From 3d9b62a6b6fbdde922cb73c262e20db4ac0d84ad Mon Sep 17 00:00:00 2001 From: Anton Khirnov Date: Fri, 13 Mar 2015 16:06:46 +0100 Subject: Initial commit. --- configuration.ccl | 2 + interface.ccl | 14 + param.ccl | 33 + schedule.ccl | 21 + src/make.code.defn | 7 + src/maximal_slicing_axi.c | 1503 +++++++++++++++++++++++++++++++++++++++++++++ 6 files changed, 1580 insertions(+) create mode 100644 configuration.ccl create mode 100644 interface.ccl create mode 100644 param.ccl create mode 100644 schedule.ccl create mode 100644 src/make.code.defn create mode 100644 src/maximal_slicing_axi.c diff --git a/configuration.ccl b/configuration.ccl new file mode 100644 index 0000000..c3ae23d --- /dev/null +++ b/configuration.ccl @@ -0,0 +1,2 @@ +# Configuration definition for thorn MaximalSlicingAxi + diff --git a/interface.ccl b/interface.ccl new file mode 100644 index 0000000..cec39a3 --- /dev/null +++ b/interface.ccl @@ -0,0 +1,14 @@ +# Interface definition for thorn MaximalSlicingAxi +implements: MaximalSlicingAxi + +INHERITS: ADMBase grid CoordBase MethodOfLines + +CCTK_INT FUNCTION MoLRegisterConstrained(CCTK_INT IN idx) +CCTK_INT FUNCTION MoLRegisterSaveAndRestore(CCTK_INT IN idx) +CCTK_INT FUNCTION MoLRegisterSaveAndRestoreGroup(CCTK_INT IN idx) + +REQUIRES FUNCTION MoLRegisterConstrained +REQUIRES FUNCTION MoLRegisterSaveAndRestore +REQUIRES FUNCTION MoLRegisterSaveAndRestoreGroup + +CCTK_REAL alpha_coeffs TYPE=array DIM=2 SIZE=basis_order_z,basis_order_r diff --git a/param.ccl b/param.ccl new file mode 100644 index 0000000..2ca5e50 --- /dev/null +++ b/param.ccl @@ -0,0 +1,33 @@ +# Parameter definitions for thorn MaximalSlicingAxi + +SHARES: ADMBase + +EXTENDS KEYWORD lapse_evolution_method +{ + "maximal_axi" :: "Maximal slicing for an axisymmetric spacetime" +} + +RESTRICTED: +CCTK_REAL amplitude "Wave amplitude A." +{ + 0: :: "" +} 1.0 + +CCTK_INT basis_order_r "Number of the basis functions in the radial direction" STEERABLE=recover +{ + 1: :: "" +} 40 + +CCTK_INT basis_order_z "Number of the basis functions in the z direction" STEERABLE=recover +{ + 1: :: "" +} 40 + +CCTK_REAL scale_factor "Scaling factor L for the SB basis" STEERABLE=recover +{ + 0: :: "" +} 3.0 + +BOOLEAN export_coeffs "Export the coefficients of the spectral expansion in alpha_coeffs" STEERABLE=recover +{ +} "no" diff --git a/schedule.ccl b/schedule.ccl new file mode 100644 index 0000000..0d9c425 --- /dev/null +++ b/schedule.ccl @@ -0,0 +1,21 @@ +# Schedule definitions for thorn MaximalSlicingAxi +# +if (CCTK_Equals(lapse_evolution_method, "maximal_axi")) { + + SCHEDULE maximal_slicing_axi IN MoL_CalcRHS BEFORE ML_BSSN_evolCalcGroup { + LANG: C + } "Maximal slicing in axisymmetry" + + SCHEDULE maximal_slicing_axi_register AT Startup { + LANG: C + } "" + + SCHEDULE maximal_slicing_axi_register_mol IN MoL_Register { + LANG: C + } "" + + if (export_coeffs) { + STORAGE: alpha_coeffs + } +} + diff --git a/src/make.code.defn b/src/make.code.defn new file mode 100644 index 0000000..27625ce --- /dev/null +++ b/src/make.code.defn @@ -0,0 +1,7 @@ +# Main make.code.defn file for thorn MaximalSlicingAxi + +# Source files in this directory +SRCS = maximal_slicing_axi.c + +# Subdirectories containing source files +SUBDIRS = diff --git a/src/maximal_slicing_axi.c b/src/maximal_slicing_axi.c new file mode 100644 index 0000000..7d3e6f4 --- /dev/null +++ b/src/maximal_slicing_axi.c @@ -0,0 +1,1503 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include + +#include +#include + +#include "cctk.h" +#include "cctk_Arguments.h" +#include "cctk_Parameters.h" +#include "cctk_Timers.h" +#include "util_Table.h" +#include "Slicing.h" + +double ms_scalarproduct_metric_avx(int offset_r, int offset_z, const double *coeffs, + const double *basis_r, const double *basis_z); + +#define ACC_TEST 0 + +#define MAX(x, y) ((x) > (y) ? (x) : (y)) +#define MIN(x, y) ((x) > (y) ? (y) : (x)) +#define SQR(x) ((x) * (x)) +#define SGN(x) ((x) >= 0.0 ? 1.0 : -1.0) +#define ARRAY_ELEMS(arr) (sizeof(arr) / sizeof(*arr)) + +/* + * small number to avoid r=0 singularities + */ +#define EPS 1E-08 + +#include +int64_t gettime(void) +{ + struct timeval tv; + gettimeofday(&tv, NULL); + return (int64_t)tv.tv_sec * 1000000 + tv.tv_usec; +} + +/* a set of basis functions */ +typedef struct BasisSet { + /* evaluate the idx-th basis function at the specified point*/ + long double (*eval) (long double coord, int idx); + /* evaluate the first derivative of the idx-th basis function at the specified point*/ + long double (*eval_diff1)(long double coord, int idx); + /* evaluate the second derivative of the idx-th basis function at the specified point*/ + long double (*eval_diff2)(long double coord, int idx); + /** + * Get the idx-th collocation point for the specified order. + * idx runs from 0 to order - 1 (inclusive) + */ + long double (*colloc_point)(int order, int idx); +} BasisSet; + +/* + * The basis of even (n = 2 * idx) SB functions (Boyd 2000, Ch 17.9) + * SB(x, n) = sin((n + 1) arccot(|x| / L)) + * They are symmetric wrt origin and decay as 1/x in infinity. + */ + +static