HeteQuadrature/gjj/myDebug.hpp

#include <array>
#include <bitset>
#include <iostream>
#include <booluarray.hpp>


#include <cstddef>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <vector>
#include "bernstein.hpp"
#include "quadrature_multipoly.hpp"
#include "binomial.hpp"

#include "real.hpp"
#include "uvector.hpp"
#include "vector"
#include "xarray.hpp"
#include <chrono>


using namespace algoim;

// Driver method which takes a functor phi defining a single polynomial in the reference
// rectangle [xmin, xmax]^N, of Bernstein degree P, along with an integrand function,
// and performances a q-refinement convergence study, comparing the computed integral
// with the given exact answers, for 1 <= q <= qMax.
template <int N, typename Phi, typename F>
void qConv1(const Phi&      phi,
            real            xmin,
            real            xmax,
            uvector<int, N> P,
            const F&        integrand,
            int             qMax,
            real            volume_exact,
            real            surf_exact)
{
    // Construct Bernstein polynomial by mapping [0,1] onto bounding box [xmin,xmax]
    xarray<real, N> phipoly(nullptr, P);
    algoim_spark_alloc(real, phipoly);
    bernstein::bernsteinInterpolate<N>([&](const uvector<real, N>& x) { return phi(xmin + x * (xmax - xmin)); }, phipoly);

    // Build quadrature hierarchy
    ImplicitPolyQuadrature<N> ipquad(phipoly);

    // Functional to evaluate volume and surface integrals of given integrand
    real volume, surf;
    auto compute = [&](int q) {
        volume = 0.0;
        surf   = 0.0;
        // compute volume integral over {phi < 0} using AutoMixed strategy
        ipquad.integrate(AutoMixed, q, [&](const uvector<real, N>& x, real w) {
            if (bernstein::evalBernsteinPoly(phipoly, x) < 0) volume += w * integrand(xmin + x * (xmax - xmin));
        });
        // compute surface integral over {phi == 0} using AutoMixed strategy
        ipquad.integrate_surf(AutoMixed, q, [&](const uvector<real, N>& x, real w, const uvector<real, N>& wn) {
            surf += w * integrand(xmin + x * (xmax - xmin));
        });
        // scale appropriately
        volume *= pow(xmax - xmin, N);
        surf   *= pow(xmax - xmin, N - 1);
    };

    // Compute results for all q and output in a convergence table
    for (int q = 1; q <= qMax; ++q) {
        compute(q);
        std::cout << q << ' ' << volume << ' ' << surf << ' ' << std::abs(volume - volume_exact) / volume_exact << ' '
                  << std::abs(surf - surf_exact) / surf_exact << std::endl;
    }
}

enum BoolOp { Union, Intersection, Difference };

// Driver method which takes two phi functors defining two polynomials in the reference
// rectangle [xmin, xmax]^N, each of of Bernstein degree P, builds a quadrature scheme with the
// given q, and outputs it for visualisation in a set of VTP XML files
template <int N, typename F1, typename F2, typename F>
void qConvMultiPloy(const F1&              fphi1,
                    const F2&              fphi2,
                    real                   xmin,
                    real                   xmax,
                    const uvector<int, N>& P,
                    const F&               integrand,
                    int                    q,
                    BoolOp                 op)
{
    // Construct phi by mapping [0,1] onto bounding box [xmin,xmax]
    xarray<real, N> phi1(nullptr, P), phi2(nullptr, P);
    algoim_spark_alloc(real, phi1, phi2);
    bernstein::bernsteinInterpolate<N>([&](const uvector<real, N>& x) { return fphi1(xmin + x * (xmax - xmin)); }, phi1);
    bernstein::bernsteinInterpolate<N>([&](const uvector<real, N>& x) { return fphi2(xmin + x * (xmax - xmin)); }, phi2);

    // Build quadrature hierarchy
    ImplicitPolyQuadrature<N> ipquad(phi1, phi2);
    // ImplicitPolyQuadrature<N> ipquad(phi1);

