UniformGridRandomFieldGenerator.cpp

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*/
 
#include "UniformGridRandomFieldGenerator.hpp"
 
#include <iomanip>
#include <fstream>
#include <numeric>
 
#include "Exception.hpp"
#include "FileFinder.hpp"
#include "Node.hpp"
#include "OutputFileHandler.hpp"
#include "RandomNumberGenerator.hpp"
#include "Warnings.hpp"
#include "RandomFieldUtilityFunctions.hpp"
 
template <unsigned SPACE_DIM>
UniformGridRandomFieldGenerator<SPACE_DIM>::UniformGridRandomFieldGenerator(
    std::array<double, SPACE_DIM> lowerCorner,
    std::array<double, SPACE_DIM> upperCorner,
    std::array<unsigned, SPACE_DIM> numGridPts,
    std::array<bool, SPACE_DIM> periodicity,
    double lengthScale)
    : mLowerCorner(lowerCorner),
      mUpperCorner(upperCorner),
      mNumGridPts(numGridPts),
      mPeriodicity(periodicity),
      mLengthScale(lengthScale),
      mCacheDir("CachedRandomFields/")
{
    // Calculate the total number of grid points
    mNumTotalGridPts = std::accumulate(mNumGridPts.begin(),
                                       mNumGridPts.end(),
                                       1u,
                                       std::multiplies<unsigned>());
 
    // Check parameters are sensible
    for (unsigned dim = 0; dim < SPACE_DIM; ++dim)
    {
        assert(mLowerCorner[dim] < mUpperCorner[dim]);
        assert(mNumGridPts[dim] > 0);
    }
    assert(mLengthScale > 0.0);
 
    // Calculate the grid spacings
    for (unsigned dim = 0; dim < SPACE_DIM; ++dim)
    {
        mGridSpacing[dim] = (mUpperCorner[dim] - mLowerCorner[dim]) / mNumGridPts[dim];
        mOneOverGridSpacing[dim] = mNumGridPts[dim] / (mUpperCorner[dim] - mLowerCorner[dim]);
    }
 
    mOpenSimplex = OpenSimplex2S(0);
}
 
template <unsigned SPACE_DIM>
void UniformGridRandomFieldGenerator<SPACE_DIM>::SetRandomSeed(const unsigned seed)
{
    mOpenSimplex = OpenSimplex2S(seed);
}
 
template <unsigned SPACE_DIM>
std::vector<double> UniformGridRandomFieldGenerator<SPACE_DIM>::SampleRandomField()
{
    return this->SampleRandomFieldAtTime(rand());
}
 
template <unsigned SPACE_DIM>
std::vector<double> UniformGridRandomFieldGenerator<SPACE_DIM>::SampleRandomFieldAtTime(double time)
{
    std::vector<double> samples(mNumTotalGridPts);
 
    switch(SPACE_DIM)
    {
        case 1:
        {
            for (unsigned x = 0; x < mNumGridPts[0]; x++)
            {
                samples[x] = random_field::Reshape(mOpenSimplex.noise2_XBeforeY(x * mLengthScale, time));
            }
            break;
        }
        case 2:
        {
            for (unsigned x = 0; x < mNumGridPts[0]; x++)
            {
                for (unsigned y = 0; y < mNumGridPts[1]; y++)
                {
                    samples[mNumGridPts[1] * y + x] = random_field::Reshape(mOpenSimplex.noise3_XYBeforeZ(x * mLengthScale, y * mLengthScale, time));
                }
            }
            break;
        }
        case 3:
        {
            for (unsigned x = 0; x < mNumGridPts[0]; x++)
            {
                for (unsigned y = 0; y < mNumGridPts[1]; y++)
                {
                    for (unsigned z = 0; z < mNumGridPts[2]; z++)
                    {
                        samples[mNumGridPts[2] * z * y + mNumGridPts[1] * y + x] = random_field::Reshape(mOpenSimplex.noise4_XYBeforeZW(x * mLengthScale, y * mLengthScale, z * mLengthScale, time));
                    }
                }
            }
            break;
        }
        default:
            NEVER_REACHED;
            break;
    }
 
    return samples;
}
 
template <unsigned SPACE_DIM>
double UniformGridRandomFieldGenerator<SPACE_DIM>::Interpolate(const std::vector<double>& rRandomField,
                                                               const c_vector<double, SPACE_DIM>& rLocation) const
{
    assert(mNumTotalGridPts == rRandomField.size());
 
