#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include <cblas.h>
#include <lapacke.h>

#include <cl.h>
#include <clBLAS.h>

#include "qms.h"

static int construct_matrix(MaximalSlicingContext *ms)
{
    double *mat = ms->mat;
    int idx_coeff, idx_grid;

#pragma omp parallel for
    for (idx_coeff = 0; idx_coeff < ms->nb_coeffs; idx_coeff++)
        for (idx_grid = 0; idx_grid < ms->nb_colloc_points; idx_grid++) {
            const int idx      = idx_grid + ms->nb_colloc_points * idx_coeff;

            mat[idx] = ms->eq_coeff_00[idx_grid] * ms->basis_val_00[idx] +
                       ms->eq_coeff_10[idx_grid] * ms->basis_val_10[idx] +
                       ms->eq_coeff_01[idx_grid] * ms->basis_val_01[idx] +
                       ms->eq_coeff_11[idx_grid] * ms->basis_val_11[idx] +
                       ms->eq_coeff_20[idx_grid] * ms->basis_val_20[idx] +
                       ms->eq_coeff_02[idx_grid] * ms->basis_val_02[idx];
        }

    return 0;
}

/* interpolate the cactus gridfunctions onto the pseudospectral grid */
static int interp_geometry(MaximalSlicingContext *ms)
{
    int ret;

    ret = CCTK_InterpGridArrays(ms->gh, 3, ms->interp_operator, ms->interp_params,
                                ms->coord_system, ms->nb_colloc_points, CCTK_VARIABLE_REAL,
                                (const void * const *)ms->interp_coords, ARRAY_ELEMS(ms->interp_vars_indices), ms->interp_vars_indices,
                                ARRAY_ELEMS(ms->interp_values), ms->interp_value_codes, (void * const *)ms->interp_values_prefilter);
    if (ret < 0)
        CCTK_WARN(0, "Error interpolating");

    CCTK_TimerStart("MaximalSlicingAxi_filter_input");
    for (int i = 0; i < ARRAY_ELEMS(ms->interp_values); i++) {
        cblas_dgemv(CblasColMajor, CblasNoTrans, ms->nb_colloc_points, ms->nb_colloc_points, 1.0,
                    ms->input_filter, ms->nb_colloc_points, ms->interp_values_prefilter[i], 1, 0.0,
                    ms->interp_values[i], 1);
    }
    CCTK_TimerStop("MaximalSlicingAxi_filter_input");

    return 0;
}

static int calc_eq_coeffs(MaximalSlicingContext *ms, double *prhs_max)
{
    double rhs_max = 0.0;
//#pragma omp parallel for schedule(dynamic, ms->nb_colloc_points_x) reduction(max : rhs_max)
    for (int i = 0; i < ms->nb_colloc_points; i++) {
        const double x = ms->interp_coords[0][i];
        const double z = ms->interp_coords[2][i];
        const int zaxis = x <= EPS;

        double Am[3][3], K[3][3], Km[3][3], Ku[3][3], gtu[3][3];
        double k2, kij_dij_alpha, k_kdot, k3;

        const double gtxx = ms->interp_values[I_GTXX][i];
        const double gtyy = ms->interp_values[I_GTYY][i];
        const double gtzz = ms->interp_values[I_GTZZ][i];
        const double gtxy = ms->interp_values[I_GTXY][i];
        const double gtxz = ms->interp_values[I_GTXZ][i];
        const double gtyz = ms->interp_values[I_GTYZ][i];

        const double gt[3][3] = {{ gtxx, gtxy, gtxz },
                                 { gtxy, gtyy, gtyz },
                                 { gtxz, gtyz, gtzz }};

        const double Atxx = ms->interp_values[I_ATXX][i];
        const double Atyy = ms->interp_values[I_ATYY][i];
        const double Atzz = ms->interp_values[I_ATZZ][i];
        const double Atxy = ms->interp_values[I_ATXY][i];
        const double Atxz = ms->interp_values[I_ATXZ][i];
        const double Atyz = ms->interp_values[I_ATYZ][i];

