, s, dM.dval, dM.ld, dc.dval, 1, queues[1] );
//---------------------------------------
        }

        // 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;
        }

        // sync Q0 --> v = r
        magma_queue_sync( queues[0] );
    }
    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_scopyvector_async( x->num_rows, dxs.dval, 1, x->dval, 1, queue );

        // r = rs
        magma_scopyvector_async( dr.num_rows, drs.dval, 1, dr.dval, 1, queue );
    }

cudaProfilerStop();

    // 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_sresidualvec( 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_smfree( &dxs, queue );
        magma_smfree( &drs, queue ); 
        magma_smfree( &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_smfree( &dr, queue );
    magma_smfree( &dP, queue );
    magma_smfree( &dP1, queue );
    magma_smfree( &dG, queue );
    magma_smfree( &dGcol, queue );
    magma_smfree( &dU, queue );
    magma_smfree( &dM, queue );
    magma_smfree( &df, queue );
    magma_smfree( &dt, queue );
    magma_smfree( &dc, queue );
    magma_smfree( &dv, queue );
    magma_smfree( &dskp, queue );
    magma_smfree( &dalpha, queue );
    magma_smfree( &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_sidr_strms */
}
Ejemplo n.º 14
0
extern "C" magma_int_t
magma_slsqr(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_solver_par *solver_par,
    magma_s_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
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_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_s_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
    
    // GPU workspace
    magma_s_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_svinit( &r, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &v, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &z, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &d, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &vt,Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &q, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &w, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));

    
    // transpose the matrix
    magma_smtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
    magma_smconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
    magma_smfree(&Ah1, queue );
    magma_smtransposeconjugate( Ah2, &Ah1, queue );
    magma_smfree(&Ah2, queue );
    Ah2.blocksize = A.blocksize;
    Ah2.alignment = A.alignment;
    magma_smconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
    magma_smfree(&Ah1, queue );
    magma_smtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
    magma_smfree(&Ah2, queue );
    

    
    // solver setup
    CHECK(  magma_sresidualvec( A, b, *x, &r, &nom0, queue));
    solver_par->init_res = nom0;
    nomb = magma_snrm2( 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_scopy( m, b.dval, 1, u.dval, 1, queue );  
    beta = magma_snrm2( m, u.dval, 1, queue );
    magma_sscal( m, MAGMA_S_MAKE(1./beta, 0.0 ), u.dval, 1, queue );
    normr = beta;
    c = 1.0;
    s = 0.0;
    phibar = beta;
    CHECK( magma_s_spmv( c_one, AT, u, c_zero, v, queue ));
    
    if( precond_par->solver == Magma_NONE ){
        ;
    } else {
      CHECK( magma_s_applyprecond_right( MagmaTrans, A, v, &zt, precond_par, queue ));
      CHECK( magma_s_applyprecond_left( MagmaTrans, A, zt, &v, precond_par, queue ));
    }
    alpha = magma_snrm2( n, v.dval, 1, queue );
    magma_sscal( n, MAGMA_S_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_scopy( n, v.dval, 1 , z.dval, 1, queue );    
        } else {
            CHECK( magma_s_applyprecond_left( MagmaNoTrans, A, v, &zt, precond_par, queue ));
            CHECK( magma_s_applyprecond_right( MagmaNoTrans, A, zt, &z, precond_par, queue ));
        }
        //CHECK( magma_s_spmv( c_one, A, z, MAGMA_S_MAKE(-alpha,0.0), u, queue ));
        CHECK( magma_s_spmv( c_one, A, z, c_zero, zt, queue ));
        magma_sscal( m, MAGMA_S_MAKE(-alpha, 0.0 ), u.dval, 1, queue ); 
        magma_saxpy( m, c_one, zt.dval, 1, u.dval, 1, queue );
        
        solver_par->spmv_count++;
        beta = magma_snrm2( m, u.dval, 1, queue );
        magma_sscal( m, MAGMA_S_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_sscal( n, MAGMA_S_MAKE(-thet, 0.0 ), d.dval, 1, queue ); 
        magma_saxpy( n, c_one, z.dval, 1, d.dval, 1, queue );
        magma_sscal( n, MAGMA_S_MAKE(1./rho, 0.0 ), d.dval, 1, queue );
        normd = magma_snrm2( 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_saxpy( n, MAGMA_S_MAKE( phi, 0.0 ), d.dval, 1, x->dval, 1, queue );
        normr = fabs(s) * normr;
        CHECK( magma_s_spmv( c_one, AT, u, c_zero, vt, queue ));
        solver_par->spmv_count++;
        if( precond_par->solver == Magma_NONE ){
            ;    
        } else {
            CHECK( magma_s_applyprecond_right( MagmaTrans, A, vt, &zt, precond_par, queue ));
            CHECK( magma_s_applyprecond_left( MagmaTrans, A, zt, &vt, precond_par, queue ));
        }