    // Find the nearest node
    std::array<long, SPACE_DIM> lower_left;
 
    for (unsigned dim = 0; dim < SPACE_DIM; ++dim)
    {
        lower_left[dim] = std::floor((rLocation[dim] - mLowerCorner[dim]) / mGridSpacing[dim]);
 
        if (lower_left[dim] < 0)
        {
            lower_left[dim] = 0;
            WARN_ONCE_ONLY("Interpolating outside random field grid: does the random field need to be larger?");
        }
        else if (lower_left[dim] >= mNumGridPts[dim])
        {
            lower_left[dim] = mNumGridPts[dim] - 1;
            WARN_ONCE_ONLY("Interpolating outside random field grid: does the random field need to be larger?");
        }
    }
 
    double interpolated_value{};
 
    // Perform the interpolation
    switch(SPACE_DIM)
    {
        case 1:
        {
            // The value of the field at points either side of rLocation
            std::array<long, SPACE_DIM> upper_idx = lower_left;
            upper_idx[0] =  (upper_idx[0] + 1) % mNumGridPts[0];
 
            const double field_at_lower = rRandomField[GetLinearIndex(lower_left)];
            const double field_at_upper = rRandomField[GetLinearIndex(upper_idx)];
 
            // Perform a simple linear interpolation
            const std::array<double, SPACE_DIM> lower_location = GetPositionUsingGridIndex(lower_left);
            const double interpolant = (rLocation[0] - lower_location[0]) * mOneOverGridSpacing[0];
 
            interpolated_value = field_at_lower * (1.0 - interpolant) + field_at_upper * interpolant;
            break;
        }
        case 2:
        {
            // The value of the field at the four points of the square containing rLocation
            std::array<long, SPACE_DIM> x_upper = lower_left;
            x_upper[0] = (x_upper[0] + 1) % mNumGridPts[0];
 
            std::array<long, SPACE_DIM> y_upper = lower_left;
            y_upper[1] = (y_upper[1] + 1) % mNumGridPts[1];
 
            std::array<long, SPACE_DIM> xy_upper = x_upper;
            xy_upper[1] = y_upper[1];
 
            const double field_xy_lower = rRandomField[GetLinearIndex(lower_left)];
            const double field_x_upper = rRandomField[GetLinearIndex(x_upper)];
            const double field_y_upper = rRandomField[GetLinearIndex(y_upper)];
            const double field_xy_upper = rRandomField[GetLinearIndex(xy_upper)];
 
            // Perform a simple bilinear interpolation
            const std::array<double, SPACE_DIM> lower_location = GetPositionUsingGridIndex(lower_left);
            const double dist_x_lower = rLocation[0] - lower_location[0];
            const double dist_x_upper = mGridSpacing[0] - dist_x_lower;
            const double dist_y_lower = rLocation[1] - lower_location[1];
            const double dist_y_upper = mGridSpacing[1] - dist_y_lower;
 
            interpolated_value = mOneOverGridSpacing[0] * mOneOverGridSpacing[1] * (field_xy_lower * dist_x_upper * dist_y_upper +
                                                                                    field_x_upper * dist_x_lower * dist_y_upper +
                                                                                    field_y_upper * dist_x_upper * dist_y_lower +
                                                                                    field_xy_upper * dist_x_lower * dist_y_lower);
 
            break;
        }
        case 3:
        {
            // The value of the field at the eight points of the cube containing rLocation
            std::array<long, SPACE_DIM> x_upper = lower_left;
            x_upper[0] = (x_upper[0] + 1) % mNumGridPts[0];
 
            std::array<long, SPACE_DIM> y_upper = lower_left;
            y_upper[1] = (y_upper[1] + 1) % mNumGridPts[1];
 