        const double phi  = ms->interp_values[I_PHI][i];

        const double phidot = ms->interp_values[I_PHIDOT][i];
        const double phidot_dx = ms->interp_values[I_PHIDOT_DX][i];
        const double phidot_dz = ms->interp_values[I_PHIDOT_DZ][i];

        const double At[3][3] = {{ Atxx, Atxy, Atxz },
                                 { Atxy, Atyy, Atyz },
                                 { Atxz, Atyz, Atzz }};

        const double trK  = ms->interp_values[I_K][i];
        const double kdot_xx = ms->interp_values[I_KDOT_XX][i];
        const double kdot_yy = ms->interp_values[I_KDOT_YY][i];
        const double kdot_zz = ms->interp_values[I_KDOT_ZZ][i];
        const double kdot_xy = ms->interp_values[I_KDOT_XY][i];
        const double kdot_xz = ms->interp_values[I_KDOT_XZ][i];
        const double kdot_yz = ms->interp_values[I_KDOT_YZ][i];

        const double kdot[3][3] = {{ kdot_xx, kdot_xy, kdot_xz },
                                   { kdot_xy, kdot_yy, kdot_yz },
                                   { kdot_xz, kdot_yz, kdot_zz }};

        const double alpha     = ms->interp_values[I_ALPHA][i];
        const double dx_alpha  = ms->interp_values[I_ALPHA_DX][i];
        const double dz_alpha  = ms->interp_values[I_ALPHA_DZ][i];
        const double dxx_alpha = ms->interp_values[I_ALPHA_DXX][i];
        const double dzz_alpha = ms->interp_values[I_ALPHA_DZZ][i];
        const double dxz_alpha = ms->interp_values[I_ALPHA_DXZ][i];

        const double dij_alpha[3][3] = {{ dxx_alpha,                                0, dxz_alpha },
                                        {         0, zaxis ? dxx_alpha : dx_alpha / x,         0 },
                                        { dxz_alpha,                                0, dzz_alpha }};

        const double Xtx  = ms->interp_values[I_XTX][i];
        const double Xtz  = ms->interp_values[I_XTZ][i];

        const double Xtdot_x  = ms->interp_values[I_XTDOT_X][i];
        const double Xtdot_z  = ms->interp_values[I_XTDOT_Z][i];

        const double det = gtxx * gtyy * gtzz + 2 * gtxy * gtyz * gtxz - gtzz * SQR(gtxy) - SQR(gtxz) * gtyy - gtxx * SQR(gtyz);

        // \tilde{γ}^{ij}
        gtu[0][0] =  (gtyy * gtzz - SQR(gtyz)) / det;
        gtu[1][1] =  (gtxx * gtzz - SQR(gtxz)) / det;
        gtu[2][2] =  (gtxx * gtyy - SQR(gtxy)) / det;
        gtu[0][1] = -(gtxy * gtzz - gtyz * gtxz) / det;
        gtu[0][2] =  (gtxy * gtyz - gtyy * gtxz) / det;
        gtu[1][2] = -(gtxx * gtyz - gtxy * gtxz) / det;
        gtu[1][0] = gtu[0][1];
        gtu[2][0] = gtu[0][2];
        gtu[2][1] = gtu[1][2];

        // K_{ij}
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++)
                K[j][k] = At[j][k] / SQR(phi) + gt[j][k] * trK;

        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++) {
                double val = 0.0;
                for (int l = 0; l < 3; l++)
                    val += SQR(phi) * gtu[j][l] * K[l][k];
                Km[j][k] = val;
            }

        // K^{ij}
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++) {
                double val = 0.0;
                for (int l = 0; l < 3; l++)
                    val += SQR(phi) * gtu[j][l] * Km[k][l];
                Ku[j][k] = val;
            }