    // Functional to evaluate volume and surface integrals of given integrand
    real volume, surf;
    auto compute = [&](int q) {
        volume = 0.0;
        surf   = 0.0;
        // compute volume integral over {phi < 0} using AutoMixed strategy
        ipquad.integrate(AutoMixed, q, [&](const uvector<real, N>& x, real w) {
            if (op == Union) {
                if (bernstein::evalBernsteinPoly(phi1, x) < 0 || bernstein::evalBernsteinPoly(phi2, x) < 0)
                    volume += w * integrand(xmin + x * (xmax - xmin));
            } else if (op == Intersection) {
                if (bernstein::evalBernsteinPoly(phi1, x) < 0 && bernstein::evalBernsteinPoly(phi2, x) < 0)
                    volume += w * integrand(xmin + x * (xmax - xmin));
            } else if (op == Difference) {
                if (bernstein::evalBernsteinPoly(phi1, x) < 0 && bernstein::evalBernsteinPoly(phi2, x) > 0)
                    volume += w * integrand(xmin + x * (xmax - xmin));
            }
            // if (bernstein::evalBernsteinPoly(phi1, x) < 0) volume += w * integrand(xmin + x * (xmax - xmin));
        });
        // compute surface integral over {phi == 0} using AutoMixed strategy
        ipquad.integrate_surf(AutoMixed, q, [&](const uvector<real, N>& x, real w, const uvector<real, N>& wn) {
            surf += w * integrand(xmin + x * (xmax - xmin));
        });
        // scale appropriately
        volume *= pow(xmax - xmin, N);
        surf   *= pow(xmax - xmin, N - 1);
    };
    compute(q);
    std::cout << "q volume: " << volume << std::endl;
}

template <int N, typename F>
void qConvMultiPloy2(real xmin, real xmax, const uvector<int, N>& P, const F& integrand, int q, std::string qfile)
{
    // Construct phi by mapping [0,1] onto bounding box [xmin,xmax]

    // bernstein::bernsteinInterpolate<N>([&](const uvector<real, N>& x) { return fphi1(xmin + x * (xmax - xmin)); }, phi1);
    // bernstein::bernsteinInterpolate<N>([&](const uvector<real, N>& x) { return fphi2(xmin + x * (xmax - xmin)); }, phi2);

    std::vector<xarray<real, N>> phis; // 大量sphere
    for (int i = 0; i < 100; i++) {
        real centerX = 1.0 - rand() % 20 / 10.0, centerY = 1.0 - rand() % 20 / 10.0, centerZ = 1.0 - rand() % 20 / 10.0;
        real r    = 0.1 + rand() % 9 / 10.0;
        auto fphi = [&](const uvector<real, 3>& xx) {
            real x = xx(0) - centerX;
            real y = xx(1) - centerY;
            real z = xx(2) - centerZ;
            return x * x + y * y + z * z - r * r;
        };
        xarray<real, N> phi(nullptr, P);
        algoim_spark_alloc(real, phi);
        bernstein::bernsteinInterpolate<N>([&](const uvector<real, N>& x) { return fphi(xmin + x * (xmax - xmin)); }, phi);
    }
    auto t = std::chrono::system_clock::now();

    ImplicitPolyQuadrature<N> ipquad(phis);


    // Build quadrature hierarchy
    // ImplicitPolyQuadrature<N> ipquad(phi1, phi2);
    // ImplicitPolyQuadrature<N> ipquad(phi1);

    // Functional to evaluate volume and surface integrals of given integrand
    real volume, surf;
    auto compute = [&](int q) {
        volume = 0.0;
        surf   = 0.0;
        // compute volume integral over {phi < 0} using AutoMixed strategy
        ipquad.integrate(AutoMixed, q, [&](const uvector<real, N>& x, real w) {
            // if (bernstein::evalBernsteinPoly(phi1, x) < 0 && bernstein::evalBernsteinPoly(phi2, x) < 0) volume += w *
            // integrand(xmin + x * (xmax - xmin)); if (bernstein::evalBernsteinPoly(phi1, x) < 0) volume += w * integrand(xmin
            // + x * (xmax - xmin));
            volume += w * integrand(xmin + x * (xmax - xmin));
        });
        // compute surface integral over {phi == 0} using AutoMixed strategy
        // ipquad.integrate_surf(AutoMixed, q, [&](const uvector<real, N>& x, real w, const uvector<real, N>& wn) {
        //     surf += w * integrand(xmin + x * (xmax - xmin));
        // });
        // scale appropriately
        volume *= pow(xmax - xmin, N);
        surf   *= pow(xmax - xmin, N - 1);
    };
    compute(q);

