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// nvcc -O3 CholeskyDecomp_t.cu --expt-relaxed-constexpr -gencode arch=compute_61,code=sm_61 --compiler-options="-Ofast -march=native"
// add -DDOPROF to run nvprof --metrics all
#include <algorithm>
#include <cassert>
#include <chrono>
#include <iomanip>
#include <iostream>
#include <limits>
#include <memory>
#include <random>
#include <Eigen/Core>
#include <Eigen/Eigenvalues>
#include "DataFormats/Math/interface/choleskyInversion.h"
constexpr int stride() { return 5 * 1024; }
template <int DIM>
using MXN = Eigen::Matrix<double, DIM, DIM>;
template <int DIM>
using MapMX = Eigen::Map<MXN<DIM>, 0, Eigen::Stride<DIM * stride(), stride()> >;
// generate matrices
template <class M>
void genMatrix(M& m) {
using T = typename std::remove_reference<decltype(m(0, 0))>::type;
int n = M::ColsAtCompileTime;
std::mt19937 eng;
// std::mt19937 eng2;
std::uniform_real_distribution<T> rgen(0., 1.);
// generate first diagonal elemets
for (int i = 0; i < n; ++i) {
double maxVal = i * 10000 / (n - 1) + 1; // max condition is 10^4
m(i, i) = maxVal * rgen(eng);
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < i; ++j) {
double v = 0.3 * std::sqrt(m(i, i) * m(j, j)); // this makes the matrix pos defined
m(i, j) = v * rgen(eng);
m(j, i) = m(i, j);
}
}
}
template <int N>
void go(bool soa) {
constexpr unsigned int DIM = N;
using MX = MXN<DIM>;
std::cout << "testing Matrix of dimension " << DIM << " size " << sizeof(MX) << " in " << (soa ? "SOA" : "AOS")
<< " mode" << std::endl;
auto start = std::chrono::high_resolution_clock::now();
auto delta = start - start;
constexpr unsigned int SIZE = 4 * 1024;
alignas(128) MX mm[stride()]; // just storage in case of SOA
double* __restrict__ p = (double*)__builtin_assume_aligned(mm, 128);
if (soa) {
for (unsigned int i = 0; i < SIZE; ++i) {
MapMX<N> m(p + i);
genMatrix(m);
}
} else {
for (auto& m : mm)
genMatrix(m);
}
std::cout << mm[SIZE / 2](1, 1) << std::endl;
if (soa)
for (unsigned int i = 0; i < SIZE; ++i) {
MapMX<N> m(p + i);
math::cholesky::invert(m, m);
math::cholesky::invert(m, m);
}
else
for (auto& m : mm) {
math::cholesky::invert(m, m);
math::cholesky::invert(m, m);
}
std::cout << mm[SIZE / 2](1, 1) << std::endl;
constexpr int NKK =
#ifdef DOPROF
2;
#else
1000;
#endif
for (int kk = 0; kk < NKK; ++kk) {
delta -= (std::chrono::high_resolution_clock::now() - start);
if (soa)
#ifdef USE_VECTORIZATION_PRAGMA
#pragma GCC ivdep
#ifdef __clang__
#pragma clang loop vectorize(enable) interleave(enable)
#endif
#endif
for (unsigned int i = 0; i < SIZE; ++i) {
MapMX<N> m(p + i);
math::cholesky::invert(m, m);
}
else
#ifdef USE_VECTORIZATION_PRAGMA
#pragma GCC ivdep
#ifdef __clang__
#pragma clang loop vectorize(enable) interleave(enable)
#endif
#endif
for (auto& m : mm) {
math::cholesky::invert(m, m);
}
delta += (std::chrono::high_resolution_clock::now() - start);
}
std::cout << mm[SIZE / 2](1, 1) << std::endl;
double DNNK = NKK;
std::cout << "x86 computation took " << std::chrono::duration_cast<std::chrono::milliseconds>(delta).count() / DNNK
<< ' ' << " ms" << std::endl;
}
int main() {
go<2>(false);
go<3>(false);
go<4>(false);
go<5>(false);
go<6>(false);
go<2>(true);
go<3>(true);
go<4>(true);
go<5>(true);
go<6>(true);
go<10>(false);
go<10>(true);
return 0;
}
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