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#ifdef NEWSMATRIX
// #include "DataFormats/Math/interface/MulSymMatrix.h"
#define SMATRIX_USE_CONSTEXPR
#include "Math/SMatrix.h"
typedef unsigned int IndexType;
//typedef unsigned long long IndexType;
namespace ROOT {
namespace Math {
constexpr int fOff15x15[] = {
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 1, 2, 4, 7, 11, 16,
22, 29, 37, 46, 56, 67, 79, 92, 106, 3, 4, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68,
80, 93, 107, 6, 7, 8, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 10, 11, 12,
13, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 15, 16, 17, 18, 19, 20, 26, 33, 41,
50, 60, 71, 83, 96, 110, 21, 22, 23, 24, 25, 26, 27, 34, 42, 51, 61, 72, 84, 97, 111,
28, 29, 30, 31, 32, 33, 34, 35, 43, 52, 62, 73, 85, 98, 112, 36, 37, 38, 39, 40, 41,
42, 43, 44, 53, 63, 74, 86, 99, 113, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 75,
87, 100, 114, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 76, 88, 101, 115, 66, 67, 68,
69, 70, 71, 72, 73, 74, 75, 76, 77, 89, 102, 116, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 88, 89, 90, 103, 117, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 118,
105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119};
constexpr int const* pfOff15x15[] = {fOff15x15 + 0,
fOff15x15 + 15,
fOff15x15 + 2 * 15,
fOff15x15 + 3 * 15,
fOff15x15 + 4 * 15,
fOff15x15 + 5 * 15,
fOff15x15 + 6 * 15,
fOff15x15 + 7 * 15,
fOff15x15 + 8 * 15,
fOff15x15 + 9 * 15,
fOff15x15 + 10 * 15,
fOff15x15 + 11 * 15,
fOff15x15 + 12 * 15,
fOff15x15 + 13 * 15,
fOff15x15 + 14 * 15};
template <>
struct RowOffsets<15> {
RowOffsets() {}
int operator()(unsigned int i, unsigned int j) const { return pfOff15x15[i][j]; } // fOff15x15[i*15+j]; }
int apply(unsigned int i) const { return fOff15x15[i]; }
};
/**
Force Expression evaluation from general to symmetric.
To be used when is known (like in similarity products) that the result
is symmetric
Note this is function used in the simmilarity product: no check for temporary is
done since in that case is not needed
*/
struct AssignAsSym {
/// assign a symmetric matrix from an expression
template <class T, IndexType D, class A, class R>
static void Evaluate(SMatrix<T, D, D, MatRepStd<T, D> >& lhs, const Expr<A, T, D, D, R>& rhs) {
//for(unsigned int i=0; i<D1*D2; ++i) lhs.fRep[i] = rhs.apply(i);
for (IndexType i = 0; i < D; ++i)
// storage of symmetric matrix is in lower block
for (IndexType j = 0; j <= i; ++j) {
lhs(i, j) = rhs(i, j);
}
}
/// assign the symmetric matric from a general matrix
template <class T, IndexType D, class R>
static void Evaluate(SMatrix<T, D, D, MatRepStd<T, D> >& lhs, const SMatrix<T, D, D, R>& rhs) {
//for(unsigned int i=0; i<D1*D2; ++i) lhs.fRep[i] = rhs.apply(i);
for (IndexType i = 0; i < D; ++i)
// storage of symmetric matrix is in lower block
for (IndexType j = 0; j <= i; ++j) {
lhs(i, j) = rhs(i, j);
}
}
}; // struct AssignSym
template <class T, IndexType D1, IndexType D2, class R>
inline SMatrix<T, D1, D1, MatRepSym<T, D1> > Similarity(const SMatrix<T, D1, D2, R>& lhs,
const SMatrix<T, D2, D2, MatRepStd<T, D2> >& rhs) {
SMatrix<T, D1, D2, MatRepStd<T, D1, D2> > tmp = lhs * rhs;
typedef SMatrix<T, D1, D1, MatRepSym<T, D1> > SMatrixSym;
SMatrixSym mret;
AssignSym::Evaluate(mret, tmp * Transpose(lhs));
return mret;
}
} // namespace Math
} // namespace ROOT
template <typename T, IndexType N>
inline void mult(ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepSym<T, N> >& a,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepSym<T, N> > const& rh,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepSym<T, N> > const& lh) {
// a(i,j) = r(i,k)*l(k,j)
for (IndexType i = 0; i != N; ++i) {
IndexType off_i = a.fRep.offset(i, 0);
for (IndexType k = 0; k != N; ++k) {
IndexType off_k = a.fRep.offset(k, 0);