        magma_sscal( n, MAGMA_S_MAKE(-beta, 0.0 ), v.dval, 1, queue ); 
        magma_saxpy( n, c_one, vt.dval, 1, v.dval, 1, queue );
        alpha = magma_snrm2( n, v.dval, 1, queue );
        magma_sscal( n, MAGMA_S_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_sresidualvec( 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_smfree(&r, queue );
    magma_smfree(&v,  queue );
    magma_smfree(&z,  queue );
    magma_smfree(&zt, queue );
    magma_smfree(&d,  queue );
    magma_smfree(&vt,  queue );
    magma_smfree(&q,  queue );
    magma_smfree(&u,  queue );
    magma_smfree(&w,  queue );
    magma_smfree(&AT, queue );
    magma_smfree(&Ah1, queue );
    magma_smfree(&Ah2, queue );

    
    solver_par->info = info;
    return info;
}   /* magma_sqmr */
Ejemplo n.º 15
0
extern "C" magma_int_t
magma_scg_merge(
    magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
    magma_s_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
    float alpha, beta, gamma, rho, tmp1, *skp_h={0};
    float nom, nom0, betanom, den, nomb;

    // some useful variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE;
    magma_int_t dofs = A.num_rows*b.num_cols;

    magma_s_matrix r={Magma_CSR}, d={Magma_CSR}, z={Magma_CSR}, B={Magma_CSR}, C={Magma_CSR};
    float *d1=NULL, *d2=NULL, *skp=NULL;

    // GPU workspace
    CHECK( magma_svinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    CHECK( magma_svinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
    
    CHECK( magma_smalloc( &d1, dofs*(1) ));
    CHECK( magma_smalloc( &d2, dofs*(1) ));
    // array for the parameters
    CHECK( magma_smalloc( &skp, 6 ));
    // skp = [alpha|beta|gamma|rho|tmp1|tmp2]
    
    // solver setup
    magma_sscal( dofs, c_zero, x->dval, 1, queue );                      // x = 0
    //CHECK(  magma_sresidualvec( A, b, *x, &r, nom0, queue));
    magma_scopy( dofs, b.dval, 1, r.dval, 1, queue );                    // r = b
    magma_scopy( dofs, r.dval, 1, d.dval, 1, queue );                    // d = r
    nom0 = betanom = magma_snrm2( dofs, r.dval, 1, queue );
    nom = nom0 * nom0;                                           // nom = r' * r
    CHECK( magma_s_spmv( c_one, A, d, c_zero, z, queue ));              // z = A d
    den = MAGMA_S_ABS( magma_sdot( dofs, d.dval, 1, z.dval, 1, queue ) ); // den = d'* z
    solver_par->init_res = nom0;
    
    nomb = magma_snrm2( dofs, b.dval, 1, queue );
    if ( nomb == 0.0 ){
        nomb=1.0;
    }       
    
    // array on host for the parameters
    CHECK( magma_smalloc_cpu( &skp_h, 6 ));
    
    alpha = rho = gamma = tmp1 = c_one;
    beta =  magma_sdot( 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_S_MAKE(nom, 0.0);

    magma_ssetvector( 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_scgmerge_spmv1(  A, d1, d2, d.dval, z.dval, skp, queue ));
        solver_par->spmv_count++;
        // updates x, r, computes scalars and updates d
        CHECK( magma_scgmerge_xrbeta( dofs, d1, d2, x->dval, r.dval, d.dval, z.dval, skp, queue ));

        // check stopping criterion (asynchronous copy)
        magma_sgetvector( 1 , skp+1, 1, skp_h+1, 1, queue );
        betanom = sqrt(MAGMA_S_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_sresidualvec( 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_smfree(&r, queue );
    magma_smfree(&z, queue );
    magma_smfree(&d, queue );
    magma_smfree(&B, queue );
    magma_smfree(&C, queue );

    magma_free( d1 );
    magma_free( d2 );
    magma_free( skp );
    magma_free_cpu( skp_h );

    solver_par->info = info;
    return info;
}   /* magma_scg_merge */
Ejemplo n.º 16
0
magma_int_t
magma_spcg( magma_s_sparse_matrix A, magma_s_vector b, magma_s_vector *x,  
            magma_s_solver_par *solver_par, 
            magma_s_preconditioner *precond_par ){