    auto                          tAfter          = std::chrono::system_clock::now();
    std::chrono::duration<double> elapsed_seconds = tAfter - t;
    std::cout << "elapsed time: " << elapsed_seconds.count() << "s\n";
    std::cout << "q volume: " << volume << std::endl;
}

void fromCommon2Bernstein() {}

void testMultiPolys()
{
    // Visusalisation of a 2D implicitly-defined domain involving the intersection of two polynomials; this example
    // corresponds to the top-left example of Figure 15, https://doi.org/10.1016/j.jcp.2021.110720
    if (true) {
        auto phi0 = [](const uvector<real, 3>& xx) {
            real x = xx(0);
            real y = xx(1);
            real z = xx(2);
            return x * x + y * y + z * z - 1;
        };
        auto phi1 = [](const uvector<real, 3>& xx) {
            // real x = xx(0);
            // real y = xx(1);
            // real z = xx(2);
            // return x * x + y * y + z * z - 1;
            real x = xx(0);
            real y = xx(1);
            real z = xx(2);
            return x * y * z;
        };
        // auto phi0 = [](const uvector<real, 3>& xx) {
        //     real x = xx(0) * 2 - 1;
        //     real y = xx(1) * 2 - 1;
        //     return 0.014836540349115947 + 0.7022484024095262 * y + 0.09974561176434385 * y * y
        //            + x * (0.6863910464417281 + 0.03805619999999999 * y - 0.09440658332756446 * y * y)
        //            + x * x * (0.19266932968830816 - 0.2325190091204104 * y + 0.2957473125000001 * y * y);
        // };
        // auto phi1 = [](const uvector<real, 3>& xx) {
        //     real x = xx(0) * 2 - 1;
        //     real y = xx(1) * 2 - 1;
        //     return -0.18792528379702625 + 0.6713882473904913 * y + 0.3778666084723582 * y * y
        //            + x * x * (-0.14480813208127946 + 0.0897755603159206 * y - 0.141199875 * y * y)
        //            + x * (-0.6169311810674598 - 0.19449299999999994 * y - 0.005459163675646665 * y * y);
        // };
        auto integrand = [](const uvector<real, 3>& x) { return 1.0; };
        // qConvMultiPloy<3>(phi0, phi1, -1.0, 1.0, 3, integrand, 3, "exampleC");
        qConvMultiPloy2<3>(-1.0, 1.0, 3, integrand, 10, "exampleC");
    }
}

template <int N>
void power2BernsteinTensorProduct(const xarray<real, N>& phiPower, xarray<real, N>& phiBernsetin)
{
    for (auto i = phiPower.loop(); ~i; ++i) {
        // phi.l(i) = powerFactors.l(i);
        real factorBase = phiPower.l(i);
        if (factorBase == 0) continue;
        auto                           traverseRange = phiPower.ext() - i();
        std::vector<std::vector<real>> decompFactors(N, std::vector<real>(max(traverseRange), 0.));
        for (int dim = 0; dim < N; ++dim) {
            // Sigma
            size_t      nDim      = phiPower.ext()(dim) - 1;
            const real* binomNDim = Binomial::row(nDim);
            for (int j = i(dim); j <= nDim; ++j) {
                const real* binomJ             = Binomial::row(j);
                decompFactors[dim][j - i(dim)] = binomJ[i(dim)] / binomNDim[i(dim)];
            }
        }
        xarray<real, N> subgrid(nullptr, traverseRange);
        // algoim_spark_alloc(real, subgrid);

        for (auto ii = subgrid.loop(); ~ii; ++ii) {
            real factor = factorBase;
            for (int dim = 0; dim < N; ++dim) { factor *= decompFactors[dim][ii(dim)]; }
            phiBernsetin.m(i() + ii()) += factor;
        }
    }
}

template <int N>
real powerEvaluation(const xarray<real, N>& phi, const uvector<real, N>& x)
{
    real res = 0;
    for (auto i = phi.loop(); ~i; ++i) {
        real item = phi.l(i);
        auto exps = i();
        for (int dim = 0; dim < N; ++dim) { item *= pow(x(dim), exps(dim)); }
        res += item;
    }
    return res;
}