if (k < i) {
for (IndexType j = 0; j != (k + 1); ++j)
a.Array()[off_i + j] += rh(i, k) * lh.Array()[off_k + j];
for (IndexType j = k + 1; j != (i + 1); ++j)
a.Array()[off_i + j] += rh(i, k) * lh(k, j);
} else
for (IndexType j = 0; j != (i + 1); ++j)
a.Array()[off_i + j] += rh(i, k) * lh.Array()[off_k + j];
}
}
}
template <typename T, IndexType N>
inline void mult(ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> >& a,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > const& rh,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > const& lh) {
// a(i,j) = r(i,k)*l(k,j)
for (IndexType i = 0; i != N; ++i) {
for (IndexType j = 0; j <= i; ++j) {
// a(i,j)=0;
// a(i,j) += rh(i,k)*lh(k,j);
for (IndexType k = 0; k != N; ++k)
a(i, j) += rh(i, k) * lh(j, k);
}
}
for (IndexType i = 0; i != N - 1; ++i)
for (IndexType j = i + 1; j != N; ++j)
a(i, j) = a(j, i);
}
// U(i,k) * A(k,l) * U(j,l)
template <typename T, IndexType N>
inline void similarity(ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> >& b,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > const& u,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > const& a) {
for (IndexType i = 0; i != N; ++i)
for (IndexType j = 0; j <= i; ++j)
for (IndexType k = 0; k != N; ++k)
for (IndexType l = 0; l != N; ++l)
b(i, j) += u(i, k) * a(k, l) * u(j, l);
/*
T s[N];
for (IndexType i=0; i!=N; ++i)
for (IndexType j=0; j<=i; ++j) {
for (IndexType k=0; k!=N; ++k) {
s[k]=0;
for (IndexType l=0; l!=N; ++l)
s[k] += a(k,l)*u(j,l);
}
for (IndexType k=0; k!=N; ++k)
b(i,j) += u(i,k)*s[k];
}
*/
for (IndexType i = 0; i != N - 1; ++i)
for (IndexType j = i + 1; j != N; ++j)
b(i, j) = b(j, i);
}
// U(k,i) * A(k,l) * U(l,j)
template <typename T, IndexType N>
inline void similarityT(ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> >& b,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > const& u,
ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > const& a) {
for (IndexType i = 0; i != N; ++i)
for (IndexType j = 0; j <= i; ++j)
for (IndexType k = 0; k != N; ++k)
for (IndexType l = 0; l != N; ++l)
b(i, j) += u(k, i) * a(k, l) * u(l, j);
for (IndexType i = 0; i != N - 1; ++i)
for (IndexType j = i + 1; j != N; ++j)
b(i, j) = b(j, i);
}
template <typename M1, typename M2>
double eps(M1 const& m1, M2 const& m2) {
IndexType N = M1::kRows;
double ret = 0.;
for (IndexType i = 0; i != N; ++i)
for (IndexType j = 0; j != N; ++j)
ret = std::max(ret, std::abs(m1(i, j) - m2(i, j)));
return ret;
}
template <typename M>
bool isSym(M const& m) {
IndexType N = M::kRows;
for (IndexType i = 0; i != N; ++i)
for (IndexType j = 0; j <= i; ++j)
if (m(i, j) != m(j, i))
return false;
return true;
}
#include <iostream>
#include "FWCore/Utilities/interface/HRRealTime.h"
#include <random>
namespace {
std::mt19937 eng;
std::uniform_real_distribution<double> rgen(-5., 5.);
template <typename T, IndexType N>
inline void fillRandom(ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> >& a) {
for (IndexType k = 0; k != N; ++k) {
a(k, k) = std::abs(rgen(eng));
for (IndexType j = 0; j < k; ++j)
a(k, j) = rgen(eng);
}
for (IndexType i = 0; i != N - 1; ++i)
for (IndexType j = i + 1; j != N; ++j)
a(i, j) = -a(j, i);
}
} // namespace
template <typename T, IndexType N>
void go(edm::HRTimeType& s1,
edm::HRTimeType& s2,
edm::HRTimeType& s3,
edm::HRTimeType& s4,
edm::HRTimeType& s5,
edm::HRTimeType& s6,
edm::HRTimeType& s7,
edm::HRTimeType& s8,
bool print) {
typedef ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepStd<T, N> > Matrix;
typedef ROOT::Math::SMatrix<T, N, N, ROOT::Math::MatRepSym<T, N> > SymMatrix;
ROOT::Math::SMatrixIdentity id;
Matrix im1(id);
Matrix im2(id);
/*
fillRandom(im1);
im1 = im1*ROOT::Math::Transpose(im1);
im1 *=im1;
Matrix im2; fillRandom(im2);
im2 = im2*ROOT::Math::Transpose(im2);
im2 *=im2;
*/
SymMatrix is1;