        // \tilde{A}_{i}^j
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++) {
                double val = 0.0;
                for (int l = 0; l < 3; l++)
                    val += gtu[j][l] * At[l][k];
                Am[j][k] = val;
            }

        kij_dij_alpha = 0.0;
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++)
                kij_dij_alpha += Ku[j][k] * dij_alpha[j][k];

        k_kdot = 0.0;
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++)
                k_kdot += kdot[j][k] * Ku[j][k];

        k3 = 0.0;
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++) {
                double val = 0.0;
                for (int l = 0; l < 3; l++)
                    val += Km[k][l] * Ku[l][j];
                k3 += val * K[j][k];
            }

        // K_{ij} K^{ij}
        k2 = 0.0;
        for (int j = 0; j < 3; j++)
            for (int k = 0; k < 3; k++)
                k2 += Km[j][k] * Km[k][j];

        {
            const double gtuxx         = gtu[0][0];
            const double gtuyy         = gtu[1][1];
            const double gtuzz         = gtu[2][2];
            const double gtuxz         = gtu[0][2];

            const double phi_dx        = ms->interp_values[I_PHI_DX][i];
            const double phi_dz        = ms->interp_values[I_PHI_DZ][i];

            const double Xtx           = ms->interp_values[I_XTX][i];
            const double Xtz           = ms->interp_values[I_XTZ][i];

            //const double k2            = a2 + SQR(trK) / 3.;

            const double trk_dx        = ms->interp_values[I_K_DX][i];
            const double trk_dz        = ms->interp_values[I_K_DZ][i];

            const double betax         = ms->interp_values[I_BETAX][i];
            const double betaz         = ms->interp_values[I_BETAZ][i];

            const double Xx = SQR(phi) * (Xtx + (phi_dx * gtuxx + phi_dz * gtuxz) / phi);
            const double Xz = SQR(phi) * (Xtz + (phi_dx * gtuxz + phi_dz * gtuzz) / phi);

            const double Xdot_x = 2 * phi * phidot * Xtx + SQR(phi) * Xtdot_x + phi * (phidot_dx * gtuxx + phidot_dz * gtuxz) -
                                  phidot * (phi_dx * gtuxx + phi_dz * gtuxz) + 2 * alpha * (phi_dx * Ku[0][0] + phi_dz * Ku[0][2]) / phi;
            const double Xdot_z = 2 * phi * phidot * Xtz + SQR(phi) * Xtdot_z + phi * (phidot_dz * gtuzz + phidot_dx * gtuxz) -
                                  phidot * (phi_dz * gtuzz + phi_dx * gtuxz) + 2 * alpha * (phi_dz * Ku[2][2] + phi_dx * Ku[0][2]) / phi;

            ms->eq_coeff_20[i] = SQR(phi) * (gtuxx + ((x <= EPS) ? gtuyy : 0.0));
            ms->eq_coeff_02[i] = SQR(phi) * gtuzz;
            ms->eq_coeff_11[i] = SQR(phi) * gtuxz * 2;
            ms->eq_coeff_10[i] = -Xx + ((x > EPS) ? SQR(phi) * gtuyy / x : 0.0);
            ms->eq_coeff_01[i] = -Xz;
            ms->eq_coeff_00[i] = -k2;

            ms->rhs[i] = -2 * alpha * kij_dij_alpha + Xdot_x * dx_alpha + Xdot_z * dz_alpha +
                         2 * (k_kdot + 2 * alpha * k3) * alpha;

            rhs_max = MAX(rhs_max, fabs(ms->rhs[i]));
        }
    }

    *prhs_max = rhs_max;

    return 0;
}

// based on the wikipedia article
// and http://www.netlib.org/templates/matlab/bicgstab.m
static int solve_bicgstab(BiCGSTABContext *ctx, const int N,
                          double *mat, double *rhs, double *x)
{
    const double rhs_norm = cblas_dnrm2(N, rhs, 1);

    double rho, rho_prev = 1.0;
    double omega = 1.0;
    double alpha = 1.0;

    double err;
    int i;

    double *k = ctx->k;
    double *p = ctx->p, *v = ctx->v, *y = ctx->y, *z = ctx->z, *t = ctx->t;
    double *res = ctx->res, *res0 = ctx->res0;