CCTK_REAL scale_factor; + +#define SCALE_FACTOR scale_factor + +static long double sb_even_eval(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + + idx *= 2; // even only + + return sinl((idx + 1) * val); +} + +static long double sb_even_eval_diff1(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + + idx *= 2; // even only + + return - SCALE_FACTOR * (idx + 1) * SGN(coord) * cosl((idx + 1) * val) / (SQR(SCALE_FACTOR) + SQR(coord)); +} + +static long double sb_even_eval_diff2(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + + idx *= 2; // even only + + return SCALE_FACTOR * (idx + 1) * SGN(coord) * (2 * fabsl(coord) * cosl((idx + 1) * val) - SCALE_FACTOR * (idx + 1) * sinl((idx + 1) * val)) / SQR(SQR(SCALE_FACTOR) + SQR(coord)); +} + +static long double sb_even_colloc_point(int order, int idx) +{ + long double t; + + idx = order - idx - 1; + //order *= 2; + + //t = (idx + 2) * M_PI / (order + 4); + t = (idx + 2) * M_PI / (2 * order + 2); + return SCALE_FACTOR / tanl(t); +} + +static const BasisSet sb_even_basis = { + .eval = sb_even_eval, + .eval_diff1 = sb_even_eval_diff1, + .eval_diff2 = sb_even_eval_diff2, + .colloc_point = sb_even_colloc_point, +}; + +static long double tb_even_eval(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + + idx++; + idx *= 2; // even only + + return cosl(idx * val) - 1.0; +} + +static long double tb_even_eval_diff1(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + + idx++; + idx *= 2; // even only + + return SCALE_FACTOR * idx * SGN(coord) * sinl(idx * val) / (SQR(SCALE_FACTOR) + SQR(coord)); +} + +static long double tb_even_eval_diff2(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + + idx++; + idx *= 2; // even only + + return -SCALE_FACTOR * idx * SGN(coord) * (2 * fabsl(coord) * sinl(idx * val) + SCALE_FACTOR * idx * cosl(idx * val)) / SQR(SQR(SCALE_FACTOR) + SQR(coord)); +} + +static long double tb_even_colloc_point(int order, int idx) +{ + long double t; + + idx = order - idx - 1; + //order *= 2; + + //t = (idx + 2) * M_PI / (order + 4); + t = (idx + 3) * M_PI / (2 * (order + 2)); + return SCALE_FACTOR / tanl(t); +} + +static const BasisSet tb_even_basis = { + .eval = tb_even_eval, + .eval_diff1 = tb_even_eval_diff1, + .eval_diff2 = tb_even_eval_diff2, + .colloc_point = tb_even_colloc_point, +}; + +static long double full_eval(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + int flag = idx & 1; + + idx /= 2; + + if (flag) return sinl((2 * idx + 1) * 4 * val); + else return cosl((2 * idx + 2) * 4 * val) - 1; +} + +static long double full_eval_diff1(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + int flag = idx & 1; + + idx /= 2; + + if (flag) { + idx = 2 * idx + 1; + return -4 * idx * SCALE_FACTOR * cosl(idx * 4 * val) / (SQR(SCALE_FACTOR) + SQR(coord)); + } else { + idx = 2 * (idx + 1); + return 4 * idx * SCALE_FACTOR * sinl(idx * 4 * val) / (SQR(SCALE_FACTOR) + SQR(coord)); + } +} + +static long double full_eval_diff2(long double coord, int idx) +{ + long double val = (coord == 0.0) ? M_PI_2 : atanl(SCALE_FACTOR / fabsl(coord)); + int flag = idx & 1; + + idx /= 2; + + if (flag) { + idx = 2 * idx + 1; + return (16 * SQR(idx * SCALE_FACTOR) * cosl(idx * 4 * val) - 4 * idx * SCALE_FACTOR * sinl(idx * 4 * val) * 2 * coord) / SQR(SQR(SCALE_FACTOR) + SQR(coord)); + } else { + idx = 2 * (idx + 1); + return (-16 * SQR(idx * SCALE_FACTOR) * sinl(idx * 4 * val) - 4 * idx * SCALE_FACTOR * cosl(idx * 4 * val) * 2 * coord) / SQR(SQR(SCALE_FACTOR) + SQR(coord)); + } +} + +static long double full_colloc_point(int order, int idx) +{ + long double t; + + idx = order - idx - 1; + + t = (idx + 0.5) * M_PI / (2 * order); + + return SCALE_FACTOR / tanl(t); + +} + +static const BasisSet full_basis = { + .eval = full_eval, + .eval_diff1 = full_eval_diff1, + .eval_diff2 = full_eval_diff2, + .colloc_point = full_colloc_point, +}; + +static long double cheb_eval(long double coord, int idx) +{ + return cosl(2 * idx * acosl(coord / SCALE_FACTOR)); +} + +static long double cheb_eval_diff1(long double coord, int idx) +{ + return 2 * idx * sinl(2 * idx * acosl(coord / SCALE_FACTOR)) / sqrtl(SQR(SCALE_FACTOR) - SQR(coord)); +} + +static long double cheb_eval_diff2(long double coord, int idx) +{ + long double t = acosl(coord / SCALE_FACTOR); + return 2 * idx * (cosl(2 * idx * t) * 2 * idx / (SQR(SCALE_FACTOR) - SQR(coord)) + sinl(2 * idx * t) * coord / pow(SQR(SCALE_FACTOR) - SQR(coord), 1.5)); +} + +static long double cheb_colloc_point(int order, int idx) +{ + return SCALE_FACTOR * cosl((idx + 0.01) * M_PI / (4 * order + 4)); +} + +static const BasisSet cheb_basis = { + .eval = cheb_eval, + .eval_diff1 = cheb_eval_diff1, + .eval_diff2 = cheb_eval_diff2, + .colloc_point = cheb_colloc_point, +}; + +/* indices (in our code, not cactus structs) of the grid functions which we'll need to + * interpolate on the pseudospectral grid */ +enum MetricVars { + GTXX = 0, + GTYY, + GTZZ, + GTXY, + GTXZ, + GTYZ, + PHI, + ATXX, + ATYY, + ATZZ, + ATXY, + ATXZ, + ATYZ, + K, + XTX, + XTY, + XTZ, + BETAX, + BETAY, + BETAZ, + NB_METRIC_VARS, +}; + +/* indices of the interpolated