ROOT::Math::AssignSym::Evaluate(is1, im1);
SymMatrix is2;
ROOT::Math::AssignSym::Evaluate(is2, im2);
Matrix j1;
fillRandom(j1);
Matrix j2;
fillRandom(j2);
SymMatrix rh;
s6 = edm::hrRealTime();
rh = ROOT::Math::Similarity(j1, is1);
s6 = edm::hrRealTime() - s6;
SymMatrix rh2;
s7 = edm::hrRealTime();
rh2 = ROOT::Math::Similarity(j1, im1);
s7 = edm::hrRealTime() - s7;
Matrix mrh;
s8 = edm::hrRealTime();
similarity(mrh, j1, im1);
s8 = edm::hrRealTime() - s8;
SymMatrix lh = ROOT::Math::SimilarityT(j2, is1);
Matrix mlh;
similarityT(mlh, j2, im1);
SymMatrix a;
s1 = edm::hrRealTime();
mult(a, lh, rh);
s1 = edm::hrRealTime() - s1;
SymMatrix b;
s2 = edm::hrRealTime();
ROOT::Math::AssignSym::Evaluate(b, lh * rh);
s2 = edm::hrRealTime() - s2;
Matrix m0 = b;
Matrix m;
s3 = edm::hrRealTime();
m = mlh * mrh;
s3 = edm::hrRealTime() - s3;
SymMatrix sm;
s4 = edm::hrRealTime();
ROOT::Math::AssignSym::Evaluate(sm, mlh * mrh);
s4 = edm::hrRealTime() - s4;
Matrix m2;
s5 = edm::hrRealTime();
mult(m2, mlh, mrh);
s5 = edm::hrRealTime() - s5;
SymMatrix smm;
ROOT::Math::AssignSym::Evaluate(smm, m);
SymMatrix smm2;
ROOT::Math::AssignSym::Evaluate(smm2, m2);
if (print) {
if (!isSym(im1))
std::cout << " im is not sym" << std::endl;
if (!isSym(mrh))
std::cout << " rh is not sym" << std::endl;
if (!isSym(mlh))
std::cout << " lh is not sym" << std::endl;
if (!isSym(m))
std::cout << " m is not sym" << std::endl;
if (!isSym(m2))
std::cout << "m2 is not sym" << std::endl;
std::cout << "eps sim " << eps(rh, mrh) << std::endl;
std::cout << "eps sim " << eps(rh, rh2) << std::endl;
std::cout << "eps simT " << eps(lh, mlh) << std::endl;
std::cout << "eps s m " << eps(m, b) << std::endl;
std::cout << "eps s sm " << eps(m2, b) << std::endl;
// std::cout << b << std::endl;
// std::cout << m << std::endl;
if (m != m0)
std::cout << "problem with SMatrix Assign " << eps(m, m0) << std::endl;
if (smm != b)
std::cout << "problem with SMatrix * " << eps(smm, b) << std::endl;
if (sm != b)
std::cout << "problem with SMatrix evaluate " << eps(sm, b) << std::endl;
if (a != b)
std::cout << "problem with MulSymMatrix " << eps(a, b) << std::endl;
if (a != smm)
std::cout << "problem with MulSymMatrix twice " << eps(a, smm) << std::endl;
if (m != m2)
std::cout << "problem with MulMatrix " << eps(m, m2) << std::endl;
if (smm != smm2)
std::cout << "problem with MulMatrix twice " << eps(smm, smm2) << std::endl;
std::cout << "sym mult " << s1 << std::endl;
std::cout << "sym * " << s2 << std::endl;
std::cout << "mat * " << s3 << std::endl;
std::cout << "mat as sym " << s4 << std::endl;
std::cout << "mat mult " << s5 << std::endl;
std::cout << "sym sim " << s6 << std::endl;
std::cout << "std sim " << s7 << std::endl;
std::cout << "loop sim " << s8 << std::endl;
}
}
int main() {
edm::HRTimeType s1 = 0, s2 = 0, s3 = 0, s4 = 0, s5 = 0, s6 = 0, s7 = 0, s8 = 0;
go<double, 3>(s1, s2, s3, s4, s5, s6, s7, s8, true);
go<double, 15>(s1, s2, s3, s4, s5, s6, s7, s8, true);
edm::HRTimeType t1 = 0;
edm::HRTimeType t2 = 0;
edm::HRTimeType t3 = 0;
edm::HRTimeType t4 = 0;
edm::HRTimeType t5 = 0;
edm::HRTimeType t6 = 0;
edm::HRTimeType t7 = 0;
edm::HRTimeType t8 = 0;
for (int i = 0; i != 50000; ++i) {
go<double, 15>(s1, s2, s3, s4, s5, s6, s7, s8, false);
t1 += s1;
t2 += s2;
t3 += s3;
t4 += s4;
t5 += s5;
t6 += s6;
t7 += s7;
t8 += s8;
}
std::cout << "sym mult " << t1 / 50000 << std::endl;
std::cout << "sym * " << t2 / 50000 << std::endl;
std::cout << "mat * " << t3 / 50000 << std::endl;
std::cout << "mat as sym " << t4 / 50000 << std::endl;
std::cout << "mat mult " << t5 / 50000 << std::endl;
std::cout << "sym sim " << t6 / 50000 << std::endl;
std::cout << "std sim " << t7 / 50000 << std::endl;
std::cout << "loop sim " << t8 / 50000 << std::endl;
return 0;
}
#else
int main() { return 0; }
#endif
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