auto xarray2StdVector(const xarray<real, 3>& array)
{
    auto                                        ext = array.ext();
    std::vector<std::vector<std::vector<real>>> v(ext(0), std::vector<std::vector<real>>(ext(1), std::vector<real>(ext(2), 0)));
    for (int i = 0; i < ext(0); ++i) {
        for (int j = 0; j < ext(1); ++j) {
            for (int k = 0; k < ext(2); ++k) { v[i][j][k] = array.m(uvector<int, 3>(i, j, k)); }
        }
    }
    return v;
}

template <int N, typename F>
void qConvBernstein(const xarray<real, N>&                  phi,
                    real                                    xmin,
                    real                                    xmax,
                    const F&                                integrand,
                    int                                     q,
                    const std::vector<std::array<real, 4>>& halfFaces)
{
    uvector<real, 3> testX(0., 0., 0.5);
    real             testEvalBernstein = bernstein::evalBernsteinPoly(phi, testX);
    auto             vec1              = xarray2StdVector(phi);
    std::cout << "eval bernstein without interpolation:" << testEvalBernstein << std::endl;

    // Build quadrature hierarchy
    ImplicitPolyQuadrature<N> ipquad(phi);
    // ImplicitPolyQuadrature<N> ipquad(phi1);

    // Functional to evaluate volume and surface integrals of given integrand
    real volume;
    auto compute = [&](int q) {
        volume = 0.0;
        // compute volume integral over {phi < 0} using AutoMixed strategy
        if (!halfFaces.empty()) {
            ipquad.integrate(AutoMixed, q, [&](const uvector<real, N>& x, real w) {
                if (bernstein::evalBernsteinPoly(phi, x) >= 0) return;
                bool in = true;
                for (int i = 0; i < halfFaces.size(); ++i) {
                    uvector<real, 3> factors(halfFaces[i][0], halfFaces[i][1], halfFaces[i][2]);
                    if (prod(factors * x) + halfFaces[i][3] > 0) {
                        in = false;
                        break;
                    }
                }
                if (in) volume += w * integrand(xmin + x * (xmax - xmin));
            });

        } else
            ipquad.integrate(AutoMixed, q, [&](const uvector<real, N>& x, real w) {
                if (bernstein::evalBernsteinPoly(phi, x) < 0) volume += w * integrand(xmin + x * (xmax - xmin));
            });
        // scale appropriately
        volume *= pow(xmax - xmin, N);
    };
    compute(q);
    std::cout << "q volume: " << volume << std::endl;
}

template <typename T, int N>
void xarrayInit(xarray<T, N>& arr)
{
    for (auto i = arr.loop(); ~i; ++i) { arr.l(i) = 0; }
}

void testSpherePowerDirectly()
{
    // a_x(x-c_x)^2 + a_y(y-c_y)^2 + a_z(x-c_z)^2 - r^2
    uvector<real, 3> xmin = -1, xmax = 1;
    uvector<real, 3> range = xmax - xmin;
    assert(all(range != 0));
    // uvector<real, 3> k    = 1 / range;
    // uvector<real, 3> bias = -k * xmin;
    uvector<real, 3> k    = range;
    uvector<real, 3> bias = xmin;
    real             a[3] = {1, 1, 1};
    real             c[3] = {0, 0, 0};
    real             r    = 1;
    uvector<int, 3>  ext  = 3;
    xarray<real, 3>  phiPower(nullptr, ext), phiBernstein(nullptr, ext);
    algoim_spark_alloc(real, phiPower, phiBernstein);
    xarrayInit(phiPower);
    xarrayInit(phiBernstein);
    auto v  = xarray2StdVector(phiPower);
    auto vv = xarray2StdVector(phiBernstein);
    for (int dim = 0; dim < 3; ++dim) {
        uvector<int, 3> idx  = 0;
        phiPower.m(idx)     += a[dim] * (bias(dim) - c[dim]) * (bias(dim) - c[dim]);
        idx(dim)             = 1;
        phiPower.m(idx)      = 2 * a[dim] * k(dim) * (bias(dim) - c[dim]);
        idx(dim)             = 2;
        phiPower.m(idx)      = a[dim] * k(dim) * k(dim);
    }
    phiPower.m(0)  -= r * r;
    auto integrand  = [](const uvector<real, 3>& x) { return 1.0; };
    power2BernsteinTensorProduct(phiPower, phiBernstein);