values of the above grid functions and their derivatives */ +enum InterpMetricVars { + I_GTXX = 0, + I_GTXX_DX, + I_GTXX_DY, + I_GTXX_DZ, + I_GTYY, + I_GTYY_DX, + I_GTYY_DY, + I_GTYY_DZ, + I_GTZZ, + I_GTZZ_DX, + I_GTZZ_DY, + I_GTZZ_DZ, + I_GTXY, + I_GTXY_DX, + I_GTXY_DY, + I_GTXY_DZ, + I_GTXZ, + I_GTXZ_DX, + I_GTXZ_DY, + I_GTXZ_DZ, + I_GTYZ, + I_GTYZ_DX, + I_GTYZ_DY, + I_GTYZ_DZ, + I_PHI, + I_PHI_DX, + I_PHI_DY, + I_PHI_DZ, + I_ATXX, + I_ATYY, + I_ATZZ, + I_ATXY, + I_ATXZ, + I_ATYZ, + I_K, + I_K_DX, + I_K_DY, + I_K_DZ, + I_XTX, + I_XTY, + I_XTZ, + I_BETAX, + I_BETAY, + I_BETAZ, + NB_INTERP_VARS, +}; + +/* mapping between our indices and thorn names */ +static const char *metric_vars[] = { + [GTXX] = "ML_BSSN::gt11", + [GTYY] = "ML_BSSN::gt22", + [GTZZ] = "ML_BSSN::gt33", + [GTXY] = "ML_BSSN::gt12", + [GTXZ] = "ML_BSSN::gt13", + [GTYZ] = "ML_BSSN::gt23", + [ATXX] = "ML_BSSN::At11", + [ATYY] = "ML_BSSN::At22", + [ATZZ] = "ML_BSSN::At33", + [ATXY] = "ML_BSSN::At12", + [ATXZ] = "ML_BSSN::At13", + [ATYZ] = "ML_BSSN::At23", + [PHI] = "ML_BSSN::phi", + [K] = "ML_BSSN::trK", + [XTX] = "ML_BSSN::Xt1", + [XTY] = "ML_BSSN::Xt2", + [XTZ] = "ML_BSSN::Xt3", + [BETAX] = "ML_BSSN::beta1", + [BETAY] = "ML_BSSN::beta2", + [BETAZ] = "ML_BSSN::beta3", +}; + +/* mapping between the cactus grid values and interpolated values */ +static const CCTK_INT interp_operation_indices[] = { + [I_GTXX] = GTXX, + [I_GTXX_DX] = GTXX, + [I_GTXX_DY] = GTXX, + [I_GTXX_DZ] = GTXX, + [I_GTYY] = GTYY, + [I_GTYY_DX] = GTYY, + [I_GTYY_DY] = GTYY, + [I_GTYY_DZ] = GTYY, + [I_GTZZ] = GTZZ, + [I_GTZZ_DX] = GTZZ, + [I_GTZZ_DY] = GTZZ, + [I_GTZZ_DZ] = GTZZ, + [I_GTXY] = GTXY, + [I_GTXY_DX] = GTXY, + [I_GTXY_DY] = GTXY, + [I_GTXY_DZ] = GTXY, + [I_GTXZ] = GTXZ, + [I_GTXZ_DX] = GTXZ, + [I_GTXZ_DY] = GTXZ, + [I_GTXZ_DZ] = GTXZ, + [I_GTYZ] = GTYZ, + [I_GTYZ_DX] = GTYZ, + [I_GTYZ_DY] = GTYZ, + [I_GTYZ_DZ] = GTYZ, + [I_PHI] = PHI, + [I_PHI_DX] = PHI, + [I_PHI_DY] = PHI, + [I_PHI_DZ] = PHI, + [I_ATXX] = ATXX, + [I_ATYY] = ATYY, + [I_ATZZ] = ATZZ, + [I_ATXY] = ATXY, + [I_ATXZ] = ATXZ, + [I_ATYZ] = ATYZ, + [I_K] = K, + [I_K_DX] = K, + [I_K_DY] = K, + [I_K_DZ] = K, + [I_XTX] = XTX, + [I_XTY] = XTY, + [I_XTZ] = XTZ, + [I_BETAX] = BETAX, + [I_BETAY] = BETAY, + [I_BETAZ] = BETAZ, +}; + +/* the operation (plain value or x/y/z-derivative) to apply during interpolation */ +static const CCTK_INT interp_operation_codes[] = { + [I_GTXX] = 0, + [I_GTXX_DX] = 1, + [I_GTXX_DY] = 2, + [I_GTXX_DZ] = 3, + [I_GTYY] = 0, + [I_GTYY_DX] = 1, + [I_GTYY_DY] = 2, + [I_GTYY_DZ] = 3, + [I_GTZZ] = 0, + [I_GTZZ_DX] = 1, + [I_GTZZ_DY] = 2, + [I_GTZZ_DZ] = 3, + [I_GTXY] = 0, + [I_GTXY_DX] = 1, + [I_GTXY_DY] = 2, + [I_GTXY_DZ] = 3, + [I_GTXZ] = 0, + [I_GTXZ_DX] = 1, + [I_GTXZ_DY] = 2, + [I_GTXZ_DZ] = 3, + [I_GTYZ] = 0, + [I_GTYZ_DX] = 1, + [I_GTYZ_DY] = 2, + [I_GTYZ_DZ] = 3, + [I_PHI] = 0, + [I_PHI_DX] = 1, + [I_PHI_DY] = 2, + [I_PHI_DZ] = 3, + [I_ATXX] = 0, + [I_ATYY] = 0, + [I_ATZZ] = 0, + [I_ATXY] = 0, + [I_ATXZ] = 0, + [I_ATYZ] = 0, + [I_K] = 0, + [I_K_DX] = 1, + [I_K_DY] = 2, + [I_K_DZ] = 3, + [I_XTX] = 0, + [I_XTY] = 0, + [I_XTZ] = 0, + [I_BETAX] = 0, + [I_BETAY] = 0, + [I_BETAZ] = 0, +}; + +/* precomputed values for a given refined grid */ +typedef struct CoordPatch { + CCTK_REAL origin[3]; + CCTK_REAL delta[3]; + CCTK_INT size[3]; + + // basis values on the grid + double *basis_val_r; + double *basis_val_z; + + double *transform_z; + double *one; +} CoordPatch; + +typedef struct ExpansionThreadData { + struct MaximalSlicingContext *ms; + CoordPatch *cp; + double *alp; + double *vec_tmp; + int start, end; +} ExpansionThreadData; + +/* state and scratch storage for the BiCGSTAB solver */ +typedef struct BiCGSTABContext { + double *p, *v, *y, *z, *t; + double *res, *res0; + double *k; + + cl_mem cl_p, cl_v, cl_y, cl_z, cl_t; + cl_mem cl_res, cl_res0; + cl_mem cl_k, cl_mat; + cl_mem cl_rho, cl_alpha, cl_beta, cl_omega, cl_omega1; + cl_mem cl_tmp, cl_tmp1; + + int64_t solve_total; + int64_t iter_total; + int64_t time_total; +} BiCGSTABContext; + +typedef struct MaximalSlicingContext { + cGH *gh; + const BasisSet *basis; + + BiCGSTABContext bicgstab; + int steps_since_inverse; + + int64_t lu_solves_total; + int64_t lu_solves_time; + + // the grid of collocation points + CCTK_REAL *grid_x; + CCTK_REAL *grid_z; + + // interpolation parameters + int coord_system; + int interp_operator; + int interp_params; + + CCTK_REAL *interp_coords[3]; + + int interp_vars_indices[NB_METRIC_VARS]; + + CCTK_REAL *interp_values[NB_INTERP_VARS]; + CCTK_INT interp_value_codes[NB_INTERP_VARS]; + + CCTK_REAL *metric_u[6]; + + CCTK_REAL *kij_kij; + CCTK_REAL *trk; + + int nb_coeffs_x; + int nb_coeffs_z; + int nb_coeffs; + + int nb_colloc_points_x; + int nb_colloc_points_z; + int nb_colloc_points; + + int colloc_grid_order_x; + int colloc_grid_order_z; + + double *mat; + double *mat_f; + double *rhs; + double *coeffs; + int *ipiv; + double *basis_x_val; + double *basis_x_dval; + double *basis_x_d2val; + + double *basis_z_val; + double *basis_z_dval; + double *basis_z_d2val; + + double *basis_val_00; + double *basis_val_20; + double *basis_val_02; + double *basis_val_11; + double *basis_val_10; + double *basis_val_01; + + CoordPatch *patches; + int nb_patches; + + // OpenCL / CLBLAS stuff + cl_context cl_ctx; + cl_command_queue cl_queue; + + cl_mem ocl_coeffs; +} MaximalSlicingContext; + +static int construct_matrix(MaximalSlicingContext *ms, double *mat, + double *rhs, double *prhs_max) +{ + int idx_coeff_x, idx_coeff_z, idx_grid_x, idx_grid_z; + double rhs_max = 0.0; + +#define BASIS_X (ms->basis_x_val [idx_grid_x * ms->nb_coeffs_x + idx_coeff_x]) +#define DBASIS_X (ms->basis_x_dval [idx_grid_x * ms->nb_coeffs_x + idx_coeff_x]) +#define D2BASIS_X (ms->basis_x_d2val[idx_grid_x * ms->nb_coeffs_x + idx_coeff_x]) +#define BASIS_Z (ms->basis_z_val [idx_grid_z * ms->nb_coeffs_z + idx_coeff_z]) +#define DBASIS_Z (ms->basis_z_dval [idx_grid_z * ms->nb_coeffs_z + idx_coeff_z]) +#define D2BASIS_Z (ms->basis_z_d2val[idx_grid_z * ms->nb_coeffs_z + idx_coeff_z]) + + //memset(mat, 0, sizeof(*mat) * ms->nb_coeffs * ms->nb_colloc_points); + +#pragma omp parallel for reduction(max : rhs_max) + for (idx_grid_z = 0; idx_grid_z < ms->nb_colloc_points_z; idx_grid_z++) { + for (idx_grid_x = 0; idx_grid_x < ms->nb_colloc_points_x; idx_grid_x++) { + CCTK_REAL x_physical = ms->grid_x[idx_grid_x]; + int idx_grid = idx_grid_z * ms->nb_colloc_points_x + idx_grid_x; + + const double gtuxx = ms->metric_u[0][idx_grid]; + const double gtuyy = ms->metric_u[1][idx_grid]; + const double gtuzz = ms->metric_u[2][idx_grid]; + const double gtuxz = ms->metric_u[4][idx_grid]; + + const double phi = ms->interp_values[I_PHI][idx_grid]; + const double phi_dx = ms->interp_values[I_PHI_DX][idx_grid]; + const double phi_dz = ms->interp_values[I_PHI_DZ][idx_grid]; + + const double Xtx = ms->interp_values[I_XTX][idx_grid]; + const double Xtz = ms->interp_values[I_XTZ][idx_grid]; + + const double k2 = ms->kij_kij[idx_grid]; + const double trk = ms->interp_values[I_K][idx_grid]; + + const double trk_dx = ms->interp_values[I_K_DX][idx_grid]; + const double trk_dz = ms->interp_values[I_K_DZ][idx_grid]; + + const double betax = ms->interp_values[I_BETAX][idx_grid]; + const double betaz = ms->interp_values[I_BETAZ][idx_grid]; + + 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 coeff_20 = SQR(phi) * (gtuxx + (x_physical <= EPS) * gtuyy); + const double coeff_02 = SQR(phi) * gtuzz; + const double coeff_11 = SQR(phi) * gtuxz * 2; + const double coeff_10 = -Xx + (x_physical > EPS) * SQR(phi) * gtuyy / x_physical; + const double coeff_01 = -Xz; + const double coeff_00 = -k2; + +#if 1 + for (idx_coeff_z = 0; idx_coeff_z < ms->nb_coeffs_z; idx_coeff_z++) + for (idx_coeff_x = 0; idx_coeff_x < ms->nb_coeffs_x; idx_coeff_x++) { + const int idx_coeff = idx_coeff_z * ms->nb_coeffs_x + idx_coeff_x; + + //double d2alpha = gtuxx * D2BASIS_X * BASIS_Z + // + gtuzz * BASIS_X * D2BASIS_Z + // + 2 * gtuxz * DBASIS_X * DBASIS_Z; + //if (x_physical > EPS) + // d2alpha += gtuyy * DBASIS_X * BASIS_Z / x_physical; + //else + // d2alpha += gtuyy * D2BASIS_X * BASIS_Z; + + //double curv_term = Xx * DBASIS_X * BASIS_Z + Xz * BASIS_X * DBASIS_Z; + + + //double D2alpha = SQR(phi) * d2alpha - curv_term; + + //mat[idx_grid + ms->nb_colloc_points * idx_coeff] = D2alpha - BASIS_X * BASIS_Z * k2; + mat[idx_grid + ms->nb_colloc_points * idx_coeff] = coeff_00 * BASIS_X * BASIS_Z + + coeff_10 * DBASIS_X * BASIS_Z + + coeff_01 * BASIS_X * DBASIS_Z + + coeff_11 * DBASIS_X * DBASIS_Z + + coeff_20 * D2BASIS_X * BASIS_Z + + coeff_02 * BASIS_X * D2BASIS_Z; + } +#else + + const double coeff_20 = SQR(phi) * (gtuxx + (x_physical <= EPS) * gtuyy); + const double coeff_02 = SQR(phi) * gtuzz; + const double coeff_11 = SQR(phi) * gtuxz * 2; + const double coeff_10 = SQR(phi) * (Xtx + (phi_dx * gtuxx + phi_dz * gtuxz) / phi + (x_physical > EPS) * gtuyy); + const double coeff_01 = SQR(phi) * (Xtz + (phi_dx * gtuxz + phi_dz * gtuzz) / phi); + const double coeff_00 = -k2; + cblas_daxpy(ms->nb_coeffs, coeff_20, ms->basis_val_20 + idx_grid, ms->nb_colloc_points, mat + idx_grid, ms->nb_colloc_points); + cblas_daxpy(ms->nb_coeffs, coeff_02, ms->basis_val_02 + idx_grid, ms->nb_colloc_points, mat + idx_grid, ms->nb_colloc_points); + cblas_daxpy(ms->nb_coeffs, coeff_11, ms->basis_val_11 + idx_grid, ms->nb_colloc_points, mat + idx_grid, ms->nb_colloc_points); + cblas_daxpy(ms->nb_coeffs, coeff_10, ms->basis_val_10 + idx_grid, ms->nb_colloc_points, mat + idx_grid, ms->nb_colloc_points); + cblas_daxpy(ms->nb_coeffs, coeff_01, ms->basis_val_01 + idx_grid, ms->nb_colloc_points, mat + idx_grid, ms->nb_colloc_points); + cblas_daxpy(ms->nb_coeffs, coeff_00, ms->basis_val_00 + idx_grid, ms->nb_colloc_points, mat + idx_grid, ms->nb_colloc_points); +#endif + + rhs[idx_grid] = k2 + trk ;// betax * trk_dx + betaz * trk_dz; + //rhs[idx_grid] = k2; + rhs_max = MAX(rhs_max, fabs(rhs[idx_grid])); + //rhs_max = fabs(rhs[idx_grid]); + } + } + + //memcpy(rhs, ms->kij_kij, sizeof(*rhs) * ms->nb_colloc_points); + //cblas_daxpy(ms->nb_colloc_points, 1.0, ms->interp_values[I_K], 1, rhs, 1); + //cblas_dsbmv(CblasColMajor, CblasUpper, ms->nb_colloc_points, 