/*
 * Copyright 2014 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/>.
 */

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

enum BDQFuncType {
    /**
     * q(ρ, z) = A ρ^2 exp(-ρ^2 - z^2)
     */
    BD_Q_FUNC_GUNDLACH,
    /**
     * q(ρ, z) = A ρ^2 / (1 + r^n); where r^2 = ρ^2 + z^2
     */
    BD_Q_FUNC_EPPLEY,
};

typedef struct BDContext {
    /**
     *  private data
     */
    void *priv;

    /*******************************
     *  options, set by the caller *
     *******************************/

    /**
     * The choice of the q function in the exponent.
     * Defaults to BD_Q_FUNC_GUNDLACH.
     */
    enum BDQFuncType q_func_type;
    /**
     * The amplitude in the q function.
     * Defaults to 1.
     */
    double amplitude;
    /**
     * For BD_Q_FUNC_EPPLEY, the power in the denominator.
     * Must be >= 4.
     * Defaults to 5.
     */
    unsigned int eppley_n;

    /* the solver parameters */

    /**
     * The number of basis functions in the ρ direction.
     * Defaults to 80.
     */
    unsigned int nb_coeffs_rho;
    /**
     * The number of basis functions in the z direction. 0 means the same as
     * nb_coeffs_rho. Defaults to 0.
     * Using values other than 0 or nb_coeffs_rho is unsupported for now.
     */
    unsigned int nb_coeffs_z;

    /**
     * The difference between the number of collocation points and the number
     * of basis functions in the rho direction. I.e. the number of collocation
     * points used will be nb_coeffs_rho + overdet_rho.
     * Defaults to 0;
     */
    int overdet_rho;
    /**
     * Same as overdet_rho, but for the z direction.
     */
    int overdet_z;

    /**
     * The difference between the index of the collocation grid used for the ρ
     * direction and nb_coeffs_rho. The 'extra' collocation points furthest from
     * the origin are discarded.
     * Defaults to 3.
     */
    unsigned int colloc_grid_offset_rho;
    /**
     * Same as colloc_grid_offset_rho, but for the z direction.
     */
    unsigned int colloc_grid_offset_z;

    /**
     * The scaling factor used in the basis functions in the ρ direction.
     * Defaults to 3.
     */
    double basis_scale_factor_rho;
    /**
     * Same as basis_scale_factor_rho, but for the z direction
     */
    double basis_scale_factor_z;

    /**********
     * output *
     **********/
    /**
     * The coefficients of the solution expanded in the basis.
     * The ρ index increases along rows, z along columns.
     *
     * The data is owned and managed by this library and is read-only for
     * the caller.
     */
    double *psi_minus1_coeffs;
    /**
     * The number of array elements between two rows.
     */
    ptrdiff_t stride;
} BDContext;

/**
 * Allocate and initialize the solver.
 */
BDContext *bd_context_alloc(void);

/**
 * Free the solver and everything associated with it.
 */
void bd_context_free(BDContext **bd);

/**
 * Solve the equation for the conformal factor ψ and export the expansion coefficients in the
 * context.
 *
 * @return >= 0 on success, a negative error code on failure
 */
int bd_solve(BDContext *bd);

/**
 * Evaluate the conformal factor ψ or its derivatives at the specified rectangular grid.
 *
 * @param bd the solver context
 * @param rho the array of ρ coordinates.
 * @param nb_coords_rho the number of elements in rho.
 * @param z   the array of z coordinates.
 * @param nb_coords_z the number of elements in z.
 * @param diff_order the order of the derivatives of ψ to evaluate. The first element specifies the
 *                   derivative wrt ρ, the second wrt z. I.e. diff_order = { 0, 0 } evaluates ψ
 *                   itself, diff_order = { 0, 1 } evaluates ∂ψ/∂z etc.
 * @param psi the array into which the values of ψ will be written. ψ is evaluated on the grid
 *            formed by the outer product of the rho and z vectors.
 *            I.e. psi[j * nb_coords_rho + i] = ψ(rho[i], z[j]). The length of psi must be
 *            nb_coords_rho * nb_coords_z.
 *
 * @return >= 0 on success, a negative error code on failure.
 */
int bd_eval_psi(BDContext *bd, const double *rho, int nb_coords_rho,
                const double *z, int nb_coords_z,
                const unsigned int diff_order[2],
                double *psi);

/**
 * Evaluate the 3-metric γ_ij at the specified rectangular grid (in cylindrical
 * coordinates { ρ, z, φ }).
 *
 * @param bd the solver context
 * @param rho the array of ρ coordinates.
 * @param nb_coords_rho the number of elements in rho.
 * @param z   the array of z coordinates.
 * @param nb_coords_z the number of elements in z.
 * @param comp the component of the metric to evaluate.
 * @param diff_order the order of the derivatives of the metric to evaluate. The first element
 *                   specifies the derivative wrt ρ, the second wrt z. I.e. diff_order = { 0, 0 }
 *                   evaluates the metric itself, diff_order = { 0, 1 } evaluates ∂γ/∂z etc.
 * @param out the array into which the values of the metric will be written. The metric
 *            is evaluated on the grid formed by the outer product of the rho
 *            and z vectors. I.e. out[j * nb_coords_rho + i] = γ_comp[0]comp[1](rho[i], z[j]).
 *            The length of out must be nb_coords_rho * nb_coords_z.
 *
 * @return >= 0 on success, a negative error code on failure.
 */
int bd_eval_metric(BDContext *bd, const double *rho, int nb_coords_rho,
                   const double *z, int nb_coords_z,
                   const unsigned int comp[2], const unsigned int diff_order[2],
                   double *out);