    // initialize the residual
    memcpy(res, rhs, N * sizeof(*res));
    cblas_dgemv(CblasColMajor, CblasNoTrans, N, N, -1.0,
                mat, N, x, 1, 1.0, res, 1);

    memcpy(res0, res, N * sizeof(*res0));
    memcpy(p,    res, N * sizeof(*p));

#define MAXITER 16
#define TOL (1e-15)
    for (i = 0; i < MAXITER; i++) {
        rho = cblas_ddot(N, res, 1, res0, 1);

        if (i) {
            double beta = (rho / rho_prev) * (alpha / omega);

            cblas_daxpy(N, -omega, v, 1, p, 1);
            cblas_dscal(N, beta, p, 1);
            cblas_daxpy(N, 1, res, 1, p, 1);
        }

        cblas_dgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    k, N, p, 1, 0.0, y, 1);

        cblas_dgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    mat, N, y, 1, 0.0, v, 1);

        alpha = rho / cblas_ddot(N, res0, 1, v, 1);

        cblas_daxpy(N, -alpha, v, 1, res, 1);

        cblas_dgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    k, N, res, 1, 0.0, z, 1);
        cblas_dgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    mat, N, z, 1, 0.0, t, 1);

        omega = cblas_ddot(N, t, 1, res, 1) / cblas_ddot(N, t, 1, t, 1);

        cblas_daxpy(N, alpha, y, 1, x, 1);
        cblas_daxpy(N, omega, z, 1, x, 1);

        cblas_daxpy(N, -omega, t, 1, res, 1);

        err = cblas_dnrm2(N, res, 1) / rhs_norm;
        if (err < TOL)
            break;

        rho_prev = rho;
    }
    if (i == MAXITER)
        return -1;

    return i;
}

static int solve_bicgstab_cl(BiCGSTABContext *ctx, cl_command_queue cl_q,
                             const int N, double *mat, double *rhs, cl_mem ocl_x)
{
    const double rhs_norm = cblas_dnrm2(N, rhs, 1);

    double rho, rho_prev = 1.0;
    double omega[2] = { 1.0 };
    double alpha = 1.0;

    double err;
    int i;

    cl_event events[8];

    // the matrix, rhs, k and x are assumed to be already uploaded
    clEnqueueWriteBuffer(cl_q, ctx->cl_res, 0, 0, N * sizeof(double), rhs,     0, NULL, &events[0]);
    clEnqueueWriteBuffer(cl_q, ctx->cl_mat, 0, 0, N * N * sizeof(double), mat, 0, NULL, &events[1]);

    // initialize the residual
    clblasDgemv(CblasColMajor, CblasNoTrans, N, N, -1.0,
                ctx->cl_mat, 0, N, ocl_x, 0, 1, 1.0, ctx->cl_res, 0, 1,
                1, &cl_q, 2, events, &events[2]);
    clEnqueueCopyBuffer(cl_q, ctx->cl_res, ctx->cl_res0, 0, 0, N * sizeof(double),
                        1, &events[2], &events[3]);
    clEnqueueCopyBuffer(cl_q, ctx->cl_res, ctx->cl_p, 0, 0, N * sizeof(double),
                        1, &events[2], &events[4]);

    clWaitForEvents(5, events);
    // BARRIER

#define MAXITER 16
#define TOL (1e-15)
    for (i = 0; i < MAXITER; i++) {
        clblasDdot(N, ctx->cl_rho, 0, ctx->cl_res, 0, 1, ctx->cl_res0, 0, 1,
                   ctx->cl_tmp, 1, &cl_q, 0, NULL, &events[0]);
        clEnqueueReadBuffer(cl_q, ctx->cl_rho, 1, 0, sizeof(double), &rho,
                            1, &events[0], NULL);
        // BARRIER

        if (i) {
            double beta = (rho / rho_prev) * (alpha / omega[0]);

