/* -------------------------------------------------------------------------- *
 *                                   OpenMM                                   *
 * -------------------------------------------------------------------------- *
 * This is part of the OpenMM molecular simulation toolkit originating from   *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org.               *
 *                                                                            *
 * Portions copyright (c) 2010-2016 Stanford University and the Authors.      *
 * Authors: Peter Eastman                                                     *
 * Contributors:                                                              *
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#include "openmm/LocalEnergyMinimizer.h"
#include "openmm/OpenMMException.h"
#include "lbfgs.h"
#include "openmm/Platform.h"
#include <cmath>
#include <sstream>
#include <vector>
#include <algorithm>

using namespace OpenMM;
using namespace std;

struct MinimizerData {
    Context& context;
    double k;
    MinimizerData(Context& context, double k)
        : context(context), k(k) {}
};

static lbfgsfloatval_t evaluate(void *instance, const lbfgsfloatval_t *x, lbfgsfloatval_t *g, const int n, const lbfgsfloatval_t step) {
    MinimizerData* data = reinterpret_cast<MinimizerData*>(instance);
    Context& context = data->context;
    const System& system = context.getSystem();
    int numParticles = system.getNumParticles();

    // Compute the force and energy for this configuration.

    vector<Vec3> positions(numParticles);
    for (int i = 0; i < numParticles; i++)
        positions[i] = Vec3(x[3*i], x[3*i+1], x[3*i+2]);
    context.setPositions(positions);
    context.computeVirtualSites();
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    for (int i = 0; i < numParticles; i++) {
        if (system.getParticleMass(i) == 0) {
            g[3*i] = 0.0;
            g[3*i+1] = 0.0;
            g[3*i+2] = 0.0;
        }
        else {
            g[3*i] = -forces[i][0];
            g[3*i+1] = -forces[i][1];
            g[3*i+2] = -forces[i][2];
        }
    }
    double energy = state.getPotentialEnergy();

    // Add harmonic forces for any constraints.

    int numConstraints = system.getNumConstraints();
    double k = data->k;
    for (int i = 0; i < numConstraints; i++) {
        int particle1, particle2;
        double distance;
        system.getConstraintParameters(i, particle1, particle2, distance);
        Vec3 delta = positions[particle2]-positions[particle1];
        double r2 = delta.dot(delta);
        double r = sqrt(r2);
        delta *= 1/r;
        double dr = r-distance;
        double kdr = k*dr;
        energy += 0.5*kdr*dr;
        g[3*particle1] -= kdr*delta[0];
        g[3*particle1+1] -= kdr*delta[1];
        g[3*particle1+2] -= kdr*delta[2];
        g[3*particle2] += kdr*delta[0];
        g[3*particle2+1] += kdr*delta[1];
        g[3*particle2+2] += kdr*delta[2];
    }
    return energy;
}

void LocalEnergyMinimizer::minimize(Context& context, double tolerance, int maxIterations) {
    const System& system = context.getSystem();
    int numParticles = system.getNumParticles();
    lbfgsfloatval_t *x = lbfgs_malloc(numParticles*3);
    if (x == NULL)
        throw OpenMMException("LocalEnergyMinimizer: Failed to allocate memory");
    double constraintTol = context.getIntegrator().getConstraintTolerance();
    double workingConstraintTol = std::max(1e-4, constraintTol);
    double k = tolerance/workingConstraintTol;

    // Initialize the minimizer.

    lbfgs_parameter_t param;
    lbfgs_parameter_init(&param);
    if (!context.getPlatform().supportsDoublePrecision())
        param.xtol = 1e-7;
    param.max_iterations = maxIterations;
    param.linesearch = LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE;

    // Make sure the initial configuration satisfies all constraints.

    context.applyConstraints(workingConstraintTol);

    // Record the initial positions and determine a normalization constant for scaling the tolerance.

    vector<Vec3> initialPos = context.getState(State::Positions).getPositions();
    double norm = 0.0;
    for (int i = 0; i < numParticles; i++) {
        x[3*i] = initialPos[i][0];
        x[3*i+1] = initialPos[i][1];
        x[3*i+2] = initialPos[i][2];
        norm += initialPos[i].dot(initialPos[i]);
    }
    norm /= numParticles;
    norm = (norm < 1 ? 1 : sqrt(norm));
    param.epsilon = tolerance/norm;

    // Repeatedly minimize, steadily increasing the strength of the springs until all constraints are satisfied.

    double prevMaxError = 1e10;
    while (true) {
        // Perform the minimization.

        lbfgsfloatval_t fx;
        MinimizerData data(context, k);
        lbfgs(numParticles*3, x, &fx, evaluate, NULL, &data, &param);

        // Check whether all constraints are satisfied.

        vector<Vec3> positions = context.getState(State::Positions).getPositions();
        int numConstraints = system.getNumConstraints();
        double maxError = 0.0;
        for (int i = 0; i < numConstraints; i++) {
            int particle1, particle2;
            double distance;
            system.getConstraintParameters(i, particle1, particle2, distance);
            Vec3 delta = positions[particle2]-positions[particle1];
            double r = sqrt(delta.dot(delta));
            double error = fabs(r-distance);
            if (error > maxError)
                maxError = error;
        }
        if (maxError <= workingConstraintTol)
            break; // All constraints are satisfied.
        context.setPositions(initialPos);
        if (maxError >= prevMaxError)
            break; // Further tightening the springs doesn't seem to be helping, so just give up.
        prevMaxError = maxError;
        k *= 10;
        if (maxError > 100*workingConstraintTol) {
            // We've gotten far enough from a valid state that we might have trouble getting
            // back, so reset to the original positions.
            
            for (int i = 0; i < numParticles; i++) {
                x[3*i] = initialPos[i][0];
                x[3*i+1] = initialPos[i][1];
                x[3*i+2] = initialPos[i][2];
            }
        }
    }
    lbfgs_free(x);
    
    // If necessary, do a final constraint projection to make sure they are satisfied
    // to the full precision requested by the user.
    
    if (constraintTol < workingConstraintTol)
        context.applyConstraints(workingConstraintTol);
}