    v = xarray2StdVector(phiPower);
    uvector<real, 3> testX(0., 0., 0.5);
    real             testEval = powerEvaluation(phiPower, testX);
    std::cout << "eval power:" << testEval << std::endl;

    real testEvalBernstein = bernstein::evalBernsteinPoly(phiBernstein, testX);
    auto vec               = xarray2StdVector(phiBernstein);
    std::cout << "eval bernstein:" << testEval << std::endl;
    qConvBernstein(phiBernstein, -1, 1, integrand, 10, {});
}

void testSpherePowerDirectlyByTransformation()
{
    // a_x(x-c_x)^2 + a_y(y-c_y)^2 + a_z(x-c_z)^2 - r^2
    uvector<real, 3> xmin = -1, xmax = 1;
    uvector<real, 3> range = xmax - xmin;
    assert(all(range != 0));
    // uvector<real, 3> k    = 1 / range;
    // uvector<real, 3> bias = -k * xmin;
    uvector<real, 3> k    = range;
    uvector<real, 3> bias = xmin;
    real             a[3] = {1, 1, 1};
    real             c[3] = {0, 0, 0};
    real             r    = 1;
    uvector<int, 3>  ext  = 3;
    xarray<real, 3>  phiPower(nullptr, ext), phiBernstein(nullptr, ext);
    algoim_spark_alloc(real, phiPower, phiBernstein);
    xarrayInit(phiPower);
    xarrayInit(phiBernstein);
		std::vector<std::vector<real>> dimTransformation;
    auto v  = xarray2StdVector(phiPower);
    auto vv = xarray2StdVector(phiBernstein);
    for (int dim = 0; dim < 3; ++dim) {
        uvector<int, 3> idx  = 0;
        phiPower.m(idx)     += a[dim] * (c[dim]) * (c[dim]);
        idx(dim)             = 1;
        phiPower.m(idx)      = 2 * a[dim] * (- c[dim]);
        idx(dim)             = 2;
        phiPower.m(idx)      = a[dim];
    }
    phiPower.m(0)  -= r * r;

		for (int dim = 0; dim < 3; ++dim) {
			dimTransformation[0](std::vector<real>(ext(dim), 0));
			for (int degree = 0; degree < ext(dim); ++degree) {
				// dimTransformation[dim][degree] = 0;
				const real* binomDegree = Binomial::row(degree);
				for (int i = 0; i <= degree; ++i) {
					// 根据二项定理展开
					dimTransformation[dim][i] += binomDegree[i] * pow(k(dim), i) * pow(bias(dim), degree - i);
				}
			}
		}
		// apply transformation
		for (auto i = phiPower.loop(); ~i; ++i) {
			real item = phiPower.l(i);
			auto exps = i();
			for (int dim = 0; dim < 3; ++dim) { item += dimTransformation[dim][exps(dim)]; }
			phiPower.m(i()) = item;
		}

    auto integrand  = [](const uvector<real, 3>& x) { return 1.0; };
    power2BernsteinTensorProduct(phiPower, phiBernstein);

    v = xarray2StdVector(phiPower);
    uvector<real, 3> testX(0., 0., 0.5);
    real             testEval = powerEvaluation(phiPower, testX);
    std::cout << "eval power:" << testEval << std::endl;

    real testEvalBernstein = bernstein::evalBernsteinPoly(phiBernstein, testX);
    auto vec               = xarray2StdVector(phiBernstein);
    std::cout << "eval bernstein:" << testEval << std::endl;
    qConvBernstein(phiBernstein, -1, 1, integrand, 10, {});
}