            clblasDaxpy(N, -omega[0], ctx->cl_v, 0, 1, ctx->cl_p, 0, 1,
                        1, &cl_q, 0, NULL, &events[0]);
            clblasDscal(N, beta, ctx->cl_p, 0, 1,
                        1, &cl_q, 1, &events[0], &events[1]);
            clblasDaxpy(N, 1, ctx->cl_res, 0, 1, ctx->cl_p, 0, 1,
                        1, &cl_q, 1, &events[1], &events[0]);
            clWaitForEvents(1, &events[0]);
            // BARRIER
        }

        clblasDgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    ctx->cl_k, 0, N, ctx->cl_p, 0, 1, 0.0, ctx->cl_y, 0, 1,
                    1, &cl_q, 0, NULL, &events[0]);

        clblasDgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    ctx->cl_mat, 0, N, ctx->cl_y, 0, 1, 0.0, ctx->cl_v, 0, 1,
                    1, &cl_q, 1, &events[0], &events[1]);

        clblasDdot(N, ctx->cl_alpha, 0, ctx->cl_res0, 0, 1, ctx->cl_v, 0, 1,
                   ctx->cl_tmp, 1, &cl_q, 1, &events[1], &events[0]);
        clEnqueueReadBuffer(cl_q, ctx->cl_alpha, 1, 0, sizeof(double), &alpha,
                            1, &events[0], NULL);
        // BARRIER

        alpha = rho / alpha;

        clblasDaxpy(N, -alpha, ctx->cl_v, 0, 1, ctx->cl_res, 0, 1,
                    1, &cl_q, 0, NULL, &events[0]);

        clblasDgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    ctx->cl_k, 0, N, ctx->cl_res, 0, 1, 0.0, ctx->cl_z, 0, 1,
                    1, &cl_q, 1, &events[0], &events[1]);
        clblasDgemv(CblasColMajor, CblasNoTrans, N, N, 1.0,
                    ctx->cl_mat, 0, N, ctx->cl_z, 0, 1, 0.0, ctx->cl_t, 0, 1,
                    1, &cl_q, 1, &events[1], &events[0]);

        clblasDdot(N, ctx->cl_omega, 0, ctx->cl_t, 0, 1, ctx->cl_res, 0, 1,
                   ctx->cl_tmp, 1, &cl_q, 1, &events[0], &events[1]);
        clblasDdot(N, ctx->cl_omega, 1, ctx->cl_t, 0, 1, ctx->cl_t, 0, 1,
                   ctx->cl_tmp1, 1, &cl_q, 1, &events[0], &events[2]);

        clEnqueueReadBuffer(cl_q, ctx->cl_omega, 1, 0, sizeof(omega), omega,
                            2, &events[1], NULL);
        // BARRIER

        omega[0] /= omega[1];

        clblasDaxpy(N, alpha, ctx->cl_y, 0, 1, ocl_x, 0, 1,
                    1, &cl_q, 0, NULL, &events[0]);
        clblasDaxpy(N, omega[0], ctx->cl_z, 0, 1, ocl_x, 0, 1,
                    1, &cl_q, 1, &events[0], &events[1]);

        clblasDaxpy(N, -omega[0], ctx->cl_t, 0, 1, ctx->cl_res, 0, 1,
                    1, &cl_q, 0, NULL, &events[0]);
        clblasDnrm2(N, ctx->cl_tmp, 0, ctx->cl_res, 0, 1, ctx->cl_tmp1,
                    1, &cl_q, 1, &events[0], &events[2]);
        clEnqueueReadBuffer(cl_q, ctx->cl_tmp, 1, 0, sizeof(double), &err,
                            1, &events[2], NULL);
        clWaitForEvents(1, &events[1]);
        // BARRIER

        if (err < TOL)
            break;

        rho_prev = rho;
    }
    if (i == MAXITER)
        return -1;

    return i;
}

static int lu_invert(const int N, double *mat, double *rhs, int *ipiv)
{
    char  equed = 'N';
    double cond, ferr, berr, rpivot;

    double *mat_f, *x;
    int ret = 0;
#if 1
    LAPACKE_dgesv(LAPACK_COL_MAJOR, N, 1,
                  mat, N, ipiv, rhs, N);
    LAPACKE_dgetri(LAPACK_COL_MAJOR, N, mat, N, ipiv);
#else
    mat_f = malloc(SQR(N) * sizeof(*mat_f));
    x     = malloc(N * sizeof(*x));

