/*
 * Multigrid solver for a 2nd order 2D linear PDE.
 * Copyright 2018 Anton Khirnov <anton@khirnov.net>
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

#ifndef MG2D_H
#define MG2D_H

#include <stddef.h>
#include <stdint.h>

/**
 * Type of the boundary condition on a given boundary.
 */
enum MG2DBCType {
    /**
     * The value of the unknown function is fixed on the boundary.
     */
    MG2D_BC_TYPE_FIXVAL,
    /**
     * The normal derivative of the unkown function is fixed on the boundary.
     *
     * TODO: the only supported value of the derivative is currently zero, i.e.
     * periodic boundary conditions.
     */
    MG2D_BC_TYPE_FIXDIFF,
};

/**
 * Location of the boundary.
 */
enum MG2DBoundaryLoc {
    /**
     * coord0 lower
     */
    MG2D_BOUNDARY_0L,
    /**
     * coord0 upper
     */
    MG2D_BOUNDARY_0U,
    /**
     * coord1 lower
     */
    MG2D_BOUNDARY_1L,
    /**
     * coord1 upper
     */
    MG2D_BOUNDARY_1U,
};

/**
 * Derivative specifier.
 */
enum MG2DDiffCoeff {
    /**
     * Zeroth derivative, i.e. function value.
     */
    MG2D_DIFF_COEFF_00,
    /**
     * First derivative wrt coord1.
     */
    MG2D_DIFF_COEFF_01,
    /**
     * First derivative wrt coord0.
     */
    MG2D_DIFF_COEFF_10,
    /**
     * Second derivative, once wrt coord0 and once wrt coord1
     */
    MG2D_DIFF_COEFF_11,
    /**
     * Second derivative wrt coord1
     */
    MG2D_DIFF_COEFF_02,
    /**
     * Second derivative wrt coord0
     */
    MG2D_DIFF_COEFF_20,
    /**
     * Total number of allowed derivatives.
     */
    MG2D_DIFF_COEFF_NB,
};

enum MG2DLogLevel {
    /**
     * The log message indicates abnormal program failure. Should never happen
     * unless there are bugs or grossly invaid user input.
     * Will typically be followed by program termination.
     */
    MG2D_LOG_FATAL = 0x0,
    /**
     * The log message indicates an error state, so that requested operation
     * cannot complete successfully.
     * Will typically be followed by the API function being called returning an
     * error.
     */
    MG2D_LOG_ERROR = 0x10,
    /**
     * The log message indicates a suspicious or suboptimal program state.
     */
    MG2D_LOG_WARNING = 0x20,
    /**
     * The log message provides commonly useful information about normal program
     * behaviour.
     */
    MG2D_LOG_INFO = 0x30,
    /**
     * The log message provides detailed extra information about normal program
     * behaviour.
     */
    MG2D_LOG_VERBOSE = 0x40,
    /**
     * The log message provides highly detailed extra information about normal
     * program behaviour.
     */
    MG2D_LOG_DEBUG = 0x50,
};

typedef struct MG2DInternal MG2DInternal;

/**
 * Boundary condition definition.
 */
typedef struct MG2DBoundary {
    /**
     * Type of the boundary condition.
     */
    enum MG2DBCType type;
    /**
     * For type = MG2D_BC_TYPE_FIXVAL:
     *     Values of the unknown function on the boundary.
     *     The number of boundary layers is equal to fd_stencil.
     *     The first boundary layer has the number of points equal to the
     *     corresponding domain_size. Each subsequent boundary layer has one
     *     more boundary point at each end of the domain.
     *
     * Ignored otherwise.
     */
    double *val;
    /**
     * Number of elements between rows in val. I.e. if val[0] is the first
     * boundary point, then val[val_stride - 1] is the first boundary point in
     * the second row and so on.
     */
    size_t  val_stride;
} MG2DBoundary;

typedef struct MG2DContext {
    /**
     * Solver private data, not to be accessed in any way by the caller.
     */
    MG2DInternal *priv;

    /**
     * A callback that will be used to print diagnostic messages.
     *
     * Defaults to fprintf(stderr, ...)
     */
    void (*log_callback)(const struct MG2DContext *ctx, int level,
                         const char *fmt, va_list);

    /**
     * Arbitrary user data, e.g. to be used by the log callback.
     */
    void *opaque;

    /**
     * Number of grid points in each direction, set by mg2d_solver_alloc().
     * Read-only for the caller.
     */
    size_t domain_size;

    /**
     * Distance between the neighbouring grid points.
     * Must be set by the caller.
     */
    double step[2];

    /**
     * Order of the finite difference operators used for approximating derivatives.
     * Must be set by the caller.
     */
    size_t fd_stencil;

    /**
     * Boundary specification, indexed by MG2DBoundaryLoc.
     * To be filled by the caller.
     */
    MG2DBoundary *boundaries[4];

    /**
     * Maximum number of solver iterations.
     */
    unsigned int maxiter;

    /**
     * Value of the residual at which to consider the equation solved.
     */
    double tol;

    /**
     * Number of cycles on each subgrid.
     */
    unsigned int nb_cycles;

    /**
     * Number of relaxation steps before and after each coarser-grid solve.
     */
    unsigned int nb_relax_pre;
    unsigned int nb_relax_post;

    /**
     * Values of the unknown function.
     *
     * Allocated and initialized to zero by the solver in mg2d_solver_alloc(),
     * owned by the solver.
     * May be filled by the caller before solving to set the initial guess.
     * Afterwards updated in mg2d_solve().
     */
    double   *u;
    /**
     * Distance between neighbouring gridpoints along coord1.
     */
    ptrdiff_t u_stride;

    /**
     * Values of the right-hand side.
     *
     * Allocated by the solver in mg2d_solver_alloc(), owned by the solver.
     * Must be filled by the caller before solving.
     */
    double    *rhs;
    /**
     * Distance between neighbouring gridpoints along coord1.
     */
    ptrdiff_t  rhs_stride;

    /**
     * Coefficients C_{*} that define the differential equation.
     *
     * Allocated by the solver in mg2d_solver_alloc(), owned by the solver.
     * Must be filled by the caller before solving.
     */
    double   *diff_coeffs[MG2D_DIFF_COEFF_NB];
    /**
     * Distance between neighbouring gridpoints along coord1.
     */
    ptrdiff_t diff_coeffs_stride;

    /**
     * Number of threads to use for processing.
     *
     * Set to 0 to autodetect. Defaults to 1.
     */
    unsigned int nb_threads;
} MG2DContext;

/**
 * Allocate the solver for the given domain size.
 *
 * @return The solver context on success, NULL on failure.
 */
MG2DContext *mg2d_solver_alloc(size_t domain_size);
/**
 * Solve the equation, after all the required fields have been filled by the
 * caller.
 *
 * This function may be called more than once.
 *
 * @return 0 on success, a negative error code on failure.
 */
int mg2d_solve(MG2DContext *ctx);
/**
 * Free the solver and write NULL to the provided pointer.
 */
void mg2d_solver_free(MG2DContext **ctx);

/**
 * Print the solver timing statistics using the logging callback.
 *
 * @param prefix the string prepended to each output line, may be NULL to mean
 *               none
 */
void mg2d_print_stats(MG2DContext *ctx, const char *prefix);

#endif /* MG2D_H */