void testCylinderPowerDirectly()
{
    // a_x(x-c_x)^2 + a_y(y-c_y)^2 + a_z(x-c_z)^2 - r^2
    uvector<real, 3> xmin = -1, xmax = 1;
    uvector<real, 3> range = xmax - xmin;
    assert(all(range != 0));
    uvector<real, 3> k    = range;
    uvector<real, 3> bias = xmin;
    real             c[3] = {0, 0, 0};
    real             r = 1, h = 1;
    uvector<int, 3>  ext = 3;
    xarray<real, 3>  phiPower(nullptr, ext), phiBernstein(nullptr, ext);
    algoim_spark_alloc(real, phiPower, phiBernstein);
    xarrayInit(phiPower);
    xarrayInit(phiBernstein);
		std::vector<std::vector<real>> dimTransformation;
    auto v   = xarray2StdVector(phiPower);
    auto vv  = xarray2StdVector(phiBernstein);
    real top = c[2] + h * 0.5, bottom = c[2] - h * 0.5;
    phiPower.m(uvector<int, 3>(2, 0, 2)) = -1;
    phiPower.m(uvector<int, 3>(0, 2, 2)) = -1;
    phiPower.m(uvector<int, 3>(0, 0, 2)) = r * r;
    phiPower.m(uvector<int, 3>(2, 0, 1)) = top + bottom;
    phiPower.m(uvector<int, 3>(0, 2, 1)) = top + bottom;
    phiPower.m(uvector<int, 3>(0, 0, 1)) = -(bottom + top) * r * r;
    phiPower.m(uvector<int, 3>(1, 0, 0)) = -bottom * top;
    phiPower.m(uvector<int, 3>(0, 1, 0)) = -bottom * top;
    phiPower.m(uvector<int, 3>(0, 0, 0)) = bottom * top * r * r;

		for (int dim = 0; dim < 3; ++dim) {
			dimTransformation.push_back(std::vector<real>(ext(dim), 0));
			for (int degree = 0; degree < ext(dim); ++degree) {
				// dimTransformation[dim][degree] = 0;
				const real* binomDegree = Binomial::row(degree);
				for (int i = 0; i <= degree; ++i) {
					// 根据二项定理展开
					dimTransformation[dim][i] += binomDegree[i] * pow(k(dim), i) * pow(bias(dim), degree - i);
				}
			}
		}

		// apply transformation
		for (auto i = phiPower.loop(); ~i; ++i) {
			real item = phiPower.l(i);
			auto exps = i();
			for (int dim = 0; dim < 3; ++dim) { item *= dimTransformation[dim][exps(dim)]; }
			phiPower.m(i()) = item;
		}

    auto integrand                       = [](const uvector<real, 3>& x) { return 1.0; };
    power2BernsteinTensorProduct(phiPower, phiBernstein);

    v = xarray2StdVector(phiPower);
    uvector<real, 3> testX(0., 0., 0.5);
    real             testEval = powerEvaluation(phiPower, testX);
    std::cout << "eval power:" << testEval << std::endl;

    real testEvalBernstein = bernstein::evalBernsteinPoly(phiBernstein, testX);
    auto vec               = xarray2StdVector(phiBernstein);
    std::cout << "eval bernstein:" << testEval << std::endl;
    qConvBernstein(phiBernstein,
                   -1,
                   1,
                   integrand,
                   50,
                   {
                       {0, 0, 1,  -top},
                       {0, 0, -1, bottom    }
    });
}

void testMultiScale()
{
    auto phi0 = [](const uvector<real, 3>& xx) {
        real x = xx(0) + 100000.;
        real y = xx(1);
        real z = xx(2) - 100000.;
        real r = 800000.;
        return x * x + y * y + z * z - r * r;
    };
    auto phi1 = [](const uvector<real, 3>& xx) {
        // real x = xx(0);
        // real y = xx(1);
        // real z = xx(2);
        // return x * x + y * y + z * z - 1;
        real x = xx(0) + 100000.;
        real y = xx(1) - 800000.;
        real z = xx(2) - 100000.;
        real r = 1000.;
        return x * x + y * y + z * z - r * r;
    };
    auto integrand = [](const uvector<real, 3>& x) { return 1.0; };
    qConvMultiPloy<3>(phi0, phi1, -1000000., 1000000., 3, integrand, 20, Difference);
}

void testBitSet()
{
    std::bitset<10> set(128);
    set.set();
    std::cout << set << std::endl;
}

void testBooluarray()
{
    algoim::booluarray<2, 3> tmp;
    tmp(0) = true;
    tmp(1) = true;
    tmp(2) = true;
    std::cout << tmp.bits << std::endl;
}

void testMain()
{
    testBooluarray();
    testMultiPolys();
    testMultiScale();
    testSpherePowerDirectlyByTransformation();
    testCylinderPowerDirectly();
}