    // prepare solver feedback
    solver_par->solver = Magma_PCG;
    solver_par->numiter = 0;
    solver_par->info = 0;

    // local variables
    float c_zero = MAGMA_S_ZERO, c_one = MAGMA_S_ONE;
    
    magma_int_t dofs = A.num_rows;

    // GPU workspace
    magma_s_vector r, rt, p, q, h;
    magma_s_vinit( &r, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &rt, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &p, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &q, Magma_DEV, dofs, c_zero );
    magma_s_vinit( &h, Magma_DEV, dofs, c_zero );
    
    // solver variables
    float alpha, beta;
    float nom, nom0, r0, gammaold, gammanew, den, res;

    // solver setup
    magma_sscal( dofs, c_zero, x->val, 1) ;                     // x = 0
    magma_scopy( dofs, b.val, 1, r.val, 1 );                    // r = b

    // preconditioner
    magma_s_applyprecond_left( A, r, &rt, precond_par );
    magma_s_applyprecond_right( A, rt, &h, precond_par );

    magma_scopy( dofs, h.val, 1, p.val, 1 );                    // p = h
    nom = MAGMA_S_REAL( magma_sdot(dofs, r.val, 1, h.val, 1) );          
    nom0 = magma_snrm2( dofs, r.val, 1 );                                                 
    magma_s_spmv( c_one, A, p, c_zero, q );                     // q = A p
    den = MAGMA_S_REAL( magma_sdot(dofs, p.val, 1, q.val, 1) );// den = p dot q
    solver_par->init_res = nom0;
    
    if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE ) 
        r0 = ATOLERANCE;
    if ( nom < r0 )
        return MAGMA_SUCCESS;
    // check positive definite
    if (den <= 0.0) {
        printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
        return -100;
    }

    //Chronometry
    real_Double_t tempo1, tempo2;
    magma_device_sync(); tempo1=magma_wtime();
    if( solver_par->verbose > 0 ){
        solver_par->res_vec[0] = (real_Double_t)nom0;
        solver_par->timing[0] = 0.0;
    }
    
    // start iteration
    for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter; 
                                                    solver_par->numiter++ ){
        // preconditioner
        magma_s_applyprecond_left( A, r, &rt, precond_par );
        magma_s_applyprecond_right( A, rt, &h, precond_par );

        gammanew = MAGMA_S_REAL( magma_sdot(dofs, r.val, 1, h.val, 1) );   
                                                            // gn = < r,h>

        if( solver_par->numiter==1 ){
            magma_scopy( dofs, h.val, 1, p.val, 1 );                    // p = h            
        }else{
            beta = MAGMA_S_MAKE(gammanew/gammaold, 0.);       // beta = gn/go
            magma_sscal(dofs, beta, p.val, 1);            // p = beta*p
            magma_saxpy(dofs, c_one, h.val, 1, p.val, 1); // p = p + h 
        }

        magma_s_spmv( c_one, A, p, c_zero, q );           // q = A p
        den = MAGMA_S_REAL(magma_sdot(dofs, p.val, 1, q.val, 1));    
                // den = p dot q 

        alpha = MAGMA_S_MAKE(gammanew/den, 0.);
        magma_saxpy(dofs,  alpha, p.val, 1, x->val, 1);     // x = x + alpha p
        magma_saxpy(dofs, -alpha, q.val, 1, r.val, 1);      // r = r - alpha q
        gammaold = gammanew;

        res = magma_snrm2( dofs, r.val, 1 );
        if( solver_par->verbose > 0 ){
            magma_device_sync(); tempo2=magma_wtime();
            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;
        }
    } 
    magma_device_sync(); tempo2=magma_wtime();
    solver_par->runtime = (real_Double_t) tempo2-tempo1;
    float residual;
    magma_sresidual( A, b, *x, &residual );
    solver_par->iter_res = res;
    solver_par->final_res = residual;

    if( solver_par->numiter < solver_par->maxiter){
        solver_par->info = 0;
    }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;
            }
        }
        solver_par->info = -2;
    }
    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;
            }
        }
        solver_par->info = -1;
    }
    magma_s_vfree(&r);
    magma_s_vfree(&rt);
    magma_s_vfree(&p);
    magma_s_vfree(&q);
    magma_s_vfree(&h);

    return MAGMA_SUCCESS;
}   /* magma_scg */