            std::array<long, SPACE_DIM> z_upper = lower_left;
            z_upper[2] = (z_upper[2] + 1) % mNumGridPts[2];
 
            std::array<long, SPACE_DIM> xy_upper = x_upper;
            xy_upper[1] = y_upper[1];
 
            std::array<long, SPACE_DIM> xz_upper = x_upper;
            xz_upper[2] = z_upper[2];
 
            std::array<long, SPACE_DIM> yz_upper = y_upper;
            yz_upper[2] = z_upper[2];
 
            std::array<long, SPACE_DIM> xyz_upper = xy_upper;
            xyz_upper[2] = z_upper[2];
 
            const double field_xyz_lower = rRandomField[GetLinearIndex(lower_left)];
            const double field_x_upper = rRandomField[GetLinearIndex(x_upper)];
            const double field_y_upper = rRandomField[GetLinearIndex(y_upper)];
            const double field_z_upper = rRandomField[GetLinearIndex(z_upper)];
            const double field_xy_upper = rRandomField[GetLinearIndex(xy_upper)];
            const double field_xz_upper = rRandomField[GetLinearIndex(xz_upper)];
            const double field_yz_upper = rRandomField[GetLinearIndex(yz_upper)];
            const double field_xyz_upper = rRandomField[GetLinearIndex(xyz_upper)];
 
            // Perform a trilinear interpolation
            const std::array<double, SPACE_DIM> lower_location = GetPositionUsingGridIndex(lower_left);
            const double dist_x_lower = rLocation[0] - lower_location[0];
            const double dist_y_lower = rLocation[1] - lower_location[1];
            const double dist_z_lower = rLocation[2] - lower_location[2];
 
            const double xd = dist_x_lower / mGridSpacing[0];
            const double yd = dist_y_lower / mGridSpacing[1];
            const double zd = dist_z_lower / mGridSpacing[2];
 
            const double c00 = field_xyz_lower * (1.0 - xd) + (field_x_upper * xd);
            const double c01 = field_z_upper * (1.0 - xd) + (field_xz_upper * xd);
            const double c10 = field_y_upper * (1.0 - xd) + (field_xy_upper * xd);
            const double c11 = field_yz_upper * (1.0 - xd) + (field_xyz_upper * xd);
 
            const double c0 = c00 * (1.0 - yd) + (c10 * yd);
            const double c1 = c01 * (1.0 - yd) + (c11 * yd);
 
            const double c = c0 * (1.0 - zd) + (c1 * zd);
            interpolated_value = c;
 
            break;
        }
        default:
            NEVER_REACHED;
    }
 
    return interpolated_value;
}
 
template <unsigned SPACE_DIM>
long UniformGridRandomFieldGenerator<SPACE_DIM>::GetLinearIndex(std::array<long, SPACE_DIM> gridIndex) const
{
    long linear_index;
 
    switch(SPACE_DIM)
    {
        case 1:
        {
            linear_index = gridIndex[0];
            break;
        }
        case 2:
        {
            linear_index = gridIndex[0] +
                           gridIndex[1] * mNumGridPts[0];
            break;
        }
        case 3:
        {
            linear_index = gridIndex[0] +
                           gridIndex[1] * mNumGridPts[0] +
                           gridIndex[2] * mNumGridPts[0] * mNumGridPts[1];
            break;
        }
        default:
            NEVER_REACHED;
    }
 
    return linear_index;
}
 
template <unsigned SPACE_DIM>
std::array<double, SPACE_DIM> UniformGridRandomFieldGenerator<SPACE_DIM>::GetPositionUsingGridIndex(std::array<long, SPACE_DIM> gridIndex) const
{
    std::array<double, SPACE_DIM> position = {{}};
 
    for (unsigned dim = 0; dim < SPACE_DIM; ++dim)
    {
        position[dim] = mLowerCorner[dim] + mGridSpacing[dim] * gridIndex[dim];
    }
 
    return position;
}
 
// Explicit instantiation
template class UniformGridRandomFieldGenerator<1>;
template class UniformGridRandomFieldGenerator<2>;
template class UniformGridRandomFieldGenerator<3>;