    //{
    //    int i, j;
    //    for (i = 0; i < N; i++) {
    //        for (j = 0; j < N; j++)
    //            fprintf(stderr, "%+#010.8g\t", mat[i + j * N]);
    //        fprintf(stderr, "\n");
    //    }
    //}
    //{
    //    double *mat_copy = malloc(SQR(N) * sizeof(double));
    //    double *svd = malloc(N * sizeof(double));
    //    double *rhs_copy = malloc(N * sizeof(double));
    //    int rank;

    //    memcpy(mat_copy, mat, SQR(N) * sizeof(double));
    //    memcpy(rhs_copy, rhs, N * sizeof(double));

    //    LAPACKE_dgelsd(LAPACK_COL_MAJOR, N, N, 1, mat_copy, N, rhs_copy, N,
    //                   svd, 1e-13, &rank);

    //    free(mat_copy);
    //    for (int i = 0; i < N; i++) {
    //        if (i > 5 && i < N - 5)
    //            continue;

    //        fprintf(stderr, "%g\t", svd[i]);
    //    }
    //    fprintf(stderr, "\n rank %d\n", rank);
    //    free(svd);
    //    free(rhs_copy);

    //    if (rank < N)
    //        ret = 1;
    //}

    //LAPACKE_dgesv(LAPACK_COL_MAJOR, N, 1,
    //              mat, N, ipiv, rhs, N);
    LAPACKE_dgesvx(LAPACK_COL_MAJOR, 'N', 'N', N, 1,
                   mat, N, mat_f, N, ipiv, &equed, NULL, NULL,
                   rhs, N, x, N, &cond, &ferr, &berr, &rpivot);
    LAPACKE_dgetri(LAPACK_COL_MAJOR, N, mat_f, N, ipiv);
    memcpy(rhs, x, N * sizeof(double));
    memcpy(mat, mat_f, SQR(N) * sizeof(double));

    fprintf(stderr, "LU factorization solution to a %zdx%zd matrix: "
            "condition number %16.16g; forward error %16.16g backward error %16.16g\n",
            N, N, cond, ferr, berr);

    free(mat_f);
    free(x);
#endif

    return ret;
}

/*
 * Solve the equation
 * D²α - KᵢⱼKⁱʲα = -K
 * for the coefficients of spectral approximation of α:
 * α(ρ, z) = 1 + ΣaᵢⱼTᵢ(ρ)Tⱼ(z)
 * where i =  { 0, ... , ms->nb_coeffs_x };
 *       j =  { 0, ... , ms->nb_coeffs_z };
 * Tᵢ(x) are defined by ms->basis.
 */
int qms_maximal_solve(MaximalSlicingContext *ms)
{
    const int N = ms->nb_coeffs;
    double rhs_max;
    int64_t start;

    int ret = 0;

    /* interpolate the metric values and construct the quantities we'll need */
    CCTK_TimerStart("MaximalSlicingAxi_interp_geometry");
    start = gettime();
    ret = interp_geometry(ms);
    ms->interp_geometry_time += gettime() - start;
    ms->interp_geometry_count++;
    CCTK_TimerStop("MaximalSlicingAxi_interp_geometry");
    if (ret < 0)
        return ret;

    CCTK_TimerStart("MaximalSlicingAxi_calc_eq_coeffs");
    start = gettime();
    ret = calc_eq_coeffs(ms, &rhs_max);
    ms->calc_eq_coeffs_time += gettime() - start;
    ms->calc_eq_coeffs_count++;
    CCTK_TimerStop("MaximalSlicingAxi_calc_eq_coeffs");
    if (ret < 0)
        return ret;