0, 1.0, ms->interp_values[I_BETAX], 1, ms->interp_values[I_K_DX], 1, 1.0, rhs, 1); + //cblas_dsbmv(CblasColMajor, CblasUpper, ms->nb_colloc_points, 0, 1.0, ms->interp_values[I_BETAZ], 1, ms->interp_values[I_K_DZ], 1, 1.0, rhs, 1); + + //*prhs_max = rhs[cblas_idamax(ms->nb_colloc_points, rhs, 1)]; + *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; + + ctx->iter_total += i + 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]; + + // upload the matrix and the RHS to the GPU + // 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; + + ctx->iter_total += i + 1; + + return i; +} + +static int lu_invert(const int N, double *mat, double *rhs, int *ipiv) +{ + LAPACKE_dgesv(LAPACK_COL_MAJOR, N, 1, + mat, N, ipiv, rhs, N); + LAPACKE_dgetri(LAPACK_COL_MAJOR, N, mat, N, ipiv); + + return 0; +} + +static int calc_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); + if (ret < 0) + CCTK_WARN(0, "Error interpolating"); + +#pragma omp parallel for schedule(dynamic, ms->nb_colloc_points_x) + for (int i = 0; i < ms->nb_colloc_points; i++) { + CCTK_REAL Am[3][3], gtu[3][3]; + CCTK_REAL a2; + + CCTK_REAL gtxx = ms->interp_values[I_GTXX][i]; + CCTK_REAL gtyy = ms->interp_values[I_GTYY][i]; + CCTK_REAL gtzz = ms->interp_values[I_GTZZ][i]; + CCTK_REAL gtxy = ms->interp_values[I_GTXY][i]; + CCTK_REAL gtxz = ms->interp_values[I_GTXZ][i]; + CCTK_REAL gtyz = ms->interp_values[I_GTYZ][i]; + + CCTK_REAL Atxx = ms->interp_values[I_ATXX][i]; + CCTK_REAL Atyy = ms->interp_values[I_ATYY][i]; + CCTK_REAL Atzz = ms->interp_values[I_ATZZ][i]; + CCTK_REAL Atxy = ms->interp_values[I_ATXY][i]; + CCTK_REAL Atxz = ms->interp_values[I_ATXZ][i]; + CCTK_REAL Atyz = ms->interp_values[I_ATYZ][i]; + + CCTK_REAL At[3][3] = {{ Atxx, Atxy, Atxz }, + { Atxy, Atyy, Atyz }, + { Atxz, Atyz, Atzz }}; + + CCTK_REAL trK = ms->interp_values[I_K][i]; + + CCTK_REAL Xtx = ms->interp_values[I_XTX][i]; + CCTK_REAL Xtz = ms->interp_values[I_XTZ][i]; + + CCTK_REAL 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]; + + // \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; + } + + // K_{ij} K^{ij} + a2 = 0.0; + for (int j = 0; j < 3; j++) + for (int k = 0; k < 3; k++) + a2 += Am[j][k] * Am[k][j]; + + ms->metric_u[0][i] = gtu[0][0]; + ms->metric_u[1][i] = gtu[1][1]; + ms->metric_u[2][i] = gtu[2][2]; + ms->metric_u[3][i] = gtu[0][1]; + ms->metric_u[4][i] = gtu[0][2]; + ms->metric_u[5][i] = gtu[1][2]; + + ms->kij_kij[i] = a2 + SQR(trK) / 3.; + } + + return 0; +} + +/* + * 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. + */ +static int maximal_solve(MaximalSlicingContext *ms) +{ + const int N = ms->nb_coeffs; + double rhs_max; + + int ret = 0; + + /* interpolate the metric values and construct the quantities we'll need */ + CCTK_TimerStart("MaximalSlicingAxi_calc_geometry"); + ret = calc_geometry(ms); + CCTK_TimerStop("MaximalSlicingAxi_calc_geometry"); + if (ret < 0) + return ret; + + /* fill the matrix */ + CCTK_TimerStart("MaximalSlicingAxi_construct_matrix"); + ret = construct_matrix(ms, ms->mat, ms->rhs, &rhs_max); + CCTK_TimerStop("MaximalSlicingAxi_construct_matrix"); + if (ret < 0) + return ret; + + if (rhs_max < EPS) { + 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; + } + + /* solve for the coeffs */ + if (ms->steps_since_inverse < 128) { + 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) { + b->time_total += gettime() - start; + b->solve_total++; + ms->steps_since_inverse++; + + if (!(b->solve_total & 127)) { + fprintf(stderr, "BiCGSTAB %ld solves, %ld iterations, total time %ld, avg iterations per solve %g, avg time per solve %g, avg time per iteration %g\n", + b->solve_total, b->iter_total, b->time_total, (double)b->iter_total / b->solve_total, (double)b->time_total / b->solve_total, (double)b->time_total / b->iter_total); + fprintf(stderr, "LU %ld solves, total time %ld, avg time per solve %g\n", ms->lu_solves_total, ms->lu_solves_time, (double)ms->lu_solves_time / ms->lu_solves_total); + } +#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(); + + lu_invert(ms->nb_coeffs, ms->mat, ms->rhs, ms->ipiv); + ms->lu_solves_time += gettime() - start; + ms->lu_solves_total++; + 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 (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; + } + + + return ret; +} + +static void init_opencl(MaximalSlicingContext *ms) +{ + int err, count; + cl_platform_id platform; + cl_device_id device; + cl_context_properties props[3]; + + err = clGetPlatformIDs(1, &platform, &count); + if (err != CL_SUCCESS || count < 1) { + fprintf(stderr, "Could not get an OpenCL platform ID\n"); + return; + } + + err = clGetDeviceIDs(platform, CL_DEVICE_TYPE_GPU, 1, &device, &count); + if (err != CL_SUCCESS || count < 1) { + fprintf(stderr, "Could not get an OpenCL device ID\n"); + return; + } + + props[0] = CL_CONTEXT_PLATFORM; + props[1] = (cl_context_properties)platform; + props[2] = 0; + + ms->cl_ctx = clCreateContext(props, 1, &device, NULL, NULL, &err); + if (err != CL_SUCCESS || !ms->cl_ctx) { + fprintf(stderr, "Could not create an OpenCL