    /* fill the matrix */
    CCTK_TimerStart("MaximalSlicingAxi_construct_matrix");
    start = gettime();
    ret = construct_matrix(ms);
    ms->construct_matrix_time += gettime() - start;
    ms->construct_matrix_count++;
    CCTK_TimerStop("MaximalSlicingAxi_construct_matrix");
    if (ret < 0)
        return ret;

#if 1
    if (rhs_max < EPS) {
        fprintf(stderr, "zero rhs\n");
        memset(ms->coeffs, 0, sizeof(*ms->coeffs) * ms->nb_coeffs);
        if (ms->cl_queue) {
            clEnqueueWriteBuffer(ms->cl_queue, ms->ocl_coeffs, 1, 0, N * sizeof(double),
                                 ms->coeffs, 0, NULL, NULL);
        }
        return 0;
    }
#endif

    /* solve for the coeffs */
    if (ms->steps_since_inverse < 1024) {
        BiCGSTABContext *b = &ms->bicgstab;
        int64_t start = gettime();

        CCTK_TimerStart("MaximalSlicingAxi_solve_BiCGSTAB");
        if (ms->cl_queue) {
            ret = solve_bicgstab_cl(b, ms->cl_queue, ms->nb_coeffs, ms->mat, ms->rhs, ms->ocl_coeffs);
            clEnqueueReadBuffer(ms->cl_queue, ms->ocl_coeffs, 1, 0, sizeof(double) * N,
                                ms->coeffs, 0, NULL, NULL);
        } else
            ret = solve_bicgstab(b, ms->nb_coeffs, ms->mat, ms->rhs, ms->coeffs);
        CCTK_TimerStop("MaximalSlicingAxi_solve_BiCGSTAB");

        if (ret >= 0) {
            ms->cg_time_total += gettime() - start;
            ms->cg_solve_count++;
            ms->cg_iter_count += ret + 1;
            ms->steps_since_inverse++;

#if 0
            {
                double min, max;
                gsl_vector_memcpy(b->y, ms->rhs);
                cblas_dgemv(CblasColMajor, CblasNoTrans, ms->mat->size1, ms->mat->size2, -1.0,
                            ms->mat->data, ms->mat->tda, ms->coeffs->data, 1, 1.0, b->y->data, 1);
                gsl_vector_minmax(b->y, &min, &max);
                if (fabs(min) > 1e-11 || fabs(max) > 1e-11)
                    abort();
            }
#endif
        }
    } else
        ret = -1;

    if (ret < 0) {
        double *tmpv;
        double *tmpm;
        int64_t start;

        CCTK_TimerStart("MaximalSlicingAxi_solve_LU");
        start = gettime();

        ret = lu_invert(ms->nb_coeffs, ms->mat, ms->rhs, ms->ipiv);
        ms->lu_solves_time += gettime() - start;
        ms->lu_solves_count++;
        CCTK_TimerStop("MaximalSlicingAxi_solve_LU");

        tmpv = ms->coeffs;
        ms->coeffs = ms->rhs;
        ms->rhs = tmpv;

        tmpm = ms->mat;
        ms->mat = ms->bicgstab.k;
        ms->bicgstab.k = tmpm;

        if (ret == 1) {
            memset(ms->coeffs, 0, sizeof(*ms->coeffs) * ms->nb_coeffs);
            ms->coeffs[0] = 1.0;
        }

        if (ms->cl_queue) {
            cl_event events[2];
            clEnqueueWriteBuffer(ms->cl_queue, ms->bicgstab.cl_k, 0, 0, N * N * sizeof(double),
                                 ms->bicgstab.k, 0, NULL, &events[0]);
            clEnqueueWriteBuffer(ms->cl_queue, ms->ocl_coeffs, 0, 0, N * sizeof(double),
                                 ms->coeffs, 0, NULL, &events[1]);
            clWaitForEvents(2, events);
        }

        ms->steps_since_inverse = 0;
    }

    for (int i = 0; i < N; i++)
        ms->coeffs[i] *= ms->coeff_scale[i];

    return ret;
}