context\n"); + return; + } + + ms->cl_queue = clCreateCommandQueue(ms->cl_ctx, device, 0, &err); + if (err != CL_SUCCESS || !ms->cl_queue) { + fprintf(stderr, "Could not create an OpenCL command queue: %d\n", err); + goto fail; + } + + err = clblasSetup(); + if (err != CL_SUCCESS) { + fprintf(stderr, "Error setting up clBLAS\n"); + goto fail; + } + + ms->ocl_coeffs = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + + ms->bicgstab.cl_p = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_v = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_y = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_z = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_t = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_res = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_res0 = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_tmp = clCreateBuffer(ms->cl_ctx, 0, ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_tmp1 = clCreateBuffer(ms->cl_ctx, 0, 2 * ms->nb_coeffs * sizeof(double), NULL, &err); + + ms->bicgstab.cl_k = clCreateBuffer(ms->cl_ctx, 0, ms->nb_colloc_points * ms->nb_coeffs * sizeof(double), NULL, &err); + ms->bicgstab.cl_mat = clCreateBuffer(ms->cl_ctx, 0, ms->nb_colloc_points * ms->nb_coeffs * sizeof(double), NULL, &err); + + ms->bicgstab.cl_rho = clCreateBuffer(ms->cl_ctx, 0, sizeof(double), NULL, &err); + ms->bicgstab.cl_alpha = clCreateBuffer(ms->cl_ctx, 0, sizeof(double), NULL, &err); + ms->bicgstab.cl_beta = clCreateBuffer(ms->cl_ctx, 0, sizeof(double), NULL, &err); + ms->bicgstab.cl_omega = clCreateBuffer(ms->cl_ctx, 0, 2 * sizeof(double), NULL, &err); + ms->bicgstab.cl_omega1 = clCreateBuffer(ms->cl_ctx, 0, sizeof(double), NULL, &err); + + return; +fail: + if (ms->cl_queue) + clReleaseCommandQueue(ms->cl_queue); + ms->cl_queue = 0; + + if (ms->cl_ctx) + clReleaseContext(ms->cl_ctx); + ms->cl_ctx = 0; +} + +static MaximalSlicingContext *init_ms(cGH *cctkGH, + int basis_order_r, int basis_order_z, + double sf, + CCTK_REAL *x, CCTK_REAL *y, CCTK_REAL *z, + const int grid_size[3]) +{ + MaximalSlicingContext *ms; + int ret; + + //const double h = (x[1] - x[0]) / 8; + //fprintf(stderr, "h %g\n", h); + + //if (basis_order_r != basis_order_z) + // CCTK_WARN(0, "Different r and z basis orders are not supported."); + + ms = calloc(1, sizeof(*ms)); + + ms->gh = cctkGH; + + ms->basis = &sb_even_basis; + //ms->basis = &full_basis; + //ms->basis = &cheb_basis; + + ms->nb_coeffs_x = basis_order_r; + ms->nb_coeffs_z = basis_order_z; + + ms->nb_coeffs = ms->nb_coeffs_x * ms->nb_coeffs_z; + + ms->nb_colloc_points_x = basis_order_r; + ms->nb_colloc_points_z = basis_order_z; + + ms->nb_colloc_points = ms->nb_colloc_points_x * ms->nb_colloc_points_z; + + if (ms->nb_colloc_points != ms->nb_coeffs) + CCTK_WARN(0, "Non-square collocation matrix"); + + ms->colloc_grid_order_x = ms->nb_colloc_points_x; + ms->colloc_grid_order_z = ms->nb_colloc_points_z; + + ms->mat = malloc(sizeof(double) * ms->nb_coeffs * ms->nb_colloc_points); + ms->coeffs = malloc(sizeof(double) * ms->nb_coeffs); + ms->rhs = malloc(sizeof(double) * ms->nb_colloc_points); + + ms->mat_f = malloc(sizeof(double) * ms->nb_coeffs * ms->nb_colloc_points); + ms->ipiv = malloc(sizeof(*ms->ipiv) * ms->nb_coeffs); + +#if 1 + scale_factor = 1.0; + + scale_factor = (x[CCTK_GFINDEX3D(cctkGH, grid_size[0] - 1, 0, 0)] - 3) / ms->basis->colloc_point(ms->colloc_grid_order_x, ms->nb_colloc_points_x - 1); + //scale_factor = x[CCTK_GFINDEX3D(cctkGH, grid_size[0] - 1, 0, 0)] - 0.5; + fprintf(stderr, "scale factor %g\n", scale_factor); + +#else + scale_factor = sf; +#endif + + ms->grid_x = malloc(ms->nb_colloc_points_x * sizeof(*ms->grid_x)); + + for (int i = 0; i < ms->nb_colloc_points_x; i++) { +#if 0 + double target_val = ms->basis->colloc_point(ms->colloc_grid_order_x, i); + double best_diff = DBL_MAX, best_val = DBL_MAX; + + for (int j = 0; j < grid_size[0]; j++) { + int idx = CCTK_GFINDEX3D(cctkGH, j, 0, 0); + double val = x[idx]; + double diff = fabs(target_val - val); + + if (val > 0.0 && diff < best_diff) { + int k; + for (k = 0; k < i; k++) + if (ms->grid_x[k] == val) + break; + if (k == i) { + best_diff = diff; + best_val = val; + } + } + } + if (best_val == DBL_MAX) + abort(); + fprintf(stderr, "%d %g -> %g (%g)\n", i, target_val, best_val, target_val - best_val); + ms->grid_x[i] = best_val; +#elif 0 + double max = x[CCTK_GFINDEX3D(cctkGH, grid_size[0] - 1, 0, 0)]; + ms->grid_x[i] = max * SQR(SQR((double)i / ms->nb_colloc_points_x)) + 0.001; +#else + ms->grid_x[i] = ms->basis->colloc_point(ms->colloc_grid_order_x, i); +#endif + fprintf(stderr, "%d %g\n", i, ms->grid_x[i]); + } + + ms->grid_z = malloc(ms->nb_colloc_points_z * sizeof(*ms->grid_z)); + + for (int i = 0; i < ms->nb_colloc_points_z; i++) { + ms->grid_z[i] = ms->basis->colloc_point(ms->colloc_grid_order_z, i); + } + + /* precompute the basis values we will need */ + ms->basis_x_val = malloc(sizeof(*ms->basis_x_val) * ms->nb_colloc_points_x * ms->nb_coeffs_x); + ms->basis_x_dval = malloc(sizeof(*ms->basis_x_dval) * ms->nb_colloc_points_x * ms->nb_coeffs_x); + ms->basis_x_d2val = malloc(sizeof(*ms->basis_x_d2val) * ms->nb_colloc_points_x * ms->nb_coeffs_x); + for (int i = 0; i < ms->nb_colloc_points_x; i++) { + CCTK_REAL coord = ms->grid_x[i]; + for (int j = 0; j < ms->nb_coeffs_x; j++) { + ms->basis_x_val [i * ms->nb_coeffs_x + j] = ms->basis->eval(coord, j); + ms->basis_x_dval [i * ms->nb_coeffs_x + j] = ms->basis->eval_diff1(coord, j); + ms->basis_x_d2val[i * ms->nb_coeffs_x + j] = ms->basis->eval_diff2(coord, j); + } + } + + ms->basis_z_val = malloc(sizeof(*ms->basis_z_val) * ms->nb_colloc_points_z * ms->nb_coeffs_z); + ms->basis_z_dval = malloc(sizeof(*ms->basis_z_dval) * ms->nb_colloc_points_z * ms->nb_coeffs_z); + ms->basis_z_d2val = malloc(sizeof(*ms->basis_z_d2val) * ms->nb_colloc_points_z * ms->nb_coeffs_z); + for (int i = 0; i < ms->nb_colloc_points_z; i++) { + CCTK_REAL coord = ms->grid_z[i]; + for (int j = 0; j < ms->nb_coeffs_z; j++) { + ms->basis_z_val [i * ms->nb_coeffs_z + j] = ms->basis->eval(coord, j); + ms->basis_z_dval [i * ms->nb_coeffs_z + j] = ms->basis->eval_diff1(coord, j); + ms->basis_z_d2val[i * ms->nb_coeffs_z + j] = ms->basis->eval_diff2(coord, j); + } + } + + ms->basis_val_00 = calloc(ms->nb_colloc_points * ms->nb_coeffs, sizeof(*ms->basis_val_00)); + ms->basis_val_11 = calloc(ms->nb_colloc_points * ms->nb_coeffs, sizeof(*ms->basis_val_00)); + ms->basis_val_10 = calloc(ms->nb_colloc_points * ms->nb_coeffs, sizeof(*ms->basis_val_00)); + ms->basis_val_01 = calloc(ms->nb_colloc_points * ms->nb_coeffs, sizeof(*ms->basis_val_00)); + ms->basis_val_02 = calloc(ms->nb_colloc_points * ms->nb_coeffs, sizeof(*ms->basis_val_00)); + ms->basis_val_20 = calloc(ms->nb_colloc_points * ms->nb_coeffs, sizeof(*ms->basis_val_00)); + for (int i = 0; i < ms->nb_colloc_points_z; i++) { + const double *basis_val_z = ms->basis_z_val + i * ms->nb_coeffs_z; + const double *dbasis_val_z = ms->basis_z_dval + i * ms->nb_coeffs_z; + const double *d2basis_val_z = ms->basis_z_d2val + i * ms->nb_coeffs_z; + + for (int j = 0; j < ms->nb_colloc_points_x; j++) { + const double *basis_val_x = ms->basis_x_val + j * ms->nb_coeffs_x; + const double *dbasis_val_x = ms->basis_x_dval + j * ms->nb_coeffs_x; + const double *d2basis_val_x = ms->basis_x_d2val + j * ms->nb_coeffs_x; + const int idx_grid = i * ms->nb_colloc_points_x + j; + + for (int k = 0; k < ms->nb_coeffs_z; k++) + for (int l = 0; l < ms->nb_coeffs_x; l++) { + const int idx_coeff = k * ms->nb_coeffs_x + l; + const int idx = idx_grid + ms->nb_colloc_points * idx_coeff; + ms->basis_val_00[idx] = basis_val_x[l] * basis_val_z[k]; + ms->basis_val_11[idx] = dbasis_val_x[l] * dbasis_val_z[k]; + ms->basis_val_10[idx] = dbasis_val_x[l] * basis_val_z[k]; + ms->basis_val_01[idx] = basis_val_x[l] * dbasis_val_z[k]; + ms->basis_val_02[idx] = basis_val_x[l] * d2basis_val_z[k]; + ms->basis_val_20[idx] = d2basis_val_x[l] * basis_val_z[k]; + } + } + } + + ms->interp_coords[0] = malloc(ms->nb_colloc_points * sizeof(*ms->interp_coords[0])); + ms->interp_coords[1] = malloc(ms->nb_colloc_points * sizeof(*ms->interp_coords[1])); + ms->interp_coords[2] = malloc(ms->nb_colloc_points * sizeof(*ms->interp_coords[2])); + for (int i = 0; i < ms->nb_colloc_points_z; i++) { + CCTK_REAL z = ms->grid_z[i]; + for (int j = 0; j < ms->nb_colloc_points_x; j++) { + CCTK_REAL x = ms->grid_x[j]; + + ms->interp_coords[0][i * ms->nb_colloc_points_x + j] = x; + ms->interp_coords[1][i * ms->nb_colloc_points_x + j] = 0; + ms->interp_coords[2][i * ms->nb_colloc_points_x + j] = z; + } + } + + for (int i = 0; i < ARRAY_ELEMS(ms->metric_u); i++) + ms->metric_u[i] = malloc(ms->nb_colloc_points * sizeof(*ms->interp_values[i])); + + ms->kij_kij = malloc(ms->nb_colloc_points * sizeof(*ms->kij_kij)); + + for (int i = 0; i < ARRAY_ELEMS(ms->interp_values); i++) { + ms->interp_values[i] = malloc(ms->nb_colloc_points * sizeof(*ms->interp_values[i])); + ms->interp_value_codes[i] = CCTK_VARIABLE_REAL; + } + + for (int i = 0; i < ARRAY_ELEMS(metric_vars); i++) + ms->interp_vars_indices[i] = CCTK_VarIndex(metric_vars[i]); + + ms->coord_system = CCTK_CoordSystemHandle("cart3d"); + if (ms->coord_system < 0) + CCTK_WARN(0, "Error getting the coordinate system"); + + ms->interp_operator = CCTK_InterpHandle("Lagrange polynomial interpolation"); + if (ms->interp_operator < 0) + CCTK_WARN(0, "Error getting the interpolation operator"); + + ms->interp_params = Util_TableCreateFromString("order=2 want_global_mode=1"); + if (ms->interp_params < 0) + CCTK_WARN(0, "Error creating interpolation parameters table"); + + ret = Util_TableSetIntArray(ms->interp_params, NB_INTERP_VARS, + interp_operation_codes, "operation_codes"); + if (ret < 0) + CCTK_WARN(0, "Error setting operation codes"); + + ret = Util_TableSetIntArray(ms->interp_params, NB_INTERP_VARS, + interp_operation_indices, "operand_indices"); + if (ret < 0) + CCTK_WARN(0, "Error setting operand indices"); + + ms->bicgstab.p = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.v = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.y = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.z = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.t = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.res = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.res0 = malloc(sizeof(double) * ms->nb_coeffs); + ms->bicgstab.k = malloc(sizeof(double) * ms->nb_coeffs * ms->nb_colloc_points); + + ms->steps_since_inverse = INT_MAX; + + init_opencl(ms); + + CCTK_TimerCreate("MaximalSlicingAxi_Solve"); + CCTK_TimerCreate("MaximalSlicingAxi_Expand"); + CCTK_TimerCreate("MaximalSlicingAxi_calc_geometry"); + CCTK_TimerCreate("MaximalSlicingAxi_construct_matrix"); + CCTK_TimerCreate("MaximalSlicingAxi_solve_LU"); + CCTK_TimerCreate("MaximalSlicingAxi_solve_BiCGSTAB"); + + return ms; +} + +static CoordPatch *get_coord_patch(MaximalSlicingContext *ms, + CCTK_REAL *x, CCTK_REAL *y, CCTK_REAL *z, + CCTK_REAL *alp) +{ + cGH *cctkGH = ms->gh; + + CoordPatch *cp; + int64_t grid_size; + + for (int i = 0; i < ms->nb_patches; i++) { + cp = &ms->patches[i]; + + if (cp->origin[0] == ms->gh->cctk_origin_space[0] && + cp->origin[1] == ms->gh->cctk_origin_space[1] && + cp->origin[2] == ms->gh->cctk_origin_space[2] && + cp->size[0] == ms->gh->cctk_lsh[0] && + cp->size[1] == ms->gh->cctk_lsh[1] && + cp->size[2] == ms->gh->cctk_lsh[2] && + cp->delta[0] == ms->gh->cctk_delta_space[0] && + cp->delta[1] == ms->gh->cctk_delta_space[1] && + cp->delta[2] == ms->gh->cctk_delta_space[2]) + return cp; + } + + grid_size = cctkGH->cctk_lsh[0] * cctkGH->cctk_lsh[1] * cctkGH->cctk_lsh[2]; + + /* create a new patch */ + ms->patches = realloc(ms->patches, sizeof(*ms->patches) * (ms->nb_patches + 1)); + cp = &ms->patches[ms->nb_patches]; + + memcpy(cp->origin, ms->gh->cctk_origin_space, sizeof(cp->origin)); + memcpy(cp->size, ms->gh->cctk_lsh, sizeof(cp->size)); + memcpy(cp->delta, ms->gh->cctk_delta_space, sizeof(cp->delta)); + + posix_memalign((void**)&cp->basis_val_r, 32, sizeof(*cp->basis_val_r) * ms->nb_coeffs_x * ms->gh->cctk_lsh[1] * ms->gh->cctk_lsh[0]); + for (int j = 0; j < ms->gh->cctk_lsh[1]; j++) + for (int i = 0; i < ms->gh->cctk_lsh[0]; i++) { + CCTK_REAL xx = x[CCTK_GFINDEX3D(ms->gh, i, j, 0)]; + CCTK_REAL yy = y[CCTK_GFINDEX3D(ms->gh, i, j, 0)]; + CCTK_REAL r = sqrt(SQR(xx) + SQR(yy)); + + for (int k = 0; k < ms->nb_coeffs_x; k++) + //cp->basis_val_r [(j * ms->gh->cctk_lsh[0] + i) * ms->nb_coeffs_x + k] = ms->basis->eval(r, k); + cp->basis_val_r [(j * ms->gh->cctk_lsh[0] + i) + ms->gh->cctk_lsh[1] * ms->gh->cctk_lsh[0] * k] = ms->basis->eval(r, k); + } + + posix_memalign((void**)&cp->basis_val_z, 32, sizeof(*cp->basis_val_z) * ms->nb_coeffs_z * ms->gh->cctk_lsh[2]); + + for (int i = 0; i < ms->gh->cctk_lsh[2]; i++) { + CCTK_REAL zz = z[CCTK_GFINDEX3D(ms->gh, 0, 0, i)]; + for (int j = 0; j < ms->nb_coeffs_z; j++) + cp->basis_val_z [i * ms->nb_coeffs_z + j] = ms->basis->eval(zz, j); + //cp->basis_val_z [i + ms->gh->cctk_lsh[2] * j] = ms->basis->eval(zz, j); + } + + posix_memalign((void**)&cp->transform_z, 32, sizeof(*cp->transform_z) * cctkGH->cctk_lsh[2] * ms->nb_coeffs_x); + posix_memalign((void**)&cp->one, 32, sizeof(*cp->one) * grid_size); + for (int i = 0; i < grid_size; i++) + cp->one[i] = 1.0; + + ms->nb_patches++; + return cp; +} + +void maximal_slicing_axi(CCTK_ARGUMENTS) +{ + static MaximalSlicingContext *ms; + + CoordPatch *cp; + + DECLARE_CCTK_ARGUMENTS; + DECLARE_CCTK_PARAMETERS; + + static double total; + static int64_t count; + int64_t timer_start; + + const int64_t grid_size = cctk_lsh[2] * cctk_lsh[1] * cctk_lsh[0]; + + /* on the first run, init the solver */ + if (!ms) { + ms = init_ms(cctkGH, basis_order_r, basis_order_z, + scale_factor, x, y, z, cctk_lsh); + } + + cp = get_coord_patch(ms, x, y, z, alp); + + CCTK_TimerStart("MaximalSlicingAxi_Solve"); + maximal_solve(ms); + CCTK_TimerStop("MaximalSlicingAxi_Solve"); + + if (export_coeffs) + memcpy(alpha_coeffs, ms->coeffs, sizeof(*alpha_coeffs) * ms->nb_coeffs); + + CCTK_TimerStart("MaximalSlicingAxi_Expand"); + timer_start = gettime(); + + memcpy(alp, cp->one, cctk_lsh[0] * cctk_lsh[1] * cctk_lsh[2] * sizeof(*alp)); + cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, + ms->nb_coeffs_x, cctk_lsh[2], ms->nb_coeffs_z, 1.0, + ms->coeffs, ms->nb_coeffs_x, cp->basis_val_z, ms->nb_coeffs_z, + 0.0, cp->transform_z, ms->nb_coeffs_x); + cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, + cctk_lsh[1] * cctk_lsh[0], cctk_lsh[2], ms->nb_coeffs_x, 1.0, + cp->basis_val_r, cctk_lsh[0] * cctk_lsh[1], cp->transform_z, ms->nb_coeffs_x, + 1.0, alp, cctk_lsh[0] * cctk_lsh[1]); + + total += gettime() - timer_start; + + CCTK_TimerStop("MaximalSlicingAxi_Expand"); + + count++; + if (!(count & 15)) + fprintf(stderr, "avg %g total %g\n", total / count, total); +} + +int maximal_slicing_axi_register(void) +{ + Einstein_RegisterSlicing("maximal_axi"); + return 0; +} + +void maximal_slicing_axi_register_mol(CCTK_ARGUMENTS) +{ + MoLRegisterConstrained(CCTK_VarIndex("ADMBase::alp")); + MoLRegisterConstrained(CCTK_VarIndex("MaximalSlicingAxi::alpha_coeffs")); + + MoLRegisterSaveAndRestoreGroup(CCTK_GroupIndex("ADMBase::metric")); + MoLRegisterSaveAndRestoreGroup(CCTK_GroupIndex("ADMBase::curv")); +} -